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-rw-r--r--polly/lib/External/ppcg/gpu.c5400
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diff --git a/polly/lib/External/ppcg/gpu.c b/polly/lib/External/ppcg/gpu.c
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+/*
+ * Copyright 2010-2011 INRIA Saclay
+ * Copyright 2012-2013 Ecole Normale Superieure
+ *
+ * Use of this software is governed by the MIT license
+ *
+ * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
+ * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
+ * 91893 Orsay, France
+ * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
+ */
+
+#include <assert.h>
+#include <stdlib.h>
+#include <string.h>
+
+#include <isl/polynomial.h>
+#include <isl/union_set.h>
+#include <isl/aff.h>
+#include <isl/ilp.h>
+#include <isl/flow.h>
+#include <isl/schedule.h>
+#include <isl/schedule_node.h>
+#include <isl/options.h>
+#include <isl/ast_build.h>
+
+#include "cpu.h"
+#include "gpu.h"
+#include "gpu_array_tile.h"
+#include "gpu_group.h"
+#include "gpu_tree.h"
+#include "schedule.h"
+#include "ppcg_options.h"
+#include "print.h"
+#include "util.h"
+
+struct gpu_array_info;
+
+/* Return the name of the outer array (of structs) accessed by "access".
+ */
+static const char *get_outer_array_name(__isl_keep isl_map *access)
+{
+ isl_space *space;
+ const char *name;
+
+ space = isl_space_range(isl_map_get_space(access));
+ while (space && isl_space_is_wrapping(space))
+ space = isl_space_domain(isl_space_unwrap(space));
+ name = isl_space_get_tuple_name(space, isl_dim_set);
+ isl_space_free(space);
+
+ return name;
+}
+
+/* Collect all references to the given array and store pointers to them
+ * in array->refs.
+ */
+static void collect_references(struct gpu_prog *prog,
+ struct gpu_array_info *array)
+{
+ int i;
+ int n;
+
+ n = 0;
+ for (i = 0; i < prog->n_stmts; ++i) {
+ struct gpu_stmt *stmt = &prog->stmts[i];
+ struct gpu_stmt_access *access;
+
+ for (access = stmt->accesses; access; access = access->next) {
+ const char *name;
+ name = get_outer_array_name(access->access);
+ if (name && !strcmp(array->name, name))
+ n++;
+ }
+ }
+
+ array->n_ref = n;
+ array->refs = isl_alloc_array(prog->ctx, struct gpu_stmt_access *, n);
+ assert(array->refs);
+
+ n = 0;
+ for (i = 0; i < prog->n_stmts; ++i) {
+ struct gpu_stmt *stmt = &prog->stmts[i];
+ struct gpu_stmt_access *access;
+
+ for (access = stmt->accesses; access; access = access->next) {
+ const char *name;
+ name = get_outer_array_name(access->access);
+ if (!name || strcmp(array->name, name))
+ continue;
+
+ array->refs[n++] = access;
+ }
+ }
+}
+
+/* Compute and return the extent of "array", taking into account the set of
+ * accessed elements.
+ *
+ * In particular, the extent in the outer dimension is taken
+ * from "accessed", while the extents in the remaining dimensions
+ * are taken from array->extent.
+ *
+ * The extent in the outer dimension cannot be taken from array->extent
+ * because that may be unbounded. Furthermore, even if it is bounded,
+ * it may be larger than the piece of the array that is being accessed.
+ */
+static __isl_give isl_set *compute_extent(struct pet_array *array,
+ __isl_keep isl_set *accessed)
+{
+ int n_index;
+ isl_id *id;
+ isl_set *outer;
+ isl_set *extent;
+
+ extent = isl_set_copy(array->extent);
+
+ n_index = isl_set_dim(accessed, isl_dim_set);
+ if (n_index == 0)
+ return extent;
+
+ extent = isl_set_project_out(extent, isl_dim_set, 0, 1);
+ outer = isl_set_copy(accessed);
+ outer = isl_set_project_out(outer, isl_dim_set, 1, n_index - 1);
+ extent = isl_set_flat_product(outer, extent);
+ id = isl_set_get_tuple_id(accessed);
+ extent = isl_set_set_tuple_id(extent, id);
+
+ return extent;
+}
+
+/* Is the array "array" being extracted a read-only scalar?
+ *
+ * That is, is "array" a scalar that is never possibly written to.
+ * An array containing structures is never considered to be a scalar.
+ */
+static int is_read_only_scalar(struct gpu_array_info *array,
+ struct gpu_prog *prog)
+{
+ isl_set *space;
+ isl_union_map *write;
+ int empty;
+
+ if (array->has_compound_element)
+ return 0;
+ if (array->n_index != 0)
+ return 0;
+
+ write = isl_union_map_copy(prog->may_write);
+ space = isl_set_universe(isl_space_copy(array->space));
+ write = isl_union_map_intersect_range(write,
+ isl_union_set_from_set(space));
+ empty = isl_union_map_is_empty(write);
+ isl_union_map_free(write);
+
+ return empty;
+}
+
+/* Compute bounds on the host array "pa" based on the corresponding
+ * accessed elements in "arrays"
+ * and collect all references to the array.
+ * Store the results in "info".
+ *
+ * If the array is zero-dimensional and does not contain structures,
+ * i.e., if the array is a scalar, we check whether it is read-only.
+ * We also check whether the array is accessed at all.
+ */
+static int extract_array_info(struct gpu_prog *prog,
+ struct gpu_array_info *info, struct pet_array *pa,
+ __isl_keep isl_union_set *arrays)
+{
+ int i, empty;
+ const char *name;
+ int n_index;
+ isl_pw_aff **bounds;
+ isl_set *accessed, *extent;
+
+ n_index = isl_set_dim(pa->extent, isl_dim_set);
+ name = isl_set_get_tuple_name(pa->extent);
+ bounds = isl_alloc_array(prog->ctx, isl_pw_aff *, n_index);
+ if (!bounds)
+ return -1;
+
+ info->space = isl_set_get_space(pa->extent);
+ info->name = strdup(name);
+ info->n_index = n_index;
+ info->bound = bounds;
+ info->linearize = prog->scop->options->linearize_device_arrays;
+
+ info->type = strdup(pa->element_type);
+ info->size = pa->element_size;
+ info->local = pa->declared && !pa->exposed;
+ info->has_compound_element = pa->element_is_record;
+ info->read_only_scalar = is_read_only_scalar(info, prog);
+
+ accessed = isl_union_set_extract_set(arrays,
+ isl_space_copy(info->space));
+ empty = isl_set_is_empty(accessed);
+ extent = compute_extent(pa, accessed);
+ isl_set_free(accessed);
+ info->extent = extent;
+ if (empty < 0)
+ return -1;
+ info->accessed = !empty;
+ for (i = 0; i < n_index; ++i) {
+ isl_set *dom;
+ isl_local_space *ls;
+ isl_aff *one;
+ isl_pw_aff *bound;
+
+ dom = isl_set_copy(extent);
+ dom = isl_set_project_out(dom, isl_dim_set, i + 1,
+ n_index - (i + 1));
+ dom = isl_set_project_out(dom, isl_dim_set, 0, i);
+ if (!isl_set_dim_has_upper_bound(dom, isl_dim_set, 0)) {
+ fprintf(stderr, "unable to determine extent of '%s' "
+ "in dimension %d\n", info->name, i);
+ dom = isl_set_free(dom);
+ }
+ bound = isl_set_dim_max(dom, 0);
+ dom = isl_pw_aff_domain(isl_pw_aff_copy(bound));
+ ls = isl_local_space_from_space(isl_set_get_space(dom));
+ one = isl_aff_zero_on_domain(ls);
+ one = isl_aff_add_constant_si(one, 1);
+ bound = isl_pw_aff_add(bound, isl_pw_aff_alloc(dom, one));
+ bound = isl_pw_aff_gist(bound, isl_set_copy(prog->context));
+
+ bounds[i] = bound;
+ if (!isl_pw_aff_is_cst(bound))
+ info->linearize = 1;
+ }
+
+ collect_references(prog, info);
+
+ return 0;
+}
+
+/* Remove independence from the order constraints "order" on array "array".
+ * Since the pairs of iterations in the filter relation of an independence
+ * are guaranteed to be completely independent by the user, there is
+ * no need to ensure that live ranges are ordered along thong pairs.
+ * We make an exception for local variables, though, as the independence
+ * guarantee does not apply to those.
+ *
+ * The order constraints are used in two places.
+ * Those on scalars are used in check_scalar_live_ranges to check if
+ * we need to force the scalar to be private. Any non-local scalar
+ * should not be forced scalar if it only appears in independent loops.
+ * Those on non-scalars are added to the coincidence constraints
+ * in compute_schedule because we do not support any array expansion.
+ * Accesses to non-local arrays should not prevent a loop from being
+ * considered coincident so we should indeed remove those constraints
+ * from the order constraints.
+ */
+static __isl_give isl_union_map *remove_independences(struct gpu_prog *prog,
+ struct gpu_array_info *array, __isl_take isl_union_map *order)
+{
+ int i;
+
+ for (i = 0; i < prog->scop->pet->n_independence; ++i) {
+ struct pet_independence *pi = prog->scop->pet->independences[i];
+ if (isl_union_set_contains(pi->local, array->space))
+ continue;
+
+ order = isl_union_map_subtract(order,
+ isl_union_map_copy(pi->filter));
+ }
+
+ return order;
+}
+
+/* For each array in "prog", store the (untagged) order dependences
+ * derived from the array in array->dep_order.
+ * In particular, consider all references that access the given array
+ * and take the order dependences that have one of these references
+ * as source. (Since an order dependence relates two references to
+ * the same array, the target of these order dependences will also
+ * be one of these references.)
+ * Additionally, store the union of these array->dep_order relations
+ * for all non-scalar arrays in prog->array_order.
+ */
+void collect_order_dependences(struct gpu_prog *prog)
+{
+ int i;
+ isl_space *space;
+ isl_union_map *accesses;
+
+ space = isl_union_map_get_space(prog->read);
+ prog->array_order = isl_union_map_empty(space);
+
+ accesses = isl_union_map_copy(prog->scop->tagged_reads);
+ accesses = isl_union_map_union(accesses,
+ isl_union_map_copy(prog->scop->tagged_may_writes));
+ accesses = isl_union_map_universe(accesses);
+ accesses = isl_union_map_apply_range(accesses,
+ isl_union_map_copy(prog->to_outer));
+
+ for (i = 0; i < prog->n_array; ++i) {
+ struct gpu_array_info *array = &prog->array[i];
+ isl_set *set;
+ isl_union_set *uset;
+ isl_union_map *order;
+
+ set = isl_set_universe(isl_space_copy(array->space));
+ uset = isl_union_set_from_set(set);
+ uset = isl_union_map_domain(
+ isl_union_map_intersect_range(isl_union_map_copy(accesses),
+ uset));
+ order = isl_union_map_copy(prog->scop->tagged_dep_order);
+ order = isl_union_map_intersect_domain(order, uset);
+ order = isl_union_map_zip(order);
+ order = isl_union_set_unwrap(isl_union_map_domain(order));
+ order = remove_independences(prog, array, order);
+ array->dep_order = order;
+
+ if (gpu_array_is_scalar(array) && !array->has_compound_element)
+ continue;
+
+ prog->array_order = isl_union_map_union(prog->array_order,
+ isl_union_map_copy(array->dep_order));
+ }
+
+ isl_union_map_free(accesses);
+}
+
+/* Construct a gpu_array_info for each array referenced by prog->scop and
+ * collect them in prog->array.
+ *
+ * The sizes are based on the extents and the set of possibly accessed
+ * elements by "prog".
+ * If there are any member accesses involved, then they are first mapped
+ * to the outer arrays of structs.
+ *
+ * If we are allowing live range reordering, then also set
+ * the dep_order field. Otherwise leave it NULL.
+ */
+static int collect_array_info(struct gpu_prog *prog)
+{
+ int i;
+ int r = 0;
+ isl_union_set *arrays;
+
+ arrays = isl_union_map_range(isl_union_map_copy(prog->read));
+ arrays = isl_union_set_union(arrays,
+ isl_union_map_range(isl_union_map_copy(prog->may_write)));
+
+ arrays = isl_union_set_apply(arrays,
+ isl_union_map_copy(prog->to_outer));
+
+ arrays = isl_union_set_coalesce(arrays);
+
+ prog->n_array = prog->scop->pet->n_array;
+ prog->array = isl_calloc_array(prog->ctx,
+ struct gpu_array_info, prog->n_array);
+ assert(prog->array);
+ for (i = 0; i < prog->scop->pet->n_array; ++i)
+ if (extract_array_info(prog, &prog->array[i],
+ prog->scop->pet->arrays[i], arrays) < 0)
+ r = -1;
+
+ isl_union_set_free(arrays);
+
+ if (prog->scop->options->live_range_reordering)
+ collect_order_dependences(prog);
+
+ return r;
+}
+
+static void free_array_info(struct gpu_prog *prog)
+{
+ int i, j;
+
+ for (i = 0; i < prog->n_array; ++i) {
+ int n_index = prog->array[i].n_index;
+ free(prog->array[i].type);
+ free(prog->array[i].name);
+ for (j = 0; j < n_index; ++j)
+ isl_pw_aff_free(prog->array[i].bound[j]);
+ isl_space_free(prog->array[i].space);
+ isl_set_free(prog->array[i].extent);
+ free(prog->array[i].bound);
+ free(prog->array[i].refs);
+ isl_union_map_free(prog->array[i].dep_order);
+ }
+ free(prog->array);
+}
+
+/* Check if a gpu array is a scalar. A scalar is a value that is not stored
+ * as an array or through a pointer reference, but as a single data element.
+ * At the moment, scalars are represented as zero-dimensional arrays.
+ * Note that the single data element may be an entire structure.
+ */
+int gpu_array_is_scalar(struct gpu_array_info *array)
+{
+ return array->n_index == 0;
+}
+
+/* Is "array" a read-only scalar?
+ */
+int gpu_array_is_read_only_scalar(struct gpu_array_info *array)
+{
+ return array->read_only_scalar;
+}
+
+/* Does "array" need to be allocated on the device?
+ * If it is a read-only scalar, then it will be passed as an argument
+ * to the kernel and therefore does not require any allocation.
+ * If this device memory is not accessed at all, then it does not
+ * need to be allocated either.
+ */
+int gpu_array_requires_device_allocation(struct gpu_array_info *array)
+{
+ if (gpu_array_is_read_only_scalar(array))
+ return 0;
+ if (!array->global)
+ return 0;
+ return 1;
+}
+
+/* Return the set of parameter values for which the array has a positive
+ * size in all dimensions.
+ * If the sizes are only valid for some parameter values, then those
+ * constraints are also taken into account.
+ */
+__isl_give isl_set *gpu_array_positive_size_guard(struct gpu_array_info *array)
+{
+ int i;
+ isl_space *space;
+ isl_set *guard;
+
+ if (!array)
+ return NULL;
+
+ space = isl_space_params(isl_space_copy(array->space));
+ guard = isl_set_universe(space);
+
+ for (i = 0; i < array->n_index; ++i) {
+ isl_pw_aff *bound;
+ isl_set *guard_i, *zero;
+
+ bound = isl_pw_aff_copy(array->bound[i]);
+ guard_i = isl_pw_aff_nonneg_set(isl_pw_aff_copy(bound));
+ zero = isl_pw_aff_zero_set(bound);
+ guard_i = isl_set_subtract(guard_i, zero);
+ guard = isl_set_intersect(guard, guard_i);
+ }
+
+ return guard;
+}
+
+/* Internal data structure for extract_size_of_type.
+ * "type" specifies the name of the space that we want to extract.
+ * "res" is used to store the subset of that space.
+ */
+struct ppcg_extract_size_data {
+ const char *type;
+ isl_set *res;
+};
+
+/* This function is called for each set in a union_set.
+ * If the name of the set matches data->type, we store the
+ * set in data->res.
+ */
+static isl_stat extract_size_of_type(__isl_take isl_set *size, void *user)
+{
+ struct ppcg_extract_size_data *data = user;
+ const char *name;
+
+ name = isl_set_get_tuple_name(size);
+ if (name && !strcmp(name, data->type)) {
+ data->res = size;
+ return isl_stat_error;
+ }
+
+ isl_set_free(size);
+ return isl_stat_ok;
+}
+
+/* Given a union map { kernel[i] -> *[...] },
+ * return the range in the space called "type" for the kernel with
+ * sequence number "id".
+ */
+static __isl_give isl_set *extract_sizes(__isl_keep isl_union_map *sizes,
+ const char *type, int id)
+{
+ isl_space *space;
+ isl_set *dom;
+ isl_union_set *local_sizes;
+ struct ppcg_extract_size_data data = { type, NULL };
+
+ if (!sizes)
+ return NULL;
+
+ space = isl_union_map_get_space(sizes);
+ space = isl_space_set_from_params(space);
+ space = isl_space_add_dims(space, isl_dim_set, 1);
+ space = isl_space_set_tuple_name(space, isl_dim_set, "kernel");
+ dom = isl_set_universe(space);
+ dom = isl_set_fix_si(dom, isl_dim_set, 0, id);
+
+ local_sizes = isl_union_set_apply(isl_union_set_from_set(dom),
+ isl_union_map_copy(sizes));
+ isl_union_set_foreach_set(local_sizes, &extract_size_of_type, &data);
+ isl_union_set_free(local_sizes);
+ return data.res;
+}
+
+/* Given a singleton set, extract the first (at most *len) elements
+ * of the single integer tuple into *sizes and update *len if needed.
+ */
+static void read_sizes_from_set(__isl_take isl_set *set, int *sizes, int *len)
+{
+ int i;
+ int dim;
+
+ if (!set)
+ return;
+
+ dim = isl_set_dim(set, isl_dim_set);
+ if (dim < *len)
+ *len = dim;
+
+ for (i = 0; i < *len; ++i) {
+ isl_val *v;
+
+ v = isl_set_plain_get_val_if_fixed(set, isl_dim_set, i);
+ assert(v);
+
+ sizes[i] = isl_val_get_num_si(v);
+ isl_val_free(v);
+ }
+
+ isl_set_free(set);
+}
+
+/* Add the map { kernel[id] -> type[sizes] } to gen->used_sizes,
+ * if the option debug->dump_sizes is set.
+ */
+static void set_used_sizes(struct gpu_gen *gen, const char *type, int id,
+ int *sizes, int len)
+{
+ int i;
+ isl_space *space;
+ isl_map *map;
+
+ if (!gen->options->debug->dump_sizes)
+ return;
+
+ space = isl_union_map_get_space(gen->used_sizes);
+ space = isl_space_set_from_params(space);
+ space = isl_space_add_dims(space, isl_dim_set, 1);
+ space = isl_space_set_tuple_name(space, isl_dim_set, "kernel");
+ space = isl_space_from_domain(space);
+ space = isl_space_add_dims(space, isl_dim_out, len);
+ space = isl_space_set_tuple_name(space, isl_dim_out, type);
+
+ map = isl_map_universe(space);
+ map = isl_map_fix_si(map, isl_dim_in, 0, id);
+ for (i = 0; i < len; ++i)
+ map = isl_map_fix_si(map, isl_dim_out, i, sizes[i]);
+
+ gen->used_sizes = isl_union_map_add_map(gen->used_sizes, map);
+}
+
+/* Extract user specified "tile" sizes from the "sizes" command line option,
+ * defaulting to option->tile_size in each dimension.
+ * *tile_len contains the maximum number of tile sizes needed.
+ * Update *tile_len to the number of specified tile sizes, if any, and
+ * return a pointer to the tile sizes (or NULL on error).
+ * Add the effectively used sizes to gen->used_sizes.
+ */
+static int *read_tile_sizes(struct gpu_gen *gen, int *tile_len)
+{
+ int n;
+ int *tile_size;
+ isl_set *size;
+
+ tile_size = isl_alloc_array(gen->ctx, int, *tile_len);
+ if (!tile_size)
+ return NULL;
+ for (n = 0; n < *tile_len; ++n)
+ tile_size[n] = gen->options->tile_size;
+
+ size = extract_sizes(gen->sizes, "tile", gen->kernel_id);
+ read_sizes_from_set(size, tile_size, tile_len);
+ set_used_sizes(gen, "tile", gen->kernel_id, tile_size, *tile_len);
+
+ return tile_size;
+}
+
+/* Extract user specified "block" sizes from the "sizes" command line option,
+ * after filling in some potentially useful defaults.
+ */
+static void read_block_sizes(struct ppcg_kernel *kernel,
+ __isl_keep isl_union_map *sizes)
+{
+ isl_set *size;
+
+ if (kernel->n_block > 3)
+ kernel->n_block = 3;
+ switch (kernel->n_block) {
+ case 1:
+ kernel->block_dim[0] = 512;
+ break;
+ case 2:
+ kernel->block_dim[0] = 32;
+ kernel->block_dim[1] = 16;
+ break;
+ default:
+ kernel->block_dim[0] = 32;
+ kernel->block_dim[1] = 4;
+ kernel->block_dim[2] = 4;
+ break;
+ }
+
+ size = extract_sizes(sizes, "block", kernel->id);
+ read_sizes_from_set(size, kernel->block_dim, &kernel->n_block);
+}
+
+/* Extract user specified "grid" sizes from the "sizes" command line option,
+ * after filling in some potentially useful defaults.
+ */
+static void read_grid_sizes(struct ppcg_kernel *kernel,
+ __isl_keep isl_union_map *sizes)
+{
+ isl_set *size;
+
+ if (kernel->n_grid > 2)
+ kernel->n_grid = 2;
+ switch (kernel->n_grid) {
+ case 1:
+ kernel->grid_dim[0] = 32768;
+ break;
+ default:
+ kernel->grid_dim[0] = 256;
+ kernel->grid_dim[1] = 256;
+ break;
+ }
+
+ size = extract_sizes(sizes, "grid", kernel->id);
+ read_sizes_from_set(size, kernel->grid_dim, &kernel->n_grid);
+}
+
+/* Extract user specified grid and block sizes from the gen->sizes
+ * command line option after filling in some potentially useful defaults.
+ * Store the extracted sizes in "kernel".
+ * Add the effectively used sizes to gen->used_sizes.
+ */
+static void read_grid_and_block_sizes(struct ppcg_kernel *kernel,
+ struct gpu_gen *gen)
+{
+ read_block_sizes(kernel, gen->sizes);
+ read_grid_sizes(kernel, gen->sizes);
+ set_used_sizes(gen, "block", kernel->id,
+ kernel->block_dim, kernel->n_block);
+ set_used_sizes(gen, "grid", kernel->id,
+ kernel->grid_dim, kernel->n_grid);
+}
+
+static void *free_stmts(struct gpu_stmt *stmts, int n)
+{
+ int i;
+
+ if (!stmts)
+ return NULL;
+
+ for (i = 0; i < n; ++i) {
+ struct gpu_stmt_access *access, *next;
+
+ for (access = stmts[i].accesses; access; access = next) {
+ next = access->next;
+ isl_id_free(access->ref_id);
+ isl_map_free(access->access);
+ isl_map_free(access->tagged_access);
+ free(access);
+ }
+
+ isl_id_free(stmts[i].id);
+ }
+ free(stmts);
+
+ return NULL;
+}
+
+/* Add parameters p[i] with identifiers "ids" to "set",
+ * with bounds to 0 <= p[i] < size[i].
+ */
+__isl_give isl_set *add_bounded_parameters(__isl_take isl_set *set,
+ int *size, __isl_keep isl_id_list *ids)
+{
+ int i, len;
+ unsigned nparam;
+
+ len = isl_id_list_n_id(ids);
+ nparam = isl_set_dim(set, isl_dim_param);
+ set = isl_set_add_dims(set, isl_dim_param, len);
+
+ for (i = 0; i < len; ++i) {
+ isl_id *id;
+
+ id = isl_id_list_get_id(ids, i);
+ set = isl_set_set_dim_id(set, isl_dim_param, nparam + i, id);
+ set = isl_set_lower_bound_si(set, isl_dim_param, nparam + i, 0);
+ set = isl_set_upper_bound_si(set, isl_dim_param,
+ nparam + i, size[i] - 1);
+ }
+
+ return set;
+}
+
+/* Add "len" parameters p[i] with identifiers "ids" and intersect "set"
+ * with
+ *
+ * { : 0 <= p[i] < size[i] }
+ *
+ * or an overapproximation.
