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/*
* Copyright 2011 INRIA Saclay
*
* Use of this software is governed by the GNU LGPLv2.1 license
*
* Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
* Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
* 91893 Orsay, France
*/
#include <isl_ctx_private.h>
#include <isl_map_private.h>
#include <isl_space_private.h>
#include <isl/hash.h>
#include <isl/constraint.h>
#include <isl/schedule.h>
#include <isl_mat_private.h>
#include <isl/set.h>
#include <isl/seq.h>
#include <isl_tab.h>
#include <isl_dim_map.h>
#include <isl_hmap_map_basic_set.h>
#include <isl_qsort.h>
#include <isl_schedule_private.h>
#include <isl_band_private.h>
#include <isl_list_private.h>
#include <isl_options_private.h>
/*
* The scheduling algorithm implemented in this file was inspired by
* Bondhugula et al., "Automatic Transformations for Communication-Minimized
* Parallelization and Locality Optimization in the Polyhedral Model".
*/
/* Internal information about a node that is used during the construction
* of a schedule.
* dim represents the space in which the domain lives
* sched is a matrix representation of the schedule being constructed
* for this node
* sched_map is an isl_map representation of the same (partial) schedule
* sched_map may be NULL
* rank is the number of linearly independent rows in the linear part
* of sched
* the columns of cmap represent a change of basis for the schedule
* coefficients; the first rank columns span the linear part of
* the schedule rows
* start is the first variable in the LP problem in the sequences that
* represents the schedule coefficients of this node
* nvar is the dimension of the domain
* nparam is the number of parameters or 0 if we are not constructing
* a parametric schedule
*
* scc is the index of SCC (or WCC) this node belongs to
*
* band contains the band index for each of the rows of the schedule.
* band_id is used to differentiate between separate bands at the same
* level within the same parent band, i.e., bands that are separated
* by the parent band or bands that are independent of each other.
* zero contains a boolean for each of the rows of the schedule,
* indicating whether the corresponding scheduling dimension results
* in zero dependence distances within its band and with respect
* to the proximity edges.
*
* index, min_index and on_stack are used during the SCC detection
* index represents the order in which nodes are visited.
* min_index is the index of the root of a (sub)component.
* on_stack indicates whether the node is currently on the stack.
*/
struct isl_sched_node {
isl_space *dim;
isl_mat *sched;
isl_map *sched_map;
int rank;
isl_mat *cmap;
int start;
int nvar;
int nparam;
int scc;
int *band;
int *band_id;
int *zero;
/* scc detection */
int index;
int min_index;
int on_stack;
};
static int node_has_dim(const void *entry, const void *val)
{
struct isl_sched_node *node = (struct isl_sched_node *)entry;
isl_space *dim = (isl_space *)val;
return isl_space_is_equal(node->dim, dim);
}
/* An edge in the dependence graph. An edge may be used to
* ensure validity of the generated schedule, to minimize the dependence
* distance or both
*
* map is the dependence relation
* src is the source node
* dst is the sink node
* validity is set if the edge is used to ensure correctness
* proximity is set if the edge is used to minimize dependence distances
*
* For validity edges, start and end mark the sequence of inequality
* constraints in the LP problem that encode the validity constraint
* corresponding to this edge.
*/
struct isl_sched_edge {
isl_map *map;
struct isl_sched_node *src;
struct isl_sched_node *dst;
int validity;
int proximity;
int start;
int end;
};
/* Internal information about the dependence graph used during
* the construction of the schedule.
*
* intra_hmap is a cache, mapping dependence relations to their dual,
* for dependences from a node to itself
* inter_hmap is a cache, mapping dependence relations to their dual,
* for dependences between distinct nodes
*
* n is the number of nodes
* node is the list of nodes
* maxvar is the maximal number of variables over all nodes
* n_row is the current (maximal) number of linearly independent
* rows in the node schedules
* n_total_row is the current number of rows in the node schedules
* n_band is the current number of completed bands
* band_start is the starting row in the node schedules of the current band
* root is set if this graph is the original dependence graph,
* without any splitting
*
* sorted contains a list of node indices sorted according to the
* SCC to which a node belongs
*
* n_edge is the number of edges
* edge is the list of edges
* edge_table contains pointers into the edge array, hashed on the source
* and sink spaces; the table only contains edges that represent
* validity constraints (and that may or may not also represent proximity
* constraints)
*
* node_table contains pointers into the node array, hashed on the space
*
* region contains a list of variable sequences that should be non-trivial
*
* lp contains the (I)LP problem used to obtain new schedule rows
*
* src_scc and dst_scc are the source and sink SCCs of an edge with
* conflicting constraints
*
* scc, sp, index and stack are used during the detection of SCCs
* scc is the number of the next SCC
* stack contains the nodes on the path from the root to the current node
* sp is the stack pointer
* index is the index of the last node visited
*/
struct isl_sched_graph {
isl_hmap_map_basic_set *intra_hmap;
isl_hmap_map_basic_set *inter_hmap;
struct isl_sched_node *node;
int n;
int maxvar;
int n_row;
int *sorted;
int n_band;
int n_total_row;
int band_start;
int root;
struct isl_sched_edge *edge;
int n_edge;
struct isl_hash_table *edge_table;
struct isl_hash_table *node_table;
struct isl_region *region;
isl_basic_set *lp;
int src_scc;
int dst_scc;
/* scc detection */
int scc;
int sp;
int index;
int *stack;
};
/* Initialize node_table based on the list of nodes.
*/
static int graph_init_table(isl_ctx *ctx, struct isl_sched_graph *graph)
{
int i;
graph->node_table = isl_hash_table_alloc(ctx, graph->n);
if (!graph->node_table)
return -1;
for (i = 0; i < graph->n; ++i) {
struct isl_hash_table_entry *entry;
uint32_t hash;
hash = isl_space_get_hash(graph->node[i].dim);
entry = isl_hash_table_find(ctx, graph->node_table, hash,
&node_has_dim,
graph->node[i].dim, 1);
if (!entry)
return -1;
entry->data = &graph->node[i];
}
return 0;
}
/* Return a pointer to the node that lives within the given space,
* or NULL if there is no such node.
*/
static struct isl_sched_node *graph_find_node(isl_ctx *ctx,
struct isl_sched_graph *graph, __isl_keep isl_space *dim)
{
struct isl_hash_table_entry *entry;
uint32_t hash;
hash = isl_space_get_hash(dim);
entry = isl_hash_table_find(ctx, graph->node_table, hash,
&node_has_dim, dim, 0);
return entry ? entry->data : NULL;
}
static int edge_has_src_and_dst(const void *entry, const void *val)
{
const struct isl_sched_edge *edge = entry;
const struct isl_sched_edge *temp = val;
return edge->src == temp->src && edge->dst == temp->dst;
}
/* Initialize edge_table based on the list of edges.
* Only edges with validity set are added to the table.
*/
static int graph_init_edge_table(isl_ctx *ctx, struct isl_sched_graph *graph)
{
int i;
graph->edge_table = isl_hash_table_alloc(ctx, graph->n_edge);
if (!graph->edge_table)
return -1;
for (i = 0; i < graph->n_edge; ++i) {
struct isl_hash_table_entry *entry;
uint32_t hash;
if (!graph->edge[i].validity)
continue;
hash = isl_hash_init();
hash = isl_hash_builtin(hash, graph->edge[i].src);
hash = isl_hash_builtin(hash, graph->edge[i].dst);
entry = isl_hash_table_find(ctx, graph->edge_table, hash,
&edge_has_src_and_dst,
&graph->edge[i], 1);
if (!entry)
return -1;
entry->data = &graph->edge[i];
}
return 0;
}
/* Check whether the dependence graph has a (validity) edge
* between the given two nodes.
*/
static int graph_has_edge(struct isl_sched_graph *graph,
struct isl_sched_node *src, struct isl_sched_node *dst)
{
isl_ctx *ctx = isl_space_get_ctx(src->dim);
struct isl_hash_table_entry *entry;
uint32_t hash;
struct isl_sched_edge temp = { .src = src, .dst = dst };
struct isl_sched_edge *edge;
int empty;
hash = isl_hash_init();
hash = isl_hash_builtin(hash, temp.src);
hash = isl_hash_builtin(hash, temp.dst);
entry = isl_hash_table_find(ctx, graph->edge_table, hash,
&edge_has_src_and_dst, &temp, 0);
if (!entry)
return 0;
edge = entry->data;
empty = isl_map_plain_is_empty(edge->map);
if (empty < 0)
return -1;
return !empty;
}
static int graph_alloc(isl_ctx *ctx, struct isl_sched_graph *graph,
int n_node, int n_edge)
{
int i;
graph->n = n_node;
graph->n_edge = n_edge;
graph->node = isl_calloc_array(ctx, struct isl_sched_node, graph->n);
graph->sorted = isl_calloc_array(ctx, int, graph->n);
graph->region = isl_alloc_array(ctx, struct isl_region, graph->n);
graph->stack = isl_alloc_array(ctx, int, graph->n);
graph->edge = isl_calloc_array(ctx,
struct isl_sched_edge, graph->n_edge);
graph->intra_hmap = isl_hmap_map_basic_set_alloc(ctx, 2 * n_edge);
graph->inter_hmap = isl_hmap_map_basic_set_alloc(ctx, 2 * n_edge);
if (!graph->node || !graph->region || !graph->stack || !graph->edge ||
!graph->sorted)
return -1;
for(i = 0; i < graph->n; ++i)
graph->sorted[i] = i;
return 0;
}
static void graph_free(isl_ctx *ctx, struct isl_sched_graph *graph)
{
int i;
isl_hmap_map_basic_set_free(ctx, graph->intra_hmap);
isl_hmap_map_basic_set_free(ctx, graph->inter_hmap);
for (i = 0; i < graph->n; ++i) {
isl_space_free(graph->node[i].dim);
isl_mat_free(graph->node[i].sched);
isl_map_free(graph->node[i].sched_map);
isl_mat_free(graph->node[i].cmap);
if (graph->root) {
free(graph->node[i].band);
free(graph->node[i].band_id);
free(graph->node[i].zero);
}
}
free(graph->node);
free(graph->sorted);
for (i = 0; i < graph->n_edge; ++i)
isl_map_free(graph->edge[i].map);
free(graph->edge);
free(graph->region);
free(graph->stack);
isl_hash_table_free(ctx, graph->edge_table);
isl_hash_table_free(ctx, graph->node_table);
isl_basic_set_free(graph->lp);
}
/* Add a new node to the graph representing the given set.
