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isl_coalesce.c
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isl_coalesce.c
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/*
* Copyright 2008-2009 Katholieke Universiteit Leuven
* Copyright 2010 INRIA Saclay
* Copyright 2012-2013 Ecole Normale Superieure
* Copyright 2014 INRIA Rocquencourt
* Copyright 2016 INRIA Paris
*
* 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
*/
#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 (say "k") that is adjacent
* to some inequality of basic map "j". All the other inequalities
* are valid for "j".
* Check if basic map "j" forms an extension of basic map "i".
*
* Note that this function is only called if some of the equalities or
* inequalities of basic map "j" do cut basic map "i". The function is
* correct even if there are no such cut constraints, but in that case
* the additional checks performed by this function are overkill.
*
* In particular, we replace constraint k, say f >= 0, by constraint
* f <= -1, add the inequalities of "j" that are valid for "i"
* and check if the result is a subset of basic map "j".
* 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") and the valid constraints of "j" we therefore
* obtain a basic map that is equal to their union.
* In this case, there is no need to perform a rollback of the tableau
* since it is going to be destroyed in fuse().
*
*
* |\__ |\__
* | \__ | \__
* | \_ => | \__
* |_______| _ |_________\
*
*
* |\ |\
* | \ | \
* | \ | \
* | | | \
* | ||\ => | \
* | || \ | \
* | || | | |
* |__||_/ |_____/
*/
static enum isl_change is_adj_ineq_extension(int i, int j,
struct isl_coalesce_info *info)
{
int k;
struct isl_tab_undo *snap;
unsigned n_eq = info[i].bmap->n_eq;
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;
if (isl_tab_extend_cons(info[i].tab, 1 + info[j].bmap->n_ineq) < 0)
return isl_change_error;
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);
snap = isl_tab_snap(info[i].tab);
if (isl_tab_unrestrict(info[i].tab, n_eq + 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 < info[j].bmap->n_ineq; ++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;
}
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, NULL, 0, 0);
if (isl_tab_rollback(info[i].tab, snap) < 0)
return isl_change_error;
return isl_change_none;
}
/* Both basic maps have at least one inequality with and adjacent
* (but opposite) inequality in the other basic map.
* Check that there are no cut constraints and that there is only
* a single pair of adjacent inequalities.
* If so, we can replace the pair by a single basic map described
* by all but the pair of adjacent inequalities.
* Any additional points introduced lie strictly between the two
* adjacent hyperplanes and can therefore be integral.
*
* ____ _____
* / ||\ / \
* / || \ / \
* \ || \ => \ \
* \ || / \ /
* \___||_/ \_____/
*
* The test for a single pair of adjancent inequalities is important
* for avoiding the combination of two basic maps like the following
*
* /|
* / |
* /__|
* _____
* | |
* | |
* |___|
*
* If there are some cut constraints on one side, then we may
* still be able to fuse the two basic maps, but we need to perform
* some additional checks in is_adj_ineq_extension.
*/
static 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 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