/*
* Copyright 2008-2009 Katholieke Universiteit Leuven
* Copyright 2010 INRIA Saclay
* Copyright 2012-2013 Ecole Normale Superieure
*
* Use of this software is governed by the MIT license
*
* Written by Sven Verdoolaege, 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
* and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
*/
#include "isl_map_private.h"
#include <isl_seq.h>
#include <isl/options.h>
#include "isl_tab.h"
#include <isl_mat_private.h>
#include <isl_local_space_private.h>
#include <isl_vec_private.h>
#define STATUS_ERROR -1
#define STATUS_REDUNDANT 1
#define STATUS_VALID 2
#define STATUS_SEPARATE 3
#define STATUS_CUT 4
#define STATUS_ADJ_EQ 5
#define STATUS_ADJ_INEQ 6
static int status_in(isl_int *ineq, struct isl_tab *tab)
{
enum isl_ineq_type type = isl_tab_ineq_type(tab, ineq);
switch (type) {
default:
case isl_ineq_error: return STATUS_ERROR;
case isl_ineq_redundant: return STATUS_VALID;
case isl_ineq_separate: return STATUS_SEPARATE;
case isl_ineq_cut: return STATUS_CUT;
case isl_ineq_adj_eq: return STATUS_ADJ_EQ;
case isl_ineq_adj_ineq: return STATUS_ADJ_INEQ;
}
}
/* Compute the position of the equalities of basic map "bmap_i"
* with respect to the basic map represented by "tab_j".
* The resulting array has twice as many entries as the number
* of equalities corresponding to the two inequalties to which
* each equality corresponds.
*/
static int *eq_status_in(__isl_keep isl_basic_map *bmap_i,
struct isl_tab *tab_j)
{
int k, l;
int *eq = isl_calloc_array(bmap_i->ctx, int, 2 * bmap_i->n_eq);
unsigned dim;
if (!eq)
return NULL;
dim = isl_basic_map_total_dim(bmap_i);
for (k = 0; k < bmap_i->n_eq; ++k) {
for (l = 0; l < 2; ++l) {
isl_seq_neg(bmap_i->eq[k], bmap_i->eq[k], 1+dim);
eq[2 * k + l] = status_in(bmap_i->eq[k], tab_j);
if (eq[2 * k + l] == STATUS_ERROR)
goto error;
}
if (eq[2 * k] == STATUS_SEPARATE ||
eq[2 * k + 1] == STATUS_SEPARATE)
break;
}
return eq;
error:
free(eq);
return NULL;
}
/* Compute the position of the inequalities of basic map "bmap_i"
* (also represented by "tab_i", if not NULL) with respect to the basic map
* represented by "tab_j".
*/
static int *ineq_status_in(__isl_keep isl_basic_map *bmap_i,
struct isl_tab *tab_i, struct isl_tab *tab_j)
{
int k;
unsigned n_eq = bmap_i->n_eq;
int *ineq = isl_calloc_array(bmap_i->ctx, int, bmap_i->n_ineq);
if (!ineq)
return NULL;
for (k = 0; k < bmap_i->n_ineq; ++k) {
if (tab_i && isl_tab_is_redundant(tab_i, n_eq + k)) {
ineq[k] = STATUS_REDUNDANT;
continue;
}
ineq[k] = status_in(bmap_i->ineq[k], tab_j);
if (ineq[k] == STATUS_ERROR)
goto error;
if (ineq[k] == STATUS_SEPARATE)
break;
}
return ineq;
error:
free(ineq);
return NULL;
}
static int any(int *con, unsigned len, int status)
{
int i;
for (i = 0; i < len ; ++i)
if (con[i] == status)
return 1;
return 0;
}
static int count(int *con, unsigned len, int status)
{
int i;
int c = 0;
for (i = 0; i < len ; ++i)
if (con[i] == status)
c++;
return c;
}
static int all(int *con, unsigned len, int status)
{
int i;
for (i = 0; i < len ; ++i) {
if (con[i] == STATUS_REDUNDANT)
continue;
if (con[i] != status)
return 0;
}
return 1;
}
static void drop(struct isl_map *map, int i, struct isl_tab **tabs)
{
isl_basic_map_free(map->p[i]);
isl_tab_free(tabs[i]);
if (i != map->n - 1) {
map->p[i] = map->p[map->n - 1];
tabs[i] = tabs[map->n - 1];
}
tabs[map->n - 1] = NULL;
map->n--;
}
/* Replace the pair of basic maps i and j by the basic map bounded
* by the valid constraints in both basic maps and the constraint
* in extra (if not NULL).
*/
static int fuse(struct isl_map *map, int i, int j,
struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j,
__isl_keep isl_mat *extra)
{
int k, l;
struct isl_basic_map *fused = NULL;
struct isl_tab *fused_tab = NULL;
unsigned total = isl_basic_map_total_dim(map->p[i]);
unsigned extra_rows = extra ? extra->n_row : 0;
fused = isl_basic_map_alloc_space(isl_space_copy(map->p[i]->dim),
map->p[i]->n_div,
map->p[i]->n_eq + map->p[j]->n_eq,
map->p[i]->n_ineq + map->p[j]->n_ineq + extra_rows);
if (!fused)
goto error;
for (k = 0; k < map->p[i]->n_eq; ++k) {
if (eq_i && (eq_i[2 * k] != STATUS_VALID ||
eq_i[2 * k + 1] != STATUS_VALID))
continue;
l = isl_basic_map_alloc_equality(fused);
if (l < 0)
goto error;
isl_seq_cpy(fused->eq[l], map->p[i]->eq[k], 1 + total);
}
for (k = 0; k < map->p[j]->n_eq; ++k) {
if (eq_j && (eq_j[2 * k] != STATUS_VALID ||
eq_j[2 * k + 1] != STATUS_VALID))
continue;
l = isl_basic_map_alloc_equality(fused);
if (l < 0)
goto error;
isl_seq_cpy(fused->eq[l], map->p[j]->eq[k], 1 + total);
}
for (k = 0; k < map->p[i]->n_ineq; ++k) {
if (ineq_i[k] != STATUS_VALID)
continue;
l = isl_basic_map_alloc_inequality(fused);
if (l < 0)
goto error;
isl_seq_cpy(fused->ineq[l], map->p[i]->ineq[k], 1 + total);
}
for (k = 0; k < map->p[j]->n_ineq; ++k) {
if (ineq_j[k] != STATUS_VALID)
continue;
l = isl_basic_map_alloc_inequality(fused);
if (l < 0)
goto error;
isl_seq_cpy(fused->ineq[l], map->p[j]->ineq[k], 1 + total);
}
for (k = 0; k < map->p[i]->n_div; ++k) {
int l = isl_basic_map_alloc_div(fused);
if (l < 0)
goto error;
isl_seq_cpy(fused->div[l], map->p[i]->div[k], 1 + 1 + total);
}
for (k = 0; k < extra_rows; ++k) {
l = isl_basic_map_alloc_inequality(fused);
if (l < 0)
goto error;
isl_seq_cpy(fused->ineq[l], extra->row[k], 1 + total);
}
fused = isl_basic_map_gauss(fused, NULL);
ISL_F_SET(fused, ISL_BASIC_MAP_FINAL);
if (ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_RATIONAL) &&
ISL_F_ISSET(map->p[j], ISL_BASIC_MAP_RATIONAL))
ISL_F_SET(fused, ISL_BASIC_MAP_RATIONAL);
fused_tab = isl_tab_from_basic_map(fused, 0);
if (isl_tab_detect_redundant(fused_tab) < 0)
goto error;
isl_basic_map_free(map->p[i]);
map->p[i] = fused;
isl_tab_free(tabs[i]);
tabs[i] = fused_tab;
drop(map, j, tabs);
return 1;
error:
isl_tab_free(fused_tab);
isl_basic_map_free(fused);
return -1;
}
/* Given a pair of basic maps i and j such that all constraints are either
* "valid" or "cut", check if the facets corresponding to the "cut"
* constraints of i lie entirely within basic map j.