*/
static int extract_node(__isl_take isl_set *set, void *user)
{
int nvar, nparam;
isl_ctx *ctx;
isl_space *dim;
isl_mat *sched;
struct isl_sched_graph *graph = user;
int *band, *band_id, *zero;
ctx = isl_set_get_ctx(set);
dim = isl_set_get_space(set);
isl_set_free(set);
nvar = isl_space_dim(dim, isl_dim_set);
nparam = isl_space_dim(dim, isl_dim_param);
if (!ctx->opt->schedule_parametric)
nparam = 0;
sched = isl_mat_alloc(ctx, 0, 1 + nparam + nvar);
graph->node[graph->n].dim = dim;
graph->node[graph->n].nvar = nvar;
graph->node[graph->n].nparam = nparam;
graph->node[graph->n].sched = sched;
graph->node[graph->n].sched_map = NULL;
band = isl_alloc_array(ctx, int, graph->n_edge + nvar);
graph->node[graph->n].band = band;
band_id = isl_calloc_array(ctx, int, graph->n_edge + nvar);
graph->node[graph->n].band_id = band_id;
zero = isl_calloc_array(ctx, int, graph->n_edge + nvar);
graph->node[graph->n].zero = zero;
graph->n++;
if (!sched || !band || !band_id || !zero)
return -1;
return 0;
}
/* Add a new edge to the graph based on the given map.
* Edges are first extracted from the validity dependences,
* from which the edge_table is constructed.
* Afterwards, the proximity dependences are added. If a proximity
* dependence relation happens to be identical to one of the
* validity dependence relations added before, then we don't create
* a new edge, but instead mark the original edge as also representing
* a proximity dependence.
*/
static int extract_edge(__isl_take isl_map *map, void *user)
{
isl_ctx *ctx = isl_map_get_ctx(map);
struct isl_sched_graph *graph = user;
struct isl_sched_node *src, *dst;
isl_space *dim;
dim = isl_space_domain(isl_map_get_space(map));
src = graph_find_node(ctx, graph, dim);
isl_space_free(dim);
dim = isl_space_range(isl_map_get_space(map));
dst = graph_find_node(ctx, graph, dim);
isl_space_free(dim);
if (!src || !dst) {
isl_map_free(map);
return 0;
}
graph->edge[graph->n_edge].src = src;
graph->edge[graph->n_edge].dst = dst;
graph->edge[graph->n_edge].map = map;
graph->edge[graph->n_edge].validity = !graph->edge_table;
graph->edge[graph->n_edge].proximity = !!graph->edge_table;
graph->n_edge++;
if (graph->edge_table) {
uint32_t hash;
struct isl_hash_table_entry *entry;
struct isl_sched_edge *edge;
int is_equal;
hash = isl_hash_init();
hash = isl_hash_builtin(hash, src);
hash = isl_hash_builtin(hash, dst);
entry = isl_hash_table_find(ctx, graph->edge_table, hash,
&edge_has_src_and_dst,
&graph->edge[graph->n_edge - 1], 0);
if (!entry)
return 0;
edge = entry->data;
is_equal = isl_map_plain_is_equal(map, edge->map);
if (is_equal < 0)
return -1;
if (!is_equal)
return 0;
graph->n_edge--;
edge->proximity = 1;
isl_map_free(map);
}
return 0;
}
/* Check whether there is a validity dependence from src to dst,
* forcing dst to follow src.
*/
static int node_follows(struct isl_sched_graph *graph,
struct isl_sched_node *dst, struct isl_sched_node *src)
{
return graph_has_edge(graph, src, dst);
}
/* Perform Tarjan's algorithm for computing the strongly connected components
* in the dependence graph (only validity edges).
* If directed is not set, we consider the graph to be undirected and
* we effectively compute the (weakly) connected components.
*/
static int detect_sccs_tarjan(struct isl_sched_graph *g, int i, int directed)
{
int j;
g->node[i].index = g->index;
g->node[i].min_index = g->index;
g->node[i].on_stack = 1;
g->index++;
g->stack[g->sp++] = i;
for (j = g->n - 1; j >= 0; --j) {
int f;
if (j == i)
continue;
if (g->node[j].index >= 0 &&
(!g->node[j].on_stack ||
g->node[j].index > g->node[i].min_index))
continue;
f = node_follows(g, &g->node[i], &g->node[j]);
if (f < 0)
return -1;
if (!f && !directed) {
f = node_follows(g, &g->node[j], &g->node[i]);
if (f < 0)
return -1;
}
if (!f)
continue;
if (g->node[j].index < 0) {
detect_sccs_tarjan(g, j, directed);
if (g->node[j].min_index < g->node[i].min_index)
g->node[i].min_index = g->node[j].min_index;
} else if (g->node[j].index < g->node[i].min_index)
g->node[i].min_index = g->node[j].index;
}
if (g->node[i].index != g->node[i].min_index)
return 0;
do {
j = g->stack[--g->sp];
g->node[j].on_stack = 0;
g->node[j].scc = g->scc;
} while (j != i);
g->scc++;
return 0;
}
static int detect_ccs(struct isl_sched_graph *graph, int directed)
{
int i;
graph->index = 0;
graph->sp = 0;
graph->scc = 0;
for (i = graph->n - 1; i >= 0; --i)
graph->node[i].index = -1;
for (i = graph->n - 1; i >= 0; --i) {
if (graph->node[i].index >= 0)
continue;
if (detect_sccs_tarjan(graph, i, directed) < 0)
return -1;
}
return 0;
}
/* Apply Tarjan's algorithm to detect the strongly connected components
* in the dependence graph.
*/
static int detect_sccs(struct isl_sched_graph *graph)
{
return detect_ccs(graph, 1);
}
/* Apply Tarjan's algorithm to detect the (weakly) connected components
* in the dependence graph.
*/
static int detect_wccs(struct isl_sched_graph *graph)
{
return detect_ccs(graph, 0);
}
static int cmp_scc(const void *a, const void *b, void *data)
{
struct isl_sched_graph *graph = data;
const int *i1 = a;
const int *i2 = b;
return graph->node[*i1].scc - graph->node[*i2].scc;
}
/* Sort the elements of graph->sorted according to the corresponding SCCs.
*/
static void sort_sccs(struct isl_sched_graph *graph)
{
isl_quicksort(graph->sorted, graph->n, sizeof(int), &cmp_scc, graph);
}
/* Given a dependence relation R from a node to itself,
* construct the set of coefficients of valid constraints for elements
* in that dependence relation.
* In particular, the result contains tuples of coefficients
* c_0, c_n, c_x such that
*
* c_0 + c_n n + c_x y - c_x x >= 0 for each (x,y) in R
*
* or, equivalently,
*
* c_0 + c_n n + c_x d >= 0 for each d in delta R = { y - x | (x,y) in R }
*
* We choose here to compute the dual of delta R.
* Alternatively, we could have computed the dual of R, resulting
* in a set of tuples c_0, c_n, c_x, c_y, and then
* plugged in (c_0, c_n, c_x, -c_x).
*/
static __isl_give isl_basic_set *intra_coefficients(
struct isl_sched_graph *graph, __isl_take isl_map *map)
{
isl_ctx *ctx = isl_map_get_ctx(map);
isl_set *delta;
isl_basic_set *coef;
if (isl_hmap_map_basic_set_has(ctx, graph->intra_hmap, map))
return isl_hmap_map_basic_set_get(ctx, graph->intra_hmap, map);
delta = isl_set_remove_divs(isl_map_deltas(isl_map_copy(map)));
coef = isl_set_coefficients(delta);
isl_hmap_map_basic_set_set(ctx, graph->intra_hmap, map,
isl_basic_set_copy(coef));
return coef;
}
/* Given a dependence relation R, * construct the set of coefficients
* of valid constraints for elements in that dependence relation.
* In particular, the result contains tuples of coefficients
* c_0, c_n, c_x, c_y such that
*
* c_0 + c_n n + c_x x + c_y y >= 0 for each (x,y) in R
*
*/
static __isl_give isl_basic_set *inter_coefficients(
struct isl_sched_graph *graph, __isl_take isl_map *map)
{
isl_ctx *ctx = isl_map_get_ctx(map);
isl_set *set;
isl_basic_set *coef;
if (isl_hmap_map_basic_set_has(ctx, graph->inter_hmap, map))
return isl_hmap_map_basic_set_get(ctx, graph->inter_hmap, map);
set = isl_map_wrap(isl_map_remove_divs(isl_map_copy(map)));
coef = isl_set_coefficients(set);
isl_hmap_map_basic_set_set(ctx, graph->inter_hmap, map,
isl_basic_set_copy(coef));
return coef;
}
/* Add constraints to graph->lp that force validity for the given
* dependence from a node i to itself.
* That is, add constraints that enforce
*
* (c_i_0 + c_i_n n + c_i_x y) - (c_i_0 + c_i_n n + c_i_x x)
* = c_i_x (y - x) >= 0
*
* for each (x,y) in R.
* We obtain general constraints on coefficients (c_0, c_n, c_x)
* of valid constraints for (y - x) and then plug in (0, 0, c_i_x^+ - c_i_x^-),
* where c_i_x = c_i_x^+ - c_i_x^-, with c_i_x^+ and c_i_x^- non-negative.
* In graph->lp, the c_i_x^- appear before their c_i_x^+ counterpart.
*
* Actually, we do not construct constraints for the c_i_x themselves,
* but for the coefficients of c_i_x written as a linear combination
* of the columns in node->cmap.
*/
static int add_intra_validity_constraints(struct isl_sched_graph *graph,
struct isl_sched_edge *edge)
{
unsigned total;
isl_map *map = isl_map_copy(edge->map);
isl_ctx *ctx = isl_map_get_ctx(map);
isl_space *dim;
isl_dim_map *dim_map;
isl_basic_set *coef;
struct isl_sched_node *node = edge->src;
coef = intra_coefficients(graph, map);
dim = isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef)));
coef = isl_basic_set_transform_dims(coef, isl_dim_set,
isl_space_dim(dim, isl_dim_set), isl_mat_copy(node->cmap));
total = isl_basic_set_total_dim(graph->lp);
dim_map = isl_dim_map_alloc(ctx, total);
isl_dim_map_range(dim_map, node->start + 2 * node->nparam + 1, 2,
isl_space_dim(dim, isl_dim_set), 1,
node->nvar, -1);
isl_dim_map_range(dim_map, node->start + 2 * node->nparam + 2, 2,
isl_space_dim(dim, isl_dim_set), 1,
node->nvar, 1);
graph->lp = isl_basic_set_extend_constraints(graph->lp,
coef->n_eq, coef->n_ineq);
graph->lp = isl_basic_set_add_constraints_dim_map(graph->lp,
coef, dim_map);
isl_space_free(dim);
return 0;
}
/* Add constraints to graph->lp that force validity for the given
* dependence from node i to node j.