+ */
+static __isl_give isl_set *add_bounded_parameters_dynamic(
+ __isl_take isl_set *set, __isl_keep isl_multi_pw_aff *size,
+ __isl_keep isl_id_list *ids)
+{
+ int i, len;
+ unsigned nparam;
+ isl_space *space;
+ isl_local_space *ls;
+
+ len = isl_multi_pw_aff_dim(size, isl_dim_out);
+ nparam = isl_set_dim(set, isl_dim_param);
+ set = isl_set_add_dims(set, isl_dim_param, len);
+
+ for (i = 0; i < len; ++i) {
+ isl_id *id;
+
+ id = isl_id_list_get_id(ids, i);
+ set = isl_set_set_dim_id(set, isl_dim_param, nparam + i, id);
+ }
+
+ space = isl_space_params(isl_set_get_space(set));
+ ls = isl_local_space_from_space(space);
+ for (i = 0; i < len; ++i) {
+ isl_pw_aff *param, *size_i, *zero;
+ isl_set *bound;
+
+ param = isl_pw_aff_var_on_domain(isl_local_space_copy(ls),
+ isl_dim_param, nparam + i);
+
+ size_i = isl_multi_pw_aff_get_pw_aff(size, i);
+ bound = isl_pw_aff_lt_set(isl_pw_aff_copy(param), size_i);
+ bound = isl_set_from_basic_set(isl_set_simple_hull(bound));
+ set = isl_set_intersect_params(set, bound);
+
+ zero = isl_pw_aff_zero_on_domain(isl_local_space_copy(ls));
+ bound = isl_pw_aff_ge_set(param, zero);
+ set = isl_set_intersect_params(set, bound);
+ }
+ isl_local_space_free(ls);
+
+ return set;
+}
+
+/* Return the union of all tagged access relations in the group.
+ */
+static __isl_give isl_union_map *group_tagged_access_relation(
+ struct gpu_array_ref_group *group)
+{
+ int i;
+ isl_union_map *access;
+
+ access = isl_union_map_empty(isl_map_get_space(group->access));
+ for (i = 0; i < group->n_ref; ++i) {
+ isl_map *map_i;
+
+ map_i = isl_map_copy(group->refs[i]->tagged_access);
+ access = isl_union_map_union(access,
+ isl_union_map_from_map(map_i));
+ }
+
+ return access;
+}
+
+/* Return the extent of "array", recomputed from the bounds.
+ * The recomputed extent may be simpler than the original extent.
+ */
+static __isl_give isl_set *array_extent(struct gpu_array_info *array)
+{
+ int i;
+ isl_id *id;
+ isl_space *space;
+ isl_local_space *ls;
+ isl_set *extent;
+
+ id = isl_set_get_tuple_id(array->extent);
+ space = isl_set_get_space(array->extent);
+ extent = isl_set_universe(isl_space_copy(space));
+ ls = isl_local_space_from_space(space);
+ for (i = 0; i < array->n_index; ++i) {
+ isl_pw_aff *bound;
+ isl_aff *aff;
+ isl_pw_aff *index;
+ isl_set *lt;
+
+ extent = isl_set_lower_bound_si(extent, isl_dim_set, i, 0);
+
+ aff = isl_aff_var_on_domain(isl_local_space_copy(ls),
+ isl_dim_set, i);
+ index = isl_pw_aff_from_aff(aff);
+ bound = isl_pw_aff_copy(array->bound[i]);
+ bound = isl_pw_aff_from_range(bound);
+ bound = isl_pw_aff_add_dims(bound, isl_dim_in, array->n_index);
+ bound = isl_pw_aff_set_tuple_id(bound, isl_dim_in,
+ isl_id_copy(id));
+ lt = isl_pw_aff_lt_set(index, bound);
+ extent = isl_set_intersect(extent, lt);
+ }
+ isl_local_space_free(ls);
+ isl_id_free(id);
+
+ return extent;
+}
+
+/* Return a map from the first group->depth dimensions of the computed
+ * schedule to the array tile in
+ * global memory that corresponds to the shared memory copy.
+ *
+ * In particular, return a map
+ *
+ * { D[i] -> A[a] }
+ *
+ * with constraints
+ *
+ * tile_offset(i) <= a <= tile_offset(i) + tile_size - 1 (1)
+ *
+ * and
+ *
+ * 0 <= a <= array_size - 1 (2)
+ *
+ * Note that if some stride has been detected (i.e., when
+ * group->shared_tile->bound[i].shift is set), then a in (1) refers
+ * to the shifted and scaled down version.
+ *
+ * Constraints (1) are obtained by mapping the size constraints on the
+ * shared/private memory tile back to the access relation.
+ * Constraints (2) are obtained from the (recomputed) extent.
+ */
+static __isl_give isl_map *group_tile(struct gpu_array_ref_group *group)
+{
+ int i;
+ int n_index = group->array->n_index;
+ isl_map *tile;
+ isl_space *space;
+ isl_set *local;
+ isl_set *extent;
+
+ space = isl_multi_aff_get_space(group->shared_tile->tiling);
+ space = isl_space_range(space);
+ local = isl_set_universe(space);
+ for (i = 0; i < n_index; ++i) {
+ isl_val *bound;
+
+ local = isl_set_lower_bound_si(local, isl_dim_set, i, 0);
+ bound = isl_val_copy(group->shared_tile->bound[i].size);
+ bound = isl_val_sub_ui(bound, 1);
+ local = isl_set_upper_bound_val(local, isl_dim_set, i, bound);
+ }
+ local = isl_set_preimage_multi_aff(local,
+ isl_multi_aff_copy(group->shared_tile->tiling));
+ tile = isl_set_unwrap(local);
+ extent = array_extent(group->array);
+ tile = isl_map_intersect_range(tile, extent);
+
+ return tile;
+}
+
+/* Given a mapping "iterator_map" from the AST schedule to a domain,
+ * return the corresponding mapping from the AST schedule to
+ * to the outer kernel->shared_schedule_dim dimensions of
+ * the schedule computed by PPCG for this kernel.
+ *
+ * Note that kernel->shared_schedule_dim is at least as large as
+ * the largest depth of any array reference group associated to the kernel.
+ * This is needed as the returned schedule is used to extract a mapping
+ * to the outer group->depth dimensions in transform_index.
+ */
+static __isl_give isl_pw_multi_aff *compute_sched_to_shared(
+ struct ppcg_kernel *kernel, __isl_take isl_pw_multi_aff *iterator_map)
+{
+ isl_union_pw_multi_aff *upma;
+ isl_pw_multi_aff *pma;
+ isl_space *space;
+
+ space = isl_space_range(isl_pw_multi_aff_get_space(iterator_map));
+ space = isl_space_from_domain(space);
+ space = isl_space_add_dims(space, isl_dim_out,
+ kernel->shared_schedule_dim);
+
+ upma = isl_union_pw_multi_aff_copy(kernel->shared_schedule);
+ pma = isl_union_pw_multi_aff_extract_pw_multi_aff(upma, space);
+ isl_union_pw_multi_aff_free(upma);
+
+ return isl_pw_multi_aff_pullback_pw_multi_aff(pma, iterator_map);
+}
+
+/* If max_shared_memory is not set to infinity (-1), then make
+ * sure that the total amount of shared memory required by the
+ * array reference groups mapped to shared memory by "kernel"
+ * is no larger than this maximum.
+ *
+ * We apply a greedy approach and discard (keep in global memory)
+ * those groups that would result in a total memory size that
+ * is larger than the maximum.
+ *
+ * This function should be called after any function that may
+ * affect the decision on whether to place a reference group
+ * in private, shared or global memory.
+ */
+static void check_shared_memory_bound(struct ppcg_kernel *kernel)
+{
+ int i, j;
+ isl_val *left, *size;
+
+ if (kernel->options->max_shared_memory < 0)
+ return;
+
+ left = isl_val_int_from_si(kernel->ctx,
+ kernel->options->max_shared_memory);
+
+ for (i = 0; i < kernel->n_array; ++i) {
+ struct gpu_local_array_info *local = &kernel->array[i];
+
+ for (j = 0; j < local->n_group; ++j) {
+ struct gpu_array_ref_group *group;
+
+ group = local->groups[j];
+ if (group->private_tile)
+ continue;
+ if (!group->shared_tile)
+ continue;
+
+ size = gpu_array_tile_size(group->shared_tile);
+ size = isl_val_mul_ui(size, local->array->size);
+
+ if (isl_val_le(size, left)) {
+ left = isl_val_sub(left, size);
+ continue;
+ }
+ isl_val_free(size);
+
+ group->shared_tile =
+ gpu_array_tile_free(group->shared_tile);
+ }
+ }
+
+ isl_val_free(left);
+}
+
+/* Mark all arrays of "kernel" that have an array reference group
+ * that is not mapped to private or shared memory as
+ * accessing the corresponding global device memory.
+ */
+static void mark_global_arrays(struct ppcg_kernel *kernel)
+{
+ int i, j;
+
+ for (i = 0; i < kernel->n_array; ++i) {
+ struct gpu_local_array_info *local = &kernel->array[i];
+
+ if (local->global)
+ continue;
+ for (j = 0; j < local->n_group; ++j) {
+ if (gpu_array_ref_group_tile(local->groups[j]))
+ continue;
+
+ local->global = 1;
+ local->array->global = 1;
+ break;
+ }
+ }
+}
+
+/* Compute a tiling for all the array reference groups in "kernel".
+ */
+static void compute_group_tilings(struct ppcg_kernel *kernel)
+{
+ int i, j;
+
+ for (i = 0; i < kernel->n_array; ++i) {
+ struct gpu_local_array_info *array = &kernel->array[i];
+
+ for (j = 0; j < array->n_group; ++j)
+ gpu_array_ref_group_compute_tiling(array->groups[j]);
+ }
+}
+
+/* Compute the size of a bounding box around the origin and "set",
+ * where "set" is assumed to contain only non-negative elements.
+ * In particular, compute the maximal value of "set" in each direction
+ * and add one.
+ */
+static __isl_give isl_multi_pw_aff *extract_size(__isl_take isl_set *set,
+ __isl_take isl_set *context)
+{
+ int i, n;
+ isl_multi_pw_aff *mpa;
+
+ context = isl_set_params(context);
+ n = isl_set_dim(set, isl_dim_set);
+ mpa = isl_multi_pw_aff_zero(isl_set_get_space(set));
+ for (i = 0; i < n; ++i) {
+ isl_space *space;
+ isl_aff *one;
+ isl_pw_aff *bound;
+
+ bound = isl_set_dim_max(isl_set_copy(set), i);
+ bound = isl_pw_aff_coalesce(bound);
+ bound = isl_pw_aff_gist(bound, isl_set_copy(context));
+
+ space = isl_pw_aff_get_domain_space(bound);
+ one = isl_aff_zero_on_domain(isl_local_space_from_space(space));
+ one = isl_aff_add_constant_si(one, 1);
+ bound = isl_pw_aff_add(bound, isl_pw_aff_from_aff(one));
+ mpa = isl_multi_pw_aff_set_pw_aff(mpa, i, bound);
+ }
+ isl_set_free(set);
+ isl_set_free(context);
+
+ return mpa;
+}
+
+/* Compute the effective grid size as a list of the sizes in each dimension.
+ *
+ * The grid size specified by the user or set by default
+ * in read_grid_sizes() and applied by the block filter,
+ * may be too large for the given code in the sense that
+ * it may contain blocks that don't need to execute anything.
+ * We therefore don't return this grid size, but instead the
+ * smallest grid size that ensures that all blocks that actually
+ * execute code are included in the grid.
+ *
+ * We first extract a description of the grid, i.e., the possible values
+ * of the block ids, from the domain elements in "domain" and
+ * kernel->block_filter.
+ * The block ids are parameters in kernel->block_filter.
+ * We simply need to change them into set dimensions.
+ *
+ * Then, for each block dimension, we compute the maximal value of the block id
+ * and add one.
+ */
+static __isl_give isl_multi_pw_aff *extract_grid_size(
+ struct ppcg_kernel *kernel, __isl_take isl_union_set *domain)
+{
+ int i;
+ isl_set *grid;
+
+ domain = isl_union_set_intersect(domain,
+ isl_union_set_copy(kernel->block_filter));
+ grid = isl_union_set_params(domain);
+ grid = isl_set_from_params(grid);
+ grid = isl_set_add_dims(grid, isl_dim_set, kernel->n_grid);
+ for (i = 0; i < kernel->n_grid; ++i) {
+ int pos;
+ isl_id *id;
+
+ id = isl_id_list_get_id(kernel->block_ids, i);
+ pos = isl_set_find_dim_by_id(grid, isl_dim_param, id);
+ isl_id_free(id);
+ assert(pos >= 0);
+ grid = isl_set_equate(grid, isl_dim_param, pos, isl_dim_set, i);
+ grid = isl_set_project_out(grid, isl_dim_param, pos, 1);
+ }
+
+ return extract_size(grid, isl_set_copy(kernel->context));
+}
+
+/* Compute the size of a fixed bounding box around the origin and "set",
+ * where "set" is assumed to contain only non-negative elements,
+ * and store the results in "size".
+ * In particular, compute the maximal value of "set" in each direction
+ * and add one.
+ */
+static void extract_fixed_size(__isl_take isl_set *set, int *size)
+{
+ int i, n;
+ isl_local_space *ls;
+ isl_aff *obj;
+
+ n = isl_set_dim(set, isl_dim_set);
+ ls = isl_local_space_from_space(isl_set_get_space(set));
+ obj = isl_aff_zero_on_domain(ls);
+ for (i = 0; i < n; ++i) {
+ isl_val *max;
+
+ obj = isl_aff_set_coefficient_si(obj, isl_dim_in, i, 1);
+ max = isl_set_max_val(set, obj);
+ size[i] = isl_val_get_num_si(max) + 1;
+ isl_val_free(max);
+ obj = isl_aff_set_coefficient_si(obj, isl_dim_in, i, 0);
+ }
+ isl_aff_free(obj);
+ isl_set_free(set);
+}
+
+/* Compute the effective block size as a list of the sizes in each dimension
+ * and store the sizes in kernel->block_dim.
+ *
+ * The block size specified by the user or set by default
+ * in read_block_sizes() and applied by the thread filter,
+ * may be too large for the given code in the sense that
+ * it may contain threads that don't need to execute anything.
+ * We therefore update this block size in kernel->block_dim
+ * to the smallest block size that ensures that all threads
+ * that actually execute code are included in the block.
+ *
+ * The possible values of the thread ids is obtained from
+ * the domain elements "domain" and kernel->thread_filter.
+ * The current implementation eliminates all parameters, ensuring
+ * that the size is a fixed constant in each dimension.
+ * In principle we could also compute parametric sizes.
+ * We would have to make sure to project out all b%d and t%d parameters,
+ * however.
+ */
+static void extract_block_size(struct ppcg_kernel *kernel,
+ __isl_take isl_union_set *domain)
+{
+ int i;
+ int nparam;
+ isl_set *block;
+
+ domain = isl_union_set_intersect(domain,
+ isl_union_set_copy(kernel->thread_filter));
+ block = isl_union_set_params(domain);
+ block = isl_set_from_params(block);
+ block = isl_set_add_dims(block, isl_dim_set, kernel->n_block);
+ for (i = 0; i < kernel->n_block; ++i) {
+ int pos;
+ isl_id *id;
+
+ id = isl_id_list_get_id(kernel->thread_ids, i);
+ pos = isl_set_find_dim_by_id(block, isl_dim_param, id);
+ isl_id_free(id);
+ assert(pos >= 0);
+ block = isl_set_equate(block, isl_dim_param, pos,
+ isl_dim_set, i);
+ }
+ nparam = isl_set_dim(block, isl_dim_param);
+ block = isl_set_project_out(block, isl_dim_param, 0, nparam);
+
+ extract_fixed_size(block, kernel->block_dim);
+}
+
+struct ppcg_kernel *ppcg_kernel_free(struct ppcg_kernel *kernel)
+{
+ int i, j;
+
+ if (!kernel)
+ return NULL;
+
+ isl_id_list_free(kernel->block_ids);
+ isl_id_list_free(kernel->thread_ids);
+ isl_multi_pw_aff_free(kernel->grid_size);
+ isl_set_free(kernel->context);
+ isl_union_set_free(kernel->core);
+ isl_union_set_free(kernel->arrays);
+ isl_space_free(kernel->space);
+ isl_ast_node_free(kernel->tree);
+ isl_union_set_free(kernel->block_filter);
+ isl_union_set_free(kernel->thread_filter);
+ isl_union_pw_multi_aff_free(kernel->shared_schedule);
+ isl_union_set_free(kernel->sync_writes);
+
+ for (i = 0; i < kernel->n_array; ++i) {
+ struct gpu_local_array_info *array = &kernel->array[i];
+
+ for (j = 0; j < array->n_group; ++j)
+ gpu_array_ref_group_free(array->groups[j]);
+ free(array->groups);
+
+ isl_pw_aff_list_free(array->bound);
+ }
+ free(kernel->array);
+
+ for (i = 0; i < kernel->n_var; ++i) {
+ free(kernel->var[i].name);
+ isl_vec_free(kernel->var[i].size);
+ }
+ free(kernel->var);
+
+ free(kernel);
+
+ return NULL;
+}
+
+/* Wrapper around ppcg_kernel_free for use as a isl_id_set_free_user callback.
+ */
+static void ppcg_kernel_free_wrap(void *user)
+{
+ struct ppcg_kernel *kernel = user;
+
+ ppcg_kernel_free(kernel);
+}
+
+static void create_kernel_var(isl_ctx *ctx, struct gpu_array_ref_group *group,
+ struct ppcg_kernel_var *var)
+{
+ int j;
+ struct gpu_array_tile *tile;
+ isl_printer *p;
+ char *name;
+
+ var->array = group->array;
+
+ tile = group->private_tile;
+ var->type = ppcg_access_private;
+ if (!tile) {
+ tile = group->shared_tile;
+ var->type = ppcg_access_shared;
+ }
+
+ p = isl_printer_to_str(ctx);
+ p = gpu_array_ref_group_print_name(group, p);
+ var->name = isl_printer_get_str(p);
+ isl_printer_free(p);
+
+ var->size = isl_vec_alloc(ctx, group->array->n_index);
+
+ for (j = 0; j < group->array->n_index; ++j)
+ var->size = isl_vec_set_element_val(var->size, j,
+ isl_val_copy(tile->bound[j].size));
+}
+
+static int create_kernel_vars(struct ppcg_kernel *kernel)
+{
+ int i, j, n;
+
+ n = 0;
+ for (i = 0; i < kernel->n_array; ++i) {
+ struct gpu_local_array_info *array = &kernel->array[i];
+
+ for (j = 0; j < array->n_group; ++j) {
+ struct gpu_array_ref_group *group = array->groups[j];
+ if (group->private_tile || group->shared_tile)
+ ++n;
+ }
+ }
+
+ kernel->n_var = n;
+ kernel->var = isl_calloc_array(kernel->ctx, struct ppcg_kernel_var, n);
+ if (!kernel->var)
+ return -1;
+
+ n = 0;
+ for (i = 0; i < kernel->n_array; ++i) {
+ struct gpu_local_array_info *array = &kernel->array[i];
+
+ for (j = 0; j < array->n_group; ++j) {
+ struct gpu_array_ref_group *group = array->groups[j];
+ if (!group->private_tile && !group->shared_tile)
+ continue;
+ create_kernel_var(kernel->ctx, group, &kernel->var[n]);
+ ++n;
+ }
+ }
+
+ return 0;
+}
+
+/* Replace "pa" by the zero function defined over the universe domain
+ * in the space of "pa".
+ */
+static __isl_give isl_pw_aff *set_universally_zero(__isl_take isl_pw_aff *pa)
+{
+ isl_space *space;
+ isl_aff *zero;
+
+ space = isl_space_domain(isl_pw_aff_get_space(pa));
+ isl_pw_aff_free(pa);
+ zero = isl_aff_zero_on_domain(isl_local_space_from_space(space));
+
+ return isl_pw_aff_from_aff(zero);
+}
+
+/* The sizes of the arrays on the host that have been computed by
+ * extract_array_info may depend on the parameters. Use the extra
+ * constraints on the parameters that are valid at "host_domain"
+ * to simplify these expressions and store the results in kernel->array.
+ *
+ * We only need these localized bounds for arrays that are accessed
+ * by the current kernel. If we have found at least one reference group
+ * then the array is accessed by the kernel.
+ *
+ * The resulting sizes may be functions that are nowhere defined
+ * in case the access function cannot possibly access anything inside
+ * the kernel for some reason. If so, they are replaced by the zero
+ * function. Since the access function cannot actually access anything,
+ * there is no harm in printing the array sizes as zero.
+ */
+static void localize_bounds(struct ppcg_kernel *kernel,
+ __isl_keep isl_set *host_domain)
+{
+ int i, j;
+ isl_set *context;
+
+ context = isl_set_copy(host_domain);
+ context = isl_set_params(context);
+
+ for (i = 0; i < kernel->n_array; ++i) {
+ struct gpu_local_array_info *local = &kernel->array[i];
+ isl_pw_aff_list *bound;
+ int n_index;
+
+ if (local->n_group == 0)
+ continue;
+
+ n_index = local->array->n_index;
+ bound = isl_pw_aff_list_alloc(kernel->ctx, n_index);
+
+ for (j = 0; j < n_index; ++j) {
+ isl_pw_aff *pwaff;
+ int empty;
+
+ pwaff = isl_pw_aff_copy(local->array->bound[j]);
+ pwaff = isl_pw_aff_gist(pwaff, isl_set_copy(context));
+ empty = isl_pw_aff_is_empty(pwaff);
+ if (empty < 0)
+ pwaff = isl_pw_aff_free(pwaff);
+ else if (empty)
+ pwaff = set_universally_zero(pwaff);
+ bound = isl_pw_aff_list_add(bound, pwaff);
+ }
+
+ local->n_index = n_index;
+ local->bound = bound;
+ }
+ isl_set_free(context);
+}
+
+/* Create the array of gpu_local_array_info structures "array"
+ * inside "kernel". The number of elements in this array is
+ * the same as the number of arrays in "prog".
+ * Initialize the "array" field of each local array to point
+ * to the corresponding array in "prog".
+ */
+static struct ppcg_kernel *ppcg_kernel_create_local_arrays(
+ struct ppcg_kernel *kernel, struct gpu_prog *prog)
+{
+ int i;
+ isl_ctx *ctx;
+
+ ctx = isl_set_get_ctx(prog->context);
+ kernel->array = isl_calloc_array(ctx,
+ struct gpu_local_array_info, prog->n_array);
+ if (!kernel->array)
+ return ppcg_kernel_free(kernel);
+ kernel->n_array = prog->n_array;
+
+ for (i = 0; i < prog->n_array; ++i)
+ kernel->array[i].array = &prog->array[i];
+
+ return kernel;
+}
+
+/* Does "kernel" need to be passed an argument corresponding to array "i"?
+ *
+ * The argument is only needed if the kernel accesses this device memory.
+ */
+int ppcg_kernel_requires_array_argument(struct ppcg_kernel *kernel, int i)
+{
+ return kernel->array[i].global;
+}
+
+/* Find the element in gen->stmt that has the given "id".
+ * Return NULL if no such gpu_stmt can be found.
+ */
+static struct gpu_stmt *find_stmt(struct gpu_prog *prog, __isl_keep isl_id *id)
+{
+ int i;
+
+ for (i = 0; i < prog->n_stmts; ++i) {
+ if (id == prog->stmts[i].id)
+ break;
+ }
+
+ return i < prog->n_stmts ? &prog->stmts[i] : NULL;
+}
+
+void ppcg_kernel_stmt_free(void *user)
+{
+ int i;
+ struct ppcg_kernel_stmt *stmt = user;
+
+ if (!stmt)
+ return;
+
+ switch (stmt->type) {
+ case ppcg_kernel_copy:
+ isl_ast_expr_free(stmt->u.c.index);
+ isl_ast_expr_free(stmt->u.c.local_index);
+ break;
+ case ppcg_kernel_domain:
+ isl_id_to_ast_expr_free(stmt->u.d.ref2expr);
+ break;
+ case ppcg_kernel_sync:
+ break;
+ }
+
+ free(stmt);
+}
+
+/* Return the gpu_stmt_access in the list "accesses" that corresponds
+ * to "ref_id".
+ */
+static struct gpu_stmt_access *find_access(struct gpu_stmt_access *accesses,
+ __isl_keep isl_id *ref_id)
+{
+ struct gpu_stmt_access *access;
+
+ for (access = accesses; access; access = access->next)
+ if (access->ref_id == ref_id)
+ return access;
+
+ return NULL;
+}
+
+/* Return the index of the array called "name" in the list of arrays.
+ */
+static int find_array_index(struct ppcg_kernel *kernel, const char *name)
+{
+ int i;
+
+ for (i = 0; i < kernel->n_array; ++i)
+ if (!strcmp(name, kernel->array[i].array->name))
+ return i;
+
+ return -1;
+}
+
+/* Internal data structure for the index and AST expression transformation
+ * callbacks for pet_stmt_build_ast_exprs.