* If so, replace the pair by the basic map consisting of the valid
* constraints in both basic maps.
*
* To see that we are not introducing any extra points, call the
* two basic maps A and B and the resulting map U and let x
* be an element of U \setminus ( A \cup B ).
* Then there is a pair of cut constraints c_1 and c_2 in A and B such that x
* violates them. Let X be the intersection of U with the opposites
* of these constraints. Then x \in X.
* The facet corresponding to c_1 contains the corresponding facet of A.
* This facet is entirely contained in B, so c_2 is valid on the facet.
* However, since it is also (part of) a facet of X, -c_2 is also valid
* on the facet. This means c_2 is saturated on the facet, so c_1 and
* c_2 must be opposites of each other, but then x could not violate
* both of them.
*/
static int check_facets(struct isl_map *map, int i, int j,
struct isl_tab **tabs, int *ineq_i, int *ineq_j)
{
int k, l;
struct isl_tab_undo *snap;
unsigned n_eq = map->p[i]->n_eq;
snap = isl_tab_snap(tabs[i]);
for (k = 0; k < map->p[i]->n_ineq; ++k) {
if (ineq_i[k] != STATUS_CUT)
continue;
if (isl_tab_select_facet(tabs[i], n_eq + k) < 0)
return -1;
for (l = 0; l < map->p[j]->n_ineq; ++l) {
int stat;
if (ineq_j[l] != STATUS_CUT)
continue;
stat = status_in(map->p[j]->ineq[l], tabs[i]);
if (stat != STATUS_VALID)
break;
}
if (isl_tab_rollback(tabs[i], snap) < 0)
return -1;
if (l < map->p[j]->n_ineq)
break;
}
if (k < map->p[i]->n_ineq)
/* BAD CUT PAIR */
return 0;
return fuse(map, i, j, tabs, NULL, ineq_i, NULL, ineq_j, NULL);
}
/* Check if basic map "i" contains the basic map represented
* by the tableau "tab".
*/
static int contains(struct isl_map *map, int i, int *ineq_i,
struct isl_tab *tab)
{
int k, l;
unsigned dim;
dim = isl_basic_map_total_dim(map->p[i]);
for (k = 0; k < map->p[i]->n_eq; ++k) {
for (l = 0; l < 2; ++l) {
int stat;
isl_seq_neg(map->p[i]->eq[k], map->p[i]->eq[k], 1+dim);
stat = status_in(map->p[i]->eq[k], tab);
if (stat != STATUS_VALID)
return 0;
}
}
for (k = 0; k < map->p[i]->n_ineq; ++k) {
int stat;
if (ineq_i[k] == STATUS_REDUNDANT)
continue;
stat = status_in(map->p[i]->ineq[k], tab);
if (stat != STATUS_VALID)
return 0;
}
return 1;
}
/* Basic map "i" has an inequality (say "k") that is adjacent
* to some inequality of basic map "j". All the other inequalities
* are valid for "j".
* Check if basic map "j" forms an extension of basic map "i".
*
* Note that this function is only called if some of the equalities or
* inequalities of basic map "j" do cut basic map "i". The function is
* correct even if there are no such cut constraints, but in that case
* the additional checks performed by this function are overkill.
*
* In particular, we replace constraint k, say f >= 0, by constraint
* f <= -1, add the inequalities of "j" that are valid for "i"
* and check if the result is a subset of basic map "j".
* If so, then we know that this result is exactly equal to basic map "j"
* since all its constraints are valid for basic map "j".
* By combining the valid constraints of "i" (all equalities and all
* inequalities except "k") and the valid constraints of "j" we therefore
* obtain a basic map that is equal to their union.
* In this case, there is no need to perform a rollback of the tableau
* since it is going to be destroyed in fuse().
*
*
* |\__ |\__
* | \__ | \__
* | \_ => | \__
* |_______| _ |_________\
*
*
* |\ |\
* | \ | \
* | \ | \
* | | | \
* | ||\ => | \
* | || \ | \
* | || | | |
* |__||_/ |_____/
*/
static int is_adj_ineq_extension(__isl_keep isl_map *map, int i, int j,
struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
{
int k;
struct isl_tab_undo *snap;
unsigned n_eq = map->p[i]->n_eq;
unsigned total = isl_basic_map_total_dim(map->p[i]);
int r;
if (isl_tab_extend_cons(tabs[i], 1 + map->p[j]->n_ineq) < 0)
return -1;
for (k = 0; k < map->p[i]->n_ineq; ++k)
if (ineq_i[k] == STATUS_ADJ_INEQ)
break;
if (k >= map->p[i]->n_ineq)
isl_die(isl_map_get_ctx(map), isl_error_internal,
"ineq_i should have exactly one STATUS_ADJ_INEQ",
return -1);
snap = isl_tab_snap(tabs[i]);
if (isl_tab_unrestrict(tabs[i], n_eq + k) < 0)
return -1;
isl_seq_neg(map->p[i]->ineq[k], map->p[i]->ineq[k], 1 + total);
isl_int_sub_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
r = isl_tab_add_ineq(tabs[i], map->p[i]->ineq[k]);
isl_seq_neg(map->p[i]->ineq[k], map->p[i]->ineq[k], 1 + total);
isl_int_sub_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
if (r < 0)
return -1;
for (k = 0; k < map->p[j]->n_ineq; ++k) {
if (ineq_j[k] != STATUS_VALID)
continue;
if (isl_tab_add_ineq(tabs[i], map->p[j]->ineq[k]) < 0)
return -1;
}
if (contains(map, j, ineq_j, tabs[i]))
return fuse(map, i, j, tabs, eq_i, ineq_i, eq_j, ineq_j, NULL);
if (isl_tab_rollback(tabs[i], snap) < 0)
return -1;
return 0;
}
/* Both basic maps have at least one inequality with and adjacent
* (but opposite) inequality in the other basic map.
* Check that there are no cut constraints and that there is only
* a single pair of adjacent inequalities.
* If so, we can replace the pair by a single basic map described
* by all but the pair of adjacent inequalities.
* Any additional points introduced lie strictly between the two
* adjacent hyperplanes and can therefore be integral.