* That is, add constraints that enforce
*
* (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) >= 0
*
* for each (x,y) in R.
* We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
* of valid constraints for R and then plug in
* (c_j_0 - c_i_0, c_j_n^+ - c_j_n^- - (c_i_n^+ - c_i_n^-),
* c_j_x^+ - c_j_x^- - (c_i_x^+ - c_i_x^-)),
* where c_* = c_*^+ - c_*^-, with c_*^+ and c_*^- non-negative.
* In graph->lp, the c_*^- appear before their c_*^+ counterpart.
*
* Actually, we do not construct constraints for the c_*_x themselves,
* but for the coefficients of c_*_x written as a linear combination
* of the columns in node->cmap.
*/
static int add_inter_validity_constraints(struct isl_sched_graph *graph,
struct isl_sched_edge *edge)
{
unsigned total;
isl_map *map = isl_map_copy(edge->map);
isl_ctx *ctx = isl_map_get_ctx(map);
isl_space *dim;
isl_dim_map *dim_map;
isl_basic_set *coef;
struct isl_sched_node *src = edge->src;
struct isl_sched_node *dst = edge->dst;
coef = inter_coefficients(graph, map);
dim = isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef)));
coef = isl_basic_set_transform_dims(coef, isl_dim_set,
isl_space_dim(dim, isl_dim_set), isl_mat_copy(src->cmap));
coef = isl_basic_set_transform_dims(coef, isl_dim_set,
isl_space_dim(dim, isl_dim_set) + src->nvar,
isl_mat_copy(dst->cmap));
total = isl_basic_set_total_dim(graph->lp);
dim_map = isl_dim_map_alloc(ctx, total);
isl_dim_map_range(dim_map, dst->start, 0, 0, 0, 1, 1);
isl_dim_map_range(dim_map, dst->start + 1, 2, 1, 1, dst->nparam, -1);
isl_dim_map_range(dim_map, dst->start + 2, 2, 1, 1, dst->nparam, 1);
isl_dim_map_range(dim_map, dst->start + 2 * dst->nparam + 1, 2,
isl_space_dim(dim, isl_dim_set) + src->nvar, 1,
dst->nvar, -1);
isl_dim_map_range(dim_map, dst->start + 2 * dst->nparam + 2, 2,
isl_space_dim(dim, isl_dim_set) + src->nvar, 1,
dst->nvar, 1);
isl_dim_map_range(dim_map, src->start, 0, 0, 0, 1, -1);
isl_dim_map_range(dim_map, src->start + 1, 2, 1, 1, src->nparam, 1);
isl_dim_map_range(dim_map, src->start + 2, 2, 1, 1, src->nparam, -1);
isl_dim_map_range(dim_map, src->start + 2 * src->nparam + 1, 2,
isl_space_dim(dim, isl_dim_set), 1,
src->nvar, 1);
isl_dim_map_range(dim_map, src->start + 2 * src->nparam + 2, 2,
isl_space_dim(dim, isl_dim_set), 1,
src->nvar, -1);
edge->start = graph->lp->n_ineq;
graph->lp = isl_basic_set_extend_constraints(graph->lp,
coef->n_eq, coef->n_ineq);
graph->lp = isl_basic_set_add_constraints_dim_map(graph->lp,
coef, dim_map);
isl_space_free(dim);
edge->end = graph->lp->n_ineq;
return 0;
}
/* Add constraints to graph->lp that bound the dependence distance for the given
* dependence from a node i to itself.
* If s = 1, we add the constraint
*
* c_i_x (y - x) <= m_0 + m_n n
*
* or
*
* -c_i_x (y - x) + m_0 + m_n n >= 0
*
* for each (x,y) in R.
* If s = -1, we add the constraint
*
* -c_i_x (y - x) <= m_0 + m_n n
*
* or
*
* c_i_x (y - x) + m_0 + m_n n >= 0
*
* for each (x,y) in R.
* We obtain general constraints on coefficients (c_0, c_n, c_x)
* of valid constraints for (y - x) and then plug in (m_0, m_n, -s * c_i_x),
* with each coefficient (except m_0) represented as a pair of non-negative
* coefficients.
*
* Actually, we do not construct constraints for the c_i_x themselves,
* but for the coefficients of c_i_x written as a linear combination
* of the columns in node->cmap.
*/
static int add_intra_proximity_constraints(struct isl_sched_graph *graph,
struct isl_sched_edge *edge, int s)
{
unsigned total;
unsigned nparam;
isl_map *map = isl_map_copy(edge->map);
isl_ctx *ctx = isl_map_get_ctx(map);
isl_space *dim;
isl_dim_map *dim_map;
isl_basic_set *coef;
struct isl_sched_node *node = edge->src;
coef = intra_coefficients(graph, map);
dim = isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef)));
coef = isl_basic_set_transform_dims(coef, isl_dim_set,
isl_space_dim(dim, isl_dim_set), isl_mat_copy(node->cmap));
nparam = isl_space_dim(node->dim, isl_dim_param);
total = isl_basic_set_total_dim(graph->lp);
dim_map = isl_dim_map_alloc(ctx, total);
isl_dim_map_range(dim_map, 1, 0, 0, 0, 1, 1);
isl_dim_map_range(dim_map, 4, 2, 1, 1, nparam, -1);
isl_dim_map_range(dim_map, 5, 2, 1, 1, nparam, 1);
isl_dim_map_range(dim_map, node->start + 2 * node->nparam + 1, 2,
isl_space_dim(dim, isl_dim_set), 1,
node->nvar, s);
isl_dim_map_range(dim_map, node->start + 2 * node->nparam + 2, 2,
isl_space_dim(dim, isl_dim_set), 1,
node->nvar, -s);
graph->lp = isl_basic_set_extend_constraints(graph->lp,
coef->n_eq, coef->n_ineq);
graph->lp = isl_basic_set_add_constraints_dim_map(graph->lp,
coef, dim_map);
isl_space_free(dim);
return 0;
}
/* Add constraints to graph->lp that bound the dependence distance for the given
* dependence from node i to node j.
* If s = 1, we add the constraint
*
* (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x)
* <= m_0 + m_n n
*
* or
*
* -(c_j_0 + c_j_n n + c_j_x y) + (c_i_0 + c_i_n n + c_i_x x) +
* m_0 + m_n n >= 0
*
* for each (x,y) in R.
* If s = -1, we add the constraint
*
* -((c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x))
* <= m_0 + m_n n
*
* or
*
* (c_j_0 + c_j_n n + c_j_x y) - (c_i_0 + c_i_n n + c_i_x x) +
* m_0 + m_n n >= 0
*
* for each (x,y) in R.
* We obtain general constraints on coefficients (c_0, c_n, c_x, c_y)
* of valid constraints for R and then plug in
* (m_0 - s*c_j_0 + s*c_i_0, m_n - s*c_j_n + s*c_i_n,
* -s*c_j_x+s*c_i_x)
* with each coefficient (except m_0, c_j_0 and c_i_0)
* represented as a pair of non-negative coefficients.
*
* Actually, we do not construct constraints for the c_*_x themselves,
* but for the coefficients of c_*_x written as a linear combination
* of the columns in node->cmap.
*/
static int add_inter_proximity_constraints(struct isl_sched_graph *graph,
struct isl_sched_edge *edge, int s)
{
unsigned total;
unsigned nparam;
isl_map *map = isl_map_copy(edge->map);
isl_ctx *ctx = isl_map_get_ctx(map);
isl_space *dim;
isl_dim_map *dim_map;
isl_basic_set *coef;
struct isl_sched_node *src = edge->src;
struct isl_sched_node *dst = edge->dst;
coef = inter_coefficients(graph, map);
dim = isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef)));
coef = isl_basic_set_transform_dims(coef, isl_dim_set,
isl_space_dim(dim, isl_dim_set), isl_mat_copy(src->cmap));
coef = isl_basic_set_transform_dims(coef, isl_dim_set,
isl_space_dim(dim, isl_dim_set) + src->nvar,
isl_mat_copy(dst->cmap));
nparam = isl_space_dim(src->dim, isl_dim_param);
total = isl_basic_set_total_dim(graph->lp);
dim_map = isl_dim_map_alloc(ctx, total);
isl_dim_map_range(dim_map, 1, 0, 0, 0, 1, 1);
isl_dim_map_range(dim_map, 4, 2, 1, 1, nparam, -1);
isl_dim_map_range(dim_map, 5, 2, 1, 1, nparam, 1);
isl_dim_map_range(dim_map, dst->start, 0, 0, 0, 1, -s);
isl_dim_map_range(dim_map, dst->start + 1, 2, 1, 1, dst->nparam, s);
isl_dim_map_range(dim_map, dst->start + 2, 2, 1, 1, dst->nparam, -s);
isl_dim_map_range(dim_map, dst->start + 2 * dst->nparam + 1, 2,
isl_space_dim(dim, isl_dim_set) + src->nvar, 1,
dst->nvar, s);
isl_dim_map_range(dim_map, dst->start + 2 * dst->nparam + 2, 2,
isl_space_dim(dim, isl_dim_set) + src->nvar, 1,
dst->nvar, -s);
isl_dim_map_range(dim_map, src->start, 0, 0, 0, 1, s);
isl_dim_map_range(dim_map, src->start + 1, 2, 1, 1, src->nparam, -s);
isl_dim_map_range(dim_map, src->start + 2, 2, 1, 1, src->nparam, s);
isl_dim_map_range(dim_map, src->start + 2 * src->nparam + 1, 2,
isl_space_dim(dim, isl_dim_set), 1,
src->nvar, -s);
isl_dim_map_range(dim_map, src->start + 2 * src->nparam + 2, 2,
isl_space_dim(dim, isl_dim_set), 1,
src->nvar, s);
graph->lp = isl_basic_set_extend_constraints(graph->lp,
coef->n_eq, coef->n_ineq);
graph->lp = isl_basic_set_add_constraints_dim_map(graph->lp,
coef, dim_map);
isl_space_free(dim);
return 0;
}
static int add_all_validity_constraints(struct isl_sched_graph *graph)
{
int i;
for (i = 0; i < graph->n_edge; ++i) {
struct isl_sched_edge *edge= &graph->edge[i];
if (!edge->validity)
continue;
if (edge->src != edge->dst)
continue;
if (add_intra_validity_constraints(graph, edge) < 0)
return -1;
}
for (i = 0; i < graph->n_edge; ++i) {
struct isl_sched_edge *edge = &graph->edge[i];
if (!edge->validity)
continue;
if (edge->src == edge->dst)
continue;
if (add_inter_validity_constraints(graph, edge) < 0)
return -1;
}
return 0;
}
/* Add constraints to graph->lp that bound the dependence distance
* for all dependence relations.