+ *
+ * "kernel" is the kernel for which are computing AST expressions and
+ * may be NULL if we are not inside a kernel.
+ * "accesses" is the list of gpu_stmt_access in the statement.
+ * "iterator_map" expresses the statement iterators in terms of
+ * the AST loop iterators.
+ * "sched2shared" expresses the outer shared_schedule_dim dimensions of
+ * the kernel schedule in terms of the AST loop iterators and
+ * may be NULL if we are not inside a kernel.
+ *
+ * The following fields are set in transform_index and used in transform_expr.
+ * "array" is the array that is being accessed.
+ * "global" is set if the global array is accessed (rather than
+ * shared/private memory).
+ * "local_array" refers to information on the array specialized
+ * to the current kernel.
+ */
+struct ppcg_transform_data {
+ struct ppcg_kernel *kernel;
+ struct gpu_stmt_access *accesses;
+ isl_pw_multi_aff *iterator_map;
+ isl_pw_multi_aff *sched2shared;
+
+ struct gpu_array_info *array;
+ int global;
+ struct gpu_local_array_info *local_array;
+};
+
+/* Return a pointer to the gpu_array_ref_group in "local"
+ * that contains the reference "access".
+ * Return NULL if no such group can be found.
+ */
+static struct gpu_array_ref_group *find_ref_group(
+ struct gpu_local_array_info *local, struct gpu_stmt_access *access)
+{
+ int i, j;
+
+ for (i = 0; i < local->n_group; ++i) {
+ struct gpu_array_ref_group *group = local->groups[i];
+
+ for (j = 0; j < group->n_ref; ++j)
+ if (group->refs[j] == access)
+ return group;
+ }
+
+ return NULL;
+}
+
+/* Index transformation callback for pet_stmt_build_ast_exprs.
+ *
+ * "index" expresses the array indices in terms of statement iterators
+ *
+ * We first reformulate "index" in terms of the AST loop iterators.
+ * Then we check if we are accessing the global array or
+ * a shared/private copy. In particular, if we are not inside a kernel
+ * then we must be accessing a global array.
+ * In the former case, we simply return
+ * the updated index. If "index" is an affine expression rather
+ * than an array access, then we also return the updated index here.
+ *
+ * If no reference groups have been computed for the array,
+ * then we can only be accessing the global array.
+ *
+ * Otherwise, we apply the tiling to the index.
+ * This tiling is of the form
+ *
+ * [D -> A] -> T
+ *
+ * where D corresponds to the outer group->depth dimensions of
+ * the kernel schedule.
+ * The index is of the form
+ *
+ * L -> A
+ *
+ * We update the tiling to refer to the AST loop iterators
+ *
+ * [L -> A] -> T
+ *
+ * and modify index to keep track of those iterators
+ *
+ * L -> [L -> A]
+ *
+ * Combining these two yields a tiled index expression in terms
+ * of the AST loop iterators
+ *
+ * L -> T
+ */
+static __isl_give isl_multi_pw_aff *transform_index(
+ __isl_take isl_multi_pw_aff *index, __isl_keep isl_id *ref_id,
+ void *user)
+{
+ struct ppcg_transform_data *data = user;
+ struct gpu_stmt_access *access;
+ struct gpu_array_ref_group *group;
+ struct gpu_array_tile *tile;
+ isl_pw_multi_aff *iterator_map;
+ int i;
+ int dim;
+ const char *name;
+ isl_space *space;
+ isl_multi_pw_aff *tiling;
+ isl_pw_multi_aff *pma;
+ isl_multi_pw_aff *mpa;
+ isl_pw_multi_aff *sched2depth;
+
+ data->array = NULL;
+
+ iterator_map = isl_pw_multi_aff_copy(data->iterator_map);
+ index = isl_multi_pw_aff_pullback_pw_multi_aff(index, iterator_map);
+
+ if (!data->kernel)
+ return index;
+
+ access = find_access(data->accesses, ref_id);
+ if (!access)
+ return index;
+ if (!isl_map_has_tuple_name(access->access, isl_dim_out))
+ return index;
+
+ name = get_outer_array_name(access->access);
+ i = find_array_index(data->kernel, name);
+ if (i < 0)
+ isl_die(isl_multi_pw_aff_get_ctx(index), isl_error_internal,
+ "cannot find array",
+ return isl_multi_pw_aff_free(index));
+ data->local_array = &data->kernel->array[i];
+ data->array = data->local_array->array;
+
+ group = find_ref_group(data->local_array, access);
+ if (!group) {
+ data->global = 1;
+ return index;
+ }
+
+ tile = group->private_tile;
+ if (!tile)
+ tile = group->shared_tile;
+ data->global = !tile;
+ if (!tile)
+ return index;
+
+ space = isl_space_range(isl_multi_pw_aff_get_space(index));
+ space = isl_space_map_from_set(space);
+ pma = isl_pw_multi_aff_identity(space);
+ sched2depth = isl_pw_multi_aff_copy(data->sched2shared);
+ dim = isl_pw_multi_aff_dim(sched2depth, isl_dim_out);
+ sched2depth = isl_pw_multi_aff_drop_dims(sched2depth, isl_dim_out,
+ group->depth, dim - group->depth);
+ pma = isl_pw_multi_aff_product(sched2depth, pma);
+ tiling = isl_multi_pw_aff_from_multi_aff(
+ isl_multi_aff_copy(tile->tiling));
+ tiling = isl_multi_pw_aff_pullback_pw_multi_aff(tiling, pma);
+
+ space = isl_space_domain(isl_multi_pw_aff_get_space(index));
+ space = isl_space_map_from_set(space);
+ mpa = isl_multi_pw_aff_identity(space);
+ index = isl_multi_pw_aff_range_product(mpa, index);
+ index = isl_multi_pw_aff_pullback_multi_pw_aff(tiling, index);
+
+ return index;
+}
+
+/* Dereference "expr" by adding an index [0].
+ * The original "expr" is assumed not to have any indices.
+ *
+ * If "expr" is a member access, then the dereferencing needs
+ * to be applied to the structure argument of this member access.
+ */
+static __isl_give isl_ast_expr *dereference(__isl_take isl_ast_expr *expr)
+{
+ isl_ctx *ctx;
+ isl_ast_expr *arg0, *res;
+ isl_ast_expr_list *list;
+
+ arg0 = isl_ast_expr_get_op_arg(expr, 0);
+ if (!arg0)
+ return isl_ast_expr_free(expr);
+ if (isl_ast_expr_get_type(arg0) == isl_ast_expr_op &&
+ isl_ast_expr_get_op_type(arg0) == isl_ast_op_member) {
+ isl_ast_expr *arg;
+
+ arg = isl_ast_expr_get_op_arg(arg0, 0);
+ arg = dereference(arg);
+ arg0 = isl_ast_expr_set_op_arg(arg0, 0, arg);
+ expr = isl_ast_expr_set_op_arg(expr, 0, arg0);
+
+ return expr;
+ }
+ isl_ast_expr_free(arg0);
+
+ ctx = isl_ast_expr_get_ctx(expr);
+ res = isl_ast_expr_from_val(isl_val_zero(ctx));
+ list = isl_ast_expr_list_from_ast_expr(res);
+ res = isl_ast_expr_get_op_arg(expr, 0);
+ res = isl_ast_expr_access(res, list);
+ isl_ast_expr_free(expr);
+
+ return res;
+}
+
+/* Linearize the index expression "expr" based on the array bounds
+ * of "array".
+ *
+ * That is, transform expression
+ *
+ * A[i_0][i_1]...[i_n]
+ *
+ * to
+ *
+ * A[(..((i_0 * b_1 + i_1) ... ) * b_n + i_n]
+ *
+ * where b_0, b_1, ..., b_n are the bounds on the array.
+ *
+ * If the base of "expr" is a member access, then the linearization needs
+ * to be applied to the structure argument of this member access.
+ *
+ * In the base case, if "expr" has no arguments (other than the name of
+ * the array), then we are passing an entire array to a function.
+ * In this case, there is nothing to linearize.
+ * Note that at this point an expression with no arguments can
+ * only be an entire array because the scalar case and
+ * the case of single struct are handled by the caller.
+ *
+ * If the number of specified index expressions in "expr"
+ * is smaller than the dimension of the accessed array,
+ * then the missing i_j also do not appear in the linearized expression.
+ * Furthermore, since such an expression does not refer to a single
+ * element while the default linearized expression would refer to
+ * a single element, we return the expression
+ *
+ * A + (..((i_0 * b_1 + i_1) ... ) * b_n]
+ *
+ * instead. Note that because of the special case handling above,
+ * we can assume here that here that there is at least one index expression.
+ */
+__isl_give isl_ast_expr *gpu_local_array_info_linearize_index(
+ struct gpu_local_array_info *array, __isl_take isl_ast_expr *expr)
+{
+ int i, n;
+ isl_ctx *ctx;
+ isl_set *context;
+ isl_ast_expr *arg0;
+ isl_ast_expr *res;
+ isl_ast_expr_list *list;
+ isl_ast_build *build;
+
+ arg0 = isl_ast_expr_get_op_arg(expr, 0);
+ if (isl_ast_expr_get_type(arg0) == isl_ast_expr_op &&
+ isl_ast_expr_get_op_type(arg0) == isl_ast_op_member) {
+ isl_ast_expr *arg;
+
+ arg = isl_ast_expr_get_op_arg(arg0, 0);
+ arg = gpu_local_array_info_linearize_index(array, arg);
+ arg0 = isl_ast_expr_set_op_arg(arg0, 0, arg);
+ expr = isl_ast_expr_set_op_arg(expr, 0, arg0);
+
+ return expr;
+ }
+ isl_ast_expr_free(arg0);
+
+ if (isl_ast_expr_get_op_n_arg(expr) == 1)
+ return expr;
+
+ ctx = isl_ast_expr_get_ctx(expr);
+ context = isl_set_universe(isl_space_params_alloc(ctx, 0));
+ build = isl_ast_build_from_context(context);
+
+ n = isl_ast_expr_get_op_n_arg(expr);
+ res = isl_ast_expr_get_op_arg(expr, 1);
+ for (i = 1; i < array->n_index; ++i) {
+ isl_pw_aff *bound_i;
+ isl_ast_expr *expr_i;
+
+ bound_i = isl_pw_aff_list_get_pw_aff(array->bound, i);
+ expr_i = isl_ast_build_expr_from_pw_aff(build, bound_i);
+ res = isl_ast_expr_mul(res, expr_i);
+
+ if (i + 1 >= n)
+ continue;
+ expr_i = isl_ast_expr_get_op_arg(expr, i + 1);
+ res = isl_ast_expr_add(res, expr_i);
+ }
+
+ isl_ast_build_free(build);
+
+ if (1 + array->n_index > n) {
+ res = isl_ast_expr_add(isl_ast_expr_get_op_arg(expr, 0), res);
+ } else {
+ list = isl_ast_expr_list_from_ast_expr(res);
+ res = isl_ast_expr_get_op_arg(expr, 0);
+ res = isl_ast_expr_access(res, list);
+ }
+
+ isl_ast_expr_free(expr);
+
+ return res;
+}
+
+/* AST expression transformation callback for pet_stmt_build_ast_exprs.
+ *
+ * If the AST expression refers to an array that is not accessed
+ * at all, then this means the value of the expression is not used,
+ * so we might as well print zero (NULL pointer) instead.
+ *
+ * If the AST expression refers to a global scalar that is not
+ * a read-only scalar, then its address was passed to the kernel and
+ * we need to dereference it.
+ *
+ * If the AST expression refers to an access to a global array,
+ * then we linearize the access exploiting the bounds in data->local_array.
+ */
+static __isl_give isl_ast_expr *transform_expr(__isl_take isl_ast_expr *expr,
+ __isl_keep isl_id *id, void *user)
+{
+ struct ppcg_transform_data *data = user;
+
+ if (!data->array)
+ return expr;
+ if (!data->array->accessed) {
+ isl_ctx *ctx;
+
+ ctx = isl_ast_expr_get_ctx(expr);
+ isl_ast_expr_free(expr);
+ return isl_ast_expr_from_val(isl_val_zero(ctx));
+ }
+ if (gpu_array_is_read_only_scalar(data->array))
+ return expr;
+ if (!data->global)
+ return expr;
+ if (data->array->n_index == 0)
+ return dereference(expr);
+ if (!data->array->linearize)
+ return expr;
+
+ return gpu_local_array_info_linearize_index(data->local_array, expr);
+}
+
+/* This function is called for each instance of a user statement
+ * in the kernel "kernel", identified by "gpu_stmt".
+ * "kernel" may be NULL if we are not inside a kernel.
+ *
+ * We attach a struct ppcg_kernel_stmt to the "node", containing
+ * a computed AST expression for each access, through an annotation
+ * with name "user".
+ * These AST expressions are computed from iterator_map,
+ * which expresses the domain
+ * elements in terms of the generated loops, and sched2shared,
+ * which expresses the outer shared_schedule_dim dimensions of
+ * the kernel schedule computed by PPCG in terms of the generated loops.
+ */
+static __isl_give isl_ast_node *create_domain_leaf(
+ struct ppcg_kernel *kernel, __isl_take isl_ast_node *node,
+ __isl_keep isl_ast_build *build, struct gpu_stmt *gpu_stmt)
+{
+ struct ppcg_transform_data data;
+ struct ppcg_kernel_stmt *stmt;
+ isl_ctx *ctx;
+ isl_id *id;
+ isl_pw_multi_aff *sched2shared;
+ isl_map *map;
+ isl_pw_multi_aff *iterator_map;
+ isl_union_map *schedule;
+
+ if (!node)
+ return NULL;
+ ctx = isl_ast_node_get_ctx(node);
+
+ stmt = isl_calloc_type(ctx, struct ppcg_kernel_stmt);
+ if (!stmt)
+ return isl_ast_node_free(node);
+
+ schedule = isl_ast_build_get_schedule(build);
+ map = isl_map_reverse(isl_map_from_union_map(schedule));
+ iterator_map = isl_pw_multi_aff_from_map(map);
+ if (kernel)
+ sched2shared = compute_sched_to_shared(kernel,
+ isl_pw_multi_aff_copy(iterator_map));
+ else
+ sched2shared = NULL;
+
+ stmt->type = ppcg_kernel_domain;
+ stmt->u.d.stmt = gpu_stmt;
+
+ data.kernel = kernel;
+ data.accesses = stmt->u.d.stmt->accesses;
+ data.iterator_map = iterator_map;
+ data.sched2shared = sched2shared;
+ stmt->u.d.ref2expr = pet_stmt_build_ast_exprs(stmt->u.d.stmt->stmt,
+ build, &transform_index, &data,
+ &transform_expr, &data);
+
+ isl_pw_multi_aff_free(iterator_map);
+ isl_pw_multi_aff_free(sched2shared);
+
+ id = isl_id_alloc(ctx, "user", stmt);
+ id = isl_id_set_free_user(id, &ppcg_kernel_stmt_free);
+ return isl_ast_node_set_annotation(node, id);
+}
+
+/* This function is called for each statement node in the AST
+ * for copying to or from shared/private memory.
+ * Attach a pointer to a ppcg_kernel_stmt representing the copy
+ * statement to the node.
+ * The statement name is "read" or "write", depending on whether we are
+ * reading from global memory or writing to global memory.
+ *
+ * The schedule is of the form
+ *
+ * type[D -> A] -> L
+ *
+ * where D corresponds to the outer group->depth dimensions of
+ * the kernel schedule, A to the global array and L to the outer
+ * generated AST schedule.
+ * We compute the inverse and strip off the type, resulting in
+ *
+ * L -> [D -> A]
+ *
+ * We combine this mapping with on the one hand the projection
+ *
+ * [D -> A] -> A
+ *
+ * and on the other hand the group tiling
+ *
+ * [D -> A] -> T
+ *
+ * resulting in
+ *
+ * L -> A and L -> T
+ *
+ * and store the corresponding expressions in stmt->index and stmt->local_index,
+ * where stmt points to the ppcg_kernel_stmt that is attached to the node.
+ */
+static __isl_give isl_ast_node *create_access_leaf(struct ppcg_kernel *kernel,
+ struct gpu_array_ref_group *group, __isl_take isl_ast_node *node,
+ __isl_keep isl_ast_build *build)
+{
+ struct ppcg_kernel_stmt *stmt;
+ struct gpu_array_tile *tile;
+ isl_id *id;
+ isl_ast_expr *expr;
+ isl_space *space;
+ isl_map *access;
+ isl_pw_multi_aff *pma, *pma2;
+ const char *type;
+
+ stmt = isl_calloc_type(kernel->ctx, struct ppcg_kernel_stmt);
+ if (!stmt)
+ return isl_ast_node_free(node);
+
+ access = isl_map_from_union_map(isl_ast_build_get_schedule(build));
+ type = isl_map_get_tuple_name(access, isl_dim_in);
+ stmt->u.c.read = !strcmp(type, "read");
+ access = isl_map_reverse(access);
+ pma = isl_pw_multi_aff_from_map(access);
+ pma = isl_pw_multi_aff_reset_tuple_id(pma, isl_dim_out);
+
+ space = isl_space_range(isl_pw_multi_aff_get_space(pma));
+ space = isl_space_unwrap(space);
+ pma2 = isl_pw_multi_aff_range_map(space);
+ pma2 = isl_pw_multi_aff_pullback_pw_multi_aff(pma2,
+ isl_pw_multi_aff_copy(pma));
+ expr = isl_ast_build_access_from_pw_multi_aff(build, pma2);
+ stmt->u.c.index = expr;
+
+ tile = gpu_array_ref_group_tile(group);
+ pma2 = isl_pw_multi_aff_from_multi_aff(
+ isl_multi_aff_copy(tile->tiling));
+ pma2 = isl_pw_multi_aff_pullback_pw_multi_aff(pma2, pma);
+ expr = isl_ast_build_access_from_pw_multi_aff(build, pma2);
+ stmt->u.c.local_index = expr;
+
+ stmt->u.c.array = group->array;
+ stmt->u.c.local_array = group->local_array;
+ stmt->type = ppcg_kernel_copy;
+
+ id = isl_id_alloc(kernel->ctx, NULL, stmt);
+ id = isl_id_set_free_user(id, &ppcg_kernel_stmt_free);
+ return isl_ast_node_set_annotation(node, id);
+}
+
+/* Create a synchronization ppcg_kernel_stmt and
+ * attach it to the node "node" representing the synchronization.
+ */
+static __isl_give isl_ast_node *create_sync_leaf(
+ struct ppcg_kernel *kernel, __isl_take isl_ast_node *node,
+ __isl_keep isl_ast_build *build)
+{
+ struct ppcg_kernel_stmt *stmt;
+ isl_id *id;
+
+ stmt = isl_calloc_type(kernel->ctx, struct ppcg_kernel_stmt);
+ if (!stmt)
+ return isl_ast_node_free(node);
+
+ stmt->type = ppcg_kernel_sync;
+ id = isl_id_alloc(kernel->ctx, NULL, stmt);
+ id = isl_id_set_free_user(id, &ppcg_kernel_stmt_free);
+ return isl_ast_node_set_annotation(node, id);
+}
+
+/* Internal data structure for at_domain.
+ *
+ * "prog" represents the entire scop.
+ * "kernel" points to the kernel to which the current schedule node
+ * belongs. It is set by before_mark and reset by after_mark.
+ * It may be NULL if we are outside any kernel.
+ */
+struct ppcg_at_domain_data {
+ struct gpu_prog *prog;
+ struct ppcg_kernel *kernel;
+};
+
+/* This function is called for each instance of a user statement
+ * in the kernel. This may be one of the original user statements
+ * or a statement introduced by PPCG.
+ *
+ * We first check if the statement id corresponds to a gpu statement,
+ * which indicates the statement is an original user statement. Any statement
+ * that is not an original user statement has been introduced by PPCG and
+ * requires special handling.
+ *
+ * If the user statement is one of the original user statements, then we call
+ * create_domain_leaf. Otherwise, we check if it is a copy or synchronization
+ * statement and call the appropriate functions. Statements that copy an array
+ * to/from the device do not need any further treatment.
+ */
+static __isl_give isl_ast_node *at_domain(__isl_take isl_ast_node *node,
+ __isl_keep isl_ast_build *build, void *user)
+{
+ struct ppcg_at_domain_data *data = user;
+ struct gpu_stmt *gpu_stmt;
+ isl_ast_expr *expr, *arg;
+ isl_id *id;
+ int is_sync;
+ const char *name;
+ void *p;
+
+ expr = isl_ast_node_user_get_expr(node);
+ arg = isl_ast_expr_get_op_arg(expr, 0);
+ id = isl_ast_expr_get_id(arg);
+ name = isl_id_get_name(id);
+ p = isl_id_get_user(id);
+ isl_ast_expr_free(expr);
+ isl_ast_expr_free(arg);
+
+ gpu_stmt = find_stmt(data->prog, id);
+ is_sync = gpu_tree_id_is_sync(id, data->kernel);
+ isl_id_free(id);
+
+ if (gpu_stmt)
+ return create_domain_leaf(data->kernel, node, build, gpu_stmt);
+
+ if (!prefixcmp(name, "to_device_") || !prefixcmp(name, "from_device_"))
+ return node;
+ if (is_sync < 0)
+ return isl_ast_node_free(node);
+ if (!strcmp(name, "read") || !strcmp(name, "write")) {
+ struct gpu_array_ref_group *group = p;
+ return create_access_leaf(data->kernel, group, node, build);
+ }
+ if (!is_sync)
+ isl_die(data->prog->ctx, isl_error_internal,
+ "unknown statement type",
+ return isl_ast_node_free(node));
+ return create_sync_leaf(data->kernel, node, build);
+}
+
+/* Given a set of wrapped references "ref", return the corresponding
+ * access relations based on the tagged access relations "tagged".
+ *
+ * The elements of "ref" are of the form
+ *
+ * [D -> R]
+ *
+ * with D an iteration domains and R a reference.
+ * The elements of "tagged" are of the form
+ *
+ * [D -> R] -> A
+ *
+ * with A an array.
+ *
+ * Extend "tagged" to include the iteration domain in the range, i.e.,
+ *
+ * [D -> R] -> [D -> A]
+ *
+ * apply the result to "ref" and then unwrap the resulting set
+ * to obtain relations of the form
+ *
+ * D -> A
+ */
+static __isl_give isl_union_map *wrapped_reference_to_access(
+ __isl_take isl_union_set *ref, __isl_take isl_union_map *tagged)
+{
+ isl_union_map *tag2access;
+
+ tag2access = isl_union_map_copy(tagged);
+ tag2access = isl_union_map_universe(tag2access);
+ tag2access = isl_union_set_unwrap(isl_union_map_domain(tag2access));
+ tag2access = isl_union_map_domain_map(tag2access);
+ tag2access = isl_union_map_range_product(tag2access, tagged);
+
+ ref = isl_union_set_coalesce(ref);
+ ref = isl_union_set_apply(ref, tag2access);
+
+ return isl_union_set_unwrap(ref);
+}
+
+/* Given an access relation "access" from one or more array reference groups,
+ * remove those reads if ("read" is 1) or writes (if "read" is 0)
+ * that are only needed to communicate data within
+ * the same iteration of "sched".
+ * "tagged" contains all tagged access relations to all
+ * the array reference groups accessed by "access" from statement
+ * instances scheduled by "sched".
+ *
+ * If the access is a read then it is either an element of
+ *
+ * live_in union (range flow)
+ *
+ * where live_in and flow may be overapproximations, or
+ * it reads an uninitialized value (that is not live-in because
+ * there is an intermediate kill) or it reads a value that was
+ * written within the same (compound) statement instance.
+ * If the access is a write then it is either an element of
+ *
+ * live_out union (domain flow)
+ *
+ * or it writes a value that is never read (and is not live-out
+ * because of an intermediate kill) or only
+ * within the same (compound) statement instance.
+ * In both cases, the access relation is also a subset of
+ * the group access relation.
+ *
+ * The cases where an uninitialized value is read or a value is written
+ * that is never read or where the dataflow occurs within a statement
+ * instance are also considered local and may also be removed.
+ *
+ * Essentially, we compute the intersection of "access" with either
+ *
+ * live_in union (range non-local-flow)
+ *
+ * or
+ *
+ * live_out union (domain non-local-flow)
+ *
+ * We first construct a relation "local"
+ *
+ * [[D -> R] -> [D' -> R']]
+ *
+ * of pairs of domain iterations accessing the reference group
+ * and references in the group that are coscheduled by "sched".
+ *
+ * If this relation does not intersect the dataflow dependences,
+ * then there is nothing we can possibly remove, unless the dataflow
+ * dependences themselves only relate a subset of the accesses.
+ * In particular, the accesses may not be involved in any dataflow
+ * dependences, either because they are uninitialized reads/dead writes
+ * or because the dataflow occurs inside a statement instance.