*
* ____ _____
* / ||\ / \
* / || \ / \
* \ || \ => \ \
* \ || / \ /
* \___||_/ \_____/
*
* The test for a single pair of adjancent inequalities is important
* for avoiding the combination of two basic maps like the following
*
* /|
* / |
* /__|
* _____
* | |
* | |
* |___|
*
* If there are some cut constraints on one side, then we may
* still be able to fuse the two basic maps, but we need to perform
* some additional checks in is_adj_ineq_extension.
*/
static int check_adj_ineq(struct isl_map *map, int i, int j,
struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
{
int count_i, count_j;
int cut_i, cut_j;
count_i = count(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_INEQ);
count_j = count(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_INEQ);
if (count_i != 1 && count_j != 1)
return 0;
cut_i = any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT) ||
any(ineq_i, map->p[i]->n_ineq, STATUS_CUT);
cut_j = any(eq_j, 2 * map->p[j]->n_eq, STATUS_CUT) ||
any(ineq_j, map->p[j]->n_ineq, STATUS_CUT);
if (!cut_i && !cut_j && count_i == 1 && count_j == 1)
return fuse(map, i, j, tabs, NULL, ineq_i, NULL, ineq_j, NULL);
if (count_i == 1 && !cut_i)
return is_adj_ineq_extension(map, i, j, tabs,
eq_i, ineq_i, eq_j, ineq_j);
if (count_j == 1 && !cut_j)
return is_adj_ineq_extension(map, j, i, tabs,
eq_j, ineq_j, eq_i, ineq_i);
return 0;
}
/* Basic map "i" has an inequality "k" that is adjacent to some equality
* of basic map "j". All the other inequalities are valid for "j".
* Check if basic map "j" forms an extension of basic map "i".
*
* In particular, we relax constraint "k", compute the corresponding
* facet and check whether it is included in the other basic map.
* If so, we know that relaxing the constraint extends the basic
* map with exactly the other basic map (we already know that this
* other basic map is included in the extension, because there
* were no "cut" inequalities in "i") and we can replace the
* two basic maps by this extension.
* ____ _____
* / || / |
* / || / |
* \ || => \ |
* \ || \ |
* \___|| \____|
*/
static int is_adj_eq_extension(struct isl_map *map, int i, int j, int k,
struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
{
int changed = 0;
int super;
struct isl_tab_undo *snap, *snap2;
unsigned n_eq = map->p[i]->n_eq;
if (isl_tab_is_equality(tabs[i], n_eq + k))
return 0;
snap = isl_tab_snap(tabs[i]);
tabs[i] = isl_tab_relax(tabs[i], n_eq + k);
snap2 = isl_tab_snap(tabs[i]);
if (isl_tab_select_facet(tabs[i], n_eq + k) < 0)
return -1;
super = contains(map, j, ineq_j, tabs[i]);
if (super) {
if (isl_tab_rollback(tabs[i], snap2) < 0)
return -1;
map->p[i] = isl_basic_map_cow(map->p[i]);
if (!map->p[i])
return -1;
isl_int_add_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
ISL_F_SET(map->p[i], ISL_BASIC_MAP_FINAL);
drop(map, j, tabs);
changed = 1;
} else
if (isl_tab_rollback(tabs[i], snap) < 0)
return -1;
return changed;
}
/* Data structure that keeps track of the wrapping constraints
* and of information to bound the coefficients of those constraints.
*
* bound is set if we want to apply a bound on the coefficients
* mat contains the wrapping constraints
* max is the bound on the coefficients (if bound is set)
*/
struct isl_wraps {
int bound;
isl_mat *mat;
isl_int max;
};
/* Update wraps->max to be greater than or equal to the coefficients
* in the equalities and inequalities of bmap that can be removed if we end up
* applying wrapping.
*/
static void wraps_update_max(struct isl_wraps *wraps,
__isl_keep isl_basic_map *bmap, int *eq, int *ineq)
{
int k;
isl_int max_k;
unsigned total = isl_basic_map_total_dim(bmap);
isl_int_init(max_k);
for (k = 0; k < bmap->n_eq; ++k) {
if (eq[2 * k] == STATUS_VALID &&
eq[2 * k + 1] == STATUS_VALID)
continue;
isl_seq_abs_max(bmap->eq[k] + 1, total, &max_k);
if (isl_int_abs_gt(max_k, wraps->max))
isl_int_set(wraps->max, max_k);
}
for (k = 0; k < bmap->n_ineq; ++k) {
if (ineq[k] == STATUS_VALID || ineq[k] == STATUS_REDUNDANT)
continue;
isl_seq_abs_max(bmap->ineq[k] + 1, total, &max_k);
if (isl_int_abs_gt(max_k, wraps->max))
isl_int_set(wraps->max, max_k);
}
isl_int_clear(max_k);
}
/* Initialize the isl_wraps data structure.
* If we want to bound the coefficients of the wrapping constraints,
* we set wraps->max to the largest coefficient
* in the equalities and inequalities that can be removed if we end up
* applying wrapping.
*/
static void wraps_init(struct isl_wraps *wraps, __isl_take isl_mat *mat,
__isl_keep isl_map *map, int i, int j,
int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
{
isl_ctx *ctx;
wraps->bound = 0;
wraps->mat = mat;
if (!mat)
return;
ctx = isl_mat_get_ctx(mat);
wraps->bound = isl_options_get_coalesce_bounded_wrapping(ctx);
if (!wraps->bound)
return;
isl_int_init(wraps->max);
isl_int_set_si(wraps->max, 0);
wraps_update_max(wraps, map->p[i], eq_i, ineq_i);
wraps_update_max(wraps, map->p[j], eq_j, ineq_j);
}
/* Free the contents of the isl_wraps data structure.
*/
static void wraps_free(struct isl_wraps *wraps)
{
isl_mat_free(wraps->mat);
if (wraps->bound)
isl_int_clear(wraps->max);
}
/* Is the wrapping constraint in row "row" allowed?
*
* If wraps->bound is set, we check that none of the coefficients
* is greater than wraps->max.
*/
static int allow_wrap(struct isl_wraps *wraps, int row)
{
int i;
if (!wraps->bound)
return 1;
for (i = 1; i < wraps->mat->n_col; ++i)
if (isl_int_abs_gt(wraps->mat->row[row][i], wraps->max))
return 0;
return 1;
}
/* For each non-redundant constraint in "bmap" (as determined by "tab"),
* wrap the constraint around "bound" such that it includes the whole
* set "set" and append the resulting constraint to "wraps".
* "wraps" is assumed to have been pre-allocated to the appropriate size.
* wraps->n_row is the number of actual wrapped constraints that have
* been added.
* If any of the wrapping problems results in a constraint that is
* identical to "bound", then this means that "set" is unbounded in such
* way that no wrapping is possible. If this happens then wraps->n_row
* is reset to zero.
* Similarly, if we want to bound the coefficients of the wrapping
* constraints and a newly added wrapping constraint does not
* satisfy the bound, then wraps->n_row is also reset to zero.
