Viewing file:  isl_coalesce.c (129.64 KB) -rw-r--r--
Select action/file-type:
 (+) |  (+) |  (+) | Code (+) | Session (+) |  (+) | SDB (+) |  (+) |  (+) |  (+) |  (+) |  (+) |
/*
* Copyright 2008-2009 Katholieke Universiteit Leuven
* Copyright 2010 INRIA Saclay
* Copyright 2012-2013 Ecole Normale Superieure
* Copyright 2014 INRIA Rocquencourt
* Copyright 2016 INRIA Paris
* Copyright 2020 Cerebras Systems
*
* 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
* and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
* B.P. 105 - 78153 Le Chesnay, France
* and Centre de Recherche Inria de Paris, 2 rue Simone Iff - Voie DQ12,
* CS 42112, 75589 Paris Cedex 12, France
* and Cerebras Systems, 175 S San Antonio Rd, Los Altos, CA, USA
*/
#include <isl_ctx_private.h>
#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_val_private.h>
#include <isl_vec_private.h>
#include <isl_aff_private.h>
#include <isl_equalities.h>
#include <isl_constraint_private.h>
#include <set_to_map.c>
#include <set_from_map.c>
#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 inequalities 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_size dim;
dim = isl_basic_map_dim(bmap_i, isl_dim_all);
if (dim < 0)
return NULL;
eq = isl_calloc_array(bmap_i->ctx, int, 2 * bmap_i->n_eq);
if (!eq)
return NULL;
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;
}
}
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;
}
/* Return the first position of "status" in the list "con" of length "len".
* Return -1 if there is no such entry.
*/
static int find(int *con, unsigned len, int status)
{
int i;
for (i = 0; i < len ; ++i)
if (con[i] == status)
return i;
return -1;
}
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;
}
/* Internal information associated to a basic map in a map
* that is to be coalesced by isl_map_coalesce.
*
* "bmap" is the basic map itself (or NULL if "removed" is set)
* "tab" is the corresponding tableau (or NULL if "removed" is set)
* "hull_hash" identifies the affine space in which "bmap" lives.
* "modified" is set if this basic map may not be identical
* to any of the basic maps in the input.
* "removed" is set if this basic map has been removed from the map
* "simplify" is set if this basic map may have some unknown integer
* divisions that were not present in the input basic maps. The basic
* map should then be simplified such that we may be able to find
* a definition among the constraints.
*
* "eq" and "ineq" are only set if we are currently trying to coalesce
* this basic map with another basic map, in which case they represent
* the position of the inequalities of this basic map with respect to
* the other basic map. The number of elements in the "eq" array
* is twice the number of equalities in the "bmap", corresponding
* to the two inequalities that make up each equality.
*/
struct isl_coalesce_info {
isl_basic_map *bmap;
struct isl_tab *tab;
uint32_t hull_hash;
int modified;
int removed;
int simplify;
int *eq;
int *ineq;
};
/* Is there any (half of an) equality constraint in the description
* of the basic map represented by "info" that
* has position "status" with respect to the other basic map?
*/
static int any_eq(struct isl_coalesce_info *info, int status)
{
isl_size n_eq;
n_eq = isl_basic_map_n_equality(info->bmap);
return any(info->eq, 2 * n_eq, status);
}
/* Is there any inequality constraint in the description
* of the basic map represented by "info" that
* has position "status" with respect to the other basic map?
*/
static int any_ineq(struct isl_coalesce_info *info, int status)
{
isl_size n_ineq;
n_ineq = isl_basic_map_n_inequality(info->bmap);
return any(info->ineq, n_ineq, status);
}
/* Return the position of the first half on an equality constraint
* in the description of the basic map represented by "info" that
* has position "status" with respect to the other basic map.
* The returned value is twice the position of the equality constraint
* plus zero for the negative half and plus one for the positive half.
* Return -1 if there is no such entry.
*/
static int find_eq(struct isl_coalesce_info *info, int status)
{
isl_size n_eq;
n_eq = isl_basic_map_n_equality(info->bmap);
return find(info->eq, 2 * n_eq, status);
}
/* Return the position of the first inequality constraint in the description
* of the basic map represented by "info" that
* has position "status" with respect to the other basic map.
* Return -1 if there is no such entry.
*/
static int find_ineq(struct isl_coalesce_info *info, int status)
{
isl_size n_ineq;
n_ineq = isl_basic_map_n_inequality(info->bmap);
return find(info->ineq, n_ineq, status);
}
/* Return the number of (halves of) equality constraints in the description
* of the basic map represented by "info" that
* have position "status" with respect to the other basic map.
*/
static int count_eq(struct isl_coalesce_info *info, int status)
{
isl_size n_eq;
n_eq = isl_basic_map_n_equality(info->bmap);
return count(info->eq, 2 * n_eq, status);
}
/* Return the number of inequality constraints in the description
* of the basic map represented by "info" that
* have position "status" with respect to the other basic map.
*/
static int count_ineq(struct isl_coalesce_info *info, int status)
{
isl_size n_ineq;
n_ineq = isl_basic_map_n_inequality(info->bmap);
return count(info->ineq, n_ineq, status);
}
/* Are all non-redundant constraints of the basic map represented by "info"
* either valid or cut constraints with respect to the other basic map?
*/
static int all_valid_or_cut(struct isl_coalesce_info *info)
{
int i;
for (i = 0; i < 2 * info->bmap->n_eq; ++i) {
if (info->eq[i] == STATUS_REDUNDANT)
continue;
if (info->eq[i] == STATUS_VALID)
continue;
if (info->eq[i] == STATUS_CUT)
continue;
return 0;
}
for (i = 0; i < info->bmap->n_ineq; ++i) {
if (info->ineq[i] == STATUS_REDUNDANT)
continue;
if (info->ineq[i] == STATUS_VALID)
continue;
if (info->ineq[i] == STATUS_CUT)
continue;
return 0;
}
return 1;
}
/* Compute the hash of the (apparent) affine hull of info->bmap (with
* the existentially quantified variables removed) and store it
* in info->hash.
*/
static int coalesce_info_set_hull_hash(struct isl_coalesce_info *info)
{
isl_basic_map *hull;
isl_size n_div;
hull = isl_basic_map_copy(info->bmap);
hull = isl_basic_map_plain_affine_hull(hull);
n_div = isl_basic_map_dim(hull, isl_dim_div);
if (n_div < 0)
hull = isl_basic_map_free(hull);
hull = isl_basic_map_drop_constraints_involving_dims(hull,
isl_dim_div, 0, n_div);
info->hull_hash = isl_basic_map_get_hash(hull);
isl_basic_map_free(hull);
return hull ? 0 : -1;
}
/* Free all the allocated memory in an array
* of "n" isl_coalesce_info elements.
*/
static void clear_coalesce_info(int n, struct isl_coalesce_info *info)
{
int i;
if (!info)
return;
for (i = 0; i < n; ++i) {
isl_basic_map_free(info[i].bmap);
isl_tab_free(info[i].tab);
}
free(info);
}
/* Clear the memory associated to "info".
*/
static void clear(struct isl_coalesce_info *info)
{
info->bmap = isl_basic_map_free(info->bmap);
isl_tab_free(info->tab);
info->tab = NULL;
}
/* Drop the basic map represented by "info".
* That is, clear the memory associated to the entry and
* mark it as having been removed.
*/
static void drop(struct isl_coalesce_info *info)
{
clear(info);
info->removed = 1;
}
/* Exchange the information in "info1" with that in "info2".
*/
static void exchange(struct isl_coalesce_info *info1,
struct isl_coalesce_info *info2)
{
struct isl_coalesce_info info;
info = *info1;
*info1 = *info2;
*info2 = info;
}
/* This type represents the kind of change that has been performed
* while trying to coalesce two basic maps.
*
* isl_change_none: nothing was changed
* isl_change_drop_first: the first basic map was removed
* isl_change_drop_second: the second basic map was removed
* isl_change_fuse: the two basic maps were replaced by a new basic map.
*/
enum isl_change {
isl_change_error = -1,
isl_change_none = 0,
isl_change_drop_first,
isl_change_drop_second,
isl_change_fuse,
};
/* Update "change" based on an interchange of the first and the second
* basic map. That is, interchange isl_change_drop_first and
* isl_change_drop_second.
*/
static enum isl_change invert_change(enum isl_change change)
{
switch (change) {
case isl_change_error:
return isl_change_error;
case isl_change_none:
return isl_change_none;
case isl_change_drop_first:
return isl_change_drop_second;
case isl_change_drop_second:
return isl_change_drop_first;
case isl_change_fuse:
return isl_change_fuse;
}
return isl_change_error;
}
/* Add the valid constraints of the basic map represented by "info"
* to "bmap". "len" is the size of the constraints.
* If only one of the pair of inequalities that make up an equality
* is valid, then add that inequality.
*/
static __isl_give isl_basic_map *add_valid_constraints(
__isl_take isl_basic_map *bmap, struct isl_coalesce_info *info,
unsigned len)
{
int k, l;
if (!bmap)
return NULL;
for (k = 0; k < info->bmap->n_eq; ++k) {
if (info->eq[2 * k] == STATUS_VALID &&
info->eq[2 * k + 1] == STATUS_VALID) {
l = isl_basic_map_alloc_equality(bmap);
if (l < 0)
return isl_basic_map_free(bmap);
isl_seq_cpy(bmap->eq[l], info->bmap->eq[k], len);
} else if (info->eq[2 * k] == STATUS_VALID) {
l = isl_basic_map_alloc_inequality(bmap);
if (l < 0)
return isl_basic_map_free(bmap);
isl_seq_neg(bmap->ineq[l], info->bmap->eq[k], len);
} else if (info->eq[2 * k + 1] == STATUS_VALID) {
l = isl_basic_map_alloc_inequality(bmap);
if (l < 0)
return isl_basic_map_free(bmap);
isl_seq_cpy(bmap->ineq[l], info->bmap->eq[k], len);
}
}
for (k = 0; k < info->bmap->n_ineq; ++k) {
if (info->ineq[k] != STATUS_VALID)
continue;
l = isl_basic_map_alloc_inequality(bmap);
if (l < 0)
return isl_basic_map_free(bmap);
isl_seq_cpy(bmap->ineq[l], info->bmap->ineq[k], len);
}
return bmap;
}
/* Is "bmap" defined by a number of (non-redundant) constraints that
* is greater than the number of constraints of basic maps i and j combined?
* Equalities are counted as two inequalities.
*/
static int number_of_constraints_increases(int i, int j,
struct isl_coalesce_info *info,
__isl_keep isl_basic_map *bmap, struct isl_tab *tab)
{
int k, n_old, n_new;
n_old = 2 * info[i].bmap->n_eq + info[i].bmap->n_ineq;
n_old += 2 * info[j].bmap->n_eq + info[j].bmap->n_ineq;
n_new = 2 * bmap->n_eq;
for (k = 0; k < bmap->n_ineq; ++k)
if (!isl_tab_is_redundant(tab, bmap->n_eq + k))
++n_new;
return n_new > n_old;
}
/* Replace the pair of basic maps i and j by the basic map bounded
* by the valid constraints in both basic maps and the constraints
* in extra (if not NULL).
* Place the fused basic map in the position that is the smallest of i and j.
*
* If "detect_equalities" is set, then look for equalities encoded
* as pairs of inequalities.
* If "check_number" is set, then the original basic maps are only
* replaced if the total number of constraints does not increase.
* While the number of integer divisions in the two basic maps
* is assumed to be the same, the actual definitions may be different.
* We only copy the definition from one of the basic map if it is
* the same as that of the other basic map. Otherwise, we mark
* the integer division as unknown and simplify the basic map
* in an attempt to recover the integer division definition.
* If any extra constraints get introduced, then these may
* involve integer divisions with a unit coefficient.
* Eliminate those that do not appear with any other coefficient
* in other constraints, to ensure they get eliminated completely,
* improving the chances of further coalescing.
*/
static enum isl_change fuse(int i, int j, struct isl_coalesce_info *info,
__isl_keep isl_mat *extra, int detect_equalities, int check_number)
{
int k, l;
struct isl_basic_map *fused = NULL;
struct isl_tab *fused_tab = NULL;
isl_size total = isl_basic_map_dim(info[i].bmap, isl_dim_all);
unsigned extra_rows = extra ? extra->n_row : 0;
unsigned n_eq, n_ineq;
int simplify = 0;
if (total < 0)
return isl_change_error;
if (j < i)
return fuse(j, i, info, extra, detect_equalities, check_number);
n_eq = info[i].bmap->n_eq + info[j].bmap->n_eq;
n_ineq = info[i].bmap->n_ineq + info[j].bmap->n_ineq;
fused = isl_basic_map_alloc_space(isl_space_copy(info[i].bmap->dim),
info[i].bmap->n_div, n_eq, n_eq + n_ineq + extra_rows);
fused = add_valid_constraints(fused, &info[i], 1 + total);
fused = add_valid_constraints(fused, &info[j], 1 + total);
if (!fused)
goto error;
if (ISL_F_ISSET(info[i].bmap, ISL_BASIC_MAP_RATIONAL) &&
ISL_F_ISSET(info[j].bmap, ISL_BASIC_MAP_RATIONAL))
ISL_F_SET(fused, ISL_BASIC_MAP_RATIONAL);
for (k = 0; k < info[i].bmap->n_div; ++k) {
int l = isl_basic_map_alloc_div(fused);
if (l < 0)
goto error;
if (isl_seq_eq(info[i].bmap->div[k], info[j].bmap->div[k],
1 + 1 + total)) {
isl_seq_cpy(fused->div[l], info[i].bmap->div[k],
1 + 1 + total);
} else {
isl_int_set_si(fused->div[l][0], 0);
simplify = 1;
}
}
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);
}
if (detect_equalities)
fused = isl_basic_map_detect_inequality_pairs(fused, NULL);
fused = isl_basic_map_gauss(fused, NULL);
if (simplify || info[j].simplify) {
fused = isl_basic_map_simplify(fused);
info[i].simplify = 0;
} else if (extra_rows > 0) {
fused = isl_basic_map_eliminate_pure_unit_divs(fused);
}
fused = isl_basic_map_finalize(fused);
fused_tab = isl_tab_from_basic_map(fused, 0);
if (isl_tab_detect_redundant(fused_tab) < 0)
goto error;
if (check_number &&
number_of_constraints_increases(i, j, info, fused, fused_tab)) {
isl_tab_free(fused_tab);
isl_basic_map_free(fused);
return isl_change_none;
}
clear(&info[i]);
info[i].bmap = fused;
info[i].tab = fused_tab;
info[i].modified = 1;
drop(&info[j]);
return isl_change_fuse;
error:
isl_tab_free(fused_tab);
isl_basic_map_free(fused);
return isl_change_error;
}
/* 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.
* Checking whether the facet lies entirely within basic map j
* is performed by checking whether the constraints of basic map j
* are valid for the facet. These tests are performed on a rational
* tableau to avoid the theoretical possibility that a constraint
* that was considered to be a cut constraint for the entire basic map i
* happens to be considered to be a valid constraint for the facet,
* even though it cuts off the same rational points.
*
* 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 ).