+ *
+ * Since the computation below may break up the access relation
+ * into smaller pieces, we only perform the intersection with
+ * the non-local dependent accesses if the local pairs
+ * intersect the dataflow dependences. Otherwise, we intersect
+ * with the universe of the non-local dependent accesses.
+ * This should at least remove accesses from statements that
+ * do not participate in any dependences.
+ *
+ * In particular, we remove the "local" dataflow dependences from
+ * the set of all dataflow dependences, or at least those
+ * that may contribute to a domain/range that intersects
+ * the domain of "access".
+ * Note that if the potential dataflow dependences are an overapproximation
+ * of the actual dataflow dependences, then the result remains an
+ * overapproximation of the non-local dataflow dependences.
+ * Copying to/from global memory is only needed for the references
+ * in the domain/range of the result or for accesses that are live out/in
+ * for the entire scop.
+ *
+ * We therefore map the domain/range of the "external" relation
+ * to the corresponding access relation and take the union with
+ * the live out/in relation.
+ */
+static __isl_give isl_union_map *remove_local_accesses(
+ struct gpu_prog *prog, __isl_take isl_union_map *tagged,
+ __isl_take isl_union_map *access, __isl_take isl_union_map *sched,
+ int read)
+{
+ int empty;
+ isl_union_pw_multi_aff *tagger;
+ isl_union_set *domain, *access_domain;
+ isl_union_map *local, *external, *universe;
+ isl_union_set *tag_set;
+
+ if (isl_union_map_is_empty(access)) {
+ isl_union_map_free(sched);
+ isl_union_map_free(tagged);
+ return access;
+ }
+
+ tagger = isl_union_pw_multi_aff_copy(prog->scop->tagger);
+ domain = isl_union_map_domain(isl_union_map_copy(tagged));
+ tagger = isl_union_pw_multi_aff_intersect_domain(tagger,
+ isl_union_set_copy(domain));
+ sched = isl_union_map_preimage_domain_union_pw_multi_aff(sched, tagger);
+
+ local = isl_union_map_apply_range(sched,
+ isl_union_map_reverse(isl_union_map_copy(sched)));
+ local = isl_union_map_intersect(local,
+ isl_union_map_copy(prog->scop->tagged_dep_flow));
+
+ empty = isl_union_map_is_empty(local);
+
+ external = isl_union_map_copy(prog->scop->tagged_dep_flow);
+ universe = isl_union_map_universe(isl_union_map_copy(access));
+ access_domain = isl_union_map_domain(universe);
+ domain = isl_union_set_universe(domain);
+ universe = isl_union_set_unwrap(domain);
+ universe = isl_union_map_intersect_domain(universe, access_domain);
+ domain = isl_union_map_wrap(universe);
+ if (read)
+ external = isl_union_map_intersect_range(external, domain);
+ else
+ external = isl_union_map_intersect_domain(external, domain);
+ external = isl_union_map_intersect_params(external,
+ isl_set_copy(prog->scop->context));
+ external = isl_union_map_subtract(external, local);
+
+ if (read) {
+ tag_set = isl_union_map_range(external);
+ external = wrapped_reference_to_access(tag_set, tagged);
+ external = isl_union_map_union(external,
+ isl_union_map_copy(prog->scop->live_in));
+ } else {
+ tag_set = isl_union_map_domain(external);
+ external = wrapped_reference_to_access(tag_set, tagged);
+ external = isl_union_map_union(external,
+ isl_union_map_copy(prog->scop->live_out));
+ }
+
+ if (empty < 0)
+ external = isl_union_map_free(external);
+ else if (empty)
+ external = isl_union_map_universe(external);
+
+ access = isl_union_map_intersect(access, external);
+
+ return access;
+}
+
+/* Given an access relation "access" from "group", remove those reads
+ * if ("read" is 1) or writes (if "read" is 0) that are only needed to
+ * communicate data within the same iteration of the schedule at the
+ * position where the copying of the group is inserted.
+ * "node" points to this position, i.e., the depth at "node"
+ * is equal to group->depth.
+ *
+ * We extract a schedule that picks out the iterations of the outer
+ * group->depth dimensions and call remove_local_accesses.
+ */
+static __isl_give isl_union_map *remove_local_accesses_group(
+ struct ppcg_kernel *kernel, struct gpu_array_ref_group *group,
+ __isl_take isl_union_map *access, __isl_keep isl_schedule_node *node,
+ int read)
+{
+ isl_union_map *sched, *tagged;
+
+ if (isl_union_map_is_empty(access))
+ return access;
+
+ tagged = group_tagged_access_relation(group);
+ sched = isl_schedule_node_get_prefix_schedule_relation(node);
+
+ return remove_local_accesses(kernel->prog, tagged, access, sched, read);
+}
+
+/* This function is called before the AST generator starts traversing
+ * the schedule subtree of a node with mark "mark".
+ *
+ * If the mark is called "kernel", store the kernel pointer in data->kernel
+ * for use in at_domain.
+ */
+static int before_mark(__isl_keep isl_id *mark,
+ __isl_keep isl_ast_build *build, void *user)
+{
+ struct ppcg_at_domain_data *data = user;
+
+ if (!mark)
+ return -1;
+ if (!strcmp(isl_id_get_name(mark), "kernel"))
+ data->kernel = isl_id_get_user(mark);
+ return 0;
+}
+
+/* This function is called after the AST generator has finished traversing
+ * the schedule subtree of a mark node. "node" points to the corresponding
+ * mark AST node.
+ *
+ * If the mark is called "kernel", then replace "node" by a user node
+ * that "calls" the kernel, representing the launch of the kernel.
+ * The original "node" is stored inside the kernel object so that
+ * it can be used to print the device code.
+ * Note that this assumes that a kernel is only launched once.
+ * Also clear data->kernel.
+ */
+static __isl_give isl_ast_node *after_mark(__isl_take isl_ast_node *node,
+ __isl_keep isl_ast_build *build, void *user)
+{
+ isl_ctx *ctx;
+ isl_id *id;
+ isl_ast_expr *expr;
+ isl_ast_expr_list *list;
+ struct ppcg_kernel *kernel;
+ struct ppcg_at_domain_data *data = user;
+
+ ctx = isl_ast_node_get_ctx(node);
+ id = isl_ast_node_mark_get_id(node);
+ if (!id)
+ return isl_ast_node_free(node);
+ if (strcmp(isl_id_get_name(id), "kernel") || !data->kernel) {
+ isl_id_free(id);
+ return node;
+ }
+ kernel = data->kernel;
+ data->kernel = NULL;
+ kernel->space = isl_ast_build_get_schedule_space(build);
+ kernel->tree = isl_ast_node_mark_get_node(node);
+ isl_ast_node_free(node);
+
+ expr = isl_ast_expr_from_id(isl_id_copy(id));
+ list = isl_ast_expr_list_alloc(ctx, 0);
+ expr = isl_ast_expr_call(expr, list);
+ node = isl_ast_node_alloc_user(expr);
+ node = isl_ast_node_set_annotation(node, id);
+
+ return node;
+}
+
+static isl_bool update_depth(__isl_keep isl_schedule_node *node, void *user)
+{
+ int *depth = user;
+ int node_depth;
+
+ if (isl_schedule_node_get_type(node) != isl_schedule_node_leaf)
+ return isl_bool_true;
+ node_depth = isl_schedule_node_get_schedule_depth(node);
+ if (node_depth > *depth)
+ *depth = node_depth;
+
+ return isl_bool_false;
+}
+
+/* Use isl to generate code for both the host and the device
+ * from "schedule".
+ * The device code is marked by "kernel" mark nodes in the schedule tree,
+ * containing a pointer to a ppcg_kernel object.
+ * The returned AST only contains the AST for the host code.
+ * The ASTs for the device code are embedded in ppcg_kernel objects
+ * attached to the leaf nodes that call "kernel".
+ */
+static __isl_give isl_ast_node *generate_code(struct gpu_gen *gen,
+ __isl_take isl_schedule *schedule)
+{
+ struct ppcg_at_domain_data data;
+ isl_ast_build *build;
+ isl_ast_node *tree;
+ isl_id_list *iterators;
+ int depth;
+
+ data.prog = gen->prog;
+ data.kernel = NULL;
+
+ depth = 0;
+ if (isl_schedule_foreach_schedule_node_top_down(schedule, &update_depth,
+ &depth) < 0)
+ return NULL;
+ build = isl_ast_build_alloc(gen->prog->ctx);
+ iterators = ppcg_scop_generate_names(gen->prog->scop, depth, "c");
+ build = isl_ast_build_set_iterators(build, iterators);
+ build = isl_ast_build_set_at_each_domain(build, &at_domain, &data);
+ build = isl_ast_build_set_before_each_mark(build, &before_mark, &data);
+ build = isl_ast_build_set_after_each_mark(build, &after_mark, &data);
+ if (gen->prog->scop->options->debug->dump_final_schedule)
+ isl_schedule_dump(schedule);
+ tree = isl_ast_build_node_from_schedule(build, schedule);
+ isl_ast_build_free(build);
+
+ return tree;
+}
+
+__isl_give isl_union_map *extract_sizes_from_str(isl_ctx *ctx, const char *str)
+{
+ if (!str)
+ return NULL;
+ return isl_union_map_read_from_str(ctx, str);
+}
+
+/* Can "node" be tiled and then mapped to block and thread identifiers?
+ * That is, is it permutable with at least one coincident dimension?
+ */
+static int is_permutable(__isl_keep isl_schedule_node *node)
+{
+ if (!node)
+ return -1;
+
+ if (isl_schedule_node_get_type(node) != isl_schedule_node_band)
+ return 0;
+ if (!isl_schedule_node_band_get_permutable(node))
+ return 0;
+ if (isl_schedule_node_band_n_member(node) < 1)
+ return 0;
+ if (!isl_schedule_node_band_member_get_coincident(node, 0))
+ return 0;
+
+ return 1;
+}
+
+/* A isl_schedule_foreach_schedule_node_top_down callback
+ * for setting *any_permutable and aborting the search
+ * if "node" is a permutable band with coincident dimensions.
+ * Otherwise, continue searching.
+ */
+static isl_bool set_permutable(__isl_keep isl_schedule_node *node, void *user)
+{
+ int *any_permutable = user;
+ int permutable;
+
+ permutable = is_permutable(node);
+ if (permutable < 0)
+ return isl_bool_error;
+ if (!permutable)
+ return isl_bool_true;
+
+ *any_permutable = 1;
+
+ return isl_bool_error;
+}
+
+/* Does "schedule" contain any permutable band with at least one coincident
+ * member?
+ */
+static int has_any_permutable_node(__isl_keep isl_schedule *schedule)
+{
+ int any_permutable = 0;
+
+ if (isl_schedule_foreach_schedule_node_top_down(schedule,
+ &set_permutable, &any_permutable) < 0 &&
+ !any_permutable)
+ return -1;
+
+ return any_permutable;
+}
+
+/* Is "node" a leaf or can it be tiled and then mapped to
+ * block and thread identifiers?
+ */
+static int is_leaf_or_tilable(__isl_keep isl_schedule_node *node)
+{
+ if (isl_schedule_node_get_type(node) == isl_schedule_node_leaf)
+ return 1;
+ return is_permutable(node);
+}
+
+/* Is "node" the outermost node in its branch that can be tiled
+ * and then mapped to block and thread identifiers?
+ * If there are no such nodes in the branch and if "node" is a leaf,
+ * then it is accepted too.
+ */
+static int is_outer_tilable(__isl_keep isl_schedule_node *node)
+{
+ int tilable;
+ isl_schedule_node *ancestor;
+
+ tilable = is_leaf_or_tilable(node);
+ if (tilable < 0)
+ return -1;
+ if (!tilable)
+ return 0;
+
+ tilable = 0;
+ ancestor = isl_schedule_node_copy(node);
+ while (isl_schedule_node_has_parent(ancestor)) {
+ ancestor = isl_schedule_node_parent(ancestor);
+
+ tilable = is_permutable(ancestor);
+ if (tilable < 0 || tilable)
+ break;
+ }
+
+ isl_schedule_node_free(ancestor);
+ return tilable < 0 ? -1 : !tilable;
+}
+
+/* Collect the references to all writes in "group".
+ * Each reference is represented by a universe set in a space
+ *
+ * [S[i,j] -> R[]]
+ *
+ * with S[i,j] the statement instance space and R[] the array reference.
+ */
+static __isl_give isl_union_set *group_tagged_writes(
+ struct gpu_array_ref_group *group)
+{
+ int i;
+ isl_space *space;
+ isl_union_set *writes;
+
+ space = isl_map_get_space(group->access);
+ writes = isl_union_set_empty(space);
+ for (i = 0; i < group->n_ref; ++i) {
+ isl_space *space;
+ isl_set *writes_i;
+
+ if (!group->refs[i]->write)
+ continue;
+
+ space = isl_map_get_space(group->refs[i]->tagged_access);
+ space = isl_space_domain(space);
+ writes_i = isl_set_universe(space);
+ writes = isl_union_set_add_set(writes, writes_i);
+ }
+
+ return writes;
+}
+
+/* Is there any write access in "group" that requires synchronization
+ * on a write to global memory?
+ * We currently take into account all writes that would require
+ * synchronization at the thread level depth, but if the copying
+ * for this group is performed at an outer level, then we do not
+ * actually need to take into account dependences at intermediate levels.
+ */
+static int any_sync_writes_in_group(struct ppcg_kernel *kernel,
+ struct gpu_array_ref_group *group)
+{
+ isl_union_set *writes;
+ int empty, disjoint;
+
+ empty = isl_union_set_is_empty(kernel->sync_writes);
+ if (empty < 0)
+ return -1;
+ if (empty)
+ return 0;
+
+ writes = group_tagged_writes(group);
+ disjoint = isl_union_set_is_disjoint(kernel->sync_writes, writes);
+ isl_union_set_free(writes);
+
+ return disjoint < 0 ? -1 : !disjoint;
+}
+
+/* Collect the references to all writes in "kernel" that write directly
+ * to global or shared memory, i.e., that are not mapped to private memory.
+ * Each reference is represented by a universe set in a space
+ *
+ * [S[i,j] -> R[]]
+ *
+ * with S[i,j] the statement instance space and R[] the array reference.
+ */
+static __isl_give isl_union_set *collect_non_private_tagged_writes(
+ struct ppcg_kernel *kernel)
+{
+ isl_union_set *writes;
+ int i, j;
+
+ writes = isl_union_set_empty(isl_union_set_get_space(kernel->arrays));
+
+ for (i = 0; i < kernel->n_array; ++i) {
+ struct gpu_local_array_info *array = &kernel->array[i];
+
+ for (j = 0; j < array->n_group; ++j) {
+ struct gpu_array_ref_group *group = array->groups[j];
+ isl_union_set *writes_ij;
+
+ if (!group->write)
+ continue;
+ if (group->private_tile)
+ continue;
+ writes_ij = group_tagged_writes(group);
+ writes = isl_union_set_union(writes, writes_ij);
+ }
+ }
+
+ return writes;
+}
+
+/* Are there any direct writes to global memory that require
+ * synchronization?
+ */
+static int any_global_or_shared_sync_writes(struct ppcg_kernel *kernel)
+{
+ isl_union_set *writes;
+ int empty, disjoint;
+
+ empty = isl_union_set_is_empty(kernel->sync_writes);
+ if (empty < 0)
+ return -1;
+ if (empty)
+ return 0;
+
+ writes = collect_non_private_tagged_writes(kernel);
+ disjoint = isl_union_set_is_disjoint(kernel->sync_writes, writes);
+ isl_union_set_free(writes);
+
+ return disjoint < 0 ? -1 : !disjoint;
+}
+
+/* Construct an isl_multi_val for use as tile sizes for tiling "node"
+ * from the elements in "tile_size".
+ */
+static __isl_give isl_multi_val *construct_band_tiles_sizes(
+ __isl_keep isl_schedule_node *node, int *tile_size)
+{
+ int i, n;
+ isl_ctx *ctx;
+ isl_space *space;
+ isl_multi_val *mv;
+
+ if (!node)
+ return NULL;
+
+ ctx = isl_schedule_node_get_ctx(node);
+ space = isl_schedule_node_band_get_space(node);
+ n = isl_schedule_node_band_n_member(node);
+ mv = isl_multi_val_zero(space);
+ for (i = 0; i < n; ++i) {
+ isl_val *v;
+
+ v = isl_val_int_from_si(ctx, tile_size[i]);
+ mv = isl_multi_val_set_val(mv, i, v);
+ }
+
+ return mv;
+}
+
+/* Replace the partial schedule S of the band node "node" by
+ *
+ * floor(S/f)
+ *
+ * or
+ *
+ * f * floor(S/f)
+ *
+ * if scale_tile_loops is set, with f the integers in "factor".
+ * The list that "factor" points to is assumed to contain at least
+ * as many elements as the number of members in the band.
+ */
+static __isl_give isl_schedule_node *snap_band_to_sizes(
+ __isl_take isl_schedule_node *node, int *factor,
+ struct ppcg_options *options)
+{
+ isl_multi_val *mv;
+
+ mv = construct_band_tiles_sizes(node, factor);
+ node = isl_schedule_node_band_scale_down(node, isl_multi_val_copy(mv));
+ if (options->scale_tile_loops)
+ node = isl_schedule_node_band_scale(node,
+ isl_multi_val_copy(mv));
+ isl_multi_val_free(mv);
+
+ return node;
+}
+
+/* Tile "band" with tile size specified by "sizes".
+ *
+ * Since the tile loops will be mapped to block ids, we forcibly
+ * turn off tile loop scaling. We may want to enable tile loop scaling
+ * at some later point, but then we would have to support the detection
+ * of strides during the mapping to block ids.
+ * Similarly, since the point loops will be mapped to thread ids,
+ * we forcibly shift the point loops so that they start at zero.
+ */
+static __isl_give isl_schedule_node *tile_band(
+ __isl_take isl_schedule_node *node, __isl_take isl_multi_val *sizes)
+{
+ isl_ctx *ctx = isl_schedule_node_get_ctx(node);
+ int scale_tile;
+ int shift_point;
+
+ scale_tile = isl_options_get_tile_scale_tile_loops(ctx);
+ isl_options_set_tile_scale_tile_loops(ctx, 0);
+ shift_point = isl_options_get_tile_shift_point_loops(ctx);
+ isl_options_set_tile_shift_point_loops(ctx, 1);
+
+ node = isl_schedule_node_band_tile(node, sizes);
+
+ isl_options_set_tile_scale_tile_loops(ctx, scale_tile);
+ isl_options_set_tile_shift_point_loops(ctx, shift_point);
+
+ return node;
+}
+
+/* Extract the set of parameter values and outer schedule dimensions
+ * for which any statement instance
+ * in the kernel inserted at "node" needs to be executed.
+ * Intersect the set of parameter values derived from the host schedule
+ * relation with the context of "prog".
+ */
+static __isl_give isl_set *extract_context(__isl_keep isl_schedule_node *node,
+ struct gpu_prog *prog)
+{
+ isl_union_map *schedule;
+ isl_union_set *schedule_domain;
+ isl_set *context;
+ int empty;
+
+ schedule = isl_schedule_node_get_prefix_schedule_relation(node);
+ schedule_domain = isl_union_map_range(schedule);
+ empty = isl_union_set_is_empty(schedule_domain);
+ if (empty < 0) {
+ isl_union_set_free(schedule_domain);
+ return NULL;
+ }
+ if (empty) {
+ int depth;
+ isl_space *space;
+
+ space = isl_union_set_get_space(schedule_domain);
+ isl_union_set_free(schedule_domain);
+ space = isl_space_set_from_params(space);
+ depth = isl_schedule_node_get_schedule_depth(node);
+ space = isl_space_add_dims(space, isl_dim_set, depth);
+ context = isl_set_empty(space);
+ } else {
+ context = isl_set_from_union_set(schedule_domain);
+ }
+ context = isl_set_intersect_params(context,
+ isl_set_copy(prog->context));
+
+ return context;
+}
+
+/* Return the set of outer array elements accessed by
+ * by the statement instance in "domain" in "prog".
+ */
+static __isl_give isl_union_set *accessed_by_domain(
+ __isl_take isl_union_set *domain, struct gpu_prog *prog)
+{
+ isl_union_map *access;
+ isl_union_set *arrays;
+
+ access = isl_union_map_union(isl_union_map_copy(prog->read),
+ isl_union_map_copy(prog->may_write));
+ access = isl_union_map_intersect_domain(access, domain);
+ arrays = isl_union_map_range(access);
+ arrays = isl_union_set_apply(arrays,
+ isl_union_map_copy(prog->to_outer));
+
+ return arrays;
+}
+
+/* Return the number of outer band members of the band node "node"
+ * that are marked coincident.
+ */
+static int n_outer_coincidence(__isl_keep isl_schedule_node *node)
+{
+ int i, n;
+
+ n = isl_schedule_node_band_n_member(node);
+
+ for (i = 0; i < n; ++i)
+ if (!isl_schedule_node_band_member_get_coincident(node, i))
+ break;
+
+ return i;
+}
+
+/* If the band node "node" has more than "n" members, then split off
+ * the first "n" of them.
+ */
+static __isl_give isl_schedule_node *split_band(
+ __isl_take isl_schedule_node *node, int n)
+{
+ int dim;
+
+ dim = isl_schedule_node_band_n_member(node);
+ if (n < dim)
+ node = isl_schedule_node_band_split(node, n);
+
+ return node;
+}
+
+/* Scale a band node that may have been split by split_band.
+ * "sizes" are the scaling factors for the original node.
+ * "node" either points to the original band node, or the outer
+ * of the two pieces after splitting.
+ *
+ * If the number of elements in "node" is smaller than the number of
+ * elements in "sizes", then some splitting has occurred and we split
+ * "sizes" in the same way.
+ */
+static __isl_give isl_schedule_node *scale_band(
+ __isl_take isl_schedule_node *node, __isl_take isl_multi_val *sizes)
+{
+ int n, dim;
+
+ n = isl_multi_val_dim(sizes, isl_dim_set);
+ dim = isl_schedule_node_band_n_member(node);
+ if (n > dim) {
+ isl_multi_val *sizes2;
+
+ sizes2 = isl_multi_val_copy(sizes);
+ sizes = isl_multi_val_drop_dims(sizes,
+ isl_dim_set, dim, n - dim);
+ sizes2 = isl_multi_val_drop_dims(sizes2, isl_dim_set, 0, dim);
+ node = isl_schedule_node_child(node, 0);
+ node = isl_schedule_node_band_scale(node, sizes2);
+ node = isl_schedule_node_parent(node);
+ }
+
+ return isl_schedule_node_band_scale(node, sizes);
+}
+
+/* Return an isl_multi_aff, with as elements the parameters in "space"
+ * that have the names specified by the elements in "names".
+ * If (some of) these parameters do not already appear in "space",
+ * then they are added first.
+ */
+static __isl_give isl_multi_aff *parameter_vector(__isl_take isl_space *space,
+ __isl_keep isl_id_list *names)
+{
+ int i, n;
+ isl_local_space *ls;
+ isl_multi_aff *ma;
+
+ if (!names)
+ space = isl_space_free(space);
+
+ n = isl_id_list_n_id(names);
+ for (i = 0; i < n; ++i) {
+ int pos;
+ isl_id *id;
+
+ id = isl_id_list_get_id(names, i);
+ pos = isl_space_find_dim_by_id(space, isl_dim_param, id);
+ if (pos >= 0) {
+ isl_id_free(id);
+ continue;
+ }
+ pos = isl_space_dim(space, isl_dim_param);
+ space = isl_space_add_dims(space, isl_dim_param, 1);
+ space = isl_space_set_dim_id(space, isl_dim_param, pos, id);
+ }
+ ma = isl_multi_aff_zero(isl_space_copy(space));
+ ls = isl_local_space_from_space(isl_space_domain(space));
+ for (i = 0; i < n; ++i) {
+ int pos;
+ isl_id *id;
+ isl_aff *aff;
+
+ id = isl_id_list_get_id(names, i);
+ pos = isl_space_find_dim_by_id(space, isl_dim_param, id);
+ isl_id_free(id);
+ aff = isl_aff_var_on_domain(isl_local_space_copy(ls),
+ isl_dim_param, pos);
+ ma = isl_multi_aff_set_aff(ma, i, aff);
+ }
+ isl_local_space_free(ls);
+
+ return ma;
+}
+
+/* Return constraints on the domain elements that equate a sequence of
+ * parameters called "names", to the partial schedule
+ * of "node" modulo the integers in "size".
+ * The number of elements in the array "size" should be equal
+ * to the number of elements in "names".
+ * The number of members of the band node "node" should be smaller
+ * than or equal to this number. If it is smaller, then the first
+ * elements of "names" are equated to zero.