*/
static int add_wraps(struct isl_wraps *wraps, __isl_keep isl_basic_map *bmap,
struct isl_tab *tab, isl_int *bound, __isl_keep isl_set *set)
{
int l;
int w;
unsigned total = isl_basic_map_total_dim(bmap);
w = wraps->mat->n_row;
for (l = 0; l < bmap->n_ineq; ++l) {
if (isl_seq_is_neg(bound, bmap->ineq[l], 1 + total))
continue;
if (isl_seq_eq(bound, bmap->ineq[l], 1 + total))
continue;
if (isl_tab_is_redundant(tab, bmap->n_eq + l))
continue;
isl_seq_cpy(wraps->mat->row[w], bound, 1 + total);
if (!isl_set_wrap_facet(set, wraps->mat->row[w], bmap->ineq[l]))
return -1;
if (isl_seq_eq(wraps->mat->row[w], bound, 1 + total))
goto unbounded;
if (!allow_wrap(wraps, w))
goto unbounded;
++w;
}
for (l = 0; l < bmap->n_eq; ++l) {
if (isl_seq_is_neg(bound, bmap->eq[l], 1 + total))
continue;
if (isl_seq_eq(bound, bmap->eq[l], 1 + total))
continue;
isl_seq_cpy(wraps->mat->row[w], bound, 1 + total);
isl_seq_neg(wraps->mat->row[w + 1], bmap->eq[l], 1 + total);
if (!isl_set_wrap_facet(set, wraps->mat->row[w],
wraps->mat->row[w + 1]))
return -1;
if (isl_seq_eq(wraps->mat->row[w], bound, 1 + total))
goto unbounded;
if (!allow_wrap(wraps, w))
goto unbounded;
++w;
isl_seq_cpy(wraps->mat->row[w], bound, 1 + total);
if (!isl_set_wrap_facet(set, wraps->mat->row[w], bmap->eq[l]))
return -1;
if (isl_seq_eq(wraps->mat->row[w], bound, 1 + total))
goto unbounded;
if (!allow_wrap(wraps, w))
goto unbounded;
++w;
}
wraps->mat->n_row = w;
return 0;
unbounded:
wraps->mat->n_row = 0;
return 0;
}
/* Check if the constraints in "wraps" from "first" until the last
* are all valid for the basic set represented by "tab".
* If not, wraps->n_row is set to zero.
*/
static int check_wraps(__isl_keep isl_mat *wraps, int first,
struct isl_tab *tab)
{
int i;
for (i = first; i < wraps->n_row; ++i) {
enum isl_ineq_type type;
type = isl_tab_ineq_type(tab, wraps->row[i]);
if (type == isl_ineq_error)
return -1;
if (type == isl_ineq_redundant)
continue;
wraps->n_row = 0;
return 0;
}
return 0;
}
/* Return a set that corresponds to the non-redudant constraints
* (as recorded in tab) of bmap.
*
* It's important to remove the redundant constraints as some
* of the other constraints may have been modified after the
* constraints were marked redundant.
* In particular, a constraint may have been relaxed.
* Redundant constraints are ignored when a constraint is relaxed
* and should therefore continue to be ignored ever after.
* Otherwise, the relaxation might be thwarted by some of
* these constraints.
*/
static __isl_give isl_set *set_from_updated_bmap(__isl_keep isl_basic_map *bmap,
struct isl_tab *tab)
{
bmap = isl_basic_map_copy(bmap);
bmap = isl_basic_map_cow(bmap);
bmap = isl_basic_map_update_from_tab(bmap, tab);
return isl_set_from_basic_set(isl_basic_map_underlying_set(bmap));
}
/* Given a basic set i with a constraint k that is adjacent to either the
* whole of basic set j or a facet of basic set j, check if we can wrap
* both the facet corresponding to k and the facet of j (or the whole of j)
* around their ridges to include the other set.
* If so, replace the pair of basic sets by their union.
*
* All constraints of i (except k) are assumed to be valid for j.
*
* However, the constraints of j may not be valid for i and so
* we have to check that the wrapping constraints for j are valid for i.
*
* In the case where j has a facet adjacent to i, tab[j] is assumed
* to have been restricted to this facet, so that the non-redundant
* constraints in tab[j] are the ridges of the facet.
* Note that for the purpose of wrapping, it does not matter whether
* we wrap the ridges of i around the whole of j or just around
* the facet since all the other constraints are assumed to be valid for j.
* In practice, we wrap to include the whole of j.
* ____ _____
* / | / \
* / || / |
* \ || => \ |
* \ || \ |
* \___|| \____|
*
*/
static int can_wrap_in_facet(struct isl_map *map, int i, int j, int k,
struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
{
int changed = 0;
struct isl_wraps wraps;
isl_mat *mat;
struct isl_set *set_i = NULL;
struct isl_set *set_j = NULL;
struct isl_vec *bound = NULL;
unsigned total = isl_basic_map_total_dim(map->p[i]);
struct isl_tab_undo *snap;
int n;
set_i = set_from_updated_bmap(map->p[i], tabs[i]);
set_j = set_from_updated_bmap(map->p[j], tabs[j]);
mat = isl_mat_alloc(map->ctx, 2 * (map->p[i]->n_eq + map->p[j]->n_eq) +
map->p[i]->n_ineq + map->p[j]->n_ineq,
1 + total);
wraps_init(&wraps, mat, map, i, j, eq_i, ineq_i, eq_j, ineq_j);
bound = isl_vec_alloc(map->ctx, 1 + total);
if (!set_i || !set_j || !wraps.mat || !bound)
goto error;
isl_seq_cpy(bound->el, map->p[i]->ineq[k], 1 + total);
isl_int_add_ui(bound->el[0], bound->el[0], 1);
isl_seq_cpy(wraps.mat->row[0], bound->el, 1 + total);
wraps.mat->n_row = 1;
if (add_wraps(&wraps, map->p[j], tabs[j], bound->el, set_i) < 0)
goto error;
if (!wraps.mat->n_row)
goto unbounded;
snap = isl_tab_snap(tabs[i]);
if (isl_tab_select_facet(tabs[i], map->p[i]->n_eq + k) < 0)
goto error;
if (isl_tab_detect_redundant(tabs[i]) < 0)
goto error;
isl_seq_neg(bound->el, map->p[i]->ineq[k], 1 + total);
n = wraps.mat->n_row;
if (add_wraps(&wraps, map->p[i], tabs[i], bound->el, set_j) < 0)
goto error;
if (isl_tab_rollback(tabs[i], snap) < 0)
goto error;
if (check_wraps(wraps.mat, n, tabs[i]) < 0)
goto error;
if (!wraps.mat->n_row)
goto unbounded;
changed = fuse(map, i, j, tabs, eq_i, ineq_i, eq_j, ineq_j, wraps.mat);
unbounded:
wraps_free(&wraps);
isl_set_free(set_i);
isl_set_free(set_j);
isl_vec_free(bound);
return changed;
error:
wraps_free(&wraps);
isl_vec_free(bound);
isl_set_free(set_i);
isl_set_free(set_j);
return -1;
}
/* Set the is_redundant property of the "n" constraints in "cuts",
* except "k" to "v".