* A line connecting x with an element of A \cup B meets a facet F
* of either A or B. Assume it is a facet of B and let c_1 be
* the corresponding facet constraint. We have c_1(x) < 0 and
* so c_1 is a cut constraint. This implies that there is some
* (possibly rational) point x' satisfying the constraints of A
* and the opposite of c_1 as otherwise c_1 would have been marked
* valid for A. The line connecting x and x' meets a facet of A
* in a (possibly rational) point that also violates c_1, but this
* is impossible since all cut constraints of B are valid for all
* cut facets of A.
* In case F is a facet of A rather than B, then we can apply the
* above reasoning to find a facet of B separating x from A \cup B first.
*/
static enum isl_change check_facets(int i, int j,
struct isl_coalesce_info *info)
{
int k, l;
struct isl_tab_undo *snap, *snap2;
unsigned n_eq = info[i].bmap->n_eq;
snap = isl_tab_snap(info[i].tab);
if (isl_tab_mark_rational(info[i].tab) < 0)
return isl_change_error;
snap2 = isl_tab_snap(info[i].tab);
for (k = 0; k < info[i].bmap->n_ineq; ++k) {
if (info[i].ineq[k] != STATUS_CUT)
continue;
if (isl_tab_select_facet(info[i].tab, n_eq + k) < 0)
return isl_change_error;
for (l = 0; l < info[j].bmap->n_ineq; ++l) {
int stat;
if (info[j].ineq[l] != STATUS_CUT)
continue;
stat = status_in(info[j].bmap->ineq[l], info[i].tab);
if (stat < 0)
return isl_change_error;
if (stat != STATUS_VALID)
break;
}
if (isl_tab_rollback(info[i].tab, snap2) < 0)
return isl_change_error;
if (l < info[j].bmap->n_ineq)
break;
}
if (k < info[i].bmap->n_ineq) {
if (isl_tab_rollback(info[i].tab, snap) < 0)
return isl_change_error;
return isl_change_none;
}
return fuse(i, j, info, NULL, 0, 0);
}
/* Check if info->bmap contains the basic map represented
* by the tableau "tab".
* For each equality, we check both the constraint itself
* (as an inequality) and its negation. Make sure the
* equality is returned to its original state before returning.
*/
static isl_bool contains(struct isl_coalesce_info *info, struct isl_tab *tab)
{
int k;
isl_size dim;
isl_basic_map *bmap = info->bmap;
dim = isl_basic_map_dim(bmap, isl_dim_all);
if (dim < 0)
return isl_bool_error;
for (k = 0; k < bmap->n_eq; ++k) {
int stat;
isl_seq_neg(bmap->eq[k], bmap->eq[k], 1 + dim);
stat = status_in(bmap->eq[k], tab);
isl_seq_neg(bmap->eq[k], bmap->eq[k], 1 + dim);
if (stat < 0)
return isl_bool_error;
if (stat != STATUS_VALID)
return isl_bool_false;
stat = status_in(bmap->eq[k], tab);
if (stat < 0)
return isl_bool_error;
if (stat != STATUS_VALID)
return isl_bool_false;
}
for (k = 0; k < bmap->n_ineq; ++k) {
int stat;
if (info->ineq[k] == STATUS_REDUNDANT)
continue;
stat = status_in(bmap->ineq[k], tab);
if (stat < 0)
return isl_bool_error;
if (stat != STATUS_VALID)
return isl_bool_false;
}
return isl_bool_true;
}
/* Basic map "i" has an inequality "k" that is adjacent
* to some inequality of basic map "j". All the other inequalities
* are valid for "j".
* If not NULL, then "extra" contains extra wrapping constraints that are valid
* for both "i" and "j".
* Check if basic map "j" forms an extension of basic map "i",
* taking into account the extra constraints, if any.
*
* 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",
* as well as the "extra" constraints, if any,
* and check if the result is a subset of basic map "j".
* To improve the chances of the subset relation being detected,
* any variable that only attains a single integer value
* in the tableau of "i" is first fixed to that value.
* If the result is a subset, 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"), the valid constraints of "j" and
* the "extra" constraints, if any, 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 enum isl_change is_adj_ineq_extension_with_wraps(int i, int j, int k,
struct isl_coalesce_info *info, __isl_keep isl_mat *extra)
{
struct isl_tab_undo *snap;
isl_size n_eq_i, n_ineq_j, n_extra;
isl_size total = isl_basic_map_dim(info[i].bmap, isl_dim_all);
isl_stat r;
isl_bool super;
if (total < 0)
return isl_change_error;
n_eq_i = isl_basic_map_n_equality(info[i].bmap);
n_ineq_j = isl_basic_map_n_inequality(info[j].bmap);
n_extra = isl_mat_rows(extra);
if (n_eq_i < 0 || n_ineq_j < 0 || n_extra < 0)
return isl_change_error;
if (isl_tab_extend_cons(info[i].tab, 1 + n_ineq_j + n_extra) < 0)
return isl_change_error;
snap = isl_tab_snap(info[i].tab);
if (isl_tab_unrestrict(info[i].tab, n_eq_i + k) < 0)
return isl_change_error;
isl_seq_neg(info[i].bmap->ineq[k], info[i].bmap->ineq[k], 1 + total);
isl_int_sub_ui(info[i].bmap->ineq[k][0], info[i].bmap->ineq[k][0], 1);
r = isl_tab_add_ineq(info[i].tab, info[i].bmap->ineq[k]);
isl_seq_neg(info[i].bmap->ineq[k], info[i].bmap->ineq[k], 1 + total);
isl_int_sub_ui(info[i].bmap->ineq[k][0], info[i].bmap->ineq[k][0], 1);
if (r < 0)
return isl_change_error;
for (k = 0; k < n_ineq_j; ++k) {
if (info[j].ineq[k] != STATUS_VALID)
continue;
if (isl_tab_add_ineq(info[i].tab, info[j].bmap->ineq[k]) < 0)
return isl_change_error;
}
for (k = 0; k < n_extra; ++k) {
if (isl_tab_add_ineq(info[i].tab, extra->row[k]) < 0)
return isl_change_error;
}
if (isl_tab_detect_constants(info[i].tab) < 0)
return isl_change_error;
super = contains(&info[j], info[i].tab);
if (super < 0)
return isl_change_error;
if (super)
return fuse(i, j, info, extra, 0, 0);
if (isl_tab_rollback(info[i].tab, snap) < 0)
return isl_change_error;
return isl_change_none;
}
/* Given an affine transformation matrix "T", does row "row" represent
* anything other than a unit vector (possibly shifted by a constant)
* that is not involved in any of the other rows?
*
* That is, if a constraint involves the variable corresponding to
* the row, then could its preimage by "T" have any coefficients
* that are different from those in the original constraint?
*/
static int not_unique_unit_row(__isl_keep isl_mat *T, int row)
{
int i, j;
int len = T->n_col - 1;
i = isl_seq_first_non_zero(T->row[row] + 1, len);
if (i < 0)
return 1;
if (!isl_int_is_one(T->row[row][1 + i]) &&
!isl_int_is_negone(T->row[row][1 + i]))
return 1;
j = isl_seq_first_non_zero(T->row[row] + 1 + i + 1, len - (i + 1));
if (j >= 0)
return 1;
for (j = 1; j < T->n_row; ++j) {
if (j == row)
continue;
if (!isl_int_is_zero(T->row[j][1 + i]))
return 1;
}
return 0;
}
/* Does inequality constraint "ineq" of "bmap" involve any of
* the variables marked in "affected"?
* "total" is the total number of variables, i.e., the number
* of entries in "affected".
*/
static isl_bool is_affected(__isl_keep isl_basic_map *bmap, int ineq,
int *affected, int total)
{
int i;
for (i = 0; i < total; ++i) {
if (!affected[i])
continue;
if (!isl_int_is_zero(bmap->ineq[ineq][1 + i]))
return isl_bool_true;
}
return isl_bool_false;
}
/* Given the compressed version of inequality constraint "ineq"
* of info->bmap in "v", check if the constraint can be tightened,
* where the compression is based on an equality constraint valid
* for info->tab.
* If so, add the tightened version of the inequality constraint
* to info->tab. "v" may be modified by this function.
*
* That is, if the compressed constraint is of the form
*
* m f() + c >= 0
*
* with 0 < c < m, then it is equivalent to
*
* f() >= 0
*
* This means that c can also be subtracted from the original,
* uncompressed constraint without affecting the integer points
* in info->tab. Add this tightened constraint as an extra row
* to info->tab to make this information explicitly available.
*/
static __isl_give isl_vec *try_tightening(struct isl_coalesce_info *info,
int ineq, __isl_take isl_vec *v)
{
isl_ctx *ctx;
isl_stat r;
if (!v)
return NULL;
ctx = isl_vec_get_ctx(v);
isl_seq_gcd(v->el + 1, v->size - 1, &ctx->normalize_gcd);
if (isl_int_is_zero(ctx->normalize_gcd) ||
isl_int_is_one(ctx->normalize_gcd)) {
return v;
}
v = isl_vec_cow(v);
if (!v)
return NULL;
isl_int_fdiv_r(v->el[0], v->el[0], ctx->normalize_gcd);
if (isl_int_is_zero(v->el[0]))
return v;
if (isl_tab_extend_cons(info->tab, 1) < 0)
return isl_vec_free(v);
isl_int_sub(info->bmap->ineq[ineq][0],
info->bmap->ineq[ineq][0], v->el[0]);
r = isl_tab_add_ineq(info->tab, info->bmap->ineq[ineq]);
isl_int_add(info->bmap->ineq[ineq][0],
info->bmap->ineq[ineq][0], v->el[0]);
if (r < 0)
return isl_vec_free(v);
return v;
}
/* Tighten the (non-redundant) constraints on the facet represented
* by info->tab.
* In particular, on input, info->tab represents the result
* of relaxing the "n" inequality constraints of info->bmap in "relaxed"
* by one, i.e., replacing f_i >= 0 by f_i + 1 >= 0, and then
* replacing the one at index "l" by the corresponding equality,
* i.e., f_k + 1 = 0, with k = relaxed[l].
*
* Compute a variable compression from the equality constraint f_k + 1 = 0
* and use it to tighten the other constraints of info->bmap
* (that is, all constraints that have not been relaxed),
* updating info->tab (and leaving info->bmap untouched).
* The compression handles essentially two cases, one where a variable
* is assigned a fixed value and can therefore be eliminated, and one
* where one variable is a shifted multiple of some other variable and
* can therefore be replaced by that multiple.
* Gaussian elimination would also work for the first case, but for
* the second case, the effectiveness would depend on the order
* of the variables.
* After compression, some of the constraints may have coefficients
* with a common divisor. If this divisor does not divide the constant
* term, then the constraint can be tightened.
* The tightening is performed on the tableau info->tab by introducing
* extra (temporary) constraints.
*
* Only constraints that are possibly affected by the compression are
* considered. In particular, if the constraint only involves variables
* that are directly mapped to a distinct set of other variables, then
* no common divisor can be introduced and no tightening can occur.
*
* It is important to only consider the non-redundant constraints
* since the facet constraint has been relaxed prior to the call
* to this function, meaning that the constraints that were redundant
* prior to the relaxation may no longer be redundant.
* These constraints will be ignored in the fused result, so
* the fusion detection should not exploit them.
*/
static isl_stat tighten_on_relaxed_facet(struct isl_coalesce_info *info,
int n, int *relaxed, int l)
{
isl_size total;
isl_ctx *ctx;
isl_vec *v = NULL;
isl_mat *T;
int i;
int k;
int *affected;
k = relaxed[l];
ctx = isl_basic_map_get_ctx(info->bmap);
total = isl_basic_map_dim(info->bmap, isl_dim_all);
if (total < 0)
return isl_stat_error;
isl_int_add_ui(info->bmap->ineq[k][0], info->bmap->ineq[k][0], 1);
T = isl_mat_sub_alloc6(ctx, info->bmap->ineq, k, 1, 0, 1 + total);
T = isl_mat_variable_compression(T, NULL);
isl_int_sub_ui(info->bmap->ineq[k][0], info->bmap->ineq[k][0], 1);
if (!T)
return isl_stat_error;
if (T->n_col == 0) {
isl_mat_free(T);
return isl_stat_ok;
}
affected = isl_alloc_array(ctx, int, total);
if (!affected)
goto error;
for (i = 0; i < total; ++i)
affected[i] = not_unique_unit_row(T, 1 + i);
for (i = 0; i < info->bmap->n_ineq; ++i) {
isl_bool handle;
if (any(relaxed, n, i))
continue;
if (info->ineq[i] == STATUS_REDUNDANT)
continue;
handle = is_affected(info->bmap, i, affected, total);
if (handle < 0)
goto error;
if (!handle)
continue;
v = isl_vec_alloc(ctx, 1 + total);
if (!v)
goto error;
isl_seq_cpy(v->el, info->bmap->ineq[i], 1 + total);
v = isl_vec_mat_product(v, isl_mat_copy(T));
v = try_tightening(info, i, v);
isl_vec_free(v);
if (!v)
goto error;
}
isl_mat_free(T);
free(affected);
return isl_stat_ok;
error:
isl_mat_free(T);
free(affected);
return isl_stat_error;
}
/* Replace the basic maps "i" and "j" by an extension of "i"
* along the "n" inequality constraints in "relax" by one.
* The tableau info[i].tab has already been extended.
* Extend info[i].bmap accordingly by relaxing all constraints in "relax"
* by one.
* Each integer division that does not have exactly the same
* definition in "i" and "j" is marked unknown and the basic map
* is scheduled to be simplified in an attempt to recover
* the integer division definition.
* Place the extension in the position that is the smallest of i and j.
*/
static enum isl_change extend(int i, int j, int n, int *relax,
struct isl_coalesce_info *info)
{
int l;
isl_size total;
info[i].bmap = isl_basic_map_cow(info[i].bmap);
total = isl_basic_map_dim(info[i].bmap, isl_dim_all);
if (total < 0)
return isl_change_error;
for (l = 0; l < info[i].bmap->n_div; ++l)
if (!isl_seq_eq(info[i].bmap->div[l],
info[j].bmap->div[l], 1 + 1 + total)) {
isl_int_set_si(info[i].bmap->div[l][0], 0);
info[i].simplify = 1;
}
for (l = 0; l < n; ++l)
isl_int_add_ui(info[i].bmap->ineq[relax[l]][0],
info[i].bmap->ineq[relax[l]][0], 1);
ISL_F_CLR(info[i].bmap, ISL_BASIC_MAP_NO_REDUNDANT);
ISL_F_SET(info[i].bmap, ISL_BASIC_MAP_FINAL);
drop(&info[j]);
info[i].modified = 1;
if (j < i)
exchange(&info[i], &info[j]);
return isl_change_fuse;
}
/* Basic map "i" has "n" inequality constraints (collected in "relax")
* that are such that they include basic map "j" if they are relaxed
* by one. All the other inequalities are valid for "j".
* Check if basic map "j" forms an extension of basic map "i".
*
* In particular, relax the constraints in "relax", compute the corresponding
* facets one by one and check whether each of these is included
* in the other basic map.
* Before testing for inclusion, the constraints on each facet
* are tightened to increase the chance of an inclusion being detected.
* (Adding the valid constraints of "j" to the tableau of "i", as is done
* in is_adj_ineq_extension, may further increase those chances, but this
* is not currently done.)
* If each facet is included, we know that relaxing the constraints extends
* the basic map with exactly the other basic map (we already know that this
* other basic map is included in the extension, because all other
* inequality constraints are valid of "j") and we can replace the
* two basic maps by this extension.
