detect some modulo expressions when extracting a function

[isl.git] / isl_ast_graft.c

/*
 * Copyright 2012      Ecole Normale Superieure
 * Copyright 2014      INRIA Rocquencourt
 * Copyright 2019      Cerebras Systems
 *
 * Use of this software is governed by the MIT license
 *
 * Written by Sven Verdoolaege,
 * Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
 * B.P. 105 - 78153 Le Chesnay, France
 * and Cerebras Systems, 175 S San Antonio Rd, Los Altos, CA, USA
 */

#include <isl/id.h>
#include <isl/space.h>
#include <isl/stream.h>
#include <isl_ast_private.h>
#include <isl_ast_build_expr.h>
#include <isl_ast_build_private.h>
#include <isl_ast_graft_private.h>
#include "isl_set_to_ast_graft_list.h"

static __isl_give isl_ast_graft *isl_ast_graft_copy(
        __isl_keep isl_ast_graft *graft);
static __isl_give isl_ast_graft *isl_stream_read_ast_graft(
        __isl_keep isl_stream *s);

#undef EL_BASE
#define EL_BASE ast_graft

#include <isl_list_templ.c>
#include <isl_list_read_templ.c>

#undef BASE
#define BASE ast_graft
#include <print_templ.c>

isl_ctx *isl_ast_graft_get_ctx(__isl_keep isl_ast_graft *graft)
{
        if (!graft)
                return NULL;
        return isl_basic_set_get_ctx(graft->enforced);
}

__isl_give isl_ast_node *isl_ast_graft_get_node(
        __isl_keep isl_ast_graft *graft)
{
        return graft ? isl_ast_node_copy(graft->node) : NULL;
}

/* Create a graft for "node" with guards "guard" and
 * enforced conditions "enforced".
 */
static isl_ast_graft *graft_alloc(__isl_take isl_ast_node *node,
        __isl_take isl_set *guard, __isl_take isl_basic_set *enforced)
{
        isl_ctx *ctx;
        isl_ast_graft *graft;

        if (!node || !guard || !enforced)
                goto error;

        ctx = isl_ast_node_get_ctx(node);
        graft = isl_calloc_type(ctx, isl_ast_graft);
        if (!graft)
                goto error;

        graft->ref = 1;
        graft->node = node;
        graft->guard = guard;
        graft->enforced = enforced;

        return graft;
error:
        isl_ast_node_free(node);
        isl_set_free(guard);
        isl_basic_set_free(enforced);
        return NULL;
}

/* Create a graft for "node" with no guards and no enforced conditions.
 */
__isl_give isl_ast_graft *isl_ast_graft_alloc(
        __isl_take isl_ast_node *node, __isl_keep isl_ast_build *build)
{
        isl_space *space;
        isl_set *guard;
        isl_basic_set *enforced;

        if (!node)
                return NULL;

        space = isl_ast_build_get_space(build, 1);

        guard = isl_set_universe(isl_space_copy(space));
        enforced = isl_basic_set_universe(space);

        return graft_alloc(node, guard, enforced);
}

/* Create a graft with no guards and no enforced conditions
 * encapsulating a call to the domain element specified by "executed".
 * "executed" is assumed to be single-valued.
 */
__isl_give isl_ast_graft *isl_ast_graft_alloc_domain(
        __isl_take isl_map *executed, __isl_keep isl_ast_build *build)
{
        isl_ast_node *node;

        node = isl_ast_build_call_from_executed(build, executed);

        return isl_ast_graft_alloc(node, build);
}

static __isl_give isl_ast_graft *isl_ast_graft_copy(
        __isl_keep isl_ast_graft *graft)
{
        if (!graft)
                return NULL;

        graft->ref++;
        return graft;
}

/* Do all the grafts in "list" have the same guard and is this guard
 * independent of the current depth?
 */
static isl_bool equal_independent_guards(__isl_keep isl_ast_graft_list *list,
        __isl_keep isl_ast_build *build)
{
        int i;
        isl_size n;
        isl_size depth;
        isl_size dim;
        isl_ast_graft *graft_0;
        isl_bool equal = isl_bool_true;
        isl_bool skip;