+ */
+static __isl_give isl_union_set *set_schedule_modulo(
+ __isl_keep isl_schedule_node *node, __isl_keep isl_id_list *names,
+ int *size)
+{
+ int n, n_zero;
+ isl_space *space;
+ isl_multi_aff *ma;
+ isl_multi_union_pw_aff *mupa, *mupa2;
+ isl_multi_val *mv;
+ isl_union_set *domain;
+
+ if (!node)
+ return NULL;
+ n = isl_id_list_n_id(names);
+ if (n == 0)
+ return isl_schedule_node_get_universe_domain(node);
+ n_zero = n - isl_schedule_node_band_n_member(node);
+
+ mupa = isl_schedule_node_band_get_partial_schedule(node);
+ mv = construct_band_tiles_sizes(node, size + n_zero);
+ mupa = isl_multi_union_pw_aff_mod_multi_val(mupa, mv);
+
+ space = isl_multi_union_pw_aff_get_space(mupa);
+ space = isl_space_params(space);
+ space = isl_space_set_from_params(space);
+ space = isl_space_add_dims(space, isl_dim_set, n_zero);
+ ma = isl_multi_aff_zero(space);
+
+ domain = isl_schedule_node_get_universe_domain(node);
+ mupa2 = isl_multi_union_pw_aff_multi_aff_on_domain(
+ isl_union_set_copy(domain), ma);
+ mupa = isl_multi_union_pw_aff_range_product(mupa2, mupa);
+
+ space = isl_multi_union_pw_aff_get_space(mupa);
+ ma = parameter_vector(space, names);
+
+ mupa2 = isl_multi_union_pw_aff_multi_aff_on_domain(domain, ma);
+ mupa = isl_multi_union_pw_aff_sub(mupa, mupa2);
+
+ return isl_multi_union_pw_aff_zero_union_set(mupa);
+}
+
+/* Insert a context node at "node" introducing the block and thread
+ * identifiers along with their bounds, which are stored in kernel->grid_size
+ * and kernel->block_dim.
+ * Note that the bounds on the block identifiers may implicitly impose
+ * constraints on the parameters. A guard needs to be inserted
+ * in the schedule tree to ensure that those bounds hold at "node".
+ * This guard is inserted in insert_guard.
+ */
+static __isl_give isl_schedule_node *insert_context(struct ppcg_kernel *kernel,
+ __isl_take isl_schedule_node *node)
+{
+ isl_set *context;
+
+ context = isl_set_universe(isl_set_get_space(kernel->context));
+
+ context = add_bounded_parameters_dynamic(context,
+ kernel->grid_size, kernel->block_ids);
+ context = add_bounded_parameters(context,
+ kernel->block_dim, kernel->thread_ids);
+
+ node = isl_schedule_node_insert_context(node, context);
+
+ return node;
+}
+
+/* Insert a guard that eliminates kernel launches where the kernel
+ * obviously does not have any work to do.
+ *
+ * In particular, eliminate kernel launches where there are obviously
+ * zero blocks.
+ * Use the same block size constraints that are used to create the context
+ * to ensure that all constraints implicit in the constructed context
+ * are imposed by the guard.
+ *
+ * Additionally, add other constraints that are valid
+ * for each executed instance ("context"), as long as this does not result
+ * in a disjunction.
+ */
+static __isl_give isl_schedule_node *insert_guard(
+ __isl_take isl_schedule_node *node, __isl_keep isl_set *context,
+ __isl_keep isl_multi_pw_aff *size, struct ppcg_scop *scop)
+{
+ unsigned nparam, n;
+ isl_set *guard;
+ isl_id_list *ids;
+
+ guard = isl_set_copy(context);
+ guard = isl_set_compute_divs(guard);
+ guard = isl_set_from_basic_set(isl_set_simple_hull(guard));
+
+ nparam = isl_set_dim(guard, isl_dim_param);
+ n = isl_multi_pw_aff_dim(size, isl_dim_out);
+ ids = ppcg_scop_generate_names(scop, n, "__ppcg_tmp");
+ guard = add_bounded_parameters_dynamic(guard, size, ids);
+ isl_id_list_free(ids);
+ guard = isl_set_project_out(guard, isl_dim_param, nparam, n);
+
+ node = isl_schedule_node_insert_guard(node, guard);
+
+ return node;
+}
+
+/* Does any array reference group mapping require the band that is mapped
+ * to threads to be unrolled?
+ */
+static int kernel_requires_unroll(struct ppcg_kernel *kernel)
+{
+ int i, j;
+
+ for (i = 0; i < kernel->n_array; ++i) {
+ struct gpu_local_array_info *array = &kernel->array[i];
+
+ for (j = 0; j < array->n_group; ++j) {
+ struct gpu_array_ref_group *group = array->groups[j];
+ if (gpu_array_ref_group_requires_unroll(group))
+ return 1;
+ }
+ }
+
+ return 0;
+}
+
+/* Mark the given band node "node" for unrolling by the AST generator and
+ * then sink it to the leaves of the schedule tree.
+ * All dimensions of "node" are assumed to be coincident, such that this
+ * sinking is a valid operation.
+ */
+static __isl_give isl_schedule_node *unroll(__isl_take isl_schedule_node *node)
+{
+ int i, n;
+
+ n = isl_schedule_node_band_n_member(node);
+ for (i = 0; i < n; ++i)
+ node = isl_schedule_node_band_member_set_ast_loop_type(node, i,
+ isl_ast_loop_unroll);
+
+ node = isl_schedule_node_band_sink(node);
+
+ return node;
+}
+
+/* Insert a synchronization node in the schedule tree of "node"
+ * after the core computation of "kernel" at the level of the band
+ * that is mapped to threads, except if that level is equal to
+ * that of the band that is mapped to blocks or if there are no writes
+ * to global or shared memory in the core computation that require
+ * synchronization.
+ * If there are any writes to shared memory and the shared memory
+ * copying is performed at the same level, then synchronization
+ * is needed between the core and the copying anyway, so we might
+ * as well add it here. If the copying is performed at a higher
+ * level, then different iterations of intermediate schedule dimensions
+ * may have a different mapping from between shared memory elements and
+ * threads, such that synchronization is required after the core.
+ * "node" is assumed to point to the kernel node.
+ */
+static __isl_give isl_schedule_node *add_sync(struct ppcg_kernel *kernel,
+ __isl_take isl_schedule_node *node)
+{
+ int kernel_depth;
+ int need_sync;
+
+ need_sync = any_global_or_shared_sync_writes(kernel);
+ if (need_sync < 0)
+ return isl_schedule_node_free(node);
+ if (!need_sync)
+ return node;
+
+ kernel_depth = isl_schedule_node_get_schedule_depth(node);
+
+ node = gpu_tree_move_down_to_thread(node, kernel->core);
+ if (kernel_depth == isl_schedule_node_get_schedule_depth(node))
+ return gpu_tree_move_up_to_kernel(node);
+
+ node = gpu_tree_ensure_following_sync(node, kernel);
+
+ node = gpu_tree_move_up_to_kernel(node);
+
+ return node;
+}
+
+/* Return a read ("read" is 1) or write access relation for "group"
+ * with those accesses removed that are only needed to communicate data
+ * within the subtree of the schedule rooted at "node".
+ * Furthermore, include the prefix schedule at "node".
+ * That is, return a relation of the form
+ *
+ * S -> [D -> A]
+ *
+ * with D the outer schedule dimensions at "node".
+ */
+static __isl_give isl_union_map *anchored_non_local_accesses(
+ struct ppcg_kernel *kernel, struct gpu_array_ref_group *group,
+ __isl_take isl_schedule_node *node, int read)
+{
+ isl_union_map *access;
+ isl_union_map *prefix;
+
+ access = gpu_array_ref_group_access_relation(group, read, !read);
+ access = remove_local_accesses_group(kernel, group, access, node, read);
+ prefix = isl_schedule_node_get_prefix_schedule_relation(node);
+ access = isl_union_map_range_product(prefix, access);
+
+ return access;
+}
+
+/* Given an array reference group "group", create a mapping
+ *
+ * read[D -> A] -> [D -> A]
+ *
+ * if "read" is set or
+ *
+ * write[D -> A] -> [D -> A]
+ *
+ * if "read" is not set.
+ * D corresponds to the outer group->depth dimensions of
+ * the kernel schedule.
+ */
+static __isl_give isl_multi_aff *create_from_access(isl_ctx *ctx,
+ struct gpu_array_ref_group *group, int read)
+{
+ isl_space *space;
+ isl_id *id;
+
+ space = isl_space_copy(group->array->space);
+ space = isl_space_from_range(space);
+ space = isl_space_add_dims(space, isl_dim_in, group->depth);
+ space = isl_space_wrap(space);
+ space = isl_space_map_from_set(space);
+
+ id = isl_id_alloc(ctx, read ? "read" : "write", group);
+ space = isl_space_set_tuple_id(space, isl_dim_in, id);
+
+ return isl_multi_aff_identity(space);
+}
+
+/* If any writes in "group" require synchronization, then make sure
+ * that there is a synchronization node for "kernel" after the node
+ * following "node" in a sequence.
+ *
+ * If "shared" is set and no synchronization is needed for
+ * the writes to global memory, then add synchronization before
+ * the kernel to protect shared memory from being overwritten
+ * by the next iteration of the core computation.
+ * No additional synchronization is needed to protect against
+ * the next copy into shared memory because each element of
+ * the shared memory tile is always copied by the same thread.
+ */
+static __isl_give isl_schedule_node *add_group_write_sync(
+ __isl_take isl_schedule_node *node, struct ppcg_kernel *kernel,
+ struct gpu_array_ref_group *group, int shared)
+{
+ int need_sync;
+
+ need_sync = any_sync_writes_in_group(kernel, group);
+ if (need_sync < 0)
+ return isl_schedule_node_free(node);
+ if (need_sync) {
+ node = isl_schedule_node_parent(node);
+ node = isl_schedule_node_next_sibling(node);
+ node = isl_schedule_node_child(node, 0);
+ node = gpu_tree_ensure_following_sync(node, kernel);
+ } else if (shared) {
+ node = isl_schedule_node_parent(node);
+ node = isl_schedule_node_parent(node);
+ node = gpu_tree_move_down_to_depth(node, group->depth,
+ kernel->core);
+ node = gpu_tree_move_left_to_sync(node, kernel);
+ }
+
+ return node;
+}
+
+/* Add copy statements to the schedule tree of "node"
+ * for reading from global memory to private memory (if "read" is set) or
+ * for writing back from private memory to global memory
+ * (if "read" is not set) for the array reference group "group" that
+ * is mapped to private memory.
+ * On input, "node" points to the kernel node, and it is moved
+ * back there on output.
+ *
+ * The copies are performed in the order of the array elements.
+ * The copy statement instances include a reference to the outer
+ * group->depth dimensions of the kernel schedule for ease of
+ * combining them with the group tiling.
+ *
+ * That is, the extra schedule is of the form
+ *
+ * type[D -> A] -> A
+ *
+ * where D corresponds to the outer group->depth dimensions of
+ * the kernel schedule and A to the global array.
+ * This schedule is unrolled because registers are not addressable.
+ *
+ * The copying is inserted in the schedule tree through an extension
+ * of the form
+ *
+ * D -> type[D -> A]
+ *
+ * where the extra domain elements type[D -> A] are those accessed
+ * by the group.
+ * A filter is inserted on type[D -> A] to ensure that the element
+ * is read/written by the same thread that needs the element.
+ * This filter is obtained by applying
+ *
+ * S -> type[D -> A]
+ *
+ * to the thread filter for the core statements.
+ *
+ * The extension is inserted before the core computation in case of a read
+ * and after the core computation in case of a write.
+ * In the latter case, we also make sure that there is a synchronization
+ * node after the write to global memory, unless this write is performed
+ * at the outer level of the kernel.
+ * In principle, this synchronization could be inserted higher
+ * in the schedule tree depending on where the corresponding reads
+ * from global memory are performed.
+ */
+static __isl_give isl_schedule_node *add_copies_group_private(
+ struct ppcg_kernel *kernel, struct gpu_array_ref_group *group,
+ __isl_take isl_schedule_node *node, int read)
+{
+ isl_union_map *access;
+ isl_union_map *prefix;
+ isl_union_set *domain;
+ isl_space *space;
+ isl_multi_aff *from_access;
+ isl_multi_pw_aff *mpa;
+ isl_multi_union_pw_aff *mupa;
+ isl_schedule_node *graft;
+ isl_union_set *filter;
+ int kernel_depth;
+ int empty;
+
+ kernel_depth = isl_schedule_node_get_schedule_depth(node);
+ node = gpu_tree_move_down_to_depth(node, group->depth, kernel->core);
+
+ access = anchored_non_local_accesses(kernel, group, node, read);
+ empty = isl_union_map_is_empty(access);
+ if (empty < 0 || empty) {
+ isl_union_map_free(access);
+ if (empty < 0)
+ return isl_schedule_node_free(node);
+ return gpu_tree_move_up_to_kernel(node);
+ }
+
+ group->array->global = 1;
+ group->local_array->global = 1;
+
+ from_access = create_from_access(kernel->ctx, group, read);
+ space = isl_space_domain(isl_multi_aff_get_space(from_access));
+ access = isl_union_map_preimage_range_multi_aff(access, from_access);
+
+ filter = isl_union_set_copy(kernel->thread_filter);
+ filter = isl_union_set_apply(filter, isl_union_map_copy(access));
+ filter = isl_union_set_detect_equalities(filter);
+ filter = isl_union_set_coalesce(filter);
+
+ domain = isl_union_map_range(access);
+ access = isl_union_set_wrapped_domain_map(domain);
+ access = isl_union_map_reverse(access);
+ access = isl_union_map_coalesce(access);
+ graft = isl_schedule_node_from_extension(access);
+
+ space = isl_space_map_from_set(space);
+ mpa = isl_multi_pw_aff_identity(space);
+ mpa = isl_multi_pw_aff_range_factor_range(mpa);
+ mupa = isl_multi_union_pw_aff_from_multi_pw_aff(mpa);
+
+ graft = isl_schedule_node_child(graft, 0);
+ graft = isl_schedule_node_insert_partial_schedule(graft, mupa);
+ graft = unroll(graft);
+
+ graft = isl_schedule_node_insert_filter(graft, filter);
+
+ graft = isl_schedule_node_parent(graft);
+
+ if (read)
+ node = isl_schedule_node_graft_before(node, graft);
+ else {
+ node = isl_schedule_node_graft_after(node, graft);
+ if (kernel_depth < group->depth)
+ node = add_group_write_sync(node, kernel, group, 0);
+ }
+
+ node = gpu_tree_move_up_to_kernel(node);
+
+ return node;
+}
+
+/* Add copy statements to the schedule tree of "node"
+ * for reading from global memory to shared memory (if "read" is set) or
+ * for writing back from shared memory to global memory
+ * (if "read" is not set) for the array reference group "group" that
+ * is mapped to shared memory.
+ * On input, "node" points to the kernel node, and it is moved
+ * back there on output.
+ *
+ * The copies are performed in the order of the corresponding shared
+ * memory tile.
+ * The copy statement instances include a reference to the outer
+ * group->depth dimensions of the kernel schedule for ease of
+ * combining them with the group tiling.
+ *
+ * If we are performing a read from global memory to shared memory and
+ * if the array involved is not a scalar, then we copy
+ * the entire tile to shared memory. This may result in some extra
+ * elements getting copied, but it should lead to simpler code
+ * (which means that fewer registers may be needed) and less divergence.
+ *
+ * Otherwise, we only copy the elements that will be read or have been written
+ * in the kernel.
+ *
+ * That is, the extra schedule is of the form
+ *
+ * type[D -> A] -> T
+ *
+ * where D corresponds to the outer group->depth dimensions of
+ * the kernel schedule, A to the global array and T is the corresponding
+ * shared memory tile.
+ *
+ * The copying is inserted in the schedule tree through an extension
+ * of the form
+ *
+ * D -> type[D -> A]
+ *
+ * where the extra domain elements type[D -> A] are those accessed
+ * by the group. In the case of read from a non-scalar, this set
+ * is replaced by the entire shared memory tile.
+ *
+ * A filter is inserted on type[D -> A] to map the copy instances
+ * to the threads. In particular, the thread identifiers are
+ * equated to the position inside the shared memory tile (T)
+ * modulo the block size.
+ * We try to align the innermost tile dimension with the innermost
+ * thread identifier (x) as a heuristic to improve coalescing.
+ * In particular, if the dimension of the tile is greater than
+ * the dimension of the block, then the schedule mapping to the tile
+ * is broken up into two pieces and the filter is applied to the inner part.
+ * If, on the other hand, the dimension of the tile is smaller than
+ * the dimension of the block, then the initial thread identifiers
+ * are equated to zero and the remaining thread identifiers are
+ * matched to the memory tile.
+ *
+ * The extension is inserted before the core computation in case of a read
+ * and after the core computation in case of a write.
+ * In the case of a read, we first need to make sure there is some
+ * synchronization before the core computation such that we can put the read
+ * from global memory to shared memory before that synchronization.
+ * This ensures that all threads have finished copying into shared memory
+ * before the shared memory is used.
+ * We also need to make sure that there is a synchronization node after
+ * the core computation to ensure that the next load into shared memory
+ * only happens after all data has been used. There is no need for
+ * this synchronization if we are at the outer level since then there
+ * won't be a next load.
+ * In the case of a write, we need to make sure there is some synchronization
+ * after the core computation such taht we can put the write from shared
+ * memory to global memory after that synchronization.
+ * Unless we are at the outer level, we also need a synchronization node
+ * after the write to ensure the data is saved to global memory
+ * before the next iteration write to the same shared memory.
+ * It also makes sure the data has arrived in global memory before
+ * it is read in a subsequent iteration.
+ */
+static __isl_give isl_schedule_node *add_copies_group_shared(
+ struct ppcg_kernel *kernel, struct gpu_array_ref_group *group,
+ __isl_take isl_schedule_node *node, int read)
+{
+ struct gpu_array_tile *tile;
+ isl_union_map *access;
+ isl_union_set *domain;
+ isl_union_set *sync;
+ isl_multi_aff *ma;
+ isl_multi_aff *from_access;
+ isl_multi_pw_aff *mpa;
+ isl_multi_union_pw_aff *mupa;
+ isl_schedule_node *graft;
+ isl_union_set *filter;
+ int skip;
+ int kernel_depth;
+ int empty;
+
+ kernel_depth = isl_schedule_node_get_schedule_depth(node);
+ node = gpu_tree_move_down_to_depth(node, group->depth, kernel->core);
+
+ access = anchored_non_local_accesses(kernel, group, node, read);
+ empty = isl_union_map_is_empty(access);
+ if (empty < 0 || empty) {
+ isl_union_map_free(access);
+ if (empty < 0)
+ return isl_schedule_node_free(node);
+ return gpu_tree_move_up_to_kernel(node);
+ }
+
+ group->array->global = 1;
+ group->local_array->global = 1;
+
+ from_access = create_from_access(kernel->ctx, group, read);
+
+ tile = gpu_array_ref_group_tile(group);
+ ma = isl_multi_aff_copy(tile->tiling);
+ ma = isl_multi_aff_pullback_multi_aff(ma,
+ isl_multi_aff_copy(from_access));
+ mpa = isl_multi_pw_aff_from_multi_aff(ma);
+ mupa = isl_multi_union_pw_aff_from_multi_pw_aff(mpa);
+
+ domain = isl_union_map_range(access);
+
+ if (read && !gpu_array_is_scalar(group->array)) {
+ isl_map *map;
+ isl_union_set_free(domain);
+ map = group_tile(group);
+ domain = isl_union_set_from_set(isl_map_wrap(map));
+ }
+
+ domain = isl_union_set_preimage_multi_aff(domain, from_access);
+ access = isl_union_set_wrapped_domain_map(domain);
+ access = isl_union_map_reverse(access);
+ access = isl_union_map_coalesce(access);
+ graft = isl_schedule_node_from_extension(access);
+
+ graft = isl_schedule_node_child(graft, 0);
+
+ graft = isl_schedule_node_insert_partial_schedule(graft, mupa);
+
+ if (tile->n > kernel->n_block && kernel->n_block > 0) {
+ graft = isl_schedule_node_band_split(graft,
+ tile->n - kernel->n_block);
+ graft = isl_schedule_node_child(graft, 0);
+ }
+ if (tile->n < kernel->n_block)
+ skip = kernel->n_block - tile->n;
+ else
+ skip = 0;
+ filter = set_schedule_modulo(graft, kernel->thread_ids,
+ kernel->block_dim);
+ if (!kernel->options->wrap)
+ graft = snap_band_to_sizes(graft, kernel->block_dim + skip,
+ kernel->options);
+ if (tile->n > kernel->n_block && kernel->n_block > 0)
+ graft = isl_schedule_node_parent(graft);
+ graft = isl_schedule_node_insert_filter(graft, filter);
+
+ while (graft && isl_schedule_node_has_parent(graft))
+ graft = isl_schedule_node_parent(graft);
+
+ if (read) {
+ if (kernel_depth < group->depth)
+ node = gpu_tree_ensure_sync_after_core(node, kernel);
+ node = gpu_tree_move_left_to_sync(node, kernel);
+ node = isl_schedule_node_graft_before(node, graft);
+ } else {
+ node = gpu_tree_move_right_to_sync(node, kernel);
+ node = isl_schedule_node_graft_after(node, graft);
+ if (kernel_depth < group->depth)
+ node = add_group_write_sync(node, kernel, group, 1);
+ }
+
+ node = gpu_tree_move_up_to_kernel(node);
+
+ return node;
+}
+
+/* Check whether the array reference group "group" is mapped to
+ * private or shared memory and, if so,
+ * add copy statements to the schedule tree of "node"
+ * for reading from global memory to private or shared memory
+ * (if "read" is set) or for writing back from private or shared memory
+ * to global memory (if "read" is not set) for this group.
+ * On input, "node" points to the kernel node, and it is moved
+ * back there on output.
+ */
+static __isl_give isl_schedule_node *add_copies_group(
+ struct ppcg_kernel *kernel, struct gpu_array_ref_group *group,
+ __isl_take isl_schedule_node *node, int read)
+{
+ if (group->private_tile)
+ return add_copies_group_private(kernel, group, node, read);
+ if (group->shared_tile)
+ return add_copies_group_shared(kernel, group, node, read);
+ return node;
+}
+
+/* For each array reference group that is mapped to private or shared memory,
+ * add copy statements to the schedule tree of "node"
+ * for reading from global memory to private or shared memory
+ * and for writing back.
+ * On input, "node" points to the kernel node, and it is moved
+ * back there on output.
+ */
+static __isl_give isl_schedule_node *add_copies(struct ppcg_kernel *kernel,
+ __isl_take isl_schedule_node *node)
+{
+ int i, j;
+
+ for (i = 0; i < kernel->n_array; ++i) {
+ struct gpu_local_array_info *array = &kernel->array[i];
+
+ for (j = 0; j < array->n_group; ++j) {
+ struct gpu_array_ref_group *group = array->groups[j];
+
+ node = add_copies_group(kernel, group, node, 1);
+ if (!node)
+ return NULL;
+ node = add_copies_group(kernel, group, node, 0);
+ if (!node)
+ return NULL;
+ }
+ }
+
+ return node;
+}
+
+/* Mark all dimensions in the current band node atomic.
+ */
+static __isl_give isl_schedule_node *atomic(__isl_take isl_schedule_node *node)
+{
+ int i, n;
+
+ n = isl_schedule_node_band_n_member(node);
+ for (i = 0; i < n; ++i)
+ node = isl_schedule_node_band_member_set_ast_loop_type(node, i,
+ isl_ast_loop_atomic);
+
+ return node;
+}
+
+/* Mark "node" atomic, if it is a band node.
+ * Do the same for all ancestors.
+ * Return a pointer to "node" (in the updated schedule tree).
+ */
+static __isl_give isl_schedule_node *atomic_ancestors(
+ __isl_take isl_schedule_node *node)
+{
+ int pos;
+
+ if (!node)
+ return NULL;
+ if (!isl_schedule_node_has_parent(node))
+ return node;
+
+ pos = isl_schedule_node_get_child_position(node);
+ node = isl_schedule_node_parent(node);
+ if (isl_schedule_node_get_type(node) == isl_schedule_node_band)
+ node = atomic(node);
+ node = atomic_ancestors(node);
+ node = isl_schedule_node_child(node, pos);
+
+ return node;
+}
+
+/* Collect all write references that require synchronization.
+ * "node" is assumed to point to the kernel node.
+ * Each reference is represented by a universe set in a space
+ *
+ * [S[i,j] -> R[]]
+ *
+ * with S[i,j] the statement instance space and R[] the array reference.