*
* If any of the relaxed constraints turn out to be redundant, then bail out.
* isl_tab_select_facet refuses to handle such constraints. It may be
* possible to handle them anyway by making a distinction between
* redundant constraints with a corresponding facet that still intersects
* the set (allowing isl_tab_select_facet to handle them) and
* those where the facet does not intersect the set (which can be ignored
* because the empty facet is trivially included in the other disjunct).
* However, relaxed constraints that turn out to be redundant should
* be fairly rare and no such instance has been reported where
* coalescing would be successful.
* ____ _____
* / || / |
* / || / |
* \ || => \ |
* \ || \ |
* \___|| \____|
*
*
* \ |\
* |\\ | \
* | \\ | \
* | | => | /
* | / | /
* |/ |/
*/
static enum isl_change is_relaxed_extension(int i, int j, int n, int *relax,
struct isl_coalesce_info *info)
{
int l;
isl_bool super;
struct isl_tab_undo *snap, *snap2;
unsigned n_eq = info[i].bmap->n_eq;
for (l = 0; l < n; ++l)
if (isl_tab_is_equality(info[i].tab, n_eq + relax[l]))
return isl_change_none;
snap = isl_tab_snap(info[i].tab);
for (l = 0; l < n; ++l)
if (isl_tab_relax(info[i].tab, n_eq + relax[l]) < 0)
return isl_change_error;
for (l = 0; l < n; ++l) {
if (!isl_tab_is_redundant(info[i].tab, n_eq + relax[l]))
continue;
if (isl_tab_rollback(info[i].tab, snap) < 0)
return isl_change_error;
return isl_change_none;
}
snap2 = isl_tab_snap(info[i].tab);
for (l = 0; l < n; ++l) {
if (isl_tab_rollback(info[i].tab, snap2) < 0)
return isl_change_error;
if (isl_tab_select_facet(info[i].tab, n_eq + relax[l]) < 0)
return isl_change_error;
if (tighten_on_relaxed_facet(&info[i], n, relax, l) < 0)
return isl_change_error;
super = contains(&info[j], info[i].tab);
if (super < 0)
return isl_change_error;
if (super)
continue;
if (isl_tab_rollback(info[i].tab, snap) < 0)
return isl_change_error;
return isl_change_none;
}
if (isl_tab_rollback(info[i].tab, snap2) < 0)
return isl_change_error;
return extend(i, j, n, relax, info);
}
/* Data structure that keeps track of the wrapping constraints
* and of information to bound the coefficients of those constraints.
*
* "failed" is set if wrapping has failed.
* 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 failed;
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 info->bmap that can be removed
* if we end up applying wrapping.
*/
static isl_stat wraps_update_max(struct isl_wraps *wraps,
struct isl_coalesce_info *info)
{
int k;
isl_int max_k;
isl_size total = isl_basic_map_dim(info->bmap, isl_dim_all);
if (total < 0)
return isl_stat_error;
isl_int_init(max_k);
for (k = 0; k < info->bmap->n_eq; ++k) {
if (info->eq[2 * k] == STATUS_VALID &&
info->eq[2 * k + 1] == STATUS_VALID)
continue;
isl_seq_abs_max(info->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 < info->bmap->n_ineq; ++k) {
if (info->ineq[k] == STATUS_VALID ||
info->ineq[k] == STATUS_REDUNDANT)
continue;
isl_seq_abs_max(info->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);
return isl_stat_ok;
}
/* 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 isl_stat wraps_init(struct isl_wraps *wraps, __isl_take isl_mat *mat,
struct isl_coalesce_info *info, int i, int j)
{
isl_ctx *ctx;
wraps->failed = 0;
wraps->bound = 0;
wraps->mat = mat;
if (!mat)
return isl_stat_error;
wraps->mat->n_row = 0;
ctx = isl_mat_get_ctx(mat);
wraps->bound = isl_options_get_coalesce_bounded_wrapping(ctx);
if (!wraps->bound)
return isl_stat_ok;
isl_int_init(wraps->max);
isl_int_set_si(wraps->max, 0);
if (wraps_update_max(wraps, &info[i]) < 0)
return isl_stat_error;
if (wraps_update_max(wraps, &info[j]) < 0)
return isl_stat_error;
return isl_stat_ok;
}
/* 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);
}
/* Mark the wrapping as failed.
*/
static isl_stat wraps_mark_failed(struct isl_wraps *wraps)
{
wraps->failed = 1;
return isl_stat_ok;
}
/* 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;
}
/* Wrap "ineq" (or its opposite if "negate" is set) around "bound"
* to include "set" and add the result in position "w" of "wraps".
* "len" is the total number of coefficients in "bound" and "ineq".
* Return 1 on success, 0 on failure and -1 on error.
* Wrapping can fail if the result of wrapping is equal to "bound"
* or if we want to bound the sizes of the coefficients and
* the wrapped constraint does not satisfy this bound.
*/
static int add_wrap(struct isl_wraps *wraps, int w, isl_int *bound,
isl_int *ineq, unsigned len, __isl_keep isl_set *set, int negate)
{
isl_seq_cpy(wraps->mat->row[w], bound, len);
if (negate) {
isl_seq_neg(wraps->mat->row[w + 1], ineq, len);
ineq = wraps->mat->row[w + 1];
}
if (!isl_set_wrap_facet(set, wraps->mat->row[w], ineq))
return -1;
if (isl_seq_eq(wraps->mat->row[w], bound, len))
return 0;
if (!allow_wrap(wraps, w))
return 0;
return 1;
}
/* This function has two modes of operations.
*
* If "add_valid" is set, then all the constraints of info->bmap
* (except the opposite of "bound") are valid for the other basic map.
* In this case, attempts are made to wrap some of these valid constraints
* to more tightly fit around "set". Only successful wrappings are recorded
* and failed wrappings are ignored.
*
* If "add_valid" is not set, then some of the constraints of info->bmap
* are not valid for the other basic map, and only those are considered
* for wrapping. In this case all attempted wrappings need to succeed.
* Otherwise "wraps" is marked as failed.
* Note that the constraints that are valid for the other basic map
* will be added to the combined basic map by default, so there is
* no need to wrap them.
* The caller wrap_in_facets even relies on this function not wrapping
* any constraints that are already valid.
*
* Only consider constraints that are not redundant (as determined
* by info->tab) and that are valid or invalid depending on "add_valid".
* Wrap each 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
* a way that no wrapping is possible.
* Similarly, if we want to bound the coefficients of the wrapping
* constraints and a newly added wrapping constraint does not
* satisfy the bound, then the wrapping is considered to have failed.
* Note though that "wraps" is only marked failed if "add_valid" is not set.
*/
static isl_stat add_selected_wraps(struct isl_wraps *wraps,
struct isl_coalesce_info *info, isl_int *bound, __isl_keep isl_set *set,
int add_valid)
{
int l, m;
int w;
int added;
isl_basic_map *bmap = info->bmap;
isl_size total = isl_basic_map_dim(bmap, isl_dim_all);
unsigned len = 1 + total;
if (total < 0)
return isl_stat_error;
w = wraps->mat->n_row;
for (l = 0; l < bmap->n_ineq; ++l) {
int is_valid = info->ineq[l] == STATUS_VALID;
if ((!add_valid && is_valid) ||
info->ineq[l] == STATUS_REDUNDANT)
continue;
if (isl_seq_is_neg(bound, bmap->ineq[l], len))
continue;
if (isl_seq_eq(bound, bmap->ineq[l], len))
continue;
if (isl_tab_is_redundant(info->tab, bmap->n_eq + l))
continue;
added = add_wrap(wraps, w, bound, bmap->ineq[l], len, set, 0);
if (added < 0)
return isl_stat_error;
if (!added && !is_valid)
goto unbounded;
if (added)
++w;
}
for (l = 0; l < bmap->n_eq; ++l) {
if (isl_seq_is_neg(bound, bmap->eq[l], len))
continue;
if (isl_seq_eq(bound, bmap->eq[l], len))
continue;
for (m = 0; m < 2; ++m) {
if (info->eq[2 * l + m] == STATUS_VALID)
continue;
added = add_wrap(wraps, w, bound, bmap->eq[l], len,
set, !m);
if (added < 0)
return isl_stat_error;
if (!added)
goto unbounded;
++w;
}
}
wraps->mat->n_row = w;
return isl_stat_ok;
unbounded:
return wraps_mark_failed(wraps);
}
/* For each constraint in info->bmap that is not redundant (as determined
* by info->tab) and that is not a valid constraint for the other basic map,
* wrap the constraint around "bound" such that it includes the whole
* set "set" and append the resulting constraint to "wraps".
* Note that the constraints that are valid for the other basic map
* will be added to the combined basic map by default, so there is
* no need to wrap them.
* The caller wrap_in_facets even relies on this function not wrapping
* any constraints that are already valid.
* "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
* a way that no wrapping is possible. If this happens then "wraps"
* is marked as failed.
* 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" is also marked as failed.
*/
static isl_stat add_wraps(struct isl_wraps *wraps,
struct isl_coalesce_info *info, isl_int *bound, __isl_keep isl_set *set)
{
return add_selected_wraps(wraps, info, bound, set, 0);
}
/* Check if the constraints in "wraps" from "first" until the last
* are all valid for the basic set represented by "tab",
* dropping the invalid constraints if "keep" is set and
* marking the wrapping as failed if "keep" is not set and
* any constraint turns out to be invalid.
*/
static isl_stat check_wraps(struct isl_wraps *wraps, int first,
struct isl_tab *tab, int keep)
{
int i;
for (i = wraps->mat->n_row - 1; i >= first; --i) {
enum isl_ineq_type type;
type = isl_tab_ineq_type(tab, wraps->mat->row[i]);
if (type == isl_ineq_error)
return isl_stat_error;
if (type == isl_ineq_redundant)
continue;
if (!keep)
return wraps_mark_failed(wraps);
wraps->mat = isl_mat_drop_rows(wraps->mat, i, 1);
if (!wraps->mat)
return isl_stat_error;
}
return isl_stat_ok;
}
/* Return a set that corresponds to the non-redundant 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.
*
* Update the underlying set to ensure that the dimension doesn't change.
* Otherwise the integer divisions could get dropped if the tab
* turns out to be empty.
*/
static __isl_give isl_set *set_from_updated_bmap(__isl_keep isl_basic_map *bmap,
struct isl_tab *tab)
{
isl_basic_set *bset;
bmap = isl_basic_map_copy(bmap);
bset = isl_basic_map_underlying_set(bmap);
bset = isl_basic_set_cow(bset);
bset = isl_basic_set_update_from_tab(bset, tab);
return isl_set_from_basic_set(bset);
}
/* Does "info" have any cut constraints that are redundant?
*/
static isl_bool has_redundant_cuts(struct isl_coalesce_info *info)
{
int l;
isl_size n_eq, n_ineq;
n_eq = isl_basic_map_n_equality(info->bmap);
n_ineq = isl_basic_map_n_inequality(info->bmap);
if (n_eq < 0 || n_ineq < 0)
return isl_bool_error;
for (l = 0; l < n_ineq; ++l) {
int red;
if (info->ineq[l] != STATUS_CUT)
continue;
red = isl_tab_is_redundant(info->tab, n_eq + l);
if (red < 0)
return isl_bool_error;
if (red)
return isl_bool_true;
}
return isl_bool_false;
}
/* Wrap some constraints of info->bmap that bound the facet defined
* by inequality "k" around (the opposite of) this inequality to
* include "set". "bound" may be used to store the negated inequality.
*
* If "add_valid" is set, then all ridges are already valid and
* the purpose is to wrap "set" more tightly. In this case,
* wrapping doesn't fail, although it is possible that no constraint
* gets wrapped.
*
* If "add_valid" is not set, then some of the ridges are cut constraints
* and only those are wrapped around "set".
*
* Since the wrapped constraints are not guaranteed to contain the whole
* of info->bmap, we check them in check_wraps.
* If any of the wrapped constraints turn out to be invalid, then
* check_wraps will mark "wraps" as failed if "add_valid" is not set.
* If "add_valid" is set, then the offending constraints are
* simply removed.
*
* If any of the cut constraints of info->bmap turn out
* to be redundant with respect to other constraints
* then these will neither be wrapped nor added directly to the result.
* The result may therefore not be correct.
* Skip wrapping and mark "wraps" as failed in this case.
*/
static isl_stat add_selected_wraps_around_facet(struct isl_wraps *wraps,
struct isl_coalesce_info *info, int k, isl_int *bound,
__isl_keep isl_set *set, int add_valid)
{
isl_bool nowrap;
struct isl_tab_undo *snap;
int n;
isl_size total = isl_basic_map_dim(info->bmap, isl_dim_all);
if (total < 0)
return isl_stat_error;
snap = isl_tab_snap(info->tab);
if (isl_tab_select_facet(info->tab, info->bmap->n_eq + k) < 0)
return isl_stat_error;
if (isl_tab_detect_redundant(info->tab) < 0)
return isl_stat_error;
nowrap = has_redundant_cuts(info);
if (nowrap < 0)
return isl_stat_error;
n = wraps->mat->n_row;
if (!nowrap) {
isl_seq_neg(bound, info->bmap->ineq[k], 1 + total);
if (add_selected_wraps(wraps, info, bound, set, add_valid) < 0)
return isl_stat_error;
}
if (isl_tab_rollback(info->tab, snap) < 0)
return isl_stat_error;
if (nowrap)
return wraps_mark_failed(wraps);
if (check_wraps(wraps, n, info->tab, add_valid) < 0)
return isl_stat_error;
return isl_stat_ok;
}
/* Wrap the constraints of info->bmap that bound the facet defined
* by inequality "k" around (the opposite of) this inequality to
* include "set". "bound" may be used to store the negated inequality.
* If any of the wrapped constraints turn out to be invalid for info->bmap
* itself, then mark "wraps" as failed.
*/
static isl_stat add_wraps_around_facet(struct isl_wraps *wraps,
struct isl_coalesce_info *info, int k, isl_int *bound,
__isl_keep isl_set *set)
{
return add_selected_wraps_around_facet(wraps, info, k, bound, set, 0);
}
/* Wrap the (valid) constraints of info->bmap that bound the facet defined
* by inequality "k" around (the opposite of) this inequality to
* include "set" more tightly.
* "bound" may be used to store the negated inequality.
* Remove any wrapping constraints that turn out to be invalid
* for info->bmap itself.
*/
static isl_stat add_valid_wraps_around_facet(struct isl_wraps *wraps,
struct isl_coalesce_info *info, int k, isl_int *bound,
__isl_keep isl_set *set)
{
return add_selected_wraps_around_facet(wraps, info, k, bound, set, 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.
*
* First try and wrap the ridges of "k" around "j".