* If a given proximity dependence is identical to a validity
* dependence, then the dependence distance is already bounded
* from below (by zero), so we only need to bound the distance
* from above.
* Otherwise, we need to bound the distance both from above and from below.
*/
static int add_all_proximity_constraints(struct isl_sched_graph *graph)
{
int i;
for (i = 0; i < graph->n_edge; ++i) {
struct isl_sched_edge *edge= &graph->edge[i];
if (!edge->proximity)
continue;
if (edge->src == edge->dst &&
add_intra_proximity_constraints(graph, edge, 1) < 0)
return -1;
if (edge->src != edge->dst &&
add_inter_proximity_constraints(graph, edge, 1) < 0)
return -1;
if (edge->validity)
continue;
if (edge->src == edge->dst &&
add_intra_proximity_constraints(graph, edge, -1) < 0)
return -1;
if (edge->src != edge->dst &&
add_inter_proximity_constraints(graph, edge, -1) < 0)
return -1;
}
return 0;
}
/* Compute a basis for the rows in the linear part of the schedule
* and extend this basis to a full basis. The remaining rows
* can then be used to force linear independence from the rows
* in the schedule.
*
* In particular, given the schedule rows S, we compute
*
* S = H Q
*
* with H the Hermite normal form of S. That is, all but the
* first rank columns of Q are zero and so each row in S is
* a linear combination of the first rank rows of Q.
* The matrix Q is then transposed because we will write the
* coefficients of the next schedule row as a column vector s
* and express this s as a linear combination s = Q c of the
* computed basis.
*/
static int node_update_cmap(struct isl_sched_node *node)
{
isl_mat *H, *Q;
int n_row = isl_mat_rows(node->sched);
H = isl_mat_sub_alloc(node->sched, 0, n_row,
1 + node->nparam, node->nvar);
H = isl_mat_left_hermite(H, 0, NULL, &Q);
isl_mat_free(node->cmap);
node->cmap = isl_mat_transpose(Q);
node->rank = isl_mat_initial_non_zero_cols(H);
isl_mat_free(H);
if (!node->cmap || node->rank < 0)
return -1;
return 0;
}
/* Count the number of equality and inequality constraints
* that will be added for the given map.
* If once is set, then we count
* each edge exactly once. Otherwise, we count as follows
* validity -> 1 (>= 0)
* validity+proximity -> 2 (>= 0 and upper bound)
* proximity -> 2 (lower and upper bound)
*/
static int count_map_constraints(struct isl_sched_graph *graph,
struct isl_sched_edge *edge, __isl_take isl_map *map,
int *n_eq, int *n_ineq, int once)
{
isl_basic_set *coef;
int f = once ? 1 : edge->proximity ? 2 : 1;
if (edge->src == edge->dst)
coef = intra_coefficients(graph, map);
else
coef = inter_coefficients(graph, map);
if (!coef)
return -1;
*n_eq += f * coef->n_eq;
*n_ineq += f * coef->n_ineq;
isl_basic_set_free(coef);
return 0;
}
/* Count the number of equality and inequality constraints
* that will be added to the main lp problem.
* If once is set, then we count
* each edge exactly once. Otherwise, we count as follows
* validity -> 1 (>= 0)
* validity+proximity -> 2 (>= 0 and upper bound)
* proximity -> 2 (lower and upper bound)
*/
static int count_constraints(struct isl_sched_graph *graph,
int *n_eq, int *n_ineq, int once)
{
int i;
*n_eq = *n_ineq = 0;
for (i = 0; i < graph->n_edge; ++i) {
struct isl_sched_edge *edge= &graph->edge[i];
isl_map *map = isl_map_copy(edge->map);
if (count_map_constraints(graph, edge, map,
n_eq, n_ineq, once) < 0)
return -1;
}
return 0;
}
/* Construct an ILP problem for finding schedule coefficients
* that result in non-negative, but small dependence distances
* over all dependences.
* In particular, the dependence distances over proximity edges
* are bounded by m_0 + m_n n and we compute schedule coefficients
* with small values (preferably zero) of m_n and m_0.
*
* All variables of the ILP are non-negative. The actual coefficients
* may be negative, so each coefficient is represented as the difference
* of two non-negative variables. The negative part always appears
* immediately before the positive part.
* Other than that, the variables have the following order
*
* - sum of positive and negative parts of m_n coefficients
* - m_0
* - sum of positive and negative parts of all c_n coefficients
* (unconstrained when computing non-parametric schedules)
* - sum of positive and negative parts of all c_x coefficients
* - positive and negative parts of m_n coefficients
* - for each node
* - c_i_0
* - positive and negative parts of c_i_n (if parametric)
* - positive and negative parts of c_i_x
*
* The c_i_x are not represented directly, but through the columns of
* node->cmap. That is, the computed values are for variable t_i_x
* such that c_i_x = Q t_i_x with Q equal to node->cmap.
*
* The constraints are those from the edges plus two or three equalities
* to express the sums.
*
* If force_zero is set, then we add equalities to ensure that
* the sum of the m_n coefficients and m_0 are both zero.
*/
static int setup_lp(isl_ctx *ctx, struct isl_sched_graph *graph,
int force_zero, int max_constant_term)
{
int i, j;
int k;
unsigned nparam;
unsigned total;
isl_space *dim;
int parametric;
int param_pos;
int n_eq, n_ineq;
parametric = ctx->opt->schedule_parametric;
nparam = isl_space_dim(graph->node[0].dim, isl_dim_param);
param_pos = 4;
total = param_pos + 2 * nparam;
for (i = 0; i < graph->n; ++i) {
struct isl_sched_node *node = &graph->node[graph->sorted[i]];
if (node_update_cmap(node) < 0)
return -1;
node->start = total;
total += 1 + 2 * (node->nparam + node->nvar);
}
if (count_constraints(graph, &n_eq, &n_ineq, 0) < 0)
return -1;
dim = isl_space_set_alloc(ctx, 0, total);
isl_basic_set_free(graph->lp);
n_eq += 2 + parametric + force_zero;
if (max_constant_term != -1)
n_ineq += graph->n;
graph->lp = isl_basic_set_alloc_space(dim, 0, n_eq, n_ineq);
k = isl_basic_set_alloc_equality(graph->lp);
if (k < 0)
return -1;
isl_seq_clr(graph->lp->eq[k], 1 + total);
if (!force_zero)
isl_int_set_si(graph->lp->eq[k][1], -1);
for (i = 0; i < 2 * nparam; ++i)
isl_int_set_si(graph->lp->eq[k][1 + param_pos + i], 1);
if (force_zero) {
k = isl_basic_set_alloc_equality(graph->lp);
if (k < 0)
return -1;
isl_seq_clr(graph->lp->eq[k], 1 + total);
isl_int_set_si(graph->lp->eq[k][2], -1);
}
if (parametric) {
k = isl_basic_set_alloc_equality(graph->lp);
if (k < 0)
return -1;
isl_seq_clr(graph->lp->eq[k], 1 + total);
isl_int_set_si(graph->lp->eq[k][3], -1);
for (i = 0; i < graph->n; ++i) {
int pos = 1 + graph->node[i].start + 1;
for (j = 0; j < 2 * graph->node[i].nparam; ++j)
isl_int_set_si(graph->lp->eq[k][pos + j], 1);
}
}
k = isl_basic_set_alloc_equality(graph->lp);
if (k < 0)
return -1;
isl_seq_clr(graph->lp->eq[k], 1 + total);
isl_int_set_si(graph->lp->eq[k][4], -1);
for (i = 0; i < graph->n; ++i) {
struct isl_sched_node *node = &graph->node[i];
int pos = 1 + node->start + 1 + 2 * node->nparam;
for (j = 0; j < 2 * node->nvar; ++j)
isl_int_set_si(graph->lp->eq[k][pos + j], 1);
}
if (max_constant_term != -1)
for (i = 0; i < graph->n; ++i) {
struct isl_sched_node *node = &graph->node[i];
k = isl_basic_set_alloc_inequality(graph->lp);
if (k < 0)
return -1;
isl_seq_clr(graph->lp->ineq[k], 1 + total);
isl_int_set_si(graph->lp->ineq[k][1 + node->start], -1);
isl_int_set_si(graph->lp->ineq[k][0], max_constant_term);
}
if (add_all_validity_constraints(graph) < 0)
return -1;
if (add_all_proximity_constraints(graph) < 0)
return -1;
return 0;
}
/* Analyze the conflicting constraint found by
* isl_tab_basic_set_non_trivial_lexmin. If it corresponds to the validity
* constraint of one of the edges between distinct nodes, living, moreover
* in distinct SCCs, then record the source and sink SCC as this may
* be a good place to cut between SCCs.
*/
static int check_conflict(int con, void *user)
{
int i;
struct isl_sched_graph *graph = user;
if (graph->src_scc >= 0)
return 0;
con -= graph->lp->n_eq;
if (con >= graph->lp->n_ineq)
return 0;
for (i = 0; i < graph->n_edge; ++i) {
if (!graph->edge[i].validity)
continue;
if (graph->edge[i].src == graph->edge[i].dst)
continue;
if (graph->edge[i].src->scc == graph->edge[i].dst->scc)
continue;
if (graph->edge[i].start > con)
continue;
if (graph->edge[i].end <= con)
continue;
graph->src_scc = graph->edge[i].src->scc;
graph->dst_scc = graph->edge[i].dst->scc;
}
return 0;
}
/* Check whether the next schedule row of the given node needs to be
* non-trivial. Lower-dimensional domains may have some trivial rows,
* but as soon as the number of remaining required non-trivial rows
* is as large as the number or remaining rows to be computed,
* all remaining rows need to be non-trivial.
*/
static int needs_row(struct isl_sched_graph *graph, struct isl_sched_node *node)
{
return node->nvar - node->rank >= graph->maxvar - graph->n_row;
}
/* Solve the ILP problem constructed in setup_lp.
* For each node such that all the remaining rows of its schedule
* need to be non-trivial, we construct a non-triviality region.
* This region imposes that the next row is independent of previous rows.