* This is a fairly tricky operation as it bypasses isl_tab.c.
* The reason we want to temporarily mark some constraints redundant
* is that we want to ignore them in add_wraps.
*
* Initially all cut constraints are non-redundant, but the
* selection of a facet right before the call to this function
* may have made some of them redundant.
* Likewise, the same constraints are marked non-redundant
* in the second call to this function, before they are officially
* made non-redundant again in the subsequent rollback.
*/
static void set_is_redundant(struct isl_tab *tab, unsigned n_eq,
int *cuts, int n, int k, int v)
{
int l;
for (l = 0; l < n; ++l) {
if (l == k)
continue;
tab->con[n_eq + cuts[l]].is_redundant = v;
}
}
/* Given a pair of basic maps i and j such that j sticks out
* of i at n cut constraints, each time by at most one,
* try to compute wrapping constraints and replace the two
* basic maps by a single basic map.
* The other constraints of i are assumed to be valid for j.
*
* The facets of i corresponding to the cut constraints are
* wrapped around their ridges, except those ridges determined
* by any of the other cut constraints.
* The intersections of cut constraints need to be ignored
* as the result of wrapping one cut constraint around another
* would result in a constraint cutting the union.
* In each case, the facets are wrapped to include the union
* of the two basic maps.
*
* The pieces of j that lie at an offset of exactly one from
* one of the cut constraints of i are wrapped around their edges.
* Here, there is no need to ignore intersections because we
* are wrapping around the union of the two basic maps.
*
* If any wrapping fails, i.e., if we cannot wrap to touch
* the union, then we give up.
* Otherwise, the pair of basic maps is replaced by their union.
*/
static int wrap_in_facets(struct isl_map *map, int i, int j,
int *cuts, int n, struct isl_tab **tabs,
int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
{
int changed = 0;
struct isl_wraps wraps;
isl_mat *mat;
isl_set *set = NULL;
isl_vec *bound = NULL;
unsigned total = isl_basic_map_total_dim(map->p[i]);
int max_wrap;
int k;
struct isl_tab_undo *snap_i, *snap_j;
if (isl_tab_extend_cons(tabs[j], 1) < 0)
goto error;
max_wrap = 2 * (map->p[i]->n_eq + map->p[j]->n_eq) +
map->p[i]->n_ineq + map->p[j]->n_ineq;
max_wrap *= n;
set = isl_set_union(set_from_updated_bmap(map->p[i], tabs[i]),
set_from_updated_bmap(map->p[j], tabs[j]));
mat = isl_mat_alloc(map->ctx, max_wrap, 1 + total);
wraps_init(&wraps, mat, map, i, j, eq_i, ineq_i, eq_j, ineq_j);
bound = isl_vec_alloc(map->ctx, 1 + total);
if (!set || !wraps.mat || !bound)
goto error;
snap_i = isl_tab_snap(tabs[i]);
snap_j = isl_tab_snap(tabs[j]);
wraps.mat->n_row = 0;
for (k = 0; k < n; ++k) {
if (isl_tab_select_facet(tabs[i], map->p[i]->n_eq + cuts[k]) < 0)
goto error;
if (isl_tab_detect_redundant(tabs[i]) < 0)
goto error;
set_is_redundant(tabs[i], map->p[i]->n_eq, cuts, n, k, 1);
isl_seq_neg(bound->el, map->p[i]->ineq[cuts[k]], 1 + total);
if (!tabs[i]->empty &&
add_wraps(&wraps, map->p[i], tabs[i], bound->el, set) < 0)
goto error;
set_is_redundant(tabs[i], map->p[i]->n_eq, cuts, n, k, 0);
if (isl_tab_rollback(tabs[i], snap_i) < 0)
goto error;
if (tabs[i]->empty)
break;
if (!wraps.mat->n_row)
break;
isl_seq_cpy(bound->el, map->p[i]->ineq[cuts[k]], 1 + total);
isl_int_add_ui(bound->el[0], bound->el[0], 1);
if (isl_tab_add_eq(tabs[j], bound->el) < 0)
goto error;
if (isl_tab_detect_redundant(tabs[j]) < 0)
goto error;
if (!tabs[j]->empty &&
add_wraps(&wraps, map->p[j], tabs[j], bound->el, set) < 0)
goto error;
if (isl_tab_rollback(tabs[j], snap_j) < 0)
goto error;
if (!wraps.mat->n_row)
break;
}
if (k == n)
changed = fuse(map, i, j, tabs,
eq_i, ineq_i, eq_j, ineq_j, wraps.mat);
isl_vec_free(bound);
wraps_free(&wraps);
isl_set_free(set);
return changed;
error:
isl_vec_free(bound);
wraps_free(&wraps);
isl_set_free(set);
return -1;
}
/* Given two basic sets i and j such that i has no cut equalities,
* check if relaxing all the cut inequalities of i by one turns
* them into valid constraint for j and check if we can wrap in
* the bits that are sticking out.
* If so, replace the pair by their union.
*
* We first check if all relaxed cut inequalities of i are valid for j
* and then try to wrap in the intersections of the relaxed cut inequalities
* with j.
*
* During this wrapping, we consider the points of j that lie at a distance
* of exactly 1 from i. In particular, we ignore the points that lie in
* between this lower-dimensional space and the basic map i.
* We can therefore only apply this to integer maps.
* ____ _____
* / ___|_ / \
* / | | / |
* \ | | => \ |
* \|____| \ |
* \___| \____/
*
* _____ ______
* | ____|_ | \
* | | | | |
* | | | => | |
* |_| | | |
* |_____| \______|
*
* _______
* | |
* | |\ |
* | | \ |
* | | \ |
* | | \|
* | | \
* | |_____\
* | |
* |_______|
*
* Wrapping can fail if the result of wrapping one of the facets
* around its edges does not produce any new facet constraint.
* In particular, this happens when we try to wrap in unbounded sets.
*
* _______________________________________________________________________
* |
* | ___
* | | |
* |_| |_________________________________________________________________
* |___|
*
* The following is not an acceptable result of coalescing the above two
* sets as it includes extra integer points.
* _______________________________________________________________________
* |
* |
* |
* |
* \______________________________________________________________________
*/
static int can_wrap_in_set(struct isl_map *map, int i, int j,
struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
{
int changed = 0;
int k, m;
int n;
int *cuts = NULL;
if (ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_RATIONAL) ||
ISL_F_ISSET(map->p[j], ISL_BASIC_MAP_RATIONAL))
return 0;
n = count(ineq_i, map->p[i]->n_ineq, STATUS_CUT);
if (n == 0)
return 0;
cuts = isl_alloc_array(map->ctx, int, n);
if (!cuts)
return -1;
for (k = 0, m = 0; m < n; ++k) {
enum isl_ineq_type type;
if (ineq_i[k] != STATUS_CUT)
continue;
isl_int_add_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
type = isl_tab_ineq_type(tabs[j], map->p[i]->ineq[k]);
isl_int_sub_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
if (type == isl_ineq_error)
goto error;
if (type != isl_ineq_redundant)
break;
cuts[m] = k;
++m;
}
if (m == n)
changed = wrap_in_facets(map, i, j, cuts, n, tabs,
eq_i, ineq_i, eq_j, ineq_j);
free(cuts);
return changed;
error:
free(cuts);
return -1;
}
/* Check if either i or j has a single cut constraint that can
* be used to wrap in (a facet of) the other basic set.