* Note that those ridges are already valid for "j",
* but the wrapped versions may wrap "j" more tightly,
* increasing the chances of "j" being detected as an extension of "i"
*/
static enum isl_change is_adj_ineq_extension(int i, int j,
struct isl_coalesce_info *info)
{
int k;
enum isl_change change;
isl_size total;
isl_size n_eq_i, n_ineq_i;
struct isl_wraps wraps;
isl_ctx *ctx;
isl_mat *mat;
isl_vec *bound;
isl_set *set_j;
isl_stat r;
k = find_ineq(&info[i], STATUS_ADJ_INEQ);
if (k < 0)
isl_die(isl_basic_map_get_ctx(info[i].bmap), isl_error_internal,
"info[i].ineq should have exactly one STATUS_ADJ_INEQ",
return isl_change_error);
total = isl_basic_map_dim(info[i].bmap, isl_dim_all);
n_eq_i = isl_basic_map_n_equality(info[i].bmap);
n_ineq_i = isl_basic_map_n_inequality(info[i].bmap);
if (total < 0 || n_eq_i < 0 || n_ineq_i < 0)
return isl_change_error;
set_j = set_from_updated_bmap(info[j].bmap, info[j].tab);
ctx = isl_basic_map_get_ctx(info[i].bmap);
bound = isl_vec_alloc(ctx, 1 + total);
mat = isl_mat_alloc(ctx, 2 * n_eq_i + n_ineq_i, 1 + total);
if (wraps_init(&wraps, mat, info, i, j) < 0)
goto error;
if (!bound || !set_j)
goto error;
r = add_valid_wraps_around_facet(&wraps, &info[i], k, bound->el, set_j);
if (r < 0)
goto error;
change = is_adj_ineq_extension_with_wraps(i, j, k, info, wraps.mat);
wraps_free(&wraps);
isl_vec_free(bound);
isl_set_free(set_j);
return change;
error:
wraps_free(&wraps);
isl_vec_free(bound);
isl_set_free(set_j);
return isl_change_error;
}
/* 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 adjacent 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 enum isl_change check_adj_ineq(int i, int j,
struct isl_coalesce_info *info)
{
int count_i, count_j;
int cut_i, cut_j;
count_i = count_ineq(&info[i], STATUS_ADJ_INEQ);
count_j = count_ineq(&info[j], STATUS_ADJ_INEQ);
if (count_i != 1 && count_j != 1)
return isl_change_none;
cut_i = any_eq(&info[i], STATUS_CUT) || any_ineq(&info[i], STATUS_CUT);
cut_j = any_eq(&info[j], STATUS_CUT) || any_ineq(&info[j], STATUS_CUT);
if (!cut_i && !cut_j && count_i == 1 && count_j == 1)
return fuse(i, j, info, NULL, 0, 0);
if (count_i == 1 && !cut_i)
return is_adj_ineq_extension(i, j, info);
if (count_j == 1 && !cut_j)
return is_adj_ineq_extension(j, i, info);
return isl_change_none;
}
/* Given a basic set i with a constraint k that is adjacent to
* basic set j, check if we can wrap
* both the facet corresponding to k (if "wrap_facet" is set) and basic map j
* (always) 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 or
* cut constraints for j.
* Wrapping the cut constraints to include basic map j may result
* in constraints that are no longer valid of basic map i
* we have to check that the resulting wrapping constraints are valid for i.
* If "wrap_facet" is not set, then all constraints of i (except k)
* are assumed to be valid for j.
* ____ _____
* / | / \
* / || / |
* \ || => \ |
* \ || \ |
* \___|| \____|
*
*/
static enum isl_change can_wrap_in_facet(int i, int j, int k,
struct isl_coalesce_info *info, int wrap_facet)
{
enum isl_change change = isl_change_none;
struct isl_wraps wraps;
isl_ctx *ctx;
isl_mat *mat;
struct isl_set *set_i = NULL;
struct isl_set *set_j = NULL;
struct isl_vec *bound = NULL;
isl_size total = isl_basic_map_dim(info[i].bmap, isl_dim_all);
if (total < 0)
return isl_change_error;
set_i = set_from_updated_bmap(info[i].bmap, info[i].tab);
set_j = set_from_updated_bmap(info[j].bmap, info[j].tab);
ctx = isl_basic_map_get_ctx(info[i].bmap);
mat = isl_mat_alloc(ctx, 2 * (info[i].bmap->n_eq + info[j].bmap->n_eq) +
info[i].bmap->n_ineq + info[j].bmap->n_ineq,
1 + total);
if (wraps_init(&wraps, mat, info, i, j) < 0)
goto error;
bound = isl_vec_alloc(ctx, 1 + total);
if (!set_i || !set_j || !bound)
goto error;
isl_seq_cpy(bound->el, info[i].bmap->ineq[k], 1 + total);
isl_int_add_ui(bound->el[0], bound->el[0], 1);
isl_seq_normalize(ctx, bound->el, 1 + total);
isl_seq_cpy(wraps.mat->row[0], bound->el, 1 + total);
wraps.mat->n_row = 1;
if (add_wraps(&wraps, &info[j], bound->el, set_i) < 0)
goto error;
if (wraps.failed)
goto unbounded;
if (wrap_facet) {
if (add_wraps_around_facet(&wraps, &info[i], k,
bound->el, set_j) < 0)
goto error;
if (wraps.failed)
goto unbounded;
}
change = fuse(i, j, info, wraps.mat, 0, 0);
unbounded:
wraps_free(&wraps);
isl_set_free(set_i);
isl_set_free(set_j);
isl_vec_free(bound);
return change;
error:
wraps_free(&wraps);
isl_vec_free(bound);
isl_set_free(set_i);
isl_set_free(set_j);
return isl_change_error;
}
/* Given a cut constraint t(x) >= 0 of basic map i, stored in row "w"
* of wrap.mat, replace it by its relaxed version t(x) + 1 >= 0, and
* add wrapping constraints to wrap.mat for all constraints
* of basic map j that bound the part of basic map j that sticks out
* of the cut constraint.
* "set_i" is the underlying set of basic map i.
* If any wrapping fails, then wraps->mat.n_row is reset to zero.
*
* In particular, we first intersect basic map j with t(x) + 1 = 0.
* If the result is empty, then t(x) >= 0 was actually a valid constraint
* (with respect to the integer points), so we add t(x) >= 0 instead.
* Otherwise, we wrap the constraints of basic map j that are not
* redundant in this intersection and that are not already valid
* for basic map i over basic map i.
* Note that it is sufficient to wrap the constraints to include
* basic map i, because we will only wrap the constraints that do
* not include basic map i already. The wrapped constraint will
* therefore be more relaxed compared to the original constraint.
* Since the original constraint is valid for basic map j, so is
* the wrapped constraint.
*/
static isl_stat wrap_in_facet(struct isl_wraps *wraps, int w,
struct isl_coalesce_info *info_j, __isl_keep isl_set *set_i,
struct isl_tab_undo *snap)
{
isl_int_add_ui(wraps->mat->row[w][0], wraps->mat->row[w][0], 1);
if (isl_tab_add_eq(info_j->tab, wraps->mat->row[w]) < 0)
return isl_stat_error;
if (isl_tab_detect_redundant(info_j->tab) < 0)
return isl_stat_error;
if (info_j->tab->empty)
isl_int_sub_ui(wraps->mat->row[w][0], wraps->mat->row[w][0], 1);
else if (add_wraps(wraps, info_j, wraps->mat->row[w], set_i) < 0)
return isl_stat_error;
if (isl_tab_rollback(info_j->tab, snap) < 0)
return isl_stat_error;
return isl_stat_ok;
}
/* 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.
* "set_i" is the underlying set of basic map i.
* "wraps" has been initialized to be of the right size.
*
* For each cut constraint t(x) >= 0 of i, we add the relaxed version
* t(x) + 1 >= 0, along with wrapping constraints for all constraints
* of basic map j that bound the part of basic map j that sticks out
* of the cut constraint.
*
* 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 enum isl_change try_wrap_in_facets(int i, int j,
struct isl_coalesce_info *info, struct isl_wraps *wraps,
__isl_keep isl_set *set_i)
{
int k, l, w;
isl_size total;
struct isl_tab_undo *snap;
total = isl_basic_map_dim(info[i].bmap, isl_dim_all);
if (total < 0)
return isl_change_error;
snap = isl_tab_snap(info[j].tab);
for (k = 0; k < info[i].bmap->n_eq; ++k) {
for (l = 0; l < 2; ++l) {
if (info[i].eq[2 * k + l] != STATUS_CUT)
continue;
w = wraps->mat->n_row++;
if (l == 0)
isl_seq_neg(wraps->mat->row[w],
info[i].bmap->eq[k], 1 + total);
else
isl_seq_cpy(wraps->mat->row[w],
info[i].bmap->eq[k], 1 + total);
if (wrap_in_facet(wraps, w, &info[j], set_i, snap) < 0)
return isl_change_error;
if (wraps->failed)
return isl_change_none;
}
}
for (k = 0; k < info[i].bmap->n_ineq; ++k) {
if (info[i].ineq[k] != STATUS_CUT)
continue;
w = wraps->mat->n_row++;
isl_seq_cpy(wraps->mat->row[w],
info[i].bmap->ineq[k], 1 + total);
if (wrap_in_facet(wraps, w, &info[j], set_i, snap) < 0)
return isl_change_error;
if (wraps->failed)
return isl_change_none;
}
return fuse(i, j, info, wraps->mat, 0, 1);
}
/* 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 core computation is performed by try_wrap_in_facets.
* This function simply extracts an underlying set representation
* of basic map i and initializes the data structure for keeping
* track of wrapping constraints.
*/
static enum isl_change wrap_in_facets(int i, int j, int n,
struct isl_coalesce_info *info)
{
enum isl_change change = isl_change_none;
struct isl_wraps wraps;
isl_ctx *ctx;
isl_mat *mat;
isl_set *set_i = NULL;
isl_size total = isl_basic_map_dim(info[i].bmap, isl_dim_all);
int max_wrap;
if (total < 0)
return isl_change_error;
if (isl_tab_extend_cons(info[j].tab, 1) < 0)
return isl_change_error;
max_wrap = 1 + 2 * info[j].bmap->n_eq + info[j].bmap->n_ineq;
max_wrap *= n;
set_i = set_from_updated_bmap(info[i].bmap, info[i].tab);
ctx = isl_basic_map_get_ctx(info[i].bmap);
mat = isl_mat_alloc(ctx, max_wrap, 1 + total);
if (wraps_init(&wraps, mat, info, i, j) < 0)
goto error;
if (!set_i)
goto error;
change = try_wrap_in_facets(i, j, info, &wraps, set_i);
wraps_free(&wraps);
isl_set_free(set_i);
return change;
error:
wraps_free(&wraps);
isl_set_free(set_i);
return isl_change_error;
}
/* Return the effect of inequality "ineq" on the tableau "tab",
* after relaxing the constant term of "ineq" by one.
*/
static enum isl_ineq_type type_of_relaxed(struct isl_tab *tab, isl_int *ineq)
{
enum isl_ineq_type type;
isl_int_add_ui(ineq[0], ineq[0], 1);
type = isl_tab_ineq_type(tab, ineq);
isl_int_sub_ui(ineq[0], ineq[0], 1);
return type;
}
/* Given two basic sets i and j,
* check if relaxing all the cut constraints 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 enum isl_change can_wrap_in_set(int i, int j,
struct isl_coalesce_info *info)
{
int k, l;
int n;
isl_size total;
if (ISL_F_ISSET(info[i].bmap, ISL_BASIC_MAP_RATIONAL) ||
ISL_F_ISSET(info[j].bmap, ISL_BASIC_MAP_RATIONAL))
return isl_change_none;
n = count_eq(&info[i], STATUS_CUT) + count_ineq(&info[i], STATUS_CUT);
if (n == 0)
return isl_change_none;
total = isl_basic_map_dim(info[i].bmap, isl_dim_all);
if (total < 0)
return isl_change_error;
for (k = 0; k < info[i].bmap->n_eq; ++k) {
for (l = 0; l < 2; ++l) {
enum isl_ineq_type type;
if (info[i].eq[2 * k + l] != STATUS_CUT)
continue;
if (l == 0)
isl_seq_neg(info[i].bmap->eq[k],
info[i].bmap->eq[k], 1 + total);
type = type_of_relaxed(info[j].tab,
info[i].bmap->eq[k]);
if (l == 0)
isl_seq_neg(info[i].bmap->eq[k],
info[i].bmap->eq[k], 1 + total);
if (type == isl_ineq_error)
return isl_change_error;
if (type != isl_ineq_redundant)
return isl_change_none;
}
}
for (k = 0; k < info[i].bmap->n_ineq; ++k) {
enum isl_ineq_type type;
if (info[i].ineq[k] != STATUS_CUT)
continue;
type = type_of_relaxed(info[j].tab, info[i].bmap->ineq[k]);
if (type == isl_ineq_error)
return isl_change_error;
if (type != isl_ineq_redundant)
return isl_change_none;
}
return wrap_in_facets(i, j, n, info);
}
/* Check if either i or j has only cut constraints that can
* be used to wrap in (a facet of) the other basic set.
* if so, replace the pair by their union.
*/
static enum isl_change check_wrap(int i, int j, struct isl_coalesce_info *info)
{
enum isl_change change = isl_change_none;
change = can_wrap_in_set(i, j, info);
if (change != isl_change_none)
return change;
change = can_wrap_in_set(j, i, info);
return change;
}
/* Check if all inequality constraints of "i" that cut "j" cease
* to be cut constraints if they are relaxed by one.
* If so, collect the cut constraints in "list".
* The caller is responsible for allocating "list".
*/
static isl_bool all_cut_by_one(int i, int j, struct isl_coalesce_info *info,
int *list)
{
int l, n;
n = 0;
for (l = 0; l < info[i].bmap->n_ineq; ++l) {
enum isl_ineq_type type;
if (info[i].ineq[l] != STATUS_CUT)
continue;
type = type_of_relaxed(info[j].tab, info[i].bmap->ineq[l]);
if (type == isl_ineq_error)
return isl_bool_error;
if (type != isl_ineq_redundant)
return isl_bool_false;
list[n++] = l;
}
return isl_bool_true;
}
/* Given two basic maps such that "j" has at least one equality constraint
* that is adjacent to an inequality constraint of "i" and such that "i" has
* exactly one inequality constraint that is adjacent to an equality
* constraint of "j", check whether "i" can be extended to include "j" or
* whether "j" can be wrapped into "i".
* All remaining constraints of "i" and "j" are assumed to be valid
* or cut constraints of the other basic map.
* However, none of the equality constraints of "i" are cut constraints.
*
* If "i" has any "cut" inequality constraints, then check if relaxing
* each of them by one is sufficient for them to become valid.
* If so, check if the inequality constraint adjacent to an equality
* constraint of "j" along with all these cut constraints
* can be relaxed by one to contain exactly "j".
* Otherwise, or if this fails, check if "j" can be wrapped into "i".
*/
static enum isl_change check_single_adj_eq(int i, int j,
struct isl_coalesce_info *info)
{
enum isl_change change = isl_change_none;
int k;
int n_cut;
int *relax;
isl_ctx *ctx;
isl_bool try_relax;
n_cut = count_ineq(&info[i], STATUS_CUT);
k = find_ineq(&info[i], STATUS_ADJ_EQ);
if (n_cut > 0) {
ctx = isl_basic_map_get_ctx(info[i].bmap);
relax = isl_calloc_array(ctx, int, 1 + n_cut);
if (!relax)
return isl_change_error;
relax[0] = k;
try_relax = all_cut_by_one(i, j, info, relax + 1);
if (try_relax < 0)
change = isl_change_error;
} else {
try_relax = isl_bool_true;
relax = &k;
}
if (try_relax && change == isl_change_none)
change = is_relaxed_extension(i, j, 1 + n_cut, relax, info);
if (n_cut > 0)
free(relax);
if (change != isl_change_none)
return change;
change = can_wrap_in_facet(i, j, k, info, n_cut > 0);
return change;
}
/* At least one of the basic maps has an equality that is adjacent
* to an 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.