+ *
+ * This function should be called before block and thread filters are added.
+ *
+ * Synchronization is needed after a write if there is a subsequent read
+ * within the same block that may not be performed by the same thread.
+ * There should not be any dependences between different blocks,
+ * so we start with the flow dependences within the same kernel invocation
+ * and we subtract from these those dependences that are mapped
+ * to the same iteration of the bands where synchronization is inserted.
+ * We do not remove pairs of instances that are known to map to
+ * the same thread across different iterations of the intermediate
+ * bands because the read may be performed by a different thread
+ * than the one that needs the value if shared memory is involved.
+ *
+ * We also consider all pairs of possible writes that access the same
+ * memory location and that may be mapped to the same block but not
+ * to the same iteration of the intermediate bands.
+ * In theory, it would be possible for one thread to still be in
+ * a previous iteration of a loop in these bands.
+ * A write to global memory in this delayed thread could then overwrite
+ * a write from another thread that has already moved on to
+ * the next iteration.
+ *
+ * After computing the above writes paired off with reads or writes
+ * that depend on them, we project onto the domain writes.
+ * Sychronization is needed after writes to global memory
+ * through these references.
+ */
+static __isl_give isl_union_set *compute_sync_writes(
+ struct ppcg_kernel *kernel, __isl_keep isl_schedule_node *node)
+{
+ isl_union_map *local;
+ isl_union_map *may_writes, *shared_access;
+ isl_union_map *kernel_prefix, *thread_prefix;
+ isl_union_map *equal;
+ isl_union_set *wrap;
+ isl_union_set *domain;
+
+ domain = isl_schedule_node_get_universe_domain(node);
+ kernel_prefix = isl_schedule_node_get_prefix_schedule_union_map(node);
+ node = isl_schedule_node_copy(node);
+ node = gpu_tree_move_down_to_thread(node, kernel->core);
+ thread_prefix = isl_schedule_node_get_prefix_schedule_union_map(node);
+ isl_schedule_node_free(node);
+
+ may_writes = isl_union_map_copy(kernel->prog->scop->tagged_may_writes);
+ may_writes = isl_union_map_curry(may_writes);
+ may_writes = isl_union_map_intersect_domain(may_writes, domain);
+ may_writes = isl_union_map_uncurry(may_writes);
+ shared_access = isl_union_map_copy(may_writes);
+ shared_access = isl_union_map_apply_range(shared_access,
+ isl_union_map_reverse(may_writes));
+
+ local = isl_union_map_copy(kernel->prog->scop->tagged_dep_flow);
+ local = isl_union_map_union(local, shared_access);
+ local = isl_union_map_zip(local);
+
+ equal = isl_union_map_apply_range(kernel_prefix,
+ isl_union_map_reverse(isl_union_map_copy(kernel_prefix)));
+ wrap = isl_union_map_wrap(equal);
+ local = isl_union_map_intersect_domain(local, wrap);
+ equal = isl_union_map_apply_range(thread_prefix,
+ isl_union_map_reverse(isl_union_map_copy(thread_prefix)));
+ wrap = isl_union_map_wrap(equal);
+ local = isl_union_map_subtract_domain(local, wrap);
+
+ local = isl_union_map_zip(local);
+ local = isl_union_map_universe(local);
+
+ return isl_union_map_domain(local);
+}
+
+/* Group the domain elements into a single space, named kernelX,
+ * with X the kernel sequence number "kernel_id".
+ */
+static __isl_give isl_schedule_node *group_statements(
+ __isl_take isl_schedule_node *node, int kernel_id)
+{
+ char buffer[20];
+ isl_id *id;
+
+ if (!node)
+ return NULL;
+
+ snprintf(buffer, sizeof(buffer), "kernel%d", kernel_id);
+ id = isl_id_alloc(isl_schedule_node_get_ctx(node), buffer, NULL);
+ return isl_schedule_node_group(node, id);
+}
+
+/* Create a ppcg_kernel representing the domain instances that reach "node"
+ * and insert a mark node pointing to the ppcg_kernel before "node".
+ * The band that "node" points to is the band that needs to be mapped
+ * to block identifiers. The band that needs to be mapped to thread
+ * identifiers should be marked by a "thread" mark by the caller.
+ * This mark is removed by this function.
+ * If "scale" is set, then the band that "node" points to is scaled
+ * by "sizes".
+ *
+ * Mark all outer band nodes as atomic to ensure each kernel is only
+ * scheduled once.
+ * If the domain elements that reach "node" live in more than one space,
+ * then group the domain elements into a single space, named kernelX,
+ * with X the kernel sequence number.
+ *
+ * Insert a guard node governing the kernel node to ensure that
+ * no kernels with zero blocks are launched.
+ *
+ * Insert a context node describing the block and thread
+ * identifiers inside the kernel mark.
+ * The context node needs to be inserted after the effective block size
+ * has been determined such that the bounds on the thread identifiers
+ * would reflect the effective block size.
+ * Insert a filter node inside the context node mapping the statement
+ * instances to block identifiers. In particular, the block identifiers
+ * are equated to the partial schedule of band that was marked for mapping
+ * to blocks modulo the grid size.
+ * Insert a filter node inside the "thread" mark mapping the statement
+ * instances to thread identifiers. In particular, the thread identifiers
+ * are equated to the partial schedule of band that was marked for mapping
+ * to threads modulo the block size.
+ *
+ * Compute array reference groups for all arrays, set the local
+ * array bounds based on the set of domain instances that reach
+ * the kernel node, check the total amount of shared memory used
+ * and compute all group tilings.
+ * The array reference groups are computed after the block filter
+ * has been inserted because it affects the mapping to shared or
+ * private memory. This computation also requires the thread filter
+ * (in the ppcg_kernel object), but this thread filter should not
+ * have been added to the schedule tree yet since the computation
+ * requires the schedule of the band that needs to be mapped to
+ * threads before the privatization is applied.
+ *
+ * If any array reference group requires the band mapped to threads
+ * to be unrolled, then we perform the required unrolling.
+ *
+ * We save a copy of the schedule that may influence the mappings
+ * to shared or private memory in kernel->shared_schedule.
+ *
+ * Finally, we add synchronization and copy statements to the schedule tree,
+ * remove the "thread" mark and create representations for the local
+ * variables in the kernel.
+ *
+ * We keep a copy of the isl_id that points to the kernel to ensure
+ * that the kernel does not get destroyed if the schedule node
+ * is freed due to some error condition.
+ */
+static __isl_give isl_schedule_node *create_kernel(struct gpu_gen *gen,
+ __isl_take isl_schedule_node *node, int scale,
+ __isl_keep isl_multi_val *sizes)
+{
+ struct ppcg_kernel *kernel;
+ isl_id *id;
+ isl_schedule_node *node_thread;
+ isl_union_map *host_schedule;
+ isl_set *host_domain;
+ isl_union_set *domain;
+ int single_statement;
+
+ kernel = isl_calloc_type(gen->ctx, struct ppcg_kernel);
+ kernel = ppcg_kernel_create_local_arrays(kernel, gen->prog);
+ if (!kernel)
+ return isl_schedule_node_free(node);
+
+ domain = isl_schedule_node_get_domain(node);
+ single_statement = isl_union_set_n_set(domain) == 1;
+
+ kernel->ctx = gen->ctx;
+ kernel->prog = gen->prog;
+ kernel->options = gen->options;
+ kernel->context = extract_context(node, gen->prog);
+ kernel->core = isl_union_set_universe(isl_union_set_copy(domain));
+ kernel->arrays = accessed_by_domain(isl_union_set_copy(domain),
+ gen->prog);
+ kernel->n_grid = n_outer_coincidence(node);
+ node_thread = isl_schedule_node_copy(node);
+ node_thread = gpu_tree_move_down_to_thread(node_thread, kernel->core);
+ node_thread = isl_schedule_node_child(node_thread, 0);
+ kernel->n_block = n_outer_coincidence(node_thread);
+ isl_schedule_node_free(node_thread);
+ kernel->id = gen->kernel_id++;
+ read_grid_and_block_sizes(kernel, gen);
+
+ kernel->sync_writes = compute_sync_writes(kernel, node);
+
+ host_schedule = isl_schedule_node_get_prefix_schedule_union_map(node);
+ host_domain = isl_set_from_union_set(isl_union_map_range(
+ host_schedule));
+
+ node = atomic_ancestors(node);
+
+ id = isl_id_alloc(gen->ctx, "kernel", kernel);
+ id = isl_id_set_free_user(id, &ppcg_kernel_free_wrap);
+ node = isl_schedule_node_insert_mark(node, isl_id_copy(id));
+
+ if (!single_statement)
+ node = group_statements(node, kernel->id);
+
+ node = isl_schedule_node_child(node, 0);
+ node = split_band(node, kernel->n_grid);
+ kernel->block_ids = ppcg_scop_generate_names(gen->prog->scop,
+ kernel->n_grid, "b");
+ kernel->block_filter = set_schedule_modulo(node, kernel->block_ids,
+ kernel->grid_dim);
+ kernel->grid_size = extract_grid_size(kernel,
+ isl_union_set_copy(domain));
+ if (!kernel->options->wrap)
+ node = snap_band_to_sizes(node, kernel->grid_dim,
+ kernel->options);
+ if (scale)
+ node = scale_band(node, isl_multi_val_copy(sizes));
+ node = isl_schedule_node_parent(node);
+ if (!single_statement)
+ node = isl_schedule_node_parent(node);
+ node = insert_guard(node, kernel->context, kernel->grid_size,
+ gen->prog->scop);
+ node = gpu_tree_move_down_to_thread(node, kernel->core);
+ node = isl_schedule_node_child(node, 0);
+ node = split_band(node, kernel->n_block);
+ kernel->thread_ids = ppcg_scop_generate_names(gen->prog->scop,
+ kernel->n_block, "t");
+ kernel->thread_filter = set_schedule_modulo(node, kernel->thread_ids,
+ kernel->block_dim);
+ extract_block_size(kernel, domain);
+
+ node = gpu_tree_move_up_to_kernel(node);
+ node = isl_schedule_node_child(node, 0);
+ node = insert_context(kernel, node);
+ node = isl_schedule_node_child(node, 0);
+ node = isl_schedule_node_insert_filter(node,
+ isl_union_set_copy(kernel->block_filter));
+
+ node = gpu_tree_move_up_to_kernel(node);
+
+ if (gpu_group_references(kernel, node) < 0)
+ node = isl_schedule_node_free(node);
+ localize_bounds(kernel, host_domain);
+ isl_set_free(host_domain);
+
+ check_shared_memory_bound(kernel);
+ mark_global_arrays(kernel);
+ compute_group_tilings(kernel);
+
+ node = gpu_tree_move_down_to_thread(node, kernel->core);
+ node = isl_schedule_node_child(node, 0);
+ if (!kernel->options->wrap)
+ node = snap_band_to_sizes(node, kernel->block_dim,
+ kernel->options);
+ node = isl_schedule_node_insert_filter(node,
+ isl_union_set_copy(kernel->thread_filter));
+ if (kernel_requires_unroll(kernel)) {
+ node = isl_schedule_node_child(node, 0);
+ node = unroll(node);
+ }
+
+ node = gpu_tree_move_up_to_thread(node);
+ kernel->shared_schedule_dim =
+ isl_schedule_node_get_schedule_depth(node);
+ kernel->shared_schedule =
+ isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(node);
+
+ node = gpu_tree_move_up_to_kernel(node);
+
+ node = add_sync(kernel, node);
+ node = add_copies(kernel, node);
+
+ node = gpu_tree_move_down_to_thread(node, kernel->core);
+ node = isl_schedule_node_delete(node);
+
+ node = gpu_tree_move_up_to_kernel(node);
+
+ if (create_kernel_vars(kernel) < 0)
+ node = isl_schedule_node_free(node);
+
+ if (!single_statement)
+ node = isl_schedule_node_parent(node);
+ node = isl_schedule_node_parent(node);
+
+ isl_id_free(id);
+ return node;
+}
+
+/* Insert a zero-dimensional permutable band at "node".
+ */
+static __isl_give isl_schedule_node *insert_empty_permutable_band(
+ __isl_take isl_schedule_node *node)
+{
+ isl_space *space;
+ isl_schedule *schedule;
+ isl_union_set *domain;
+ isl_multi_union_pw_aff *mupa;
+
+ schedule = isl_schedule_node_get_schedule(node);
+ domain = isl_schedule_get_domain(schedule);
+ space = isl_union_set_get_space(domain);
+ isl_union_set_free(domain);
+ isl_schedule_free(schedule);
+
+ space = isl_space_set_from_params(space);
+ mupa = isl_multi_union_pw_aff_zero(space);
+ node = isl_schedule_node_insert_partial_schedule(node, mupa);
+ node = isl_schedule_node_band_set_permutable(node, 1);
+
+ return node;
+}
+
+/* If "node" is the outermost permutable band that can be mapped to block and
+ * thread identifiers in its branch (or a leaf with no such outer bands),
+ * then mark the band as such, attaching a ppcg_kernel to the mark.
+ *
+ * If "node" originally points to a leaf, then insert a zero-dimensional
+ * permutable band such that we can assume that "node" always
+ * points to a band node.
+ *
+ * Tile "node" using user specified tile sizes, after splitting the band
+ * if the number of specified tile sizes is smaller than the dimension
+ * of the band. Mark the point band of this tiling as the band that
+ * needs to be mapped to threads.
+ * Create a kernel representing the domain instances that reach "node" and
+ * insert a mark node pointing to the ppcg_kernel before the band node.
+ */
+static __isl_give isl_schedule_node *mark_outer_permutable(
+ __isl_take isl_schedule_node *node, void *user)
+{
+ struct gpu_gen *gen = user;
+ int outer;
+ int scale;
+ int tile_len;
+ int *tile_size;
+ isl_id *id;
+ isl_multi_val *sizes;
+
+ outer = is_outer_tilable(node);
+ if (outer < 0)
+ return isl_schedule_node_free(node);
+ if (!outer)
+ return node;
+
+ if (isl_schedule_node_get_type(node) == isl_schedule_node_leaf)
+ node = insert_empty_permutable_band(node);
+
+ tile_len = isl_schedule_node_band_n_member(node);
+ tile_size = read_tile_sizes(gen, &tile_len);
+ if (!tile_size)
+ return isl_schedule_node_free(node);
+ if (tile_len < isl_schedule_node_band_n_member(node))
+ node = isl_schedule_node_band_split(node, tile_len);
+ sizes = construct_band_tiles_sizes(node, tile_size);
+ node = tile_band(node, isl_multi_val_copy(sizes));
+ node = isl_schedule_node_child(node, 0);
+ id = isl_id_alloc(gen->ctx, "thread", NULL);
+ node = isl_schedule_node_insert_mark(node, id);
+ node = isl_schedule_node_parent(node);
+
+ scale = gen->options->scale_tile_loops;
+ node = create_kernel(gen, node, scale, sizes);
+ isl_multi_val_free(sizes);
+ free(tile_size);
+
+ return node;
+}
+
+/* Does the subtree rooted at "node" have any suitably permutable band nodes?
+ * That is, does it have any nodes that are permutable and that
+ * have a least one coincident dimension?
+ */
+static int subtree_has_permutable_bands(__isl_keep isl_schedule_node *node)
+{
+ int any_parallelism = 0;
+
+ if (isl_schedule_node_foreach_descendant_top_down(node, &set_permutable,
+ &any_parallelism) < 0 &&
+ !any_parallelism)
+ return -1;
+
+ return any_parallelism;
+}
+
+/* Mark all variables that are accessed by the statement instances in "domain"
+ * and that are local to "prog" as requiring a declaration in the host code.
+ */
+static int declare_accessed_local_variables(struct gpu_prog *prog,
+ __isl_keep isl_union_set *domain)
+{
+ isl_union_set *arrays;
+ int i;
+
+ if (!ppcg_scop_any_hidden_declarations(prog->scop))
+ return 0;
+ arrays = accessed_by_domain(isl_union_set_copy(domain), prog);
+
+ for (i = 0; i < prog->n_array; ++i) {
+ isl_space *space;
+ isl_set *set;
+ int empty;
+
+ if (!prog->array[i].local)
+ continue;
+ space = isl_set_get_space(prog->array[i].extent);
+ set = isl_union_set_extract_set(arrays, space);
+ empty = isl_set_plain_is_empty(set);
+ isl_set_free(set);
+ if (empty < 0)
+ goto error;
+ if (!empty)
+ prog->array[i].declare_local = 1;
+ }
+
+ isl_union_set_free(arrays);
+ return 0;
+error:
+ isl_union_set_free(arrays);
+ return -1;
+}
+
+/* If "node" points to a set node, then separate its children
+ * into subtrees that have suitably permutable bands and
+ * those that do not.
+ * Adjust the schedule tree in order to execute the second group
+ * after the first group and return a pointer to the first group,
+ * assuming there are any such subtrees.
+ * Mark all local variables in "prog" that are accessed by
+ * the second group as requiring a declaration on the host.
+ */
+static __isl_give isl_schedule_node *isolate_permutable_subtrees(
+ __isl_take isl_schedule_node *node, struct gpu_prog *prog)
+{
+ isl_space *space;
+ isl_union_set *filter;
+ int i, n;
+
+ if (!node)
+ return NULL;
+ if (isl_schedule_node_get_type(node) != isl_schedule_node_set)
+ return node;
+
+ n = isl_schedule_node_n_children(node);
+ if (n < 0)
+ return isl_schedule_node_free(node);
+
+ node = isl_schedule_node_child(node, 0);
+ filter = isl_schedule_node_filter_get_filter(node);
+ node = isl_schedule_node_parent(node);
+ space = isl_union_set_get_space(filter);
+ isl_union_set_free(filter);
+ filter = isl_union_set_empty(space);
+
+ for (i = 0; i < n; ++i) {
+ int parallelism;
+
+ node = isl_schedule_node_child(node, i);
+ parallelism = subtree_has_permutable_bands(node);
+ if (parallelism < 0) {
+ node = isl_schedule_node_free(node);
+ } else if (!parallelism) {
+ isl_union_set *filter_i;
+ filter_i = isl_schedule_node_filter_get_filter(node);
+ filter = isl_union_set_union(filter, filter_i);
+ }
+ node = isl_schedule_node_parent(node);
+ }
+
+ if (declare_accessed_local_variables(prog, filter) < 0)
+ node = isl_schedule_node_free(node);
+ node = isl_schedule_node_order_after(node, filter);
+
+ return node;
+}
+
+/* Replace any reference to an array element in the range of "copy"
+ * by a reference to all array elements (defined by the extent of the array).
+ */
+static __isl_give isl_union_map *approximate_copy_out(
+ __isl_take isl_union_map *copy, struct gpu_prog *prog)
+{
+ int i;
+ isl_union_map *res;
+
+ res = isl_union_map_empty(isl_union_map_get_space(copy));
+
+ for (i = 0; i < prog->n_array; ++i) {
+ isl_space *space;
+ isl_set *set;
+ isl_union_map *copy_i;
+ isl_union_set *extent, *domain;
+
+ space = isl_space_copy(prog->array[i].space);
+ extent = isl_union_set_from_set(isl_set_universe(space));
+ copy_i = isl_union_map_copy(copy);
+ copy_i = isl_union_map_intersect_range(copy_i, extent);
+ set = isl_set_copy(prog->array[i].extent);
+ extent = isl_union_set_from_set(set);
+ domain = isl_union_map_domain(copy_i);
+ copy_i = isl_union_map_from_domain_and_range(domain, extent);
+ res = isl_union_map_union(res, copy_i);
+ }
+
+ isl_union_map_free(copy);
+
+ return res;
+}
+
+/* Insert "kernel" marks that point to a ppcg_kernel structure
+ * in front of all outermost tilable band that (by construction)
+ * have at least one parallel loop.
+ */
+static __isl_give isl_schedule_node *mark_kernels(struct gpu_gen *gen,
+ __isl_take isl_schedule_node *node)
+{
+ return isl_schedule_node_map_descendant_bottom_up(node,
+ &mark_outer_permutable, gen);
+}
+
+/* Save the schedule "schedule" to a file called "filename".
+ * The schedule is printed in block style.
+ */
+static void save_schedule(__isl_keep isl_schedule *schedule,
+ const char *filename)
+{
+ FILE *file;
+ isl_ctx *ctx;
+ isl_printer *p;
+
+ if (!schedule)
+ return;
+
+ file = fopen(filename, "w");
+ if (!file) {
+ fprintf(stderr, "Unable to open '%s' for writing\n", filename);
+ return;
+ }
+ ctx = isl_schedule_get_ctx(schedule);
+ p = isl_printer_to_file(ctx, file);
+ p = isl_printer_set_yaml_style(p, ISL_YAML_STYLE_BLOCK);
+ p = isl_printer_print_schedule(p, schedule);
+ isl_printer_free(p);
+ fclose(file);
+}
+
+/* Load and return a schedule from a file called "filename".
+ */
+static __isl_give isl_schedule *load_schedule(isl_ctx *ctx,
+ const char *filename)
+{
+ FILE *file;
+ isl_schedule *schedule;
+
+ file = fopen(filename, "r");
+ if (!file) {
+ fprintf(stderr, "Unable to open '%s' for reading\n", filename);
+ return NULL;
+ }
+ schedule = isl_schedule_read_from_file(ctx, file);
+ fclose(file);
+
+ return schedule;
+}
+
+/* Construct schedule constraints from the dependences in prog->scop and
+ * the array order dependences in prog->array_order.
+ *
+ * If live range reordering is allowed, then we need to make sure
+ * that live ranges on arrays are not run in parallel since doing
+ * so would require array expansion. We therefore add the array
+ * order dependences to the coincidence dependences. Non-zero array
+ * order dependences will then prevent a schedule dimension from being
+ * considered parallel.
+ * Live ranges derived from scalars are allowed to be run in parallel
+ * since we force the scalars to be mapped to private memory in
+ * check_scalar_live_ranges.
+ * If live range reordering is allowed, then the false dependences
+ * are not added to the validity constraints as that would prevent
+ * reordering. Instead, the external false dependences that enforce that reads
+ * from potentially live-in data precede any later write and
+ * that writes of potentially live-out data follow any other earlier write
+ * are added to the validity and the coincidence constraints.
+ * The false dependences are still added to the proximity constraints
+ * for consistency with the case where live range reordering is not allowed.
+ * The coincidence constraints then consist of flow dependences,
+ * external false dependences and array order dependences.
+ * The independences can be filtered out from the first two sets.
+ * They have already been filtered out from the array order dependences
+ * on a per array basis in collect_order_dependences.
+ * There is no need for a per array handling of the other two sets
+ * as there should be no flow or external false dependence on local
+ * variables that can be filtered out.
+ */
+static __isl_give isl_schedule_constraints *construct_schedule_constraints(
+ struct gpu_prog *prog)
+{
+ isl_union_set *domain;
+ isl_union_map *dep_raw, *dep;
+ isl_union_map *validity, *proximity, *coincidence;
+ isl_schedule_constraints *sc;
+
+ domain = isl_union_set_copy(prog->scop->domain);
+ sc = isl_schedule_constraints_on_domain(domain);
+ sc = isl_schedule_constraints_set_context(sc,
+ isl_set_copy(prog->scop->context));
+ if (prog->scop->options->live_range_reordering) {
+ sc = isl_schedule_constraints_set_conditional_validity(sc,
+ isl_union_map_copy(prog->scop->tagged_dep_flow),
+ isl_union_map_copy(prog->scop->tagged_dep_order));
+ proximity = isl_union_map_copy(prog->scop->dep_flow);
+ validity = isl_union_map_copy(proximity);
+ validity = isl_union_map_union(validity,
+ isl_union_map_copy(prog->scop->dep_forced));
+ proximity = isl_union_map_union(proximity,
+ isl_union_map_copy(prog->scop->dep_false));
+ coincidence = isl_union_map_copy(validity);
+ coincidence = isl_union_map_subtract(coincidence,
+ isl_union_map_copy(prog->scop->independence));
+ coincidence = isl_union_map_union(coincidence,
+ isl_union_map_copy(prog->array_order));
+ } else {
+ dep_raw = isl_union_map_copy(prog->scop->dep_flow);
+ dep = isl_union_map_copy(prog->scop->dep_false);
+ dep = isl_union_map_union(dep, dep_raw);
+ dep = isl_union_map_coalesce(dep);
+ proximity = isl_union_map_copy(dep);
+ coincidence = isl_union_map_copy(dep);
+ validity = dep;
+ }
+ sc = isl_schedule_constraints_set_validity(sc, validity);
+ sc = isl_schedule_constraints_set_coincidence(sc, coincidence);
+ sc = isl_schedule_constraints_set_proximity(sc, proximity);
+
+ if (prog->scop->options->debug->dump_schedule_constraints)
+ isl_schedule_constraints_dump(sc);
+ return sc;
+}
+
+/* Compute an appropriate schedule based on the accesses in
+ * gen->read and gen->write.