* In particular the coefficients c_i_x are represented by t_i_x
* variables with c_i_x = Q t_i_x and Q a unimodular matrix such that
* its first columns span the rows of the previously computed part
* of the schedule. The non-triviality region enforces that at least
* one of the remaining components of t_i_x is non-zero, i.e.,
* that the new schedule row depends on at least one of the remaining
* columns of Q.
*/
static __isl_give isl_vec *solve_lp(struct isl_sched_graph *graph)
{
int i;
isl_vec *sol;
isl_basic_set *lp;
for (i = 0; i < graph->n; ++i) {
struct isl_sched_node *node = &graph->node[i];
int skip = node->rank;
graph->region[i].pos = node->start + 1 + 2*(node->nparam+skip);
if (needs_row(graph, node))
graph->region[i].len = 2 * (node->nvar - skip);
else
graph->region[i].len = 0;
}
lp = isl_basic_set_copy(graph->lp);
sol = isl_tab_basic_set_non_trivial_lexmin(lp, 2, graph->n,
graph->region, &check_conflict, graph);
return sol;
}
/* Update the schedules of all nodes based on the given solution
* of the LP problem.
* The new row is added to the current band.
* All possibly negative coefficients are encoded as a difference
* of two non-negative variables, so we need to perform the subtraction
* here. Moreover, if use_cmap is set, then the solution does
* not refer to the actual coefficients c_i_x, but instead to variables
* t_i_x such that c_i_x = Q t_i_x and Q is equal to node->cmap.
* In this case, we then also need to perform this multiplication
* to obtain the values of c_i_x.
*
* If check_zero is set, then the first two coordinates of sol are
* assumed to correspond to the dependence distance. If these two
* coordinates are zero, then the corresponding scheduling dimension
* is marked as being zero distance.
*/
static int update_schedule(struct isl_sched_graph *graph,
__isl_take isl_vec *sol, int use_cmap, int check_zero)
{
int i, j;
int zero = 0;
isl_vec *csol = NULL;
if (!sol)
goto error;
if (sol->size == 0)
isl_die(sol->ctx, isl_error_internal,
"no solution found", goto error);
if (check_zero)
zero = isl_int_is_zero(sol->el[1]) &&
isl_int_is_zero(sol->el[2]);
for (i = 0; i < graph->n; ++i) {
struct isl_sched_node *node = &graph->node[i];
int pos = node->start;
int row = isl_mat_rows(node->sched);
isl_vec_free(csol);
csol = isl_vec_alloc(sol->ctx, node->nvar);
if (!csol)
goto error;
isl_map_free(node->sched_map);
node->sched_map = NULL;
node->sched = isl_mat_add_rows(node->sched, 1);
if (!node->sched)
goto error;
node->sched = isl_mat_set_element(node->sched, row, 0,
sol->el[1 + pos]);
for (j = 0; j < node->nparam + node->nvar; ++j)
isl_int_sub(sol->el[1 + pos + 1 + 2 * j + 1],
sol->el[1 + pos + 1 + 2 * j + 1],
sol->el[1 + pos + 1 + 2 * j]);
for (j = 0; j < node->nparam; ++j)
node->sched = isl_mat_set_element(node->sched,
row, 1 + j, sol->el[1+pos+1+2*j+1]);
for (j = 0; j < node->nvar; ++j)
isl_int_set(csol->el[j],
sol->el[1+pos+1+2*(node->nparam+j)+1]);
if (use_cmap)
csol = isl_mat_vec_product(isl_mat_copy(node->cmap),
csol);
if (!csol)
goto error;
for (j = 0; j < node->nvar; ++j)
node->sched = isl_mat_set_element(node->sched,
row, 1 + node->nparam + j, csol->el[j]);
node->band[graph->n_total_row] = graph->n_band;
node->zero[graph->n_total_row] = zero;
}
isl_vec_free(sol);
isl_vec_free(csol);
graph->n_row++;
graph->n_total_row++;
return 0;
error:
isl_vec_free(sol);
isl_vec_free(csol);
return -1;
}
/* Convert node->sched into a map and return this map.
* We simply add equality constraints that express each output variable
* as the affine combination of parameters and input variables specified
* by the schedule matrix.
*
* The result is cached in node->sched_map, which needs to be released
* whenever node->sched is updated.
*/
static __isl_give isl_map *node_extract_schedule(struct isl_sched_node *node)
{
int i, j;
isl_space *dim;
isl_local_space *ls;
isl_basic_map *bmap;
isl_constraint *c;
int nrow, ncol;
isl_int v;
if (node->sched_map)
return isl_map_copy(node->sched_map);
nrow = isl_mat_rows(node->sched);
ncol = isl_mat_cols(node->sched) - 1;
dim = isl_space_from_domain(isl_space_copy(node->dim));
dim = isl_space_add_dims(dim, isl_dim_out, nrow);
bmap = isl_basic_map_universe(isl_space_copy(dim));
ls = isl_local_space_from_space(dim);
isl_int_init(v);
for (i = 0; i < nrow; ++i) {
c = isl_equality_alloc(isl_local_space_copy(ls));
isl_constraint_set_coefficient_si(c, isl_dim_out, i, -1);
isl_mat_get_element(node->sched, i, 0, &v);
isl_constraint_set_constant(c, v);
for (j = 0; j < node->nparam; ++j) {
isl_mat_get_element(node->sched, i, 1 + j, &v);
isl_constraint_set_coefficient(c, isl_dim_param, j, v);
}
for (j = 0; j < node->nvar; ++j) {
isl_mat_get_element(node->sched,
i, 1 + node->nparam + j, &v);
isl_constraint_set_coefficient(c, isl_dim_in, j, v);
}
bmap = isl_basic_map_add_constraint(bmap, c);
}
isl_int_clear(v);
isl_local_space_free(ls);
node->sched_map = isl_map_from_basic_map(bmap);
return isl_map_copy(node->sched_map);
}
/* Update the given dependence relation based on the current schedule.
* That is, intersect the dependence relation with a map expressing
* that source and sink are executed within the same iteration of
* the current schedule.
* This is not the most efficient way, but this shouldn't be a critical
* operation.
*/
static __isl_give isl_map *specialize(__isl_take isl_map *map,
struct isl_sched_node *src, struct isl_sched_node *dst)
{
isl_map *src_sched, *dst_sched, *id;
src_sched = node_extract_schedule(src);
dst_sched = node_extract_schedule(dst);
id = isl_map_apply_range(src_sched, isl_map_reverse(dst_sched));
return isl_map_intersect(map, id);
}
/* Update the dependence relations of all edges based on the current schedule.
* If a dependence is carried completely by the current schedule, then
* it is removed and edge_table is updated accordingly.
*/
static int update_edges(isl_ctx *ctx, struct isl_sched_graph *graph)
{
int i;
int reset_table = 0;
for (i = graph->n_edge - 1; i >= 0; --i) {
struct isl_sched_edge *edge = &graph->edge[i];
edge->map = specialize(edge->map, edge->src, edge->dst);
if (!edge->map)
return -1;
if (isl_map_plain_is_empty(edge->map)) {
reset_table = 1;
isl_map_free(edge->map);
if (i != graph->n_edge - 1)
graph->edge[i] = graph->edge[graph->n_edge - 1];
graph->n_edge--;
}
}
if (reset_table) {
isl_hash_table_free(ctx, graph->edge_table);
graph->edge_table = NULL;
return graph_init_edge_table(ctx, graph);
}
return 0;
}
static void next_band(struct isl_sched_graph *graph)
{
graph->band_start = graph->n_total_row;
graph->n_band++;
}
/* Topologically sort statements mapped to same schedule iteration
* and add a row to the schedule corresponding to this order.
*/
static int sort_statements(isl_ctx *ctx, struct isl_sched_graph *graph)
{
int i, j;
if (graph->n <= 1)
return 0;
if (update_edges(ctx, graph) < 0)
return -1;
if (graph->n_edge == 0)
return 0;
if (detect_sccs(graph) < 0)
return -1;
for (i = 0; i < graph->n; ++i) {
struct isl_sched_node *node = &graph->node[i];
int row = isl_mat_rows(node->sched);
int cols = isl_mat_cols(node->sched);
isl_map_free(node->sched_map);
node->sched_map = NULL;
node->sched = isl_mat_add_rows(node->sched, 1);
if (!node->sched)
return -1;
node->sched = isl_mat_set_element_si(node->sched, row, 0,
node->scc);
for (j = 1; j < cols; ++j)
node->sched = isl_mat_set_element_si(node->sched,
row, j, 0);
node->band[graph->n_total_row] = graph->n_band;
}
graph->n_total_row++;
next_band(graph);
return 0;
}
/* Construct an isl_schedule based on the computed schedule stored
* in graph and with parameters specified by dim.
*/
static __isl_give isl_schedule *extract_schedule(struct isl_sched_graph *graph,
__isl_take isl_space *dim)
{
int i;
isl_ctx *ctx;
isl_schedule *sched = NULL;
if (!dim)
return NULL;
ctx = isl_space_get_ctx(dim);
sched = isl_calloc(ctx, struct isl_schedule,
sizeof(struct isl_schedule) +
(graph->n - 1) * sizeof(struct isl_schedule_node));
if (!sched)
goto error;
sched->ref = 1;
sched->n = graph->n;
sched->n_band = graph->n_band;
sched->n_total_row = graph->n_total_row;
for (i = 0; i < sched->n; ++i) {
int r, b;
int *band_end, *band_id, *zero;
band_end = isl_alloc_array(ctx, int, graph->n_band);
band_id = isl_alloc_array(ctx, int, graph->n_band);
zero = isl_alloc_array(ctx, int, graph->n_total_row);
sched->node[i].sched = node_extract_schedule(&graph->node[i]);
sched->node[i].band_end = band_end;
sched->node[i].band_id = band_id;
sched->node[i].zero = zero;
if (!band_end || !band_id || !zero)
goto error;
for (r = 0; r < graph->n_total_row; ++r)
zero[r] = graph->node[i].zero[r];
for (r = b = 0; r < graph->n_total_row; ++r) {
if (graph->node[i].band[r] == b)
continue;
band_end[b++] = r;
if (graph->node[i].band[r] == -1)
break;
}
if (r == graph->n_total_row)
band_end[b++] = r;
sched->node[i].n_band = b;
for (--b; b >= 0; --b)
band_id[b] = graph->node[i].band_id[b];
}
sched->dim = dim;
return sched;
error:
isl_space_free(dim);
isl_schedule_free(sched);
return NULL;
}
/* Copy nodes that satisfy node_pred from the src dependence graph
* to the dst dependence graph.