* If the other basic map does not have such an inequality, then
* check if all its constraints are either valid or cut constraints
* and, if so, try wrapping in the first map into the second.
* Otherwise, try to extend one basic map with the other or
* wrap one basic map in the other.
*/
static enum isl_change check_adj_eq(int i, int j,
struct isl_coalesce_info *info)
{
if (any_eq(&info[i], STATUS_ADJ_INEQ) &&
any_eq(&info[j], STATUS_ADJ_INEQ))
/* ADJ EQ TOO MANY */
return isl_change_none;
if (any_eq(&info[i], STATUS_ADJ_INEQ))
return check_adj_eq(j, i, info);
/* j has an equality adjacent to an inequality in i */
if (count_ineq(&info[i], STATUS_ADJ_EQ) != 1) {
if (all_valid_or_cut(&info[i]))
return can_wrap_in_set(i, j, info);
return isl_change_none;
}
if (any_eq(&info[i], STATUS_CUT))
return isl_change_none;
if (any_ineq(&info[j], STATUS_ADJ_EQ) ||
any_ineq(&info[i], STATUS_ADJ_INEQ) ||
any_ineq(&info[j], STATUS_ADJ_INEQ))
/* ADJ EQ TOO MANY */
return isl_change_none;
return check_single_adj_eq(i, j, info);
}
/* Disjunct "j" lies on a hyperplane that is adjacent to disjunct "i".
* In particular, disjunct "i" has an inequality constraint that is adjacent
* to a (combination of) equality constraint(s) of disjunct "j",
* but disjunct "j" has no explicit equality constraint adjacent
* to an inequality constraint of disjunct "i".
*
* Disjunct "i" is already known not to have any equality constraints
* that are adjacent to an equality or inequality constraint.
* Check that, other than the inequality constraint mentioned above,
* all other constraints of disjunct "i" are valid for disjunct "j".
* If so, try and wrap in disjunct "j".
*/
static enum isl_change check_ineq_adj_eq(int i, int j,
struct isl_coalesce_info *info)
{
int k;
if (any_eq(&info[i], STATUS_CUT))
return isl_change_none;
if (any_ineq(&info[i], STATUS_CUT))
return isl_change_none;
if (any_ineq(&info[i], STATUS_ADJ_INEQ))
return isl_change_none;
if (count_ineq(&info[i], STATUS_ADJ_EQ) != 1)
return isl_change_none;
k = find_ineq(&info[i], STATUS_ADJ_EQ);
return can_wrap_in_facet(i, j, k, info, 0);
}
/* 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.
* _
* \\ \\
* \\ => \\
* \ \|
*
* If there is more than one equality of "i" adjacent to an equality of "j",
* then the result will satisfy one or more equalities that are a linear
* combination of these equalities. These will be encoded as pairs
* of inequalities in the wrapping constraints and need to be made
* explicit.
*/
static enum isl_change check_eq_adj_eq(int i, int j,
struct isl_coalesce_info *info)
{
int k;
enum isl_change change = isl_change_none;
int detect_equalities = 0;
struct isl_wraps wraps;
isl_ctx *ctx;
isl_mat *mat;
struct isl_set *set_i = NULL;
struct isl_set *set_j = NULL;
struct isl_vec *bound = NULL;
isl_size total = isl_basic_map_dim(info[i].bmap, isl_dim_all);
if (total < 0)
return isl_change_error;
if (count_eq(&info[i], STATUS_ADJ_EQ) != 1)
detect_equalities = 1;
k = find_eq(&info[i], STATUS_ADJ_EQ);
set_i = set_from_updated_bmap(info[i].bmap, info[i].tab);
set_j = set_from_updated_bmap(info[j].bmap, info[j].tab);
ctx = isl_basic_map_get_ctx(info[i].bmap);
mat = isl_mat_alloc(ctx, 2 * (info[i].bmap->n_eq + info[j].bmap->n_eq) +
info[i].bmap->n_ineq + info[j].bmap->n_ineq,
1 + total);
if (wraps_init(&wraps, mat, info, i, j) < 0)
goto error;
bound = isl_vec_alloc(ctx, 1 + total);
if (!set_i || !set_j || !bound)
goto error;
if (k % 2 == 0)
isl_seq_neg(bound->el, info[i].bmap->eq[k / 2], 1 + total);
else
isl_seq_cpy(bound->el, info[i].bmap->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, &info[j], bound->el, set_i) < 0)
goto error;
if (wraps.failed)
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, &info[i], bound->el, set_j) < 0)
goto error;
if (wraps.failed)
goto unbounded;
change = fuse(i, j, info, wraps.mat, detect_equalities, 0);
if (0) {
error: change = isl_change_error;
}
unbounded:
wraps_free(&wraps);
isl_set_free(set_i);
isl_set_free(set_j);
isl_vec_free(bound);
return change;
}
/* Initialize the "eq" and "ineq" fields of "info".
*/
static void init_status(struct isl_coalesce_info *info)
{
info->eq = info->ineq = NULL;
}
/* Set info->eq to the positions of the equalities of info->bmap
* with respect to the basic map represented by "tab".
* If info->eq has already been computed, then do not compute it again.
*/
static void set_eq_status_in(struct isl_coalesce_info *info,
struct isl_tab *tab)
{
if (info->eq)
return;
info->eq = eq_status_in(info->bmap, tab);
}
/* Set info->ineq to the positions of the inequalities of info->bmap
* with respect to the basic map represented by "tab".
* If info->ineq has already been computed, then do not compute it again.
*/
static void set_ineq_status_in(struct isl_coalesce_info *info,
struct isl_tab *tab)
{
if (info->ineq)
return;
info->ineq = ineq_status_in(info->bmap, info->tab, tab);
}
/* Free the memory allocated by the "eq" and "ineq" fields of "info".
* This function assumes that init_status has been called on "info" first,
* after which the "eq" and "ineq" fields may or may not have been
* assigned a newly allocated array.
*/
static void clear_status(struct isl_coalesce_info *info)
{
free(info->eq);
free(info->ineq);
}
/* Are all inequality constraints of the basic map represented by "info"
* valid for the other basic map, except for a single constraint
* that is adjacent to an inequality constraint of the other basic map?
*/
static int all_ineq_valid_or_single_adj_ineq(struct isl_coalesce_info *info)
{
int i;
int k = -1;
for (i = 0; i < info->bmap->n_ineq; ++i) {
if (info->ineq[i] == STATUS_REDUNDANT)
continue;
if (info->ineq[i] == STATUS_VALID)
continue;
if (info->ineq[i] != STATUS_ADJ_INEQ)
return 0;
if (k != -1)
return 0;
k = i;
}
return k != -1;
}
/* Basic map "i" has one or more equality constraints that separate it
* from basic map "j". Check if it happens to be an extension
* of basic map "j".
* In particular, check that all constraints of "j" are valid for "i",
* except for one inequality constraint that is adjacent
* to an inequality constraints of "i".
* If so, check for "i" being an extension of "j" by calling
* is_adj_ineq_extension.
*
* Clean up the memory allocated for keeping track of the status
* of the constraints before returning.
*/
static enum isl_change separating_equality(int i, int j,
struct isl_coalesce_info *info)
{
enum isl_change change = isl_change_none;
if (all(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_VALID) &&
all_ineq_valid_or_single_adj_ineq(&info[j]))
change = is_adj_ineq_extension(j, i, info);
clear_status(&info[i]);
clear_status(&info[j]);
return change;
}
/* 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
* isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
* Otherwise, return isl_change_none.
* The two basic maps are assumed to live in the same local space.
* The "eq" and "ineq" fields of info[i] and info[j] are assumed
* to have been initialized by the caller, either to NULL or
* to valid information.
*
* 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 inequality adjacent to 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 enum isl_change coalesce_local_pair_reuse(int i, int j,
struct isl_coalesce_info *info)
{
enum isl_change change = isl_change_none;
set_ineq_status_in(&info[i], info[j].tab);
if (info[i].bmap->n_ineq && !info[i].ineq)
goto error;
if (any_ineq(&info[i], STATUS_ERROR))
goto error;
if (any_ineq(&info[i], STATUS_SEPARATE))
goto done;
set_ineq_status_in(&info[j], info[i].tab);
if (info[j].bmap->n_ineq && !info[j].ineq)
goto error;
if (any_ineq(&info[j], STATUS_ERROR))
goto error;
if (any_ineq(&info[j], STATUS_SEPARATE))
goto done;
set_eq_status_in(&info[i], info[j].tab);
if (info[i].bmap->n_eq && !info[i].eq)
goto error;
if (any_eq(&info[i], STATUS_ERROR))
goto error;
set_eq_status_in(&info[j], info[i].tab);
if (info[j].bmap->n_eq && !info[j].eq)
goto error;
if (any_eq(&info[j], STATUS_ERROR))
goto error;
if (any_eq(&info[i], STATUS_SEPARATE))
return separating_equality(i, j, info);
if (any_eq(&info[j], STATUS_SEPARATE))
return separating_equality(j, i, info);
if (all(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_VALID) &&
all(info[i].ineq, info[i].bmap->n_ineq, STATUS_VALID)) {
drop(&info[j]);
change = isl_change_drop_second;
} else if (all(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_VALID) &&
all(info[j].ineq, info[j].bmap->n_ineq, STATUS_VALID)) {
drop(&info[i]);
change = isl_change_drop_first;
} else if (any_eq(&info[i], STATUS_ADJ_EQ)) {
change = check_eq_adj_eq(i, j, info);
} else if (any_eq(&info[j], STATUS_ADJ_EQ)) {
change = check_eq_adj_eq(j, i, info);
} else if (any_eq(&info[i], STATUS_ADJ_INEQ) ||
any_eq(&info[j], STATUS_ADJ_INEQ)) {
change = check_adj_eq(i, j, info);
} else if (any_ineq(&info[i], STATUS_ADJ_EQ)) {
change = check_ineq_adj_eq(i, j, info);
} else if (any_ineq(&info[j], STATUS_ADJ_EQ)) {
change = check_ineq_adj_eq(j, i, info);
} else if (any_ineq(&info[i], STATUS_ADJ_INEQ) ||
any_ineq(&info[j], STATUS_ADJ_INEQ)) {
change = check_adj_ineq(i, j, info);
} else {
if (!any_eq(&info[i], STATUS_CUT) &&
!any_eq(&info[j], STATUS_CUT))
change = check_facets(i, j, info);
if (change == isl_change_none)
change = check_wrap(i, j, info);
}
done:
clear_status(&info[i]);
clear_status(&info[j]);
return change;
error:
clear_status(&info[i]);
clear_status(&info[j]);
return isl_change_error;
}
/* 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
* isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
* Otherwise, return isl_change_none.
* The two basic maps are assumed to live in the same local space.
*/
static enum isl_change coalesce_local_pair(int i, int j,
struct isl_coalesce_info *info)
{
init_status(&info[i]);
init_status(&info[j]);
return coalesce_local_pair_reuse(i, j, info);
}
/* Shift the integer division at position "div" of the basic map
* represented by "info" by "shift".
*
* That is, if the integer division has the form
*
* floor(f(x)/d)
*
* then replace it by
*
* floor((f(x) + shift * d)/d) - shift
*/
static isl_stat shift_div(struct isl_coalesce_info *info, int div,
isl_int shift)
{
isl_size total, n_div;
info->bmap = isl_basic_map_shift_div(info->bmap, div, 0, shift);
if (!info->bmap)
return isl_stat_error;
total = isl_basic_map_dim(info->bmap, isl_dim_all);
n_div = isl_basic_map_dim(info->bmap, isl_dim_div);
if (total < 0 || n_div < 0)
return isl_stat_error;
total -= n_div;
if (isl_tab_shift_var(info->tab, total + div, shift) < 0)
return isl_stat_error;
return isl_stat_ok;
}
/* If the integer division at position "div" is defined by an equality,
* i.e., a stride constraint, then change the integer division expression
* to have a constant term equal to zero.
*
* Let the equality constraint be
*
* c + f + m a = 0
*
* The integer division expression is then typically of the form
*
* a = floor((-f - c')/m)
*
* The integer division is first shifted by t = floor(c/m),
* turning the equality constraint into
*
* c - m floor(c/m) + f + m a' = 0
*
* i.e.,
*
* (c mod m) + f + m a' = 0
*
* That is,
*
* a' = (-f - (c mod m))/m = floor((-f)/m)
*
* because a' is an integer and 0 <= (c mod m) < m.
* The constant term of a' can therefore be zeroed out,
* but only if the integer division expression is of the expected form.
*/
static isl_stat normalize_stride_div(struct isl_coalesce_info *info, int div)
{
isl_bool defined, valid;
isl_stat r;
isl_constraint *c;
isl_int shift, stride;
defined = isl_basic_map_has_defining_equality(info->bmap, isl_dim_div,
div, &c);
if (defined < 0)
return isl_stat_error;
if (!defined)
return isl_stat_ok;
if (!c)
return isl_stat_error;
valid = isl_constraint_is_div_equality(c, div);
isl_int_init(shift);
isl_int_init(stride);
isl_constraint_get_constant(c, &shift);
isl_constraint_get_coefficient(c, isl_dim_div, div, &stride);
isl_int_fdiv_q(shift, shift, stride);
r = shift_div(info, div, shift);
isl_int_clear(stride);
isl_int_clear(shift);
isl_constraint_free(c);
if (r < 0 || valid < 0)
return isl_stat_error;
if (!valid)
return isl_stat_ok;
info->bmap = isl_basic_map_set_div_expr_constant_num_si_inplace(
info->bmap, div, 0);
if (!info->bmap)
return isl_stat_error;
return isl_stat_ok;
}
/* The basic maps represented by "info1" and "info2" are known
* to have the same number of integer divisions.
* Check if pairs of integer divisions are equal to each other
* despite the fact that they differ by a rational constant.
*
* In particular, look for any pair of integer divisions that
* only differ in their constant terms.
* If either of these integer divisions is defined
* by stride constraints, then modify it to have a zero constant term.
* If both are defined by stride constraints then in the end they will have
* the same (zero) constant term.
*/
static isl_stat harmonize_stride_divs(struct isl_coalesce_info *info1,
struct isl_coalesce_info *info2)
{
int i;
isl_size n;
n = isl_basic_map_dim(info1->bmap, isl_dim_div);
if (n < 0)
return isl_stat_error;
for (i = 0; i < n; ++i) {
isl_bool known, harmonize;
known = isl_basic_map_div_is_known(info1->bmap, i);
if (known >= 0 && known)
known = isl_basic_map_div_is_known(info2->bmap, i);
if (known < 0)
return isl_stat_error;
if (!known)
continue;
harmonize = isl_basic_map_equal_div_expr_except_constant(
info1->bmap, i, info2->bmap, i);
if (harmonize < 0)
return isl_stat_error;
if (!harmonize)
continue;
if (normalize_stride_div(info1, i) < 0)
return isl_stat_error;
if (normalize_stride_div(info2, i) < 0)
return isl_stat_error;
}
return isl_stat_ok;
}
/* If "shift" is an integer constant, then shift the integer division
* at position "div" of the basic map represented by "info" by "shift".
* If "shift" is not an integer constant, then do nothing.
* If "shift" is equal to zero, then no shift needs to be performed either.