+ *
+ * We derive schedule constraints from the dependences in gen->prog->scop
+ * and then use isl to compute a schedule that has a parallel loop
+ * in each tilable band.
+ */
+static __isl_give isl_schedule *compute_schedule(struct gpu_gen *gen)
+{
+ isl_schedule_constraints *sc;
+ isl_schedule *schedule;
+
+ sc = construct_schedule_constraints(gen->prog);
+ schedule = isl_schedule_constraints_compute_schedule(sc);
+
+ return schedule;
+}
+
+/* If the band node "node" has exactly one member then mark it permutable.
+ */
+static __isl_give isl_schedule_node *band_set_permutable(
+ __isl_take isl_schedule_node *node,
+ __isl_keep isl_schedule_constraints *sc)
+{
+ if (isl_schedule_node_band_n_member(node) == 1)
+ node = isl_schedule_node_band_set_permutable(node, 1);
+
+ return node;
+}
+
+/* Return the coincidence constraints between pairs of instances
+ * that are scheduled together by the ancestors of "node".
+ * That is, select those coincidence constraints that relate
+ * pairs of instances that have the same value for the prefix schedule.
+ * If the schedule depth is zero, then the prefix schedule does not
+ * contain any information, so we intersect domain and range
+ * of the schedule constraints with the reaching domain elements instead.
+ */
+static __isl_give isl_union_map *get_local_coincidence(
+ __isl_keep isl_schedule_node *node,
+ __isl_keep isl_schedule_constraints *sc)
+{
+ isl_union_map *coincidence;
+ isl_multi_union_pw_aff *prefix;
+ isl_union_pw_multi_aff *contraction;
+
+ coincidence = isl_schedule_constraints_get_coincidence(sc);
+ contraction = isl_schedule_node_get_subtree_contraction(node);
+ if (isl_schedule_node_get_schedule_depth(node) == 0) {
+ isl_union_set *domain;
+
+ domain = isl_schedule_node_get_domain(node);
+ domain = isl_union_set_preimage_union_pw_multi_aff(domain,
+ contraction);
+ coincidence = isl_union_map_intersect_domain(coincidence,
+ isl_union_set_copy(domain));
+ coincidence = isl_union_map_intersect_range(coincidence,
+ domain);
+ return coincidence;
+ }
+
+ prefix = isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(node);
+ prefix = isl_multi_union_pw_aff_pullback_union_pw_multi_aff(prefix,
+ contraction);
+ return isl_union_map_eq_at_multi_union_pw_aff(coincidence, prefix);
+}
+
+/* For each member in the band node "node", determine whether
+ * it is coincident with respect to the outer nodes and mark
+ * it accordingly.
+ *
+ * That is, for each coincidence constraint between pairs
+ * of instances that are scheduled together by the outer nodes,
+ * check that domain and range are assigned the same value
+ * by the band member. This test is performed by checking
+ * that imposing the same value for the band member does not
+ * remove any elements from the set of coincidence constraints.
+ */
+static __isl_give isl_schedule_node *band_set_coincident(
+ __isl_take isl_schedule_node *node,
+ __isl_keep isl_schedule_constraints *sc)
+{
+ isl_union_map *coincidence;
+ isl_union_pw_multi_aff *contraction;
+ isl_multi_union_pw_aff *partial;
+ int i, n;
+
+ coincidence = get_local_coincidence(node, sc);
+
+ partial = isl_schedule_node_band_get_partial_schedule(node);
+ contraction = isl_schedule_node_get_subtree_contraction(node);
+ partial = isl_multi_union_pw_aff_pullback_union_pw_multi_aff(partial,
+ contraction);
+ n = isl_schedule_node_band_n_member(node);
+ for (i = 0; i < n; ++i) {
+ isl_union_map *coincidence_i;
+ isl_union_pw_aff *upa;
+ isl_multi_union_pw_aff *partial_i;
+ int subset;
+
+ upa = isl_multi_union_pw_aff_get_union_pw_aff(partial, i);
+ partial_i = isl_multi_union_pw_aff_from_union_pw_aff(upa);
+ coincidence_i = isl_union_map_copy(coincidence);
+ coincidence_i = isl_union_map_eq_at_multi_union_pw_aff(
+ coincidence_i, partial_i);
+ subset = isl_union_map_is_subset(coincidence, coincidence_i);
+ isl_union_map_free(coincidence_i);
+
+ if (subset < 0)
+ break;
+ node = isl_schedule_node_band_member_set_coincident(node, i,
+ subset);
+ }
+ if (i < n)
+ node = isl_schedule_node_free(node);
+ isl_multi_union_pw_aff_free(partial);
+ isl_union_map_free(coincidence);
+
+ return node;
+}
+
+/* If "node" is a band, then set its properties.
+ *
+ * In particular, if the band has exactly one member, then mark it permutable.
+ * Mark the band member coincident based on the coincidence constraints
+ * of "sc".
+ */
+static __isl_give isl_schedule_node *set_band_properties(
+ __isl_take isl_schedule_node *node, void *user)
+{
+ isl_schedule_constraints *sc = user;
+
+ if (isl_schedule_node_get_type(node) != isl_schedule_node_band)
+ return node;
+ if (isl_schedule_node_band_n_member(node) == 0)
+ return node;
+
+ node = band_set_permutable(node, sc);
+ node = band_set_coincident(node, sc);
+
+ return node;
+}
+
+/* Return the original schedule with all bands marked permutable and
+ * all band members marked coincident based on the coincidence constraints.
+ * The bands are explicitly marked permutable so that they will be considered
+ * by mark_outer_permutable.
+ */
+static __isl_give isl_schedule *determine_properties_original_schedule(
+ struct gpu_gen *gen)
+{
+ isl_schedule *schedule;
+ isl_schedule_constraints *sc;
+
+ schedule = isl_schedule_copy(gen->prog->scop->schedule);
+ sc = construct_schedule_constraints(gen->prog);
+ schedule = isl_schedule_map_schedule_node_bottom_up(schedule,
+ &set_band_properties, sc);
+ isl_schedule_constraints_free(sc);
+
+ return schedule;
+}
+
+/* Obtain a schedule for the scop, by reading it from
+ * a file, by computing one or by determining the properties
+ * of the original schedule.
+ */
+static __isl_give isl_schedule *get_schedule(struct gpu_gen *gen)
+{
+ isl_schedule *schedule;
+
+ if (gen->options->load_schedule_file) {
+ schedule = load_schedule(gen->ctx,
+ gen->options->load_schedule_file);
+ } else {
+ if (gen->options->reschedule)
+ schedule = compute_schedule(gen);
+ else
+ schedule = determine_properties_original_schedule(gen);
+ if (gen->options->save_schedule_file)
+ save_schedule(schedule,
+ gen->options->save_schedule_file);
+ }
+ if (gen->options->debug->dump_schedule)
+ isl_schedule_dump(schedule);
+
+ return schedule;
+}
+
+/* Construct the string "<a>_<b>".
+ */
+static char *concat(isl_ctx *ctx, const char *a, const char *b)
+{
+ isl_printer *p;
+ char *s;
+
+ p = isl_printer_to_str(ctx);
+ p = isl_printer_print_str(p, a);
+ p = isl_printer_print_str(p, "_");
+ p = isl_printer_print_str(p, b);
+ s = isl_printer_get_str(p);
+ isl_printer_free(p);
+
+ return s;
+}
+
+/* For each array in "prog" of which an element appears in "accessed" and
+ * that is not a read only scalar, create a zero-dimensional universe set
+ * of which the tuple id has name "<prefix>_<name of array>" and a user
+ * pointer pointing to the array (gpu_array_info).
+ *
+ * If the array is local to "prog", then make sure it will be declared
+ * in the host code.
+ *
+ * Return the list of these universe sets.
+ */
+static __isl_give isl_union_set_list *create_copy_filters(struct gpu_prog *prog,
+ const char *prefix, __isl_take isl_union_set *accessed)
+{
+ int i;
+ isl_ctx *ctx;
+ isl_union_set_list *filters;
+
+ ctx = prog->ctx;
+ filters = isl_union_set_list_alloc(ctx, 0);
+ for (i = 0; i < prog->n_array; ++i) {
+ struct gpu_array_info *array = &prog->array[i];
+ isl_space *space;
+ isl_set *accessed_i;
+ int empty;
+ char *name;
+ isl_id *id;
+ isl_union_set *uset;
+
+ if (gpu_array_is_read_only_scalar(array))
+ continue;
+
+ space = isl_space_copy(array->space);
+ accessed_i = isl_union_set_extract_set(accessed, space);
+ empty = isl_set_plain_is_empty(accessed_i);
+ isl_set_free(accessed_i);
+ if (empty < 0) {
+ filters = isl_union_set_list_free(filters);
+ break;
+ }
+ if (empty)
+ continue;
+
+ array->global = 1;
+ if (array->local)
+ array->declare_local = 1;
+
+ name = concat(ctx, prefix, array->name);
+ id = name ? isl_id_alloc(ctx, name, array) : NULL;
+ free(name);
+ space = isl_space_set_alloc(ctx, 0, 0);
+ space = isl_space_set_tuple_id(space, isl_dim_set, id);
+ uset = isl_union_set_from_set(isl_set_universe(space));
+
+ filters = isl_union_set_list_add(filters, uset);
+ }
+ isl_union_set_free(accessed);
+
+ return filters;
+}
+
+/* Make sure that code for the statements in "filters" that
+ * copy arrays to or from the device is only generated when
+ * the size of the corresponding array is positive.
+ * That is, add a set node underneath "graft" with "filters" as children
+ * and for each child add a guard that the selects the parameter
+ * values for which the corresponding array has a positive size.
+ * The array is available in the user pointer of the statement identifier.
+ * "depth" is the schedule depth of the position where "graft"
+ * will be added.
+ */
+static __isl_give isl_schedule_node *insert_positive_size_guards(
+ __isl_take isl_schedule_node *graft,
+ __isl_take isl_union_set_list *filters, int depth)
+{
+ int i, n;
+
+ graft = isl_schedule_node_child(graft, 0);
+ graft = isl_schedule_node_insert_set(graft, filters);
+ n = isl_schedule_node_n_children(graft);
+ for (i = 0; i < n; ++i) {
+ isl_union_set *filter;
+ isl_set *domain, *guard;
+ isl_id *id;
+ struct gpu_array_info *array;
+
+ graft = isl_schedule_node_child(graft, i);
+ filter = isl_schedule_node_filter_get_filter(graft);
+ domain = isl_set_from_union_set(filter);
+ id = isl_set_get_tuple_id(domain);
+ array = isl_id_get_user(id);
+ isl_id_free(id);
+ isl_set_free(domain);
+ guard = gpu_array_positive_size_guard(array);
+ guard = isl_set_from_params(guard);
+ guard = isl_set_add_dims(guard, isl_dim_set, depth);
+ graft = isl_schedule_node_child(graft, 0);
+ graft = isl_schedule_node_insert_guard(graft, guard);
+ graft = isl_schedule_node_parent(graft);
+ graft = isl_schedule_node_parent(graft);
+ }
+ graft = isl_schedule_node_parent(graft);
+
+ return graft;
+}
+
+/* Create a graft for copying arrays to or from the device,
+ * whenever the size of the array is strictly positive.
+ * Each statement is called "<prefix>_<name of array>" and
+ * the identifier has a user pointer pointing to the array.
+ * The graft will be added at the position specified by "node".
+ * "copy" contains the array elements that need to be copied.
+ * Only arrays of which some elements need to be copied
+ * will have a corresponding statement in the graph.
+ * Note though that each such statement will copy the entire array.
+ */
+static __isl_give isl_schedule_node *create_copy_device(struct gpu_prog *prog,
+ __isl_keep isl_schedule_node *node, const char *prefix,
+ __isl_take isl_union_set *copy)
+{
+ int depth;
+ isl_ctx *ctx;
+ isl_space *space;
+ isl_union_set *all, *domain;
+ isl_union_set_list *filters;
+ isl_union_map *extension;
+ isl_schedule_node *graft;
+
+ ctx = prog->ctx;
+ depth = isl_schedule_node_get_schedule_depth(node);
+ filters = create_copy_filters(prog, prefix, copy);
+ all = isl_union_set_list_union(isl_union_set_list_copy(filters));
+
+ space = depth < 0 ? NULL : isl_space_set_alloc(ctx, 0, depth);
+ domain = isl_union_set_from_set(isl_set_universe(space));
+ extension = isl_union_map_from_domain_and_range(domain, all);
+ graft = isl_schedule_node_from_extension(extension);
+
+ if (!filters)
+ return isl_schedule_node_free(graft);
+ if (isl_union_set_list_n_union_set(filters) == 0) {
+ isl_union_set_list_free(filters);
+ return graft;
+ }
+
+ return insert_positive_size_guards(graft, filters, depth);
+}
+
+/* Return (the universe spaces of) the arrays that are declared
+ * inside the scop corresponding to "prog" and for which all
+ * potential writes inside the scop form a subset of "domain".
+ */
+static __isl_give isl_union_set *extract_local_accesses(struct gpu_prog *prog,
+ __isl_keep isl_union_set *domain)
+{
+ int i;
+ isl_union_set *local;
+
+ local = isl_union_set_empty(isl_union_set_get_space(domain));
+
+ for (i = 0; i < prog->n_array; ++i) {
+ isl_set *set;
+ isl_union_map *to_outer;
+ isl_union_map *may_write;
+ isl_union_set *write_domain;
+ isl_union_set *fields;
+ int subset;
+
+ if (!prog->array[i].local)
+ continue;
+
+ set = isl_set_universe(isl_space_copy(prog->array[i].space));
+ to_outer = isl_union_map_copy(prog->to_outer);
+ to_outer = isl_union_map_intersect_range(to_outer,
+ isl_union_set_from_set(isl_set_copy(set)));
+ fields = isl_union_map_domain(to_outer);
+ may_write = isl_union_map_copy(prog->may_write);
+ may_write = isl_union_map_intersect_range(may_write, fields);
+ write_domain = isl_union_map_domain(may_write);
+ subset = isl_union_set_is_subset(write_domain, domain);
+ isl_union_set_free(write_domain);
+
+ if (subset < 0) {
+ isl_set_free(set);
+ return isl_union_set_free(local);
+ } else if (subset) {
+ local = isl_union_set_add_set(local, set);
+ } else {
+ isl_set_free(set);
+ }
+ }
+
+ return local;
+}
+
+/* Internal data structure for node_may_persist.
+ *
+ * "tagger" maps tagged iteration domains to the corresponding untagged
+ * iteration domain.
+ *
+ * "may_persist_flow" is the set of all tagged dataflow dependences
+ * with those dependences removed that either precede or follow
+ * the kernel launch in a sequence.
+ * "inner_band_flow" is the set of all tagged dataflow dependences
+ * that are local to a given iteration of the outer band nodes
+ * with respect to the current node.
+ * "local_flow" is equal to "inner_band_flow", except that the domain
+ * and the range have been intersected with intermediate filters
+ * on children of sets or sequences.
+ */
+struct ppcg_may_persist_data {
+ isl_union_pw_multi_aff *tagger;
+
+ isl_union_map *local_flow;
+ isl_union_map *inner_band_flow;
+ isl_union_map *may_persist_flow;
+};
+
+/* Update the information in "data" based on the band ancestor "node".
+ *
+ * In particular, we restrict the dependences in data->local_flow
+ * to those dependence where the source and the sink occur in
+ * the same iteration of the given band node.
+ * We also update data->inner_band_flow to the new value of
+ * data->local_flow.
+ */
+static int update_may_persist_at_band(__isl_keep isl_schedule_node *node,
+ struct ppcg_may_persist_data *data)
+{
+ isl_multi_union_pw_aff *partial;
+ isl_union_pw_multi_aff *contraction;
+ isl_union_map *flow;
+
+ if (isl_schedule_node_band_n_member(node) == 0)
+ return 0;
+
+ partial = isl_schedule_node_band_get_partial_schedule(node);
+ contraction = isl_schedule_node_get_subtree_contraction(node);
+ partial = isl_multi_union_pw_aff_pullback_union_pw_multi_aff(partial,
+ contraction);
+ partial = isl_multi_union_pw_aff_pullback_union_pw_multi_aff(partial,
+ isl_union_pw_multi_aff_copy(data->tagger));
+
+ flow = data->local_flow;
+ flow = isl_union_map_eq_at_multi_union_pw_aff(flow, partial);
+ data->local_flow = flow;
+
+ isl_union_map_free(data->inner_band_flow);
+ data->inner_band_flow = isl_union_map_copy(data->local_flow);
+
+ return 0;
+}
+
+/* Given a set of local reaching domain elements "domain",
+ * expand them to the corresponding leaf domain elements using "contraction"
+ * and insert the array references tags using data->tagger.
+ */
+static __isl_give isl_union_set *expand_and_tag(
+ __isl_take isl_union_set *domain,
+ __isl_take isl_union_pw_multi_aff *contraction,
+ struct ppcg_may_persist_data *data)
+{
+ domain = isl_union_set_preimage_union_pw_multi_aff(domain,
+ contraction);
+ domain = isl_union_set_preimage_union_pw_multi_aff(domain,
+ isl_union_pw_multi_aff_copy(data->tagger));
+ return domain;
+}
+
+/* Given a filter node that is the child of a set or sequence node,
+ * restrict data->local_flow to refer only to those elements
+ * in the filter of the node.
+ * "contraction" maps the leaf domain elements of the schedule tree
+ * to the corresponding domain elements at (the parent of) "node".
+ */
+static int filter_flow(__isl_keep isl_schedule_node *node,
+ struct ppcg_may_persist_data *data,
+ __isl_take isl_union_pw_multi_aff *contraction)
+{
+ isl_union_set *filter;
+ isl_union_map *flow;
+
+ flow = data->local_flow;
+ filter = isl_schedule_node_filter_get_filter(node);
+ filter = expand_and_tag(filter, contraction, data);
+ flow = isl_union_map_intersect_domain(flow, isl_union_set_copy(filter));
+ flow = isl_union_map_intersect_range(flow, filter);
+ data->local_flow = flow;
+
+ return 0;
+}
+
+/* Given a filter node "node", collect the filters on all preceding siblings
+ * (which are also filter nodes), add them to "filters" and return the result.
+ */
+static __isl_give isl_union_set *add_previous_filters(
+ __isl_take isl_union_set *filters, __isl_keep isl_schedule_node *node)
+{
+ isl_schedule_node *sibling;
+
+ sibling = isl_schedule_node_copy(node);
+ while (sibling && isl_schedule_node_has_previous_sibling(sibling)) {
+ isl_union_set *filter;
+
+ sibling = isl_schedule_node_previous_sibling(sibling);
+ filter = isl_schedule_node_filter_get_filter(sibling);
+ filters = isl_union_set_union(filters, filter);
+ }
+ isl_schedule_node_free(sibling);
+ if (!sibling)
+ return isl_union_set_free(filters);
+
+ return filters;
+}
+
+/* Given a filter node "node", collect the filters on all following siblings
+ * (which are also filter nodes), add them to "filters" and return the result.
+ */
+static __isl_give isl_union_set *add_next_filters(
+ __isl_take isl_union_set *filters, __isl_keep isl_schedule_node *node)
+{
+ isl_schedule_node *sibling;
+
+ sibling = isl_schedule_node_copy(node);
+ while (sibling && isl_schedule_node_has_next_sibling(sibling)) {
+ isl_union_set *filter;
+
+ sibling = isl_schedule_node_next_sibling(sibling);
+ filter = isl_schedule_node_filter_get_filter(sibling);
+ filters = isl_union_set_union(filters, filter);
+ }
+ isl_schedule_node_free(sibling);
+ if (!sibling)
+ return isl_union_set_free(filters);
+
+ return filters;
+}
+
+/* Remove those flow dependences from data->may_persist_flow
+ * that flow between elements of "domain" within the same iteration
+ * of all outer band nodes.
+ * "contraction" maps the leaf domain elements of the schedule tree
+ * to the corresponding elements "domain".
+ */
+static void remove_external_flow(struct ppcg_may_persist_data *data,
+ __isl_take isl_union_set *domain,
+ __isl_keep isl_union_pw_multi_aff *contraction)
+{
+ isl_union_map *flow;
+
+ contraction = isl_union_pw_multi_aff_copy(contraction);
+ domain = expand_and_tag(domain, contraction, data);
+ flow = isl_union_map_copy(data->local_flow);
+ flow = isl_union_map_intersect_domain(flow, isl_union_set_copy(domain));
+ flow = isl_union_map_intersect_range(flow, domain);
+
+ data->may_persist_flow = isl_union_map_subtract(data->may_persist_flow,
+ flow);
+}
+
+/* Update the information in "data" based on the filter ancestor "node".
+ * We only need to modify anything if the filter is the child
+ * of a set or sequence node.
+ *
+ * In the case of a sequence, we remove the dependences between
+ * statement instances that are both executed either before or
+ * after the subtree that will be mapped to a kernel, within
+ * the same iteration of outer bands.
+ *
+ * In both cases, we restrict data->local_flow to the current child.
+ */
+static int update_may_persist_at_filter(__isl_keep isl_schedule_node *node,
+ struct ppcg_may_persist_data *data)
+{
+ enum isl_schedule_node_type type;
+ isl_schedule_node *parent;
+ isl_space *space;
+ isl_union_pw_multi_aff *contraction;
+ isl_union_set *before, *after, *filter;
+ isl_union_map *flow;
+
+ type = isl_schedule_node_get_parent_type(node);
+ if (type != isl_schedule_node_sequence && type != isl_schedule_node_set)
+ return 0;
+
+ parent = isl_schedule_node_copy(node);
+ parent = isl_schedule_node_parent(parent);
+ contraction = isl_schedule_node_get_subtree_contraction(parent);
+ isl_schedule_node_free(parent);
+
+ if (type == isl_schedule_node_set)
+ return filter_flow(node, data, contraction);
+
+ filter = isl_schedule_node_filter_get_filter(node);
+ space = isl_union_set_get_space(filter);
+ isl_union_set_free(filter);
+ before = isl_union_set_empty(space);
+ after = isl_union_set_copy(before);
+ before = add_previous_filters(before, node);
+ after = add_next_filters(after, node);
+
+ remove_external_flow(data, before, contraction);
+ remove_external_flow(data, after, contraction);
+
+ return filter_flow(node, data, contraction);
+}
+
+/* Update the information in "data" based on the ancestor "node".
+ */
+static isl_stat update_may_persist_at(__isl_keep isl_schedule_node *node,
+ void *user)
+{
+ struct ppcg_may_persist_data *data = user;
+
+ switch (isl_schedule_node_get_type(node)) {
+ case isl_schedule_node_error:
+ return isl_stat_error;
+ case isl_schedule_node_context:
+ case isl_schedule_node_domain:
+ case isl_schedule_node_expansion:
+ case isl_schedule_node_extension:
+ case isl_schedule_node_guard:
+ case isl_schedule_node_leaf:
+ case isl_schedule_node_mark:
+ case isl_schedule_node_sequence:
+ case isl_schedule_node_set:
+ break;
+ case isl_schedule_node_band:
+ if (update_may_persist_at_band(node, data) < 0)
+ return isl_stat_error;
+ break;
+ case isl_schedule_node_filter:
+ if (update_may_persist_at_filter(node, data) < 0)
+ return isl_stat_error;
+ break;
+ }
+
+ return isl_stat_ok;
+}
+
+/* Determine the set of array elements that may need to be perserved
+ * by a kernel constructed from the subtree at "node".
+ * This includes the set of array elements that may need to be preserved
+ * by the entire scop (prog->may_persist) and the elements for which
+ * there is a potential flow dependence that may cross a kernel launch.
+ *
+ * To determine the second set, we start from all flow dependences.
+ * From this set of dependences, we remove those that cannot possibly
+ * require data to be preserved by a kernel launch.
+ * In particular, we consider the following sets of dependences.
+ * - dependences of which the write occurs inside the kernel.
+ * If the data is needed outside the kernel, then it will
+ * be copied out immediately after the kernel launch, so there
+ * is no need for any special care.
+ * - dependences of which the read occurs inside the kernel and the
+ * corresponding write occurs inside the same iteration of the
+ * outer band nodes. This means that the data is needed in
+ * the first kernel launch after the write, which is already
+ * taken care of by the standard copy-in. That is, the data
+ * do not need to be preserved by any intermediate call to
+ * the same kernel.
+ * - dependences of which the write and the read either both occur
+ * before the kernel launch or both occur after the kernel launch,
+ * within the same iteration of the outer band nodes with respect
+ * to the sequence that determines the ordering of the dependence
+ * and the kernel launch. Such flow dependences cannot cross
+ * any kernel launch.