*/
static int copy_nodes(struct isl_sched_graph *dst, struct isl_sched_graph *src,
int (*node_pred)(struct isl_sched_node *node, int data), int data)
{
int i;
dst->n = 0;
for (i = 0; i < src->n; ++i) {
if (!node_pred(&src->node[i], data))
continue;
dst->node[dst->n].dim = isl_space_copy(src->node[i].dim);
dst->node[dst->n].nvar = src->node[i].nvar;
dst->node[dst->n].nparam = src->node[i].nparam;
dst->node[dst->n].sched = isl_mat_copy(src->node[i].sched);
dst->node[dst->n].sched_map =
isl_map_copy(src->node[i].sched_map);
dst->node[dst->n].band = src->node[i].band;
dst->node[dst->n].band_id = src->node[i].band_id;
dst->node[dst->n].zero = src->node[i].zero;
dst->n++;
}
return 0;
}
/* Copy non-empty edges that satisfy edge_pred from the src dependence graph
* to the dst dependence graph.
*/
static int copy_edges(isl_ctx *ctx, struct isl_sched_graph *dst,
struct isl_sched_graph *src,
int (*edge_pred)(struct isl_sched_edge *edge, int data), int data)
{
int i;
dst->n_edge = 0;
for (i = 0; i < src->n_edge; ++i) {
struct isl_sched_edge *edge = &src->edge[i];
isl_map *map;
if (!edge_pred(edge, data))
continue;
if (isl_map_plain_is_empty(edge->map))
continue;
map = isl_map_copy(edge->map);
dst->edge[dst->n_edge].src =
graph_find_node(ctx, dst, edge->src->dim);
dst->edge[dst->n_edge].dst =
graph_find_node(ctx, dst, edge->dst->dim);
dst->edge[dst->n_edge].map = map;
dst->edge[dst->n_edge].validity = edge->validity;
dst->edge[dst->n_edge].proximity = edge->proximity;
dst->n_edge++;
}
return 0;
}
/* Given a "src" dependence graph that contains the nodes from "dst"
* that satisfy node_pred, copy the schedule computed in "src"
* for those nodes back to "dst".
*/
static int copy_schedule(struct isl_sched_graph *dst,
struct isl_sched_graph *src,
int (*node_pred)(struct isl_sched_node *node, int data), int data)
{
int i;
src->n = 0;
for (i = 0; i < dst->n; ++i) {
if (!node_pred(&dst->node[i], data))
continue;
isl_mat_free(dst->node[i].sched);
isl_map_free(dst->node[i].sched_map);
dst->node[i].sched = isl_mat_copy(src->node[src->n].sched);
dst->node[i].sched_map =
isl_map_copy(src->node[src->n].sched_map);
src->n++;
}
dst->n_total_row = src->n_total_row;
dst->n_band = src->n_band;
return 0;
}
/* Compute the maximal number of variables over all nodes.
* This is the maximal number of linearly independent schedule
* rows that we need to compute.
* Just in case we end up in a part of the dependence graph
* with only lower-dimensional domains, we make sure we will
* compute the required amount of extra linearly independent rows.
*/
static int compute_maxvar(struct isl_sched_graph *graph)
{
int i;
graph->maxvar = 0;
for (i = 0; i < graph->n; ++i) {
struct isl_sched_node *node = &graph->node[i];
int nvar;
if (node_update_cmap(node) < 0)
return -1;
nvar = node->nvar + graph->n_row - node->rank;
if (nvar > graph->maxvar)
graph->maxvar = nvar;
}
return 0;
}
static int compute_schedule(isl_ctx *ctx, struct isl_sched_graph *graph);
static int compute_schedule_wcc(isl_ctx *ctx, struct isl_sched_graph *graph);
/* Compute a schedule for a subgraph of "graph". In particular, for
* the graph composed of nodes that satisfy node_pred and edges that
* that satisfy edge_pred. The caller should precompute the number
* of nodes and edges that satisfy these predicates and pass them along
* as "n" and "n_edge".
* If the subgraph is known to consist of a single component, then wcc should
* be set and then we call compute_schedule_wcc on the constructed subgraph.
* Otherwise, we call compute_schedule, which will check whether the subgraph
* is connected.
*/
static int compute_sub_schedule(isl_ctx *ctx,
struct isl_sched_graph *graph, int n, int n_edge,
int (*node_pred)(struct isl_sched_node *node, int data),
int (*edge_pred)(struct isl_sched_edge *edge, int data),
int data, int wcc)
{
struct isl_sched_graph split = { 0 };
if (graph_alloc(ctx, &split, n, n_edge) < 0)
goto error;
if (copy_nodes(&split, graph, node_pred, data) < 0)
goto error;
if (graph_init_table(ctx, &split) < 0)
goto error;
if (copy_edges(ctx, &split, graph, edge_pred, data) < 0)
goto error;
if (graph_init_edge_table(ctx, &split) < 0)
goto error;
split.n_row = graph->n_row;
split.n_total_row = graph->n_total_row;
split.n_band = graph->n_band;
split.band_start = graph->band_start;
if (wcc && compute_schedule_wcc(ctx, &split) < 0)
goto error;
if (!wcc && compute_schedule(ctx, &split) < 0)
goto error;
copy_schedule(graph, &split, node_pred, data);
graph_free(ctx, &split);
return 0;
error:
graph_free(ctx, &split);
return -1;
}
static int node_scc_exactly(struct isl_sched_node *node, int scc)
{
return node->scc == scc;
}
static int node_scc_at_most(struct isl_sched_node *node, int scc)
{
return node->scc <= scc;
}
static int node_scc_at_least(struct isl_sched_node *node, int scc)
{
return node->scc >= scc;
}
static int edge_src_scc_exactly(struct isl_sched_edge *edge, int scc)
{
return edge->src->scc == scc;
}
static int edge_dst_scc_at_most(struct isl_sched_edge *edge, int scc)
{
return edge->dst->scc <= scc;
}
static int edge_src_scc_at_least(struct isl_sched_edge *edge, int scc)
{
return edge->src->scc >= scc;
}
/* Pad the schedules of all nodes with zero rows such that in the end
* they all have graph->n_total_row rows.
* The extra rows don't belong to any band, so they get assigned band number -1.
*/
static int pad_schedule(struct isl_sched_graph *graph)
{
int i, j;
for (i = 0; i < graph->n; ++i) {
struct isl_sched_node *node = &graph->node[i];
int row = isl_mat_rows(node->sched);
if (graph->n_total_row > row) {
isl_map_free(node->sched_map);
node->sched_map = NULL;
}
node->sched = isl_mat_add_zero_rows(node->sched,
graph->n_total_row - row);
if (!node->sched)
return -1;
for (j = row; j < graph->n_total_row; ++j)
node->band[j] = -1;
}
return 0;
}
/* Split the current graph into two parts and compute a schedule for each
* part individually. In particular, one part consists of all SCCs up
* to and including graph->src_scc, while the other part contains the other
* SCCS.
*
* The split is enforced in the schedule by constant rows with two different
* values (0 and 1). These constant rows replace the previously computed rows
* in the current band.
* It would be possible to reuse them as the first rows in the next
* band, but recomputing them may result in better rows as we are looking
* at a smaller part of the dependence graph.
*
* The band_id of the second group is set to n, where n is the number
* of nodes in the first group. This ensures that the band_ids over
* the two groups remain disjoint, even if either or both of the two
* groups contain independent components.
*/
static int compute_split_schedule(isl_ctx *ctx, struct isl_sched_graph *graph)
{
int i, j, n, e1, e2;
int n_total_row, orig_total_row;
int n_band, orig_band;
int drop;
drop = graph->n_total_row - graph->band_start;
graph->n_total_row -= drop;
graph->n_row -= drop;
n = 0;
for (i = 0; i < graph->n; ++i) {
struct isl_sched_node *node = &graph->node[i];
int row = isl_mat_rows(node->sched) - drop;
int cols = isl_mat_cols(node->sched);
int before = node->scc <= graph->src_scc;
if (before)
n++;
isl_map_free(node->sched_map);
node->sched_map = NULL;
node->sched = isl_mat_drop_rows(node->sched,
graph->band_start, drop);
node->sched = isl_mat_add_rows(node->sched, 1);
if (!node->sched)
return -1;
node->sched = isl_mat_set_element_si(node->sched, row, 0,
!before);
for (j = 1; j < cols; ++j)
node->sched = isl_mat_set_element_si(node->sched,
row, j, 0);
node->band[graph->n_total_row] = graph->n_band;
}
e1 = e2 = 0;
for (i = 0; i < graph->n_edge; ++i) {
if (graph->edge[i].dst->scc <= graph->src_scc)
e1++;
if (graph->edge[i].src->scc > graph->src_scc)
e2++;
}
graph->n_total_row++;
next_band(graph);
for (i = 0; i < graph->n; ++i) {
struct isl_sched_node *node = &graph->node[i];
if (node->scc > graph->src_scc)
node->band_id[graph->n_band] = n;
}
orig_total_row = graph->n_total_row;
orig_band = graph->n_band;
if (compute_sub_schedule(ctx, graph, n, e1,
&node_scc_at_most, &edge_dst_scc_at_most,
graph->src_scc, 0) < 0)
return -1;
n_total_row = graph->n_total_row;
graph->n_total_row = orig_total_row;
n_band = graph->n_band;
graph->n_band = orig_band;
if (compute_sub_schedule(ctx, graph, graph->n - n, e2,
&node_scc_at_least, &edge_src_scc_at_least,
graph->src_scc + 1, 0) < 0)
return -1;
if (n_total_row > graph->n_total_row)
graph->n_total_row = n_total_row;
if (n_band > graph->n_band)
graph->n_band = n_band;
return pad_schedule(graph);
}
/* Compute the next band of the schedule after updating the dependence
* relations based on the the current schedule.
*/
static int compute_next_band(isl_ctx *ctx, struct isl_sched_graph *graph)
{
if (update_edges(ctx, graph) < 0)
return -1;
next_band(graph);
return compute_schedule(ctx, graph);
}
/* Add constraints to graph->lp that force the dependence "map" (which
* is part of the dependence relation of "edge")
* to be respected and attempt to carry it, where the edge is one from
* a node j to itself. "pos" is the sequence number of the given map.
* That is, add constraints that enforce
*
* (c_j_0 + c_j_n n + c_j_x y) - (c_j_0 + c_j_n n + c_j_x x)
* = c_j_x (y - x) >= e_i
*
* for each (x,y) in R.
* We obtain general constraints on coefficients (c_0, c_n, c_x)
* of valid constraints for (y - x) and then plug in (-e_i, 0, c_j_x),
* with each coefficient in c_j_x represented as a pair of non-negative
* coefficients.