*
* That is, if the integer division has the form
*
* floor(f(x)/d)
*
* then replace it by
*
* floor((f(x) + shift * d)/d) - shift
*/
static isl_stat shift_if_cst_int(struct isl_coalesce_info *info, int div,
__isl_keep isl_aff *shift)
{
isl_bool cst;
isl_stat r;
isl_int d;
isl_val *c;
cst = isl_aff_is_cst(shift);
if (cst < 0 || !cst)
return cst < 0 ? isl_stat_error : isl_stat_ok;
c = isl_aff_get_constant_val(shift);
cst = isl_val_is_int(c);
if (cst >= 0 && cst)
cst = isl_bool_not(isl_val_is_zero(c));
if (cst < 0 || !cst) {
isl_val_free(c);
return cst < 0 ? isl_stat_error : isl_stat_ok;
}
isl_int_init(d);
r = isl_val_get_num_isl_int(c, &d);
if (r >= 0)
r = shift_div(info, div, d);
isl_int_clear(d);
isl_val_free(c);
return r;
}
/* Check if some of the divs in the basic map represented by "info1"
* are shifts of the corresponding divs in the basic map represented
* by "info2", taking into account the equality constraints "eq1" of "info1"
* and "eq2" of "info2". If so, align them with those of "info2".
* "info1" and "info2" are assumed to have the same number
* of integer divisions.
*
* An integer division is considered to be a shift of another integer
* division if, after simplification with respect to the equality
* constraints of the other basic map, one is equal to the other
* plus a constant.
*
* In particular, for each pair of integer divisions, if both are known,
* have the same denominator and are not already equal to each other,
* simplify each with respect to the equality constraints
* of the other basic map. If the difference is an integer constant,
* then move this difference outside.
* That is, if, after simplification, one integer division is of the form
*
* floor((f(x) + c_1)/d)
*
* while the other is of the form
*
* floor((f(x) + c_2)/d)
*
* and n = (c_2 - c_1)/d is an integer, then replace the first
* integer division by
*
* floor((f_1(x) + c_1 + n * d)/d) - n,
*
* where floor((f_1(x) + c_1 + n * d)/d) = floor((f2(x) + c_2)/d)
* after simplification with respect to the equality constraints.
*/
static isl_stat harmonize_divs_with_hulls(struct isl_coalesce_info *info1,
struct isl_coalesce_info *info2, __isl_keep isl_basic_set *eq1,
__isl_keep isl_basic_set *eq2)
{
int i;
isl_size total;
isl_local_space *ls1, *ls2;
total = isl_basic_map_dim(info1->bmap, isl_dim_all);
if (total < 0)
return isl_stat_error;
ls1 = isl_local_space_wrap(isl_basic_map_get_local_space(info1->bmap));
ls2 = isl_local_space_wrap(isl_basic_map_get_local_space(info2->bmap));
for (i = 0; i < info1->bmap->n_div; ++i) {
isl_stat r;
isl_aff *div1, *div2;
if (!isl_local_space_div_is_known(ls1, i) ||
!isl_local_space_div_is_known(ls2, i))
continue;
if (isl_int_ne(info1->bmap->div[i][0], info2->bmap->div[i][0]))
continue;
if (isl_seq_eq(info1->bmap->div[i] + 1,
info2->bmap->div[i] + 1, 1 + total))
continue;
div1 = isl_local_space_get_div(ls1, i);
div2 = isl_local_space_get_div(ls2, i);
div1 = isl_aff_substitute_equalities(div1,
isl_basic_set_copy(eq2));
div2 = isl_aff_substitute_equalities(div2,
isl_basic_set_copy(eq1));
div2 = isl_aff_sub(div2, div1);
r = shift_if_cst_int(info1, i, div2);
isl_aff_free(div2);
if (r < 0)
break;
}
isl_local_space_free(ls1);
isl_local_space_free(ls2);
if (i < info1->bmap->n_div)
return isl_stat_error;
return isl_stat_ok;
}
/* Check if some of the divs in the basic map represented by "info1"
* are shifts of the corresponding divs in the basic map represented
* by "info2". If so, align them with those of "info2".
* Only do this if "info1" and "info2" have the same number
* of integer divisions.
*
* An integer division is considered to be a shift of another integer
* division if, after simplification with respect to the equality
* constraints of the other basic map, one is equal to the other
* plus a constant.
*
* First check if pairs of integer divisions are equal to each other
* despite the fact that they differ by a rational constant.
* If so, try and arrange for them to have the same constant term.
*
* Then, extract the equality constraints and continue with
* harmonize_divs_with_hulls.
*
* If the equality constraints of both basic maps are the same,
* then there is no need to perform any shifting since
* the coefficients of the integer divisions should have been
* reduced in the same way.
*/
static isl_stat harmonize_divs(struct isl_coalesce_info *info1,
struct isl_coalesce_info *info2)
{
isl_bool equal;
isl_basic_map *bmap1, *bmap2;
isl_basic_set *eq1, *eq2;
isl_stat r;
if (!info1->bmap || !info2->bmap)
return isl_stat_error;
if (info1->bmap->n_div != info2->bmap->n_div)
return isl_stat_ok;
if (info1->bmap->n_div == 0)
return isl_stat_ok;
if (harmonize_stride_divs(info1, info2) < 0)
return isl_stat_error;
bmap1 = isl_basic_map_copy(info1->bmap);
bmap2 = isl_basic_map_copy(info2->bmap);
eq1 = isl_basic_map_wrap(isl_basic_map_plain_affine_hull(bmap1));
eq2 = isl_basic_map_wrap(isl_basic_map_plain_affine_hull(bmap2));
equal = isl_basic_set_plain_is_equal(eq1, eq2);
if (equal < 0)
r = isl_stat_error;
else if (equal)
r = isl_stat_ok;
else
r = harmonize_divs_with_hulls(info1, info2, eq1, eq2);
isl_basic_set_free(eq1);
isl_basic_set_free(eq2);
return r;
}
/* 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 isl_bool same_divs(__isl_keep isl_basic_map *bmap1,
__isl_keep isl_basic_map *bmap2)
{
int i;
isl_bool known;
isl_size total;
if (!bmap1 || !bmap2)
return isl_bool_error;
if (bmap1->n_div != bmap2->n_div)
return isl_bool_false;
if (bmap1->n_div == 0)
return isl_bool_true;
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_dim(bmap1, isl_dim_all);
if (total < 0)
return isl_bool_error;
for (i = 0; i < bmap1->n_div; ++i)
if (!isl_seq_eq(bmap1->div[i], bmap2->div[i], 2 + total))
return isl_bool_false;
return isl_bool_true;
}
/* Assuming that "tab" contains the equality constraints and
* the initial inequality constraints of "bmap", copy the remaining
* inequality constraints of "bmap" to "Tab".
*/
static isl_stat copy_ineq(struct isl_tab *tab, __isl_keep isl_basic_map *bmap)
{
int i, n_ineq;
if (!bmap)
return isl_stat_error;
n_ineq = tab->n_con - tab->n_eq;
for (i = n_ineq; i < bmap->n_ineq; ++i)
if (isl_tab_add_ineq(tab, bmap->ineq[i]) < 0)
return isl_stat_error;
return isl_stat_ok;
}
/* Description of an integer division that is added
* during an expansion.
* "pos" is the position of the corresponding variable.
* "cst" indicates whether this integer division has a fixed value.
* "val" contains the fixed value, if the value is fixed.
*/
struct isl_expanded {
int pos;
isl_bool cst;
isl_int val;
};
/* For each of the "n" integer division variables "expanded",
* if the variable has a fixed value, then add two inequality
* constraints expressing the fixed value.
* Otherwise, add the corresponding div constraints.
* The caller is responsible for removing the div constraints
* that it added for all these "n" integer divisions.
*
* The div constraints and the pair of inequality constraints
* forcing the fixed value cannot both be added for a given variable
* as the combination may render some of the original constraints redundant.
* These would then be ignored during the coalescing detection,
* while they could remain in the fused result.
*
* The two added inequality constraints are
*
* -a + v >= 0
* a - v >= 0
*
* with "a" the variable and "v" its fixed value.
* The facet corresponding to one of these two constraints is selected
* in the tableau to ensure that the pair of inequality constraints
* is treated as an equality constraint.
*
* The information in info->ineq is thrown away because it was
* computed in terms of div constraints, while some of those
* have now been replaced by these pairs of inequality constraints.
*/
static isl_stat fix_constant_divs(struct isl_coalesce_info *info,
int n, struct isl_expanded *expanded)
{
unsigned o_div;
int i;
isl_vec *ineq;
o_div = isl_basic_map_offset(info->bmap, isl_dim_div) - 1;
ineq = isl_vec_alloc(isl_tab_get_ctx(info->tab), 1 + info->tab->n_var);
if (!ineq)
return isl_stat_error;
isl_seq_clr(ineq->el + 1, info->tab->n_var);
for (i = 0; i < n; ++i) {
if (!expanded[i].cst) {
info->bmap = isl_basic_map_extend_constraints(
info->bmap, 0, 2);
info->bmap = isl_basic_map_add_div_constraints(
info->bmap, expanded[i].pos - o_div);
} else {
isl_int_set_si(ineq->el[1 + expanded[i].pos], -1);
isl_int_set(ineq->el[0], expanded[i].val);
info->bmap = isl_basic_map_add_ineq(info->bmap,
ineq->el);
isl_int_set_si(ineq->el[1 + expanded[i].pos], 1);
isl_int_neg(ineq->el[0], expanded[i].val);
info->bmap = isl_basic_map_add_ineq(info->bmap,
ineq->el);
isl_int_set_si(ineq->el[1 + expanded[i].pos], 0);
}
if (copy_ineq(info->tab, info->bmap) < 0)
break;
if (expanded[i].cst &&
isl_tab_select_facet(info->tab, info->tab->n_con - 1) < 0)
break;
}
isl_vec_free(ineq);
clear_status(info);
init_status(info);
return i < n ? isl_stat_error : isl_stat_ok;
}
/* Insert the "n" integer division variables "expanded"
* into info->tab and info->bmap and
* update info->ineq with respect to the redundant constraints
* in the resulting tableau.
* "bmap" contains the result of this insertion in info->bmap,
* while info->bmap is the original version
* of "bmap", i.e., the one that corresponds to the current
* state of info->tab. The number of constraints in info->bmap
* is assumed to be the same as the number of constraints
* in info->tab. This is required to be able to detect
* the extra constraints in "bmap".
*
* In particular, introduce extra variables corresponding
* to the extra integer divisions and add the div constraints
* that were added to "bmap" after info->tab was created
* from info->bmap.
* Furthermore, check if these extra integer divisions happen
* to attain a fixed integer value in info->tab.
* If so, replace the corresponding div constraints by pairs
* of inequality constraints that fix these
* integer divisions to their single integer values.
* Replace info->bmap by "bmap" to match the changes to info->tab.
* info->ineq was computed without a tableau and therefore
* does not take into account the redundant constraints
* in the tableau. Mark them here.
* There is no need to check the newly added div constraints
* since they cannot be redundant.
* The redundancy check is not performed when constants have been discovered
* since info->ineq is completely thrown away in this case.
*/
static isl_stat tab_insert_divs(struct isl_coalesce_info *info,
int n, struct isl_expanded *expanded, __isl_take isl_basic_map *bmap)
{
int i, n_ineq;
unsigned n_eq;
struct isl_tab_undo *snap;
int any;
if (!bmap)
return isl_stat_error;
if (info->bmap->n_eq + info->bmap->n_ineq != info->tab->n_con)
isl_die(isl_basic_map_get_ctx(bmap), isl_error_internal,
"original tableau does not correspond "
"to original basic map", goto error);
if (isl_tab_extend_vars(info->tab, n) < 0)
goto error;
if (isl_tab_extend_cons(info->tab, 2 * n) < 0)
goto error;
for (i = 0; i < n; ++i) {
if (isl_tab_insert_var(info->tab, expanded[i].pos) < 0)
goto error;
}
snap = isl_tab_snap(info->tab);
n_ineq = info->tab->n_con - info->tab->n_eq;
if (copy_ineq(info->tab, bmap) < 0)
goto error;
isl_basic_map_free(info->bmap);
info->bmap = bmap;
any = 0;
for (i = 0; i < n; ++i) {
expanded[i].cst = isl_tab_is_constant(info->tab,
expanded[i].pos, &expanded[i].val);
if (expanded[i].cst < 0)
return isl_stat_error;
if (expanded[i].cst)
any = 1;
}
if (any) {
if (isl_tab_rollback(info->tab, snap) < 0)
return isl_stat_error;
info->bmap = isl_basic_map_cow(info->bmap);
info->bmap = isl_basic_map_free_inequality(info->bmap, 2 * n);
if (info->bmap < 0)
return isl_stat_error;
return fix_constant_divs(info, n, expanded);
}
n_eq = info->bmap->n_eq;
for (i = 0; i < n_ineq; ++i) {
if (isl_tab_is_redundant(info->tab, n_eq + i))
info->ineq[i] = STATUS_REDUNDANT;
}
return isl_stat_ok;
error:
isl_basic_map_free(bmap);
return isl_stat_error;
}
/* Expand info->tab and info->bmap in the same way "bmap" was expanded
* in isl_basic_map_expand_divs using the expansion "exp" and
* update info->ineq with respect to the redundant constraints
* in the resulting tableau. info->bmap is the original version
* of "bmap", i.e., the one that corresponds to the current
* state of info->tab. The number of constraints in info->bmap
* is assumed to be the same as the number of constraints
* in info->tab. This is required to be able to detect
* the extra constraints in "bmap".
*
* Extract the positions where extra local variables are introduced
* from "exp" and call tab_insert_divs.
*/
static isl_stat expand_tab(struct isl_coalesce_info *info, int *exp,
__isl_take isl_basic_map *bmap)
{
isl_ctx *ctx;
struct isl_expanded *expanded;
int i, j, k, n;
int extra_var;
isl_size total, n_div;
unsigned pos;
isl_stat r;
total = isl_basic_map_dim(bmap, isl_dim_all);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (total < 0 || n_div < 0)
return isl_stat_error;
pos = total - n_div;
extra_var = total - info->tab->n_var;
n = n_div - extra_var;
ctx = isl_basic_map_get_ctx(bmap);
expanded = isl_calloc_array(ctx, struct isl_expanded, extra_var);
if (extra_var && !expanded)
goto error;
i = 0;
k = 0;
for (j = 0; j < n_div; ++j) {
if (i < n && exp[i] == j) {
++i;
continue;
}
expanded[k++].pos = pos + j;
}
for (k = 0; k < extra_var; ++k)
isl_int_init(expanded[k].val);
r = tab_insert_divs(info, extra_var, expanded, bmap);
for (k = 0; k < extra_var; ++k)
isl_int_clear(expanded[k].val);
free(expanded);
return r;
error:
isl_basic_map_free(bmap);
return isl_stat_error;
}
/* Check if the union of the basic maps represented by info[i] and info[j]
* can be represented by a single basic map,
* after expanding the divs of info[i] to match those of info[j].
* If so, replace the pair by the single basic map and return
* isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
* Otherwise, return isl_change_none.
*
* The caller has already checked for info[j] being a subset of info[i].
* If some of the divs of info[j] are unknown, then the expanded info[i]
* will not have the corresponding div constraints. The other patterns
* therefore cannot apply. Skip the computation in this case.
*
* The expansion is performed using the divs "div" and expansion "exp"
* computed by the caller.