* if so, replace the pair by their union.
*/
static int check_wrap(struct isl_map *map, int i, int j,
struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
{
int changed = 0;
if (!any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT))
changed = can_wrap_in_set(map, i, j, tabs,
eq_i, ineq_i, eq_j, ineq_j);
if (changed)
return changed;
if (!any(eq_j, 2 * map->p[j]->n_eq, STATUS_CUT))
changed = can_wrap_in_set(map, j, i, tabs,
eq_j, ineq_j, eq_i, ineq_i);
return changed;
}
/* At least one of the basic maps has an equality that is adjacent
* to inequality. Make sure that only one of the basic maps has
* such an equality and that the other basic map has exactly one
* inequality adjacent to an equality.
* We call the basic map that has the inequality "i" and the basic
* map that has the equality "j".
* If "i" has any "cut" (in)equality, then relaxing the inequality
* by one would not result in a basic map that contains the other
* basic map.
*/
static int check_adj_eq(struct isl_map *map, int i, int j,
struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
{
int changed = 0;
int k;
if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_INEQ) &&
any(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_INEQ))
/* ADJ EQ TOO MANY */
return 0;
if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_INEQ))
return check_adj_eq(map, j, i, tabs,
eq_j, ineq_j, eq_i, ineq_i);
/* j has an equality adjacent to an inequality in i */
if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT))
return 0;
if (any(ineq_i, map->p[i]->n_ineq, STATUS_CUT))
/* ADJ EQ CUT */
return 0;
if (count(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_EQ) != 1 ||
any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_EQ) ||
any(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_INEQ) ||
any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_INEQ))
/* ADJ EQ TOO MANY */
return 0;
for (k = 0; k < map->p[i]->n_ineq; ++k)
if (ineq_i[k] == STATUS_ADJ_EQ)
break;
changed = is_adj_eq_extension(map, i, j, k, tabs,
eq_i, ineq_i, eq_j, ineq_j);
if (changed)
return changed;
if (count(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_INEQ) != 1)
return 0;
changed = can_wrap_in_facet(map, i, j, k, tabs, eq_i, ineq_i, eq_j, ineq_j);
return changed;
}
/* The two basic maps lie on adjacent hyperplanes. In particular,
* basic map "i" has an equality that lies parallel to basic map "j".
* Check if we can wrap the facets around the parallel hyperplanes
* to include the other set.
*
* We perform basically the same operations as can_wrap_in_facet,
* except that we don't need to select a facet of one of the sets.
* _
* \\ \\
* \\ => \\
* \ \|
*
* We only allow one equality of "i" to be adjacent to an equality of "j"
* to avoid coalescing
*
* [m, n] -> { [x, y] -> [x, 1 + y] : x >= 1 and y >= 1 and
* x <= 10 and y <= 10;
* [x, y] -> [1 + x, y] : x >= 1 and x <= 20 and
* y >= 5 and y <= 15 }
*
* to
*
* [m, n] -> { [x, y] -> [x2, y2] : x >= 1 and 10y2 <= 20 - x + 10y and
* 4y2 >= 5 + 3y and 5y2 <= 15 + 4y and
* y2 <= 1 + x + y - x2 and y2 >= y and
* y2 >= 1 + x + y - x2 }
*/
static int check_eq_adj_eq(struct isl_map *map, int i, int j,
struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
{
int k;
int changed = 0;
struct isl_wraps wraps;
isl_mat *mat;
struct isl_set *set_i = NULL;
struct isl_set *set_j = NULL;
struct isl_vec *bound = NULL;
unsigned total = isl_basic_map_total_dim(map->p[i]);
if (count(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_EQ) != 1)
return 0;
for (k = 0; k < 2 * map->p[i]->n_eq ; ++k)
if (eq_i[k] == STATUS_ADJ_EQ)
break;
set_i = set_from_updated_bmap(map->p[i], tabs[i]);
set_j = set_from_updated_bmap(map->p[j], tabs[j]);
mat = isl_mat_alloc(map->ctx, 2 * (map->p[i]->n_eq + map->p[j]->n_eq) +
map->p[i]->n_ineq + map->p[j]->n_ineq,
1 + total);
wraps_init(&wraps, mat, map, i, j, eq_i, ineq_i, eq_j, ineq_j);
bound = isl_vec_alloc(map->ctx, 1 + total);
if (!set_i || !set_j || !wraps.mat || !bound)
goto error;
if (k % 2 == 0)
isl_seq_neg(bound->el, map->p[i]->eq[k / 2], 1 + total);
else
isl_seq_cpy(bound->el, map->p[i]->eq[k / 2], 1 + total);
isl_int_add_ui(bound->el[0], bound->el[0], 1);
isl_seq_cpy(wraps.mat->row[0], bound->el, 1 + total);
wraps.mat->n_row = 1;
if (add_wraps(&wraps, map->p[j], tabs[j], bound->el, set_i) < 0)
goto error;
if (!wraps.mat->n_row)
goto unbounded;
isl_int_sub_ui(bound->el[0], bound->el[0], 1);
isl_seq_neg(bound->el, bound->el, 1 + total);
isl_seq_cpy(wraps.mat->row[wraps.mat->n_row], bound->el, 1 + total);
wraps.mat->n_row++;
if (add_wraps(&wraps, map->p[i], tabs[i], bound->el, set_j) < 0)
goto error;
if (!wraps.mat->n_row)
goto unbounded;
changed = fuse(map, i, j, tabs, eq_i, ineq_i, eq_j, ineq_j, wraps.mat);
if (0) {
error: changed = -1;
}
unbounded:
wraps_free(&wraps);
isl_set_free(set_i);
isl_set_free(set_j);
isl_vec_free(bound);
return changed;
}
/* Check if the union of the given pair of basic maps
* can be represented by a single basic map.
* If so, replace the pair by the single basic map and return 1.
* Otherwise, return 0;
* The two basic maps are assumed to live in the same local space.
*
* We first check the effect of each constraint of one basic map
* on the other basic map.
* The constraint may be
* redundant the constraint is redundant in its own
* basic map and should be ignore and removed
* in the end
* valid all (integer) points of the other basic map
* satisfy the constraint
* separate no (integer) point of the other basic map
* satisfies the constraint
* cut some but not all points of the other basic map
* satisfy the constraint
* adj_eq the given constraint is adjacent (on the outside)
* to an equality of the other basic map
* adj_ineq the given constraint is adjacent (on the outside)
* to an inequality of the other basic map
*
* We consider seven cases in which we can replace the pair by a single
* basic map. We ignore all "redundant" constraints.