*/
static int add_intra_constraints(struct isl_sched_graph *graph,
struct isl_sched_edge *edge, __isl_take isl_map *map, int pos)
{
unsigned total;
isl_ctx *ctx = isl_map_get_ctx(map);
isl_space *dim;
isl_dim_map *dim_map;
isl_basic_set *coef;
struct isl_sched_node *node = edge->src;
coef = intra_coefficients(graph, map);
dim = isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef)));
total = isl_basic_set_total_dim(graph->lp);
dim_map = isl_dim_map_alloc(ctx, total);
isl_dim_map_range(dim_map, 3 + pos, 0, 0, 0, 1, -1);
isl_dim_map_range(dim_map, node->start + 2 * node->nparam + 1, 2,
isl_space_dim(dim, isl_dim_set), 1,
node->nvar, -1);
isl_dim_map_range(dim_map, node->start + 2 * node->nparam + 2, 2,
isl_space_dim(dim, isl_dim_set), 1,
node->nvar, 1);
graph->lp = isl_basic_set_extend_constraints(graph->lp,
coef->n_eq, coef->n_ineq);
graph->lp = isl_basic_set_add_constraints_dim_map(graph->lp,
coef, dim_map);
isl_space_free(dim);
return 0;
}
/* Add constraints to graph->lp that force the dependence "map" (which
* is part of the dependence relation of "edge")
* to be respected and attempt to carry it, where the edge is one from
* node j to node k. "pos" is the sequence number of the given map.
* That is, add constraints that enforce
*
* (c_k_0 + c_k_n n + c_k_x y) - (c_j_0 + c_j_n n + c_j_x x) >= e_i
*
* for each (x,y) in R.
* We obtain general constraints on coefficients (c_0, c_n, c_x)
* of valid constraints for R and then plug in
* (-e_i + c_k_0 - c_j_0, c_k_n - c_j_n, c_k_x - c_j_x)
* with each coefficient (except e_i, c_k_0 and c_j_0)
* represented as a pair of non-negative coefficients.
*/
static int add_inter_constraints(struct isl_sched_graph *graph,
struct isl_sched_edge *edge, __isl_take isl_map *map, int pos)
{
unsigned total;
isl_ctx *ctx = isl_map_get_ctx(map);
isl_space *dim;
isl_dim_map *dim_map;
isl_basic_set *coef;
struct isl_sched_node *src = edge->src;
struct isl_sched_node *dst = edge->dst;
coef = inter_coefficients(graph, map);
dim = isl_space_domain(isl_space_unwrap(isl_basic_set_get_space(coef)));
total = isl_basic_set_total_dim(graph->lp);
dim_map = isl_dim_map_alloc(ctx, total);
isl_dim_map_range(dim_map, 3 + pos, 0, 0, 0, 1, -1);
isl_dim_map_range(dim_map, dst->start, 0, 0, 0, 1, 1);
isl_dim_map_range(dim_map, dst->start + 1, 2, 1, 1, dst->nparam, -1);
isl_dim_map_range(dim_map, dst->start + 2, 2, 1, 1, dst->nparam, 1);
isl_dim_map_range(dim_map, dst->start + 2 * dst->nparam + 1, 2,
isl_space_dim(dim, isl_dim_set) + src->nvar, 1,
dst->nvar, -1);
isl_dim_map_range(dim_map, dst->start + 2 * dst->nparam + 2, 2,
isl_space_dim(dim, isl_dim_set) + src->nvar, 1,
dst->nvar, 1);
isl_dim_map_range(dim_map, src->start, 0, 0, 0, 1, -1);
isl_dim_map_range(dim_map, src->start + 1, 2, 1, 1, src->nparam, 1);
isl_dim_map_range(dim_map, src->start + 2, 2, 1, 1, src->nparam, -1);
isl_dim_map_range(dim_map, src->start + 2 * src->nparam + 1, 2,
isl_space_dim(dim, isl_dim_set), 1,
src->nvar, 1);
isl_dim_map_range(dim_map, src->start + 2 * src->nparam + 2, 2,
isl_space_dim(dim, isl_dim_set), 1,
src->nvar, -1);
graph->lp = isl_basic_set_extend_constraints(graph->lp,
coef->n_eq, coef->n_ineq);
graph->lp = isl_basic_set_add_constraints_dim_map(graph->lp,
coef, dim_map);
isl_space_free(dim);
return 0;
}
/* Add constraints to graph->lp that force all dependence
* to be respected and attempt to carry it.
*/
static int add_all_constraints(struct isl_sched_graph *graph)
{
int i, j;
int pos;
pos = 0;
for (i = 0; i < graph->n_edge; ++i) {
struct isl_sched_edge *edge= &graph->edge[i];
for (j = 0; j < edge->map->n; ++j) {
isl_basic_map *bmap;
isl_map *map;
bmap = isl_basic_map_copy(edge->map->p[j]);
map = isl_map_from_basic_map(bmap);
if (edge->src == edge->dst &&
add_intra_constraints(graph, edge, map, pos) < 0)
return -1;
if (edge->src != edge->dst &&
add_inter_constraints(graph, edge, map, pos) < 0)
return -1;
++pos;
}
}
return 0;
}
/* Count the number of equality and inequality constraints
* that will be added to the carry_lp problem.
* If once is set, then we count
* each edge exactly once. Otherwise, we count as follows
* validity -> 1 (>= 0)
* validity+proximity -> 2 (>= 0 and upper bound)
* proximity -> 2 (lower and upper bound)
*/
static int count_all_constraints(struct isl_sched_graph *graph,
int *n_eq, int *n_ineq, int once)
{
int i, j;
*n_eq = *n_ineq = 0;
for (i = 0; i < graph->n_edge; ++i) {
struct isl_sched_edge *edge= &graph->edge[i];
for (j = 0; j < edge->map->n; ++j) {
isl_basic_map *bmap;
isl_map *map;
bmap = isl_basic_map_copy(edge->map->p[j]);
map = isl_map_from_basic_map(bmap);
if (count_map_constraints(graph, edge, map,
n_eq, n_ineq, once) < 0)
return -1;
}
}
return 0;
}
/* Construct an LP problem for finding schedule coefficients
* such that the schedule carries as many dependences as possible.
* In particular, for each dependence i, we bound the dependence distance
* from below by e_i, with 0 <= e_i <= 1 and then maximize the sum
* of all e_i's. Dependence with e_i = 0 in the solution are simply
* respected, while those with e_i > 0 (in practice e_i = 1) are carried.
* Note that if the dependence relation is a union of basic maps,
* then we have to consider each basic map individually as it may only
* be possible to carry the dependences expressed by some of those
* basic maps and not all off them.
* Below, we consider each of those basic maps as a separate "edge".
*
* All variables of the LP are non-negative. The actual coefficients
* may be negative, so each coefficient is represented as the difference
* of two non-negative variables. The negative part always appears
* immediately before the positive part.
* Other than that, the variables have the following order
*
* - sum of (1 - e_i) over all edges
* - sum of positive and negative parts of all c_n coefficients
* (unconstrained when computing non-parametric schedules)
* - sum of positive and negative parts of all c_x coefficients
* - for each edge
* - e_i
* - for each node
* - c_i_0
* - positive and negative parts of c_i_n (if parametric)
* - positive and negative parts of c_i_x
*
* The constraints are those from the edges plus three equalities
* to express the sums and n_edge inequalities to express e_i <= 1.
*/
static int setup_carry_lp(isl_ctx *ctx, struct isl_sched_graph *graph)
{
int i, j;
int k;
isl_space *dim;
unsigned total;
int n_eq, n_ineq;
int n_edge;
n_edge = 0;
for (i = 0; i < graph->n_edge; ++i)
n_edge += graph->edge[i].map->n;
total = 3 + n_edge;
for (i = 0; i < graph->n; ++i) {
struct isl_sched_node *node = &graph->node[graph->sorted[i]];
node->start = total;
total += 1 + 2 * (node->nparam + node->nvar);
}
if (count_all_constraints(graph, &n_eq, &n_ineq, 1) < 0)
return -1;
dim = isl_space_set_alloc(ctx, 0, total);
isl_basic_set_free(graph->lp);
n_eq += 3;
n_ineq += n_edge;
graph->lp = isl_basic_set_alloc_space(dim, 0, n_eq, n_ineq);
graph->lp = isl_basic_set_set_rational(graph->lp);
k = isl_basic_set_alloc_equality(graph->lp);
if (k < 0)
return -1;
isl_seq_clr(graph->lp->eq[k], 1 + total);
isl_int_set_si(graph->lp->eq[k][0], -n_edge);
isl_int_set_si(graph->lp->eq[k][1], 1);
for (i = 0; i < n_edge; ++i)
isl_int_set_si(graph->lp->eq[k][4 + i], 1);
k = isl_basic_set_alloc_equality(graph->lp);
if (k < 0)
return -1;
isl_seq_clr(graph->lp->eq[k], 1 + total);
isl_int_set_si(graph->lp->eq[k][2], -1);
for (i = 0; i < graph->n; ++i) {
int pos = 1 + graph->node[i].start + 1;
for (j = 0; j < 2 * graph->node[i].nparam; ++j)
isl_int_set_si(graph->lp->eq[k][pos + j], 1);
}
k = isl_basic_set_alloc_equality(graph->lp);
if (k < 0)
return -1;
isl_seq_clr(graph->lp->eq[k], 1 + total);
isl_int_set_si(graph->lp->eq[k][3], -1);
for (i = 0; i < graph->n; ++i) {
struct isl_sched_node *node = &graph->node[i];
int pos = 1 + node->start + 1 + 2 * node->nparam;
for (j = 0; j < 2 * node->nvar; ++j)
isl_int_set_si(graph->lp->eq[k][pos + j], 1);
}
for (i = 0; i < n_edge; ++i) {
k = isl_basic_set_alloc_inequality(graph->lp);
if (k < 0)
return -1;
isl_seq_clr(graph->lp->ineq[k], 1 + total);
isl_int_set_si(graph->lp->ineq[k][4 + i], -1);
isl_int_set_si(graph->lp->ineq[k][0], 1);
}
if (add_all_constraints(graph) < 0)
return -1;
return 0;
}
/* If the schedule_split_parallel option is set and if the linear
* parts of the scheduling rows for all nodes in the graphs are the same,
* then split off the constant term from the linear part.
* The constant term is then placed in a separate band and
* the linear part is simplified.