* info[i].bmap has already been expanded and the result is passed in
* as "bmap".
* The "eq" and "ineq" fields of info[i] reflect the status of
* the constraints of the expanded "bmap" with respect to info[j].tab.
* However, inequality constraints that are redundant in info[i].tab
* have not yet been marked as such because no tableau was available.
*
* Replace info[i].bmap by "bmap" and expand info[i].tab as well,
* updating info[i].ineq with respect to the redundant constraints.
* Then try and coalesce the expanded info[i] with info[j],
* reusing the information in info[i].eq and info[i].ineq.
* If this does not result in any coalescing or if it results in info[j]
* getting dropped (which should not happen in practice, since the case
* of info[j] being a subset of info[i] has already been checked by
* the caller), then revert info[i] to its original state.
*/
static enum isl_change coalesce_expand_tab_divs(__isl_take isl_basic_map *bmap,
int i, int j, struct isl_coalesce_info *info, __isl_keep isl_mat *div,
int *exp)
{
isl_bool known;
isl_basic_map *bmap_i;
struct isl_tab_undo *snap;
enum isl_change change = isl_change_none;
known = isl_basic_map_divs_known(info[j].bmap);
if (known < 0 || !known) {
clear_status(&info[i]);
isl_basic_map_free(bmap);
return known < 0 ? isl_change_error : isl_change_none;
}
bmap_i = isl_basic_map_copy(info[i].bmap);
snap = isl_tab_snap(info[i].tab);
if (expand_tab(&info[i], exp, bmap) < 0)
change = isl_change_error;
init_status(&info[j]);
if (change == isl_change_none)
change = coalesce_local_pair_reuse(i, j, info);
else
clear_status(&info[i]);
if (change != isl_change_none && change != isl_change_drop_second) {
isl_basic_map_free(bmap_i);
} else {
isl_basic_map_free(info[i].bmap);
info[i].bmap = bmap_i;
if (isl_tab_rollback(info[i].tab, snap) < 0)
change = isl_change_error;
}
return change;
}
/* Check if the union of "bmap" and the basic map represented by info[j]
* can be represented by a single basic map,
* after expanding the divs of "bmap" to match those of info[j].
* If so, replace the pair by the single basic map and return
* isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
* Otherwise, return isl_change_none.
*
* In particular, check if the expanded "bmap" contains the basic map
* represented by the tableau info[j].tab.
* The expansion is performed using the divs "div" and expansion "exp"
* computed by the caller.
* Then we check if all constraints of the expanded "bmap" are valid for
* info[j].tab.
*
* If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
* In this case, the positions of the constraints of info[i].bmap
* with respect to the basic map represented by info[j] are stored
* in info[i].
*
* If the expanded "bmap" does not contain the basic map
* represented by the tableau info[j].tab and if "i" is not -1,
* i.e., if the original "bmap" is info[i].bmap, then expand info[i].tab
* as well and check if that results in coalescing.
*/
static enum isl_change coalesce_with_expanded_divs(
__isl_keep isl_basic_map *bmap, int i, int j,
struct isl_coalesce_info *info, __isl_keep isl_mat *div, int *exp)
{
enum isl_change change = isl_change_none;
struct isl_coalesce_info info_local, *info_i;
info_i = i >= 0 ? &info[i] : &info_local;
init_status(info_i);
bmap = isl_basic_map_copy(bmap);
bmap = isl_basic_map_expand_divs(bmap, isl_mat_copy(div), exp);
bmap = isl_basic_map_mark_final(bmap);
if (!bmap)
goto error;
info_local.bmap = bmap;
info_i->eq = eq_status_in(bmap, info[j].tab);
if (bmap->n_eq && !info_i->eq)
goto error;
if (any_eq(info_i, STATUS_ERROR))
goto error;
if (any_eq(info_i, STATUS_SEPARATE))
goto done;
info_i->ineq = ineq_status_in(bmap, NULL, info[j].tab);
if (bmap->n_ineq && !info_i->ineq)
goto error;
if (any_ineq(info_i, STATUS_ERROR))
goto error;
if (any_ineq(info_i, STATUS_SEPARATE))
goto done;
if (all(info_i->eq, 2 * bmap->n_eq, STATUS_VALID) &&
all(info_i->ineq, bmap->n_ineq, STATUS_VALID)) {
drop(&info[j]);
change = isl_change_drop_second;
}
if (change == isl_change_none && i != -1)
return coalesce_expand_tab_divs(bmap, i, j, info, div, exp);
done:
isl_basic_map_free(bmap);
clear_status(info_i);
return change;
error:
isl_basic_map_free(bmap);
clear_status(info_i);
return isl_change_error;
}
/* Check if the union of "bmap_i" and the basic map represented by info[j]
* can be represented by a single basic map,
* after aligning the divs of "bmap_i" to match those of info[j].
* If so, replace the pair by the single basic map and return
* isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
* Otherwise, return isl_change_none.
*
* In particular, check if "bmap_i" contains the basic map represented by
* info[j] after aligning the divs of "bmap_i" to those of info[j].
* Note that this can only succeed if the number of divs of "bmap_i"
* is smaller than (or equal to) the number of divs of info[j].
*
* We first check if the divs of "bmap_i" are all known and form a subset
* of those of info[j].bmap. If so, we pass control over to
* coalesce_with_expanded_divs.
*
* If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
*/
static enum isl_change coalesce_after_aligning_divs(
__isl_keep isl_basic_map *bmap_i, int i, int j,
struct isl_coalesce_info *info)
{
isl_bool known;
isl_mat *div_i, *div_j, *div;
int *exp1 = NULL;
int *exp2 = NULL;
isl_ctx *ctx;
enum isl_change change;
known = isl_basic_map_divs_known(bmap_i);
if (known < 0)
return isl_change_error;
if (!known)
return isl_change_none;
ctx = isl_basic_map_get_ctx(bmap_i);
div_i = isl_basic_map_get_divs(bmap_i);
div_j = isl_basic_map_get_divs(info[j].bmap);
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)
change = coalesce_with_expanded_divs(bmap_i,
i, j, info, div, exp1);
else
change = isl_change_none;
isl_mat_free(div);
isl_mat_free(div_i);
isl_mat_free(div_j);
free(exp2);
free(exp1);
return change;
error:
isl_mat_free(div_i);
isl_mat_free(div_j);
free(exp1);
free(exp2);
return isl_change_error;
}
/* Check if basic map "j" is a subset of basic map "i" after
* exploiting the extra equalities of "j" to simplify the divs of "i".
* If so, remove basic map "j" and return isl_change_drop_second.
*
* If "j" does not have any equalities or if they are the same
* as those of "i", then we cannot exploit them to simplify the divs.
* Similarly, if there are no divs in "i", then they cannot be simplified.
* If, on the other hand, the affine hulls of "i" and "j" do not intersect,
* then "j" cannot be a subset of "i".
*
* Otherwise, we intersect "i" with the affine hull of "j" and then
* check if "j" is a subset of the result after aligning the divs.
* If so, then "j" is definitely a subset of "i" and can be removed.
* Note that if after intersection with the affine hull of "j".
* "i" still has more divs than "j", then there is no way we can
* align the divs of "i" to those of "j".
*/
static enum isl_change coalesce_subset_with_equalities(int i, int j,
struct isl_coalesce_info *info)
{
isl_basic_map *hull_i, *hull_j, *bmap_i;
int equal, empty;
enum isl_change change;
if (info[j].bmap->n_eq == 0)
return isl_change_none;
if (info[i].bmap->n_div == 0)
return isl_change_none;
hull_i = isl_basic_map_copy(info[i].bmap);
hull_i = isl_basic_map_plain_affine_hull(hull_i);
hull_j = isl_basic_map_copy(info[j].bmap);
hull_j = isl_basic_map_plain_affine_hull(hull_j);
hull_j = isl_basic_map_intersect(hull_j, isl_basic_map_copy(hull_i));
equal = isl_basic_map_plain_is_equal(hull_i, hull_j);
empty = isl_basic_map_plain_is_empty(hull_j);
isl_basic_map_free(hull_i);
if (equal < 0 || equal || empty < 0 || empty) {
isl_basic_map_free(hull_j);
if (equal < 0 || empty < 0)
return isl_change_error;
return isl_change_none;
}
bmap_i = isl_basic_map_copy(info[i].bmap);
bmap_i = isl_basic_map_intersect(bmap_i, hull_j);
if (!bmap_i)
return isl_change_error;
if (bmap_i->n_div > info[j].bmap->n_div) {
isl_basic_map_free(bmap_i);
return isl_change_none;
}
change = coalesce_after_aligning_divs(bmap_i, -1, j, info);
isl_basic_map_free(bmap_i);
return change;
}
/* Check if the union of and the basic maps represented by info[i] and info[j]
* can be represented by a single basic map, by aligning or equating
* their integer divisions.
* If so, replace the pair by the single basic map and return
* isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
* Otherwise, return isl_change_none.
*
* Note that we only perform any test if the number of divs is different
* in the two basic maps. In case the number of divs is the same,
* we have already established that the divs are different
* in the two basic maps.
* In particular, if the number of divs of basic map i is smaller than
* the number of divs of basic map j, then we check if j is a subset of i
* and vice versa.
*/
static enum isl_change coalesce_divs(int i, int j,
struct isl_coalesce_info *info)
{
enum isl_change change = isl_change_none;
if (info[i].bmap->n_div < info[j].bmap->n_div)
change = coalesce_after_aligning_divs(info[i].bmap, i, j, info);
if (change != isl_change_none)
return change;
if (info[j].bmap->n_div < info[i].bmap->n_div)
change = coalesce_after_aligning_divs(info[j].bmap, j, i, info);
if (change != isl_change_none)
return invert_change(change);
change = coalesce_subset_with_equalities(i, j, info);
if (change != isl_change_none)
return change;
change = coalesce_subset_with_equalities(j, i, info);
if (change != isl_change_none)
return invert_change(change);
return isl_change_none;
}
/* Does "bmap" involve any divs that themselves refer to divs?
*/
static isl_bool has_nested_div(__isl_keep isl_basic_map *bmap)
{
int i;
isl_size total;
isl_size n_div;
total = isl_basic_map_dim(bmap, isl_dim_all);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (total < 0 || n_div < 0)
return isl_bool_error;
total -= n_div;
for (i = 0; i < n_div; ++i)
if (isl_seq_first_non_zero(bmap->div[i] + 2 + total,
n_div) != -1)
return isl_bool_true;
return isl_bool_false;
}
/* Return a list of affine expressions, one for each integer division
* in "bmap_i". For each integer division that also appears in "bmap_j",
* the affine expression is set to NaN. The number of NaNs in the list
* is equal to the number of integer divisions in "bmap_j".
* For the other integer divisions of "bmap_i", the corresponding
* element in the list is a purely affine expression equal to the integer
* division in "hull".
* If no such list can be constructed, then the number of elements
* in the returned list is smaller than the number of integer divisions
* in "bmap_i".
*/
static __isl_give isl_aff_list *set_up_substitutions(
__isl_keep isl_basic_map *bmap_i, __isl_keep isl_basic_map *bmap_j,
__isl_take isl_basic_map *hull)
{
isl_size n_div_i, n_div_j, total;
isl_ctx *ctx;
isl_local_space *ls;
isl_basic_set *wrap_hull;
isl_aff *aff_nan;
isl_aff_list *list;
int i, j;
n_div_i = isl_basic_map_dim(bmap_i, isl_dim_div);
n_div_j = isl_basic_map_dim(bmap_j, isl_dim_div);
total = isl_basic_map_dim(bmap_i, isl_dim_all);
if (!hull || n_div_i < 0 || n_div_j < 0 || total < 0)
return NULL;
ctx = isl_basic_map_get_ctx(hull);
total -= n_div_i;
ls = isl_basic_map_get_local_space(bmap_i);
ls = isl_local_space_wrap(ls);
wrap_hull = isl_basic_map_wrap(hull);
aff_nan = isl_aff_nan_on_domain(isl_local_space_copy(ls));
list = isl_aff_list_alloc(ctx, n_div_i);
j = 0;
for (i = 0; i < n_div_i; ++i) {
isl_aff *aff;
isl_size n_div;
if (j < n_div_j &&
isl_basic_map_equal_div_expr_part(bmap_i, i, bmap_j, j,
0, 2 + total)) {
++j;
list = isl_aff_list_add(list, isl_aff_copy(aff_nan));
continue;
}
if (n_div_i - i <= n_div_j - j)
break;
aff = isl_local_space_get_div(ls, i);
aff = isl_aff_substitute_equalities(aff,
isl_basic_set_copy(wrap_hull));
aff = isl_aff_floor(aff);
n_div = isl_aff_dim(aff, isl_dim_div);
if (n_div < 0)
goto error;
if (n_div != 0) {
isl_aff_free(aff);
break;
}
list = isl_aff_list_add(list, aff);
}
isl_aff_free(aff_nan);
isl_local_space_free(ls);
isl_basic_set_free(wrap_hull);
return list;
error:
isl_aff_free(aff_nan);
isl_local_space_free(ls);
isl_basic_set_free(wrap_hull);
isl_aff_list_free(list);
return NULL;
}
/* Add variables to info->bmap and info->tab corresponding to the elements
* in "list" that are not set to NaN.
* "extra_var" is the number of these elements.
* "dim" is the offset in the variables of "tab" where we should
* start considering the elements in "list".
* When this function returns, the total number of variables in "tab"
* is equal to "dim" plus the number of elements in "list".
*
* The newly added existentially quantified variables are not given
* an explicit representation because the corresponding div constraints
* do not appear in info->bmap. These constraints are not added
* to info->bmap because for internal consistency, they would need to
* be added to info->tab as well, where they could combine with the equality
* that is added later to result in constraints that do not hold
* in the original input.
*/
static isl_stat add_sub_vars(struct isl_coalesce_info *info,
__isl_keep isl_aff_list *list, int dim, int extra_var)
{
int i, j, d;
isl_size n;
info->bmap = isl_basic_map_cow(info->bmap);
info->bmap = isl_basic_map_extend(info->bmap, extra_var, 0, 0);
n = isl_aff_list_n_aff(list);
if (!info->bmap || n < 0)
return isl_stat_error;
for (i = 0; i < n; ++i) {
int is_nan;
isl_aff *aff;
aff = isl_aff_list_get_aff(list, i);
is_nan = isl_aff_is_nan(aff);
isl_aff_free(aff);
if (is_nan < 0)
return isl_stat_error;
if (is_nan)
continue;
if (isl_tab_insert_var(info->tab, dim + i) < 0)
return isl_stat_error;
d = isl_basic_map_alloc_div(info->bmap);
if (d < 0)
return isl_stat_error;
info->bmap = isl_basic_map_mark_div_unknown(info->bmap, d);
for (j = d; j > i; --j)
info->bmap = isl_basic_map_swap_div(info->bmap,
j - 1, j);
if (!info->bmap)
return isl_stat_error;
}
return isl_stat_ok;
}
/* For each element in "list" that is not set to NaN, fix the corresponding
* variable in "tab" to the purely affine expression defined by the element.
* "dim" is the offset in the variables of "tab" where we should
* start considering the elements in "list".
*
* This function assumes that a sufficient number of rows and
* elements in the constraint array are available in the tableau.