*
* 1. all constraints of one basic map are valid
* => the other basic map is a subset and can be removed
*
* 2. all constraints of both basic maps are either "valid" or "cut"
* and the facets corresponding to the "cut" constraints
* of one of the basic maps lies entirely inside the other basic map
* => the pair can be replaced by a basic map consisting
* of the valid constraints in both basic maps
*
* 3. there is a single pair of adjacent inequalities
* (all other constraints are "valid")
* => the pair can be replaced by a basic map consisting
* of the valid constraints in both basic maps
*
* 4. one basic map has a single adjacent inequality, while the other
* constraints are "valid". The other basic map has some
* "cut" constraints, but replacing the adjacent inequality by
* its opposite and adding the valid constraints of the other
* basic map results in a subset of the other basic map
* => the pair can be replaced by a basic map consisting
* of the valid constraints in both basic maps
*
* 5. there is a single adjacent pair of an inequality and an equality,
* the other constraints of the basic map containing the inequality are
* "valid". Moreover, if the inequality the basic map is relaxed
* and then turned into an equality, then resulting facet lies
* entirely inside the other basic map
* => the pair can be replaced by the basic map containing
* the inequality, with the inequality relaxed.
*
* 6. there is a single adjacent pair of an inequality and an equality,
* the other constraints of the basic map containing the inequality are
* "valid". Moreover, the facets corresponding to both
* the inequality and the equality can be wrapped around their
* ridges to include the other basic map
* => the pair can be replaced by a basic map consisting
* of the valid constraints in both basic maps together
* with all wrapping constraints
*
* 7. one of the basic maps extends beyond the other by at most one.
* Moreover, the facets corresponding to the cut constraints and
* the pieces of the other basic map at offset one from these cut
* constraints can be wrapped around their ridges to include
* the union of the two basic maps
* => the pair can be replaced by a basic map consisting
* of the valid constraints in both basic maps together
* with all wrapping constraints
*
* 8. the two basic maps live in adjacent hyperplanes. In principle
* such sets can always be combined through wrapping, but we impose
* that there is only one such pair, to avoid overeager coalescing.
*
* Throughout the computation, we maintain a collection of tableaus
* corresponding to the basic maps. When the basic maps are dropped
* or combined, the tableaus are modified accordingly.
*/
static int coalesce_local_pair(__isl_keep isl_map *map, int i, int j,
struct isl_tab **tabs)
{
int changed = 0;
int *eq_i = NULL;
int *eq_j = NULL;
int *ineq_i = NULL;
int *ineq_j = NULL;
eq_i = eq_status_in(map->p[i], tabs[j]);
if (map->p[i]->n_eq && !eq_i)
goto error;
if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ERROR))
goto error;
if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_SEPARATE))
goto done;
eq_j = eq_status_in(map->p[j], tabs[i]);
if (map->p[j]->n_eq && !eq_j)
goto error;
if (any(eq_j, 2 * map->p[j]->n_eq, STATUS_ERROR))
goto error;
if (any(eq_j, 2 * map->p[j]->n_eq, STATUS_SEPARATE))
goto done;
ineq_i = ineq_status_in(map->p[i], tabs[i], tabs[j]);
if (map->p[i]->n_ineq && !ineq_i)
goto error;
if (any(ineq_i, map->p[i]->n_ineq, STATUS_ERROR))
goto error;
if (any(ineq_i, map->p[i]->n_ineq, STATUS_SEPARATE))
goto done;
ineq_j = ineq_status_in(map->p[j], tabs[j], tabs[i]);
if (map->p[j]->n_ineq && !ineq_j)
goto error;
if (any(ineq_j, map->p[j]->n_ineq, STATUS_ERROR))
goto error;
if (any(ineq_j, map->p[j]->n_ineq, STATUS_SEPARATE))
goto done;
if (all(eq_i, 2 * map->p[i]->n_eq, STATUS_VALID) &&
all(ineq_i, map->p[i]->n_ineq, STATUS_VALID)) {
drop(map, j, tabs);
changed = 1;
} else if (all(eq_j, 2 * map->p[j]->n_eq, STATUS_VALID) &&
all(ineq_j, map->p[j]->n_ineq, STATUS_VALID)) {
drop(map, i, tabs);
changed = 1;
} else if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_EQ)) {
changed = check_eq_adj_eq(map, i, j, tabs,
eq_i, ineq_i, eq_j, ineq_j);
} else if (any(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_EQ)) {
changed = check_eq_adj_eq(map, j, i, tabs,
eq_j, ineq_j, eq_i, ineq_i);
} else if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_INEQ) ||
any(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_INEQ)) {
changed = check_adj_eq(map, i, j, tabs,
eq_i, ineq_i, eq_j, ineq_j);
} else if (any(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_EQ) ||
any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_EQ)) {
/* Can't happen */
/* BAD ADJ INEQ */
} else if (any(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_INEQ) ||
any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_INEQ)) {
changed = check_adj_ineq(map, i, j, tabs,
eq_i, ineq_i, eq_j, ineq_j);
} else {
if (!any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT) &&
!any(eq_j, 2 * map->p[j]->n_eq, STATUS_CUT))
changed = check_facets(map, i, j, tabs, ineq_i, ineq_j);
if (!changed)
changed = check_wrap(map, i, j, tabs,
eq_i, ineq_i, eq_j, ineq_j);
}
done:
free(eq_i);
free(eq_j);
free(ineq_i);
free(ineq_j);
return changed;
error:
free(eq_i);
free(eq_j);
free(ineq_i);
free(ineq_j);
return -1;
}
/* Do the two basic maps live in the same local space, i.e.,
* do they have the same (known) divs?
* If either basic map has any unknown divs, then we can only assume
* that they do not live in the same local space.
*/
static int same_divs(__isl_keep isl_basic_map *bmap1,
__isl_keep isl_basic_map *bmap2)
{
int i;
int known;
int total;
if (!bmap1 || !bmap2)
return -1;
if (bmap1->n_div != bmap2->n_div)
return 0;
if (bmap1->n_div == 0)
return 1;
known = isl_basic_map_divs_known(bmap1);
if (known < 0 || !known)
return known;
known = isl_basic_map_divs_known(bmap2);
if (known < 0 || !known)
return known;
total = isl_basic_map_total_dim(bmap1);
for (i = 0; i < bmap1->n_div; ++i)
if (!isl_seq_eq(bmap1->div[i], bmap2->div[i], 2 + total))
return 0;
return 1;
}
/* Given two basic maps "i" and "j", where the divs of "i" form a subset
* of those of "j", check if basic map "j" is a subset of basic map "i"
* and, if so, drop basic map "j".
*
* We first expand the divs of basic map "i" to match those of basic map "j",
* using the divs and expansion computed by the caller.
* Then we check if all constraints of the expanded "i" are valid for "j".