*/
static int split_parallel(isl_ctx *ctx, struct isl_sched_graph *graph)
{
int i;
int equal = 1;
int row, cols;
struct isl_sched_node *node0;
if (!ctx->opt->schedule_split_parallel)
return 0;
if (graph->n <= 1)
return 0;
node0 = &graph->node[0];
row = isl_mat_rows(node0->sched) - 1;
cols = isl_mat_cols(node0->sched);
for (i = 1; i < graph->n; ++i) {
struct isl_sched_node *node = &graph->node[i];
if (!isl_seq_eq(node0->sched->row[row] + 1,
node->sched->row[row] + 1, cols - 1))
return 0;
if (equal &&
isl_int_ne(node0->sched->row[row][0],
node->sched->row[row][0]))
equal = 0;
}
if (equal)
return 0;
next_band(graph);
for (i = 0; i < graph->n; ++i) {
struct isl_sched_node *node = &graph->node[i];
isl_map_free(node->sched_map);
node->sched_map = NULL;
node->sched = isl_mat_add_zero_rows(node->sched, 1);
if (!node->sched)
return -1;
isl_int_set(node->sched->row[row + 1][0],
node->sched->row[row][0]);
isl_int_set_si(node->sched->row[row][0], 0);
node->sched = isl_mat_normalize_row(node->sched, row);
if (!node->sched)
return -1;
node->band[graph->n_total_row] = graph->n_band;
}
graph->n_total_row++;
return 0;
}
/* Construct a schedule row for each node such that as many dependences
* as possible are carried and then continue with the next band.
*/
static int carry_dependences(isl_ctx *ctx, struct isl_sched_graph *graph)
{
int i;
int n_edge;
isl_vec *sol;
isl_basic_set *lp;
n_edge = 0;
for (i = 0; i < graph->n_edge; ++i)
n_edge += graph->edge[i].map->n;
if (setup_carry_lp(ctx, graph) < 0)
return -1;
lp = isl_basic_set_copy(graph->lp);
sol = isl_tab_basic_set_non_neg_lexmin(lp);
if (!sol)
return -1;
if (sol->size == 0) {
isl_vec_free(sol);
isl_die(ctx, isl_error_internal,
"error in schedule construction", return -1);
}
if (isl_int_cmp_si(sol->el[1], n_edge) >= 0) {
isl_vec_free(sol);
isl_die(ctx, isl_error_unknown,
"unable to carry dependences", return -1);
}
if (update_schedule(graph, sol, 0, 0) < 0)
return -1;
if (split_parallel(ctx, graph) < 0)
return -1;
return compute_next_band(ctx, graph);
}
/* Compute a schedule for a connected dependence graph.
* We try to find a sequence of as many schedule rows as possible that result
* in non-negative dependence distances (independent of the previous rows
* in the sequence, i.e., such that the sequence is tilable).
* If we can't find any more rows we either
* - split between SCCs and start over (assuming we found an interesting
* pair of SCCs between which to split)
* - continue with the next band (assuming the current band has at least
* one row)
* - try to carry as many dependences as possible and continue with the next
* band
*
* If we manage to complete the schedule, we finish off by topologically
* sorting the statements based on the remaining dependences.
*
* If ctx->opt->schedule_outer_zero_distance is set, then we force the
* outermost dimension in the current band to be zero distance. If this
* turns out to be impossible, we fall back on the general scheme above
* and try to carry as many dependences as possible.
*/
static int compute_schedule_wcc(isl_ctx *ctx, struct isl_sched_graph *graph)
{
int force_zero = 0;
int max_constant_term;
if (detect_sccs(graph) < 0)
return -1;
sort_sccs(graph);
if (compute_maxvar(graph) < 0)
return -1;
if (ctx->opt->schedule_outer_zero_distance)
force_zero = 1;
max_constant_term = ctx->opt->schedule_max_constant_term;
while (graph->n_row < graph->maxvar) {
isl_vec *sol;
graph->src_scc = -1;
graph->dst_scc = -1;
if (setup_lp(ctx, graph, force_zero, max_constant_term) < 0)
return -1;
sol = solve_lp(graph);
if (!sol)
return -1;
if (sol->size == 0) {
isl_vec_free(sol);
if (!ctx->opt->schedule_maximize_band_depth &&
graph->n_total_row > graph->band_start)
return compute_next_band(ctx, graph);
if (graph->src_scc >= 0)
return compute_split_schedule(ctx, graph);
if (graph->n_total_row > graph->band_start)
return compute_next_band(ctx, graph);
return carry_dependences(ctx, graph);
}
if (update_schedule(graph, sol, 1, 1) < 0)
return -1;
force_zero = 0;
}
if (graph->n_total_row > graph->band_start)
next_band(graph);
return sort_statements(ctx, graph);
}
/* Compute a schedule for each component (identified by node->scc)
* of the dependence graph separately and then combine the results.
*
* The band_id is adjusted such that each component has a separate id.
* Note that the band_id may have already been set to a value different
* from zero by compute_split_schedule.
*/
static int compute_component_schedule(isl_ctx *ctx,
struct isl_sched_graph *graph)
{
int wcc, i;
int n, n_edge;
int n_total_row, orig_total_row;
int n_band, orig_band;
n_total_row = 0;
orig_total_row = graph->n_total_row;
n_band = 0;
orig_band = graph->n_band;
for (i = 0; i < graph->n; ++i)
graph->node[i].band_id[graph->n_band] += graph->node[i].scc;
for (wcc = 0; wcc < graph->scc; ++wcc) {
n = 0;
for (i = 0; i < graph->n; ++i)
if (graph->node[i].scc == wcc)
n++;
n_edge = 0;
for (i = 0; i < graph->n_edge; ++i)
if (graph->edge[i].src->scc == wcc)
n_edge++;
if (compute_sub_schedule(ctx, graph, n, n_edge,
&node_scc_exactly,
&edge_src_scc_exactly, wcc, 1) < 0)
return -1;
if (graph->n_total_row > n_total_row)
n_total_row = graph->n_total_row;
graph->n_total_row = orig_total_row;
if (graph->n_band > n_band)
n_band = graph->n_band;
graph->n_band = orig_band;
}
graph->n_total_row = n_total_row;
graph->n_band = n_band;
return pad_schedule(graph);
}
/* Compute a schedule for the given dependence graph.
* We first check if the graph is connected (through validity dependences)
* and, if not, compute a schedule for each component separately.
*/
static int compute_schedule(isl_ctx *ctx, struct isl_sched_graph *graph)
{
if (detect_wccs(graph) < 0)
return -1;
if (graph->scc > 1)
return compute_component_schedule(ctx, graph);
return compute_schedule_wcc(ctx, graph);
}
/* Compute a schedule for the given union of domains that respects
* all the validity dependences and tries to minimize the dependence
* distances over the proximity dependences.
*/
__isl_give isl_schedule *isl_union_set_compute_schedule(
__isl_take isl_union_set *domain,
__isl_take isl_union_map *validity,
__isl_take isl_union_map *proximity)
{
isl_ctx *ctx = isl_union_set_get_ctx(domain);
isl_space *dim;
struct isl_sched_graph graph = { 0 };
isl_schedule *sched;
domain = isl_union_set_align_params(domain,
isl_union_map_get_space(validity));
domain = isl_union_set_align_params(domain,
isl_union_map_get_space(proximity));
dim = isl_union_set_get_space(domain);
validity = isl_union_map_align_params(validity, isl_space_copy(dim));
proximity = isl_union_map_align_params(proximity, dim);
if (!domain)
goto error;
graph.n = isl_union_set_n_set(domain);
if (graph.n == 0)
goto empty;
if (graph_alloc(ctx, &graph, graph.n,
isl_union_map_n_map(validity) + isl_union_map_n_map(proximity)) < 0)
goto error;
graph.root = 1;
graph.n = 0;
if (isl_union_set_foreach_set(domain, &extract_node, &graph) < 0)
goto error;
if (graph_init_table(ctx, &graph) < 0)
goto error;
graph.n_edge = 0;
if (isl_union_map_foreach_map(validity, &extract_edge, &graph) < 0)
goto error;
if (graph_init_edge_table(ctx, &graph) < 0)
goto error;
if (isl_union_map_foreach_map(proximity, &extract_edge, &graph) < 0)
goto error;
if (compute_schedule(ctx, &graph) < 0)
goto error;
empty:
sched = extract_schedule(&graph, isl_union_set_get_space(domain));
graph_free(ctx, &graph);
isl_union_set_free(domain);
isl_union_map_free(validity);
isl_union_map_free(proximity);
return sched;
error:
graph_free(ctx, &graph);
isl_union_set_free(domain);
isl_union_map_free(validity);
isl_union_map_free(proximity);
return NULL;
}
void *isl_schedule_free(__isl_take isl_schedule *sched)
{
int i;
if (!sched)
return NULL;
if (--sched->ref > 0)
return NULL;
for (i = 0; i < sched->n; ++i) {
isl_map_free(sched->node[i].sched);
free(sched->node[i].band_end);
free(sched->node[i].band_id);
free(sched->node[i].zero);
}
isl_space_free(sched->dim);
isl_band_list_free(sched->band_forest);
free(sched);
return NULL;
}
isl_ctx *isl_schedule_get_ctx(__isl_keep isl_schedule *schedule)
{
return schedule ? isl_space_get_ctx(schedule->dim) : NULL;
}
__isl_give isl_union_map *isl_schedule_get_map(__isl_keep isl_schedule *sched)
{
int i;
isl_union_map *umap;
if (!sched)
return NULL;
umap = isl_union_map_empty(isl_space_copy(sched->dim));
for (i = 0; i < sched->n; ++i)
umap = isl_union_map_add_map(umap,
isl_map_copy(sched->node[i].sched));
return umap;
}
static __isl_give isl_band_list *construct_band_list(
__isl_keep isl_schedule *schedule, __isl_keep isl_band *parent,
int band_nr, int *parent_active, int n_active);
/* Construct an isl_band structure for the band in the given schedule
* with sequence number band_nr for the n_active nodes marked by active.
* If the nodes don't have a band with the given sequence number,
* then a band without members is created.
*
* Because of the way the schedule is constructed, we know that
* the position of the band inside the schedule of a node is the same
* for all active nodes.
*/
static __isl_give isl_band *construct_band(__isl_keep isl_schedule *schedule,
__isl_keep isl_band *parent,
int band_nr, int *active, int n_active)
{
int i, j;
isl_ctx *ctx = isl_schedule_get_ctx(schedule);
isl_band *band;
unsigned start, end;
band = isl_calloc_type(ctx, isl_band);
if (!band)
return NULL;
band->ref = 1