*/
static isl_stat add_sub_equalities(struct isl_tab *tab,
__isl_keep isl_aff_list *list, int dim)
{
int i;
isl_size n;
isl_ctx *ctx;
isl_vec *sub;
isl_aff *aff;
n = isl_aff_list_n_aff(list);
if (n < 0)
return isl_stat_error;
ctx = isl_tab_get_ctx(tab);
sub = isl_vec_alloc(ctx, 1 + dim + n);
if (!sub)
return isl_stat_error;
isl_seq_clr(sub->el + 1 + dim, n);
for (i = 0; i < n; ++i) {
aff = isl_aff_list_get_aff(list, i);
if (!aff)
goto error;
if (isl_aff_is_nan(aff)) {
isl_aff_free(aff);
continue;
}
isl_seq_cpy(sub->el, aff->v->el + 1, 1 + dim);
isl_int_neg(sub->el[1 + dim + i], aff->v->el[0]);
if (isl_tab_add_eq(tab, sub->el) < 0)
goto error;
isl_int_set_si(sub->el[1 + dim + i], 0);
isl_aff_free(aff);
}
isl_vec_free(sub);
return isl_stat_ok;
error:
isl_aff_free(aff);
isl_vec_free(sub);
return isl_stat_error;
}
/* Add variables to info->tab and info->bmap corresponding to the elements
* in "list" that are not set to NaN. The value of the added variable
* in info->tab is fixed to the purely affine expression defined by the element.
* "dim" is the offset in the variables of info->tab where we should
* start considering the elements in "list".
* When this function returns, the total number of variables in info->tab
* is equal to "dim" plus the number of elements in "list".
*/
static isl_stat add_subs(struct isl_coalesce_info *info,
__isl_keep isl_aff_list *list, int dim)
{
int extra_var;
isl_size n;
n = isl_aff_list_n_aff(list);
if (n < 0)
return isl_stat_error;
extra_var = n - (info->tab->n_var - dim);
if (isl_tab_extend_vars(info->tab, extra_var) < 0)
return isl_stat_error;
if (isl_tab_extend_cons(info->tab, 2 * extra_var) < 0)
return isl_stat_error;
if (add_sub_vars(info, list, dim, extra_var) < 0)
return isl_stat_error;
return add_sub_equalities(info->tab, list, dim);
}
/* Coalesce basic map "j" into basic map "i" after adding the extra integer
* divisions in "i" but not in "j" to basic map "j", with values
* specified by "list". The total number of elements in "list"
* is equal to the number of integer divisions in "i", while the number
* of NaN elements in the list is equal to the number of integer divisions
* in "j".
*
* If no coalescing can be performed, then we need to revert basic map "j"
* to its original state. We do the same if basic map "i" gets dropped
* during the coalescing, even though this should not happen in practice
* since we have already checked for "j" being a subset of "i"
* before we reach this stage.
*/
static enum isl_change coalesce_with_subs(int i, int j,
struct isl_coalesce_info *info, __isl_keep isl_aff_list *list)
{
isl_basic_map *bmap_j;
struct isl_tab_undo *snap;
isl_size dim, n_div;
enum isl_change change;
bmap_j = isl_basic_map_copy(info[j].bmap);
snap = isl_tab_snap(info[j].tab);
dim = isl_basic_map_dim(bmap_j, isl_dim_all);
n_div = isl_basic_map_dim(bmap_j, isl_dim_div);
if (dim < 0 || n_div < 0)
goto error;
dim -= n_div;
if (add_subs(&info[j], list, dim) < 0)
goto error;
change = coalesce_local_pair(i, j, info);
if (change != isl_change_none && change != isl_change_drop_first) {
isl_basic_map_free(bmap_j);
} else {
isl_basic_map_free(info[j].bmap);
info[j].bmap = bmap_j;
if (isl_tab_rollback(info[j].tab, snap) < 0)
return isl_change_error;
}
return change;
error:
isl_basic_map_free(bmap_j);
return isl_change_error;
}
/* Check if we can coalesce basic map "j" into basic map "i" after copying
* those extra integer divisions in "i" that can be simplified away
* using the extra equalities in "j".
* All divs are assumed to be known and not contain any nested divs.
*
* We first check if there are any extra equalities in "j" that we
* can exploit. Then we check if every integer division in "i"
* either already appears in "j" or can be simplified using the
* extra equalities to a purely affine expression.
* If these tests succeed, then we try to coalesce the two basic maps
* by introducing extra dimensions in "j" corresponding to
* the extra integer divisions "i" fixed to the corresponding
* purely affine expression.
*/
static enum isl_change check_coalesce_into_eq(int i, int j,
struct isl_coalesce_info *info)
{
isl_size n_div_i, n_div_j, n;
isl_basic_map *hull_i, *hull_j;
isl_bool equal, empty;
isl_aff_list *list;
enum isl_change change;
n_div_i = isl_basic_map_dim(info[i].bmap, isl_dim_div);
n_div_j = isl_basic_map_dim(info[j].bmap, isl_dim_div);
if (n_div_i < 0 || n_div_j < 0)
return isl_change_error;
if (n_div_i <= n_div_j)
return isl_change_none;
if (info[j].bmap->n_eq == 0)
return isl_change_none;
hull_i = isl_basic_map_copy(info[i].bmap);
hull_i = isl_basic_map_plain_affine_hull(hull_i);
hull_j = isl_basic_map_copy(info[j].bmap);
hull_j = isl_basic_map_plain_affine_hull(hull_j);
hull_j = isl_basic_map_intersect(hull_j, isl_basic_map_copy(hull_i));
equal = isl_basic_map_plain_is_equal(hull_i, hull_j);
empty = isl_basic_map_plain_is_empty(hull_j);
isl_basic_map_free(hull_i);
if (equal < 0 || empty < 0)
goto error;
if (equal || empty) {
isl_basic_map_free(hull_j);
return isl_change_none;
}
list = set_up_substitutions(info[i].bmap, info[j].bmap, hull_j);
if (!list)
return isl_change_error;
n = isl_aff_list_n_aff(list);
if (n < 0)
change = isl_change_error;
else if (n < n_div_i)
change = isl_change_none;
else
change = coalesce_with_subs(i, j, info, list);
isl_aff_list_free(list);
return change;
error:
isl_basic_map_free(hull_j);
return isl_change_error;
}
/* Check if we can coalesce basic maps "i" and "j" after copying
* those extra integer divisions in one of the basic maps that can
* be simplified away using the extra equalities in the other basic map.
* We require all divs to be known in both basic maps.
* Furthermore, to simplify the comparison of div expressions,
* we do not allow any nested integer divisions.
*/
static enum isl_change check_coalesce_eq(int i, int j,
struct isl_coalesce_info *info)
{
isl_bool known, nested;
enum isl_change change;
known = isl_basic_map_divs_known(info[i].bmap);
if (known < 0 || !known)
return known < 0 ? isl_change_error : isl_change_none;
known = isl_basic_map_divs_known(info[j].bmap);
if (known < 0 || !known)
return known < 0 ? isl_change_error : isl_change_none;
nested = has_nested_div(info[i].bmap);
if (nested < 0 || nested)
return nested < 0 ? isl_change_error : isl_change_none;
nested = has_nested_div(info[j].bmap);
if (nested < 0 || nested)
return nested < 0 ? isl_change_error : isl_change_none;
change = check_coalesce_into_eq(i, j, info);
if (change != isl_change_none)
return change;
change = check_coalesce_into_eq(j, i, info);
if (change != isl_change_none)
return invert_change(change);
return isl_change_none;
}
/* 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
* isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
* Otherwise, return isl_change_none.
*
* We first check if the two basic maps live in the same local space,
* after aligning the divs that differ by only an integer constant.
* If so, we do the complete check. Otherwise, we check if they have
* the same number of integer divisions and can be coalesced, if one is
* an obvious subset of the other or if the extra integer divisions
* of one basic map can be simplified away using the extra equalities
* of the other basic map.
*
* Note that trying to coalesce pairs of disjuncts with the same
* number, but different local variables may drop the explicit
* representation of some of these local variables.
* This operation is therefore not performed when
* the "coalesce_preserve_locals" option is set.
*/
static enum isl_change coalesce_pair(int i, int j,
struct isl_coalesce_info *info)
{
int preserve;
isl_bool same;
enum isl_change change;
isl_ctx *ctx;
if (harmonize_divs(&info[i], &info[j]) < 0)
return isl_change_error;
same = same_divs(info[i].bmap, info[j].bmap);
if (same < 0)
return isl_change_error;
if (same)
return coalesce_local_pair(i, j, info);
ctx = isl_basic_map_get_ctx(info[i].bmap);
preserve = isl_options_get_coalesce_preserve_locals(ctx);
if (!preserve && info[i].bmap->n_div == info[j].bmap->n_div) {
change = coalesce_local_pair(i, j, info);
if (change != isl_change_none)
return change;
}
change = coalesce_divs(i, j, info);
if (change != isl_change_none)
return change;
return check_coalesce_eq(i, j, info);
}
/* Return the maximum of "a" and "b".
*/
static int isl_max(int a, int b)
{
return a > b ? a : b;
}
/* Pairwise coalesce the basic maps in the range [start1, end1[ of "info"
* with those in the range [start2, end2[, skipping basic maps
* that have been removed (either before or within this function).
*
* For each basic map i in the first range, we check if it can be coalesced
* with respect to any previously considered basic map j in the second range.
* If i gets dropped (because it was a subset of some j), then
* we can move on to the next basic map.
* If j gets dropped, we need to continue checking against the other
* previously considered basic maps.
* If the two basic maps got fused, then we recheck the fused basic map
* against the previously considered basic maps, starting at i + 1
* (even if start2 is greater than i + 1).
*/
static int coalesce_range(isl_ctx *ctx, struct isl_coalesce_info *info,
int start1, int end1, int start2, int end2)
{
int i, j;
for (i = end1 - 1; i >= start1; --i) {
if (info[i].removed)
continue;
for (j = isl_max(i + 1, start2); j < end2; ++j) {
enum isl_change changed;
if (info[j].removed)
continue;
if (info[i].removed)
isl_die(ctx, isl_error_internal,
"basic map unexpectedly removed",
return -1);
changed = coalesce_pair(i, j, info);
switch (changed) {
case isl_change_error:
return -1;
case isl_change_none:
case isl_change_drop_second:
continue;
case isl_change_drop_first:
j = end2;
break;
case isl_change_fuse:
j = i;
break;
}
}
}
return 0;
}
/* Pairwise coalesce the basic maps described by the "n" elements of "info".
*
* We consider groups of basic maps that live in the same apparent
* affine hull and we first coalesce within such a group before we
* coalesce the elements in the group with elements of previously
* considered groups. If a fuse happens during the second phase,
* then we also reconsider the elements within the group.
*/
static int coalesce(isl_ctx *ctx, int n, struct isl_coalesce_info *info)
{
int start, end;
for (end = n; end > 0; end = start) {
start = end - 1;
while (start >= 1 &&
info[start - 1].hull_hash == info[start].hull_hash)
start--;
if (coalesce_range(ctx, info, start, end, start, end) < 0)
return -1;
if (coalesce_range(ctx, info, start, end, end, n) < 0)
return -1;
}
return 0;
}
/* Update the basic maps in "map" based on the information in "info".
* In particular, remove the basic maps that have been marked removed and
* update the others based on the information in the corresponding tableau.
* Since we detected implicit equalities without calling
* isl_basic_map_gauss, we need to do it now.
* Also call isl_basic_map_simplify if we may have lost the definition
* of one or more integer divisions.
* If a basic map is still equal to the one from which the corresponding "info"
* entry was created, then redundant constraint and
* implicit equality constraint detection have been performed
* on the corresponding tableau and the basic map can be marked as such.
*/
static __isl_give isl_map *update_basic_maps(__isl_take isl_map *map,
int n, struct isl_coalesce_info *info)
{
int i;
if (!map)
return NULL;
for (i = n - 1; i >= 0; --i) {
if (info[i].removed) {
isl_basic_map_free(map->p[i]);
if (i != map->n - 1)
map->p[i] = map->p[map->n - 1];
map->n--;
continue;
}
info[i].bmap = isl_basic_map_update_from_tab(info[i].bmap,
info[i].tab);
info[i].bmap = isl_basic_map_gauss(info[i].bmap, NULL);
if (info[i].simplify)
info[i].bmap = isl_basic_map_simplify(info[i].bmap);
info[i].bmap = isl_basic_map_finalize(info[i].bmap);
if (!info[i].bmap)
return isl_map_free(map);
if (!info[i].modified) {
ISL_F_SET(info[i].bmap, ISL_BASIC_MAP_NO_IMPLICIT);
ISL_F_SET(info[i].bmap, ISL_BASIC_MAP_NO_REDUNDANT);
}
isl_basic_map_free(map->p[i]);
map->p[i] = info[i].bmap;
info[i].bmap = NULL;
}
return map;
}
/* 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.
*
* We factor out any (hidden) common factor from the constraint
* coefficients to improve the detection of adjacent constraints.
* Note that this function does not call isl_basic_map_gauss,
* but it does make sure that only a single copy of the basic map
* is affected. This means that isl_basic_map_gauss may have
* to be called at the end of the computation (in update_basic_maps)
* on this single copy to ensure that
* the basic maps are not left in an unexpected state.
*
* 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. If the basic map only has a single reference
* (this happens in particular if it was modified by
* isl_basic_map_reduce_coefficients), then isl_basic_map_gauss
* does not get called on the result. The call to
* isl_basic_map_gauss in update_basic_maps resolves this as well.
* For each basic map, we also compute the hash of the apparent affine hull
* for use in coalesce.
*/
__isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map)
{
int i;
unsigned n;
isl_ctx *ctx;
struct isl_coalesce_info *info = NULL;
map = isl_map_remove_empty_parts(map);
if (!map)
return NULL;
if (map->n <= 1)
return map;
ctx = isl_map_get_ctx(map);
map = isl_map_sort_divs(map);
map = isl_map_cow(map);
if (!map)
return NULL;
n = map->n;
info = isl_calloc_array(map->ctx, struct isl_coalesce_info, n);
if (!info)
goto error;
for (i = 0; i < map->n; ++i) {
map->p[i] = isl_basic_map_reduce_coefficients(map->p[i]);
if (!map->p[i])
goto error;
info[i].bmap = isl_basic_map_copy(map->p[i]);
info[i].tab = isl_tab_from_basic_map(info[i].bmap, 0);
if (!info[i].tab)
goto error;
if (!ISL_F_ISSET(info[i].bmap, ISL_BASIC_MAP_NO_IMPLICIT))
if (isl_tab_detect_implicit_equalities(info[i].tab) < 0)
goto error;
info[i].bmap = isl_tab_make_equalities_explicit(info[i].tab,
info[i].bmap);
if (!info[i].bmap)
goto error;
if (!ISL_F_ISSET(info[i].bmap, ISL_BASIC_MAP_NO_REDUNDANT))
if (isl_tab_detect_redundant(info[i].tab) < 0)
goto error;
if (coalesce_info_set_hull_hash(&info[i]) < 0)
goto error;
}
for (i = map->n - 1; i >= 0; --i)
if (info[i].tab->empty)
drop(&info[i]);
if (coalesce(ctx, n, info) < 0)
goto error;
map = update_basic_maps(map, n, info);
clear_coalesce_info(n, info);
return map;
error:
clear_coalesce_info(n, info);
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.
*/
__isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set)
{
return set_from_map(isl_map_coalesce(set_to_map(set)));
}
|