*/
static int coalesce_subset(__isl_keep isl_map *map, int i, int j,
struct isl_tab **tabs, __isl_keep isl_mat *div, int *exp)
{
isl_basic_map *bmap;
int changed = 0;
int *eq_i = NULL;
int *ineq_i = NULL;
bmap = isl_basic_map_copy(map->p[i]);
bmap = isl_basic_set_expand_divs(bmap, isl_mat_copy(div), exp);
if (!bmap)
goto error;
eq_i = eq_status_in(bmap, tabs[j]);
if (bmap->n_eq && !eq_i)
goto error;
if (any(eq_i, 2 * bmap->n_eq, STATUS_ERROR))
goto error;
if (any(eq_i, 2 * bmap->n_eq, STATUS_SEPARATE))
goto done;
ineq_i = ineq_status_in(bmap, NULL, tabs[j]);
if (bmap->n_ineq && !ineq_i)
goto error;
if (any(ineq_i, bmap->n_ineq, STATUS_ERROR))
goto error;
if (any(ineq_i, bmap->n_ineq, STATUS_SEPARATE))
goto done;
if (all(eq_i, 2 * map->p[i]->n_eq, STATUS_VALID) &&
all(ineq_i, map->p[i]->n_ineq, STATUS_VALID)) {
drop(map, j, tabs);
changed = 1;
}
done:
isl_basic_map_free(bmap);
free(eq_i);
free(ineq_i);
return 0;
error:
isl_basic_map_free(bmap);
free(eq_i);
free(ineq_i);
return -1;
}
/* Check if the basic map "j" is a subset of basic map "i",
* assuming that "i" has fewer divs that "j".
* If not, then we change the order.
*
* If the two basic maps have the same number of divs, then
* they must necessarily be different. Otherwise, we would have
* called coalesce_local_pair. We therefore don't try anything
* in this case.
*
* We first check if the divs of "i" are all known and form a subset
* of those of "j". If so, we pass control over to coalesce_subset.
*/
static int check_coalesce_subset(__isl_keep isl_map *map, int i, int j,
struct isl_tab **tabs)
{
int known;
isl_mat *div_i, *div_j, *div;
int *exp1 = NULL;
int *exp2 = NULL;
isl_ctx *ctx;
int subset;
if (map->p[i]->n_div == map->p[j]->n_div)
return 0;
if (map->p[j]->n_div < map->p[i]->n_div)
return check_coalesce_subset(map, j, i, tabs);
known = isl_basic_map_divs_known(map->p[i]);
if (known < 0 || !known)
return known;
ctx = isl_map_get_ctx(map);
div_i = isl_basic_map_get_divs(map->p[i]);
div_j = isl_basic_map_get_divs(map->p[j]);
if (!div_i || !div_j)
goto error;
exp1 = isl_alloc_array(ctx, int, div_i->n_row);
exp2 = isl_alloc_array(ctx, int, div_j->n_row);
if ((div_i->n_row && !exp1) || (div_j->n_row && !exp2))
goto error;
div = isl_merge_divs(div_i, div_j, exp1, exp2);
if (!div)
goto error;
if (div->n_row == div_j->n_row)
subset = coalesce_subset(map, i, j, tabs, div, exp1);
else
subset = 0;
isl_mat_free(div);
isl_mat_free(div_i);
isl_mat_free(div_j);
free(exp2);
free(exp1);
return subset;
error:
isl_mat_free(div_i);
isl_mat_free(div_j);
free(exp1);
free(exp2);
return -1;
}
/* Check if the union of the given pair of basic maps
* can be represented by a single basic map.
* If so, replace the pair by the single basic map and return 1.
* Otherwise, return 0;
*
* We first check if the two basic maps live in the same local space.
* If so, we do the complete check. Otherwise, we check if one is
* an obvious subset of the other.
*/
static int coalesce_pair(__isl_keep isl_map *map, int i, int j,
struct isl_tab **tabs)
{
int same;
same = same_divs(map->p[i], map->p[j]);
if (same < 0)
return -1;
if (same)
return coalesce_local_pair(map, i, j, tabs);
return check_coalesce_subset(map, i, j, tabs);
}
static struct isl_map *coalesce(struct isl_map *map, struct isl_tab **tabs)
{
int i, j;
for (i = map->n - 2; i >= 0; --i)
restart:
for (j = i + 1; j < map->n; ++j) {
int changed;
changed = coalesce_pair(map, i, j, tabs);
if (changed < 0)
goto error;
if (changed)
goto restart;
}
return map;
error:
isl_map_free(map);
return NULL;
}
/* For each pair of basic maps in the map, check if the union of the two
* can be represented by a single basic map.
* If so, replace the pair by the single basic map and start over.
*
* Since we are constructing the tableaus of the basic maps anyway,
* we exploit them to detect implicit equalities and redundant constraints.
* This also helps the coalescing as it can ignore the redundant constraints.
* In order to avoid confusion, we make all implicit equalities explicit
* in the basic maps. We don't call isl_basic_map_gauss, though,
* as that may affect the number of constraints.
* This means that we have to call isl_basic_map_gauss at the end
* of the computation to ensure that the basic maps are not left
* in an unexpected state.
*/
struct isl_map *isl_map_coalesce(struct isl_map *map)
{
int i;
unsigned n;
struct isl_tab **tabs = NULL;
map = isl_map_remove_empty_parts(map);
if (!map)
return NULL;
if (map->n <= 1)
return map;
map = isl_map_sort_divs(map);
map = isl_map_cow(map);
if (!map)
return NULL;
tabs = isl_calloc_array(map->ctx, struct isl_tab *, map->n);
if (!tabs)
goto error;
n = map->n;
for (i = 0; i < map->n; ++i) {
tabs[i] = isl_tab_from_basic_map(map->p[i], 0);
if (!tabs[i])
goto error;
if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_NO_IMPLICIT))
if (isl_tab_detect_implicit_equalities(tabs[i]) < 0)
goto error;
map->p[i] = isl_tab_make_equalities_explicit(tabs[i],
map->p[i]);
if (!map->p[i])
goto error;
if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_NO_REDUNDANT))
if (isl_tab_detect_redundant(tabs[i]) < 0)
goto error;
}
for (i = map->n - 1; i >= 0; --i)
if (tabs[i]->empty)
drop(map, i, tabs);
map = coalesce(map, tabs);
if (map)
for (i = 0; i < map->n; ++i) {
map->p[i] = isl_basic_map_update_from_tab(map->p[i],
tabs[i]);
map->p[i] = isl_basic_map_gauss(map->p[i], NULL);
map->p[i] = isl_basic_map_finalize(map->p[i]);
if (!map->p[i])
goto error;
ISL_F_SET(map->p[i], ISL_BASIC_MAP_NO_IMPLICIT);
ISL_F_SET(map->p[i], ISL_BASIC_MAP_NO_REDUNDANT);
}
for (i = 0; i < n; ++i)
isl_tab_free(tabs[i]);
free(tabs);
return map;
error:
if (tabs)
for (i = 0; i < n; ++i)
isl_tab_free(tabs[i]);
free(tabs);
isl_map_free(map);
return NULL;
}
/* For each pair of basic sets in the set, check if the union of the two
* can be represented by a single basic set.
* If so, replace the pair by the single basic set and start over.
*/
struct isl_set *isl_set_coalesce(struct isl_set *set)
{
return (struct isl_set *)isl_map_coalesce((struct isl_map *)set);
}