+ *
+ * For the remaining (tagged) dependences, we take the domain
+ * (i.e., the tagged writes) and apply the tagged access relation
+ * to obtain the accessed data elements.
+ * These are then combined with the elements that may need to be
+ * preserved by the entire scop.
+ */
+static __isl_give isl_union_set *node_may_persist(
+ __isl_keep isl_schedule_node *node, struct gpu_prog *prog)
+{
+ struct ppcg_may_persist_data data;
+ isl_schedule_node *root;
+ isl_union_pw_multi_aff *contraction;
+ isl_union_set *domain;
+ isl_union_set *persist;
+ isl_union_map *flow, *local_flow;
+
+ data.tagger = prog->scop->tagger;
+
+ flow = isl_union_map_copy(prog->scop->tagged_dep_flow);
+ data.local_flow = isl_union_map_copy(flow);
+ data.inner_band_flow = isl_union_map_copy(flow);
+ data.may_persist_flow = flow;
+ if (isl_schedule_node_foreach_ancestor_top_down(node,
+ &update_may_persist_at, &data) < 0)
+ data.may_persist_flow =
+ isl_union_map_free(data.may_persist_flow);
+ flow = data.may_persist_flow;
+ isl_union_map_free(data.local_flow);
+
+ domain = isl_schedule_node_get_domain(node);
+ contraction = isl_schedule_node_get_subtree_contraction(node);
+ domain = isl_union_set_preimage_union_pw_multi_aff(domain,
+ contraction);
+ domain = isl_union_set_preimage_union_pw_multi_aff(domain,
+ isl_union_pw_multi_aff_copy(data.tagger));
+ flow = isl_union_map_subtract_domain(flow, isl_union_set_copy(domain));
+ local_flow = data.inner_band_flow;
+ local_flow = isl_union_map_intersect_range(local_flow, domain);
+ flow = isl_union_map_subtract(flow, local_flow);
+
+ persist = isl_union_map_domain(flow);
+ persist = isl_union_set_apply(persist,
+ isl_union_map_copy(prog->scop->tagged_may_writes));
+ persist = isl_union_set_union(persist,
+ isl_union_set_copy(prog->may_persist));
+
+ return persist;
+}
+
+/* Add nodes for copying outer arrays in and out of the device
+ * before and after the subtree "node", which contains one or more kernels.
+ * "domain" contains the original reaching domain elements before
+ * the kernels were created, i.e., before the contraction that
+ * may have been performed in creating the kernels has been applied.
+ * "prefix" contains the prefix schedule at that point, in terms
+ * of the same original reaching domain elements.
+ *
+ * We first compute the sets of outer array elements that need
+ * to be copied in and out and then graft in the nodes for
+ * performing this copying.
+ *
+ * In particular, for each array that is possibly written anywhere in
+ * the subtree "node" and that may be used after "node"
+ * or that may be visible outside the corresponding scop,
+ * we copy out its entire extent.
+ *
+ * Any array elements that is read without first being written inside
+ * the subtree "node" needs to be copied in.
+ * Furthermore, if there are any array elements that
+ * are copied out, but that may not be written inside "node, then
+ * they also need to be copied in to ensure that the value after execution
+ * is the same as the value before execution, at least for those array
+ * elements that may have their values preserved by the scop or that
+ * may be written before "node" and read after "node".
+ * In case the array elements are structures, we need to take into
+ * account that all members of the structures need to be written
+ * by "node" before we can avoid copying the data structure in.
+ *
+ * Note that the may_write relation is intersected with the domain,
+ * which has been intersected with the context.
+ * This helps in those cases where the arrays are declared with a fixed size,
+ * while the accesses are parametric and the context assigns a fixed value
+ * to the parameters.
+ *
+ * If an element from a local array is read without first being written,
+ * then there is no point in copying it in since it cannot have been
+ * written prior to the scop. Warn about the uninitialized read instead.
+ */
+static __isl_give isl_schedule_node *add_to_from_device(
+ __isl_take isl_schedule_node *node, __isl_take isl_union_set *domain,
+ __isl_take isl_union_map *prefix, struct gpu_prog *prog)
+{
+ isl_union_set *local;
+ isl_union_set *to_device, *from_device, *may_persist;
+ isl_union_map *may_write, *must_write, *copy_out, *not_written;
+ isl_union_map *read, *copy_in;
+ isl_union_map *tagged;
+ isl_union_map *local_uninitialized;
+ isl_schedule_node *graft;
+
+ tagged = isl_union_map_copy(prog->scop->tagged_reads);
+ tagged = isl_union_map_union(tagged,
+ isl_union_map_copy(prog->scop->tagged_may_writes));
+
+ may_write = isl_union_map_copy(prog->may_write);
+ may_write = isl_union_map_intersect_domain(may_write,
+ isl_union_set_copy(domain));
+ may_write = remove_local_accesses(prog,
+ isl_union_map_copy(tagged), may_write,
+ isl_union_map_copy(prefix), 0);
+ may_write = isl_union_map_apply_range(may_write,
+ isl_union_map_copy(prog->to_outer));
+ may_write = isl_union_map_apply_domain(may_write,
+ isl_union_map_copy(prefix));
+ may_write = approximate_copy_out(may_write, prog);
+ copy_out = isl_union_map_copy(may_write);
+ may_write = isl_union_map_apply_range(may_write,
+ isl_union_map_copy(prog->to_inner));
+ must_write = isl_union_map_copy(prog->must_write);
+ must_write = isl_union_map_apply_domain(must_write,
+ isl_union_map_copy(prefix));
+ may_persist = node_may_persist(node, prog);
+ may_write = isl_union_map_intersect_range(may_write, may_persist);
+ not_written = isl_union_map_subtract(may_write, must_write);
+
+ local = extract_local_accesses(prog, domain);
+ read = isl_union_map_copy(prog->read);
+ read = isl_union_map_intersect_domain(read, domain);
+ read = remove_local_accesses(prog, tagged, read,
+ isl_union_map_copy(prefix), 1);
+ local = isl_union_set_apply(local, isl_union_map_copy(prog->to_inner));
+ local_uninitialized = isl_union_map_copy(prog->scop->live_in);
+ local_uninitialized = isl_union_map_intersect_range(local_uninitialized,
+ local);
+ local_uninitialized = isl_union_map_intersect(local_uninitialized,
+ isl_union_map_copy(read));
+ if (!isl_union_map_is_empty(local_uninitialized)) {
+ fprintf(stderr,
+ "possibly uninitialized reads (not copied in):\n");
+ isl_union_map_dump(local_uninitialized);
+ }
+ read = isl_union_map_subtract(read, local_uninitialized);
+ read = isl_union_map_apply_domain(read, prefix);
+ copy_in = isl_union_map_union(read, not_written);
+ copy_in = isl_union_map_apply_range(copy_in,
+ isl_union_map_copy(prog->to_outer));
+
+ graft = create_copy_device(prog, node, "to_device",
+ isl_union_map_range(copy_in));
+ node = isl_schedule_node_graft_before(node, graft);
+ graft = create_copy_device(prog, node, "from_device",
+ isl_union_map_range(copy_out));
+ node = isl_schedule_node_graft_after(node, graft);
+
+ return node;
+}
+
+/* Update "schedule" for mapping to a GPU device.
+ *
+ * In particular, insert a context node, create kernels for
+ * each outermost tilable band and introduce node for copying array
+ * in and out of the device.
+ * If the child of the initial root points to a set node,
+ * then children of this node that do not contain any tilable bands
+ * are separated from the other children and are not mapped to
+ * the device.
+ */
+static __isl_give isl_schedule *map_to_device(struct gpu_gen *gen,
+ __isl_take isl_schedule *schedule)
+{
+ isl_schedule_node *node;
+ isl_set *context;
+ isl_union_set *domain;
+ isl_union_map *prefix;
+
+ context = isl_set_copy(gen->prog->context);
+ context = isl_set_from_params(context);
+ schedule = isl_schedule_insert_context(schedule, context);
+
+ node = isl_schedule_get_root(schedule);
+ isl_schedule_free(schedule);
+ node = isl_schedule_node_child(node, 0);
+ if (isl_schedule_node_get_type(node) == isl_schedule_node_context)
+ node = isl_schedule_node_child(node, 0);
+ node = isolate_permutable_subtrees(node, gen->prog);
+ domain = isl_schedule_node_get_domain(node);
+ prefix = isl_schedule_node_get_prefix_schedule_union_map(node);
+ node = mark_kernels(gen, node);
+ node = add_to_from_device(node, domain, prefix, gen->prog);
+ schedule = isl_schedule_node_get_schedule(node);
+ isl_schedule_node_free(node);
+
+ return schedule;
+}
+
+/* Internal data structure for extract_access.
+ * "next_access" points to the end of a linked list that is extended
+ * by extract_access.
+ * "single_expression" is set if the access expressions belong to
+ * an expression statement (i.e., a statement without internal control).
+ * "any_to_outer" maps all intermediate arrays to their outer arrays.
+ */
+struct ppcg_extract_access_data {
+ struct gpu_stmt_access **next_access;
+ int single_expression;
+ isl_union_map *any_to_outer;
+};
+
+/* Given a tagged access relation to a single array "tagged", extract it
+ * as a map, taking into account that the input may be empty.
+ * If the access relation is empty, then it does not contain
+ * any space information, so we try to recover it from the index
+ * expression.
+ * The space of the index expression is of the form I -> A,
+ * with I the statement instances and A the array, or [I -> F] -> A,
+ * with F the filters corresponding to arguments.
+ * We first drop F, if present, obtaining I -> A.
+ * Then we construct I -> R, with R the reference tag,
+ * combine the two into I -> [R -> A] and uncurry to obtain
+ * the final result [I -> R] -> A.
+ * Note that the index expression may have a lower dimension
+ * than that of the array, but this dimension is not used
+ * if the access relation is empty.
+ */
+static __isl_give isl_map *extract_single_tagged_access(
+ __isl_take isl_union_map *tagged, __isl_keep pet_expr *expr)
+{
+ int empty;
+ isl_id *id;
+ isl_space *space, *space2;
+ isl_multi_pw_aff *index;
+
+ empty = isl_union_map_is_empty(tagged);
+ if (empty < 0)
+ goto error;
+ if (!empty)
+ return isl_map_from_union_map(tagged);
+ isl_union_map_free(tagged);
+
+ index = pet_expr_access_get_index(expr);
+ space = isl_multi_pw_aff_get_space(index);
+ isl_multi_pw_aff_free(index);
+ if (isl_space_domain_is_wrapping(space))
+ space = isl_space_domain_factor_domain(space);
+ space2 = isl_space_copy(space);
+ space2 = isl_space_from_domain(isl_space_domain(space));
+ id = pet_expr_access_get_ref_id(expr);
+ space2 = isl_space_set_tuple_id(space2, isl_dim_out, id);
+ space = isl_space_range_product(space2, space);
+ space = isl_space_uncurry(space);
+
+ return isl_map_empty(space);
+error:
+ isl_union_map_free(tagged);
+ return NULL;
+}
+
+/* Extract a gpu_stmt_access from "expr", append it to the list
+ * that ends in *data->next_access and update the end of the list.
+ * If the access expression performs a write, then it is considered
+ * exact only if it appears in a single expression statement and
+ * if its may access relation is equal to its must access relation.
+ *
+ * The combined set of may accesses may be union if member accesses
+ * are involved, but the entire set is derived from a single reference and
+ * therefore from a single index expression. These accesses therefore
+ * all map to the same outer array.
+ */
+static int extract_access(__isl_keep pet_expr *expr, void *user)
+{
+ struct ppcg_extract_access_data *data = user;
+ isl_union_map *tagged;
+ struct gpu_stmt_access *access;
+ isl_ctx *ctx = pet_expr_get_ctx(expr);
+ isl_multi_pw_aff *index;
+
+ access = isl_alloc_type(ctx, struct gpu_stmt_access);
+ assert(access);
+ access->next = NULL;
+ access->read = pet_expr_access_is_read(expr);
+ access->write = pet_expr_access_is_write(expr);
+ tagged = pet_expr_access_get_tagged_may_read(expr);
+ tagged = isl_union_map_union(tagged,
+ pet_expr_access_get_tagged_may_write(expr));
+ tagged = isl_union_map_apply_range(tagged,
+ isl_union_map_copy(data->any_to_outer));
+ if (!access->write) {
+ access->exact_write = 1;
+ } else if (!data->single_expression) {
+ access->exact_write = 0;
+ } else {
+ isl_union_map *must, *may;
+ may = isl_union_map_copy(tagged);
+ may = isl_union_map_domain_factor_domain(may);
+ must = pet_expr_access_get_must_write(expr);
+ access->exact_write = isl_union_map_is_equal(must, may);
+ isl_union_map_free(must);
+ isl_union_map_free(may);
+ }
+ index = pet_expr_access_get_index(expr);
+ access->n_index = isl_multi_pw_aff_dim(index, isl_dim_out);
+ isl_multi_pw_aff_free(index);
+ access->ref_id = pet_expr_access_get_ref_id(expr);
+ access->tagged_access = extract_single_tagged_access(tagged, expr);
+ access->access = isl_map_copy(access->tagged_access);
+ access->access = isl_map_domain_factor_domain(access->access);
+
+ *data->next_access = access;
+ data->next_access = &(*data->next_access)->next;
+
+ if (!access->access)
+ return -1;
+
+ return 0;
+}
+
+/* Construct a linked list of gpu_stmt_access objects,
+ * one for each access expression in the statement body.
+ * "any_to_outer" maps all intermediate arrays to their outer arrays.
+ */
+static int pet_stmt_extract_accesses(struct gpu_stmt *stmt,
+ __isl_keep isl_union_map *any_to_outer)
+{
+ struct ppcg_extract_access_data data;
+
+ stmt->accesses = NULL;
+ data.next_access = &stmt->accesses;
+ data.single_expression =
+ pet_tree_get_type(stmt->stmt->body) == pet_tree_expr;
+ data.any_to_outer = any_to_outer;
+ return pet_tree_foreach_access_expr(stmt->stmt->body,
+ &extract_access, &data);
+}
+
+/* Return an array of gpu_stmt representing the statements in "scop".
+ */
+static struct gpu_stmt *extract_stmts(isl_ctx *ctx, struct ppcg_scop *scop,
+ __isl_keep isl_set *context, __isl_keep isl_union_map *any_to_outer)
+{
+ int i;
+ struct gpu_stmt *stmts;
+
+ stmts = isl_calloc_array(ctx, struct gpu_stmt, scop->pet->n_stmt);
+ if (!stmts)
+ return NULL;
+
+ for (i = 0; i < scop->pet->n_stmt; ++i) {
+ struct gpu_stmt *s = &stmts[i];
+
+ s->id = isl_set_get_tuple_id(scop->pet->stmts[i]->domain);
+ s->stmt = scop->pet->stmts[i];
+ if (pet_stmt_extract_accesses(s, any_to_outer) < 0)
+ return free_stmts(stmts, i + 1);
+ }
+
+ return stmts;
+}
+
+/* Callback for ppcg_print_guarded that calls the callback for generate_gpu.
+ */
+static __isl_give isl_printer *print_gpu(__isl_take isl_printer *p, void *user)
+{
+ struct gpu_gen *gen = user;
+
+ return gen->print(p, gen->prog, gen->tree, &gen->types,
+ gen->print_user);
+}
+
+/* Generate CUDA code for "scop" and print it to "p".
+ * After generating an AST for the transformed scop as explained below,
+ * we call "gen->print" to print the AST in the desired output format
+ * to "p".
+ *
+ * If it turns out that it does not make sense to generate GPU code,
+ * then we generate CPU code instead.
+ *
+ * The GPU code is generated in a context where at least one
+ * statement instance is executed. The corresponding guard (if any) is printed
+ * around the entire generated GPU code, except for the declaration
+ * of the arrays that are visible outside of the scop and that therefore
+ * cannot be declared inside the body of any possible guard.
+ *
+ * We first compute a schedule that respects the dependences
+ * of the original program and select the outermost bands
+ * of tilable dimensions that have at least one parallel loop.
+ * If the --load-schedule is specified, then the loaded schedule
+ * is used instead of a computed schedule.
+ *
+ * Each of these bands B is then tiled according to "tile" sizes, resulting
+ * in two nested bands, with a kernel marker on top
+ *
+ * K
+ * |
+ * T
+ * |
+ * P
+ *
+ * We then split off at most 2 parallel dimensions from the T band and
+ * at most 3 parallel dimension from the P band
+ *
+ * K
+ * |
+ * T
+ * T1
+ * |
+ * T2
+ * |
+ * P1
+ * |
+ * P2
+ *
+ * A filter is introduced in front of T1 that maps the domain instances
+ * to block identifiers. Similarly, a filter is introduced in front of P1
+ * that maps the domain instances to thread identifiers.
+ *
+ * For each iteration of the T2 band and for each array, we compute
+ * the array elements accessed by that iteration, construct a rectangular
+ * box around it and shift it to the origin. The result is used
+ * as shared memory for the array.
+ *
+ * Copying and synchronization statements are added to this schedule tree.
+ * In principle, these are added in front of the P1 band, but some of
+ * them may get hoisted up to higher levels.
+ *
+ * The entire AST is then generated from the single resulting schedule tree.
+ * During the generation the subtrees at kernel nodes (K) are saved
+ * aside and replaced by kernel calls. The result is printed as host code
+ * while the saved subtrees are printed as device code.
+ */
+static __isl_give isl_printer *generate(__isl_take isl_printer *p,
+ struct gpu_gen *gen, struct ppcg_scop *scop,
+ struct ppcg_options *options)
+{
+ struct gpu_prog *prog;
+ isl_ctx *ctx;
+ isl_set *context, *guard;
+ isl_schedule *schedule;
+ int any_permutable;
+
+ if (!scop)
+ return isl_printer_free(p);
+
+ ctx = isl_printer_get_ctx(p);
+ prog = gpu_prog_alloc(ctx, scop);
+ if (!prog)
+ return isl_printer_free(p);
+
+ context = isl_set_copy(prog->context);
+ guard = isl_union_set_params(isl_union_set_copy(prog->scop->domain));
+ prog->context = isl_set_intersect(prog->context, isl_set_copy(guard));
+
+ gen->prog = prog;
+ schedule = get_schedule(gen);
+
+ any_permutable = has_any_permutable_node(schedule);
+ if (any_permutable < 0 || !any_permutable) {
+ isl_set_free(context);
+ isl_set_free(guard);
+ if (any_permutable < 0)
+ p = isl_printer_free(p);
+ else
+ p = print_cpu(p, scop, options);
+ isl_schedule_free(schedule);
+ } else {
+ schedule = map_to_device(gen, schedule);
+ gen->tree = generate_code(gen, schedule);
+ p = isl_ast_op_type_print_macro(isl_ast_op_fdiv_q, p);
+ p = ppcg_print_exposed_declarations(p, prog->scop);
+ p = ppcg_print_guarded(p, guard, context, &print_gpu, gen);
+ isl_ast_node_free(gen->tree);
+ }
+
+ gpu_prog_free(prog);
+
+ return p;
+}
+
+/* Wrapper around generate for use as a ppcg_transform callback.
+ */
+static __isl_give isl_printer *generate_wrap(__isl_take isl_printer *p,
+ struct ppcg_scop *scop, void *user)
+{
+ struct gpu_gen *gen = user;
+
+ return generate(p, gen, scop, gen->options);
+}
+
+/* Transform the code in the file called "input" by replacing
+ * all scops by corresponding GPU code and write the results to "out".
+ */
+int generate_gpu(isl_ctx *ctx, const char *input, FILE *out,
+ struct ppcg_options *options,
+ __isl_give isl_printer *(*print)(__isl_take isl_printer *p,
+ struct gpu_prog *prog, __isl_keep isl_ast_node *tree,
+ struct gpu_types *types, void *user), void *user)
+{
+ struct gpu_gen gen;
+ int r;
+ int i;
+
+ gen.ctx = ctx;
+ gen.sizes = extract_sizes_from_str(ctx, options->sizes);
+ gen.options = options;
+ gen.kernel_id = 0;
+ gen.print = print;
+ gen.print_user = user;
+ gen.types.n = 0;
+ gen.types.name = NULL;
+
+ if (options->debug->dump_sizes) {
+ isl_space *space = isl_space_params_alloc(ctx, 0);
+ gen.used_sizes = isl_union_map_empty(space);
+ }
+
+ r = ppcg_transform(ctx, input, out, options, &generate_wrap, &gen);
+
+ if (options->debug->dump_sizes) {
+ isl_union_map_dump(gen.used_sizes);
+ isl_union_map_free(gen.used_sizes);
+ }
+
+ isl_union_map_free(gen.sizes);
+ for (i = 0; i < gen.types.n; ++i)
+ free(gen.types.name[i]);
+ free(gen.types.name);
+
+ return r;
+}
+
+/* Compute the set of inner array elements that may have their values
+ * preserved by "prog". In particular, collect the array elements of
+ * arrays that are not local to "prog" and remove those elements that
+ * are definitely killed or definitely written by "prog".
+ */
+static __isl_give isl_union_set *compute_may_persist(struct gpu_prog *prog)
+{
+ int i;
+ isl_union_set *may_persist, *killed;
+ isl_union_map *must_kill;
+
+ may_persist = isl_union_set_empty(isl_set_get_space(prog->context));
+ for (i = 0; i < prog->n_array; ++i) {
+ isl_set *extent;
+
+ if (prog->array[i].local)
+ continue;
+
+ extent = isl_set_copy(prog->array[i].extent);
+ may_persist = isl_union_set_add_set(may_persist, extent);
+ }
+
+ may_persist = isl_union_set_intersect_params(may_persist,
+ isl_set_copy(prog->context));
+ may_persist = isl_union_set_apply(may_persist,
+ isl_union_map_copy(prog->to_inner));
+ must_kill = isl_union_map_copy(prog->tagged_must_kill);
+ killed = isl_union_map_range(must_kill);
+ must_kill = isl_union_map_copy(prog->must_write);
+ killed = isl_union_set_union(killed, isl_union_map_range(must_kill));
+
+ may_persist = isl_union_set_subtract(may_persist, killed);
+ return may_persist;
+}
+
+struct gpu_prog *gpu_prog_alloc(isl_ctx *ctx, struct ppcg_scop *scop)
+{
+ struct gpu_prog *prog;
+ isl_space *space;
+ isl_map *id;
+
+ if (!scop)
+ return NULL;
+
+ prog = isl_calloc_type(ctx, struct gpu_prog);
+ assert(prog);
+
+ prog->ctx = ctx;
+ prog->scop = scop;
+ prog->context = isl_set_copy(scop->context);
+ prog->n_stmts = scop->pet->n_stmt;
+ prog->any_to_outer = pet_scop_compute_outer_to_any(scop->pet);
+ prog->any_to_outer = isl_union_map_reverse(prog->any_to_outer);
+ space = isl_union_map_get_space(prog->any_to_outer);
+ space = isl_space_set_from_params(space);
+ space = isl_space_add_dims(space, isl_dim_set, 1);
+ space = isl_space_map_from_set(space);
+ id = isl_map_identity(space);
+ prog->any_to_outer = isl_union_map_add_map(prog->any_to_outer, id);
+ prog->stmts = extract_stmts(ctx, scop,
+ prog->context, prog->any_to_outer);
+ prog->read = isl_union_map_copy(scop->reads);
+ prog->may_write = isl_union_map_copy(scop->may_writes);
+ prog->must_write = isl_union_map_copy(scop->must_writes);
+ prog->tagged_must_kill = isl_union_map_copy(scop->tagged_must_kills);
+ prog->to_inner = pet_scop_compute_outer_to_inner(scop->pet);
+ prog->to_outer = isl_union_map_copy(prog->to_inner);
+ prog->to_outer = isl_union_map_reverse(prog->to_outer);
+
+ if (!prog->stmts)
+ return gpu_prog_free(prog);
+
+ if (collect_array_info(prog) < 0)
+ return gpu_prog_free(prog);
+ prog->may_persist = compute_may_persist(prog);
+
+ return prog;
+}
+
+void *gpu_prog_free(struct gpu_prog *prog)
+{
+ if (!prog)
+ return NULL;
+ free_array_info(prog);
+ free_stmts(prog->stmts, prog->n_stmts);
+ isl_union_map_free(prog->any_to_outer);
+ isl_union_map_free(prog->to_outer);
+ isl_union_map_free(prog->to_inner);
+ isl_union_map_free(prog->read);
+ isl_union_map_free(prog->may_write);
+ isl_union_map_free(prog->must_write);
+ isl_union_map_free(prog->tagged_must_kill);
+ isl_union_map_free(prog->array_order);
+ isl_union_set_free(prog->may_persist);
+ isl_set_free(prog->context);
+ free(prog);
+ return NULL;
+}
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