        n = isl_ast_graft_list_n_ast_graft(list);
        depth = isl_ast_build_get_depth(build);
        if (n < 0 || depth < 0)
                return isl_bool_error;
        graft_0 = isl_ast_graft_list_get_ast_graft(list, 0);
        if (!graft_0)
                return isl_bool_error;

        dim = isl_set_dim(graft_0->guard, isl_dim_set);
        if (dim < 0)
                skip = isl_bool_error;
        else if (dim <= depth)
                skip = isl_bool_false;
        else
                skip = isl_set_involves_dims(graft_0->guard,
                                                isl_dim_set, depth, 1);
        if (skip < 0 || skip) {
                isl_ast_graft_free(graft_0);
                return isl_bool_not(skip);
        }

        for (i = 1; i < n; ++i) {
                isl_ast_graft *graft;
                graft = isl_ast_graft_list_get_ast_graft(list, i);
                if (!graft)
                        equal = isl_bool_error;
                else
                        equal = isl_set_is_equal(graft_0->guard, graft->guard);
                isl_ast_graft_free(graft);
                if (equal < 0 || !equal)
                        break;
        }

        isl_ast_graft_free(graft_0);

        return equal;
}

/* Hoist "guard" out of the current level (given by "build").
 *
 * In particular, eliminate the dimension corresponding to the current depth.
 */
static __isl_give isl_set *hoist_guard(__isl_take isl_set *guard,
        __isl_keep isl_ast_build *build)
{
        isl_size depth;
        isl_size dim;

        depth = isl_ast_build_get_depth(build);
        dim = isl_set_dim(guard, isl_dim_set);
        if (depth < 0 || dim < 0)
                return isl_set_free(guard);
        if (depth < dim) {
                guard = isl_set_remove_divs_involving_dims(guard,
                                                isl_dim_set, depth, 1);
                guard = isl_set_eliminate(guard, isl_dim_set, depth, 1);
                guard = isl_set_compute_divs(guard);
        }

        return guard;
}

/* Extract a common guard from the grafts in "list" that can be hoisted
 * out of the current level.  If no such guard can be found, then return
 * a universal set.
 *
 * If all the grafts in the list have the same guard and if this guard
 * is independent of the current level, then it can be hoisted out.
 * If there is only one graft in the list and if its guard
 * depends on the current level, then we eliminate this level and
 * return the result.
 *
 * Otherwise, we return the unshifted simple hull of the guards.
 * In order to be able to hoist as many constraints as possible,
 * but at the same time avoid hoisting constraints that did not
 * appear in the guards in the first place, we intersect the guards
 * with all the information that is available (i.e., the domain
 * from the build and the enforced constraints of the graft) and
 * compute the unshifted hull of the result using only constraints
 * from the original guards.
 * In particular, intersecting the guards with other known information
 * allows us to hoist guards that are only explicit is some of
 * the grafts and implicit in the others.
 *
 * The special case for equal guards is needed in case those guards
 * are non-convex.  Taking the simple hull would remove information
 * and would not allow for these guards to be hoisted completely.
 */
__isl_give isl_set *isl_ast_graft_list_extract_hoistable_guard(
        __isl_keep isl_ast_graft_list *list, __isl_keep isl_ast_build *build)
{
        int i;
        isl_size n;
        isl_bool equal;
        isl_ctx *ctx;
        isl_set *guard;
        isl_set_list *set_list;
        isl_basic_set *hull;

        if (!list || !build)
                return NULL;

        n = isl_ast_graft_list_n_ast_graft(list);
        if (n < 0)
                return NULL;
        if (n == 0)
                return isl_set_universe(isl_ast_build_get_space(build, 1));

        equal = equal_independent_guards(list, build);
        if (equal < 0)
                return NULL;

        if (equal || n == 1) {
                isl_ast_graft *graft_0;

                graft_0 = isl_ast_graft_list_get_ast_graft(list, 0);
                if (!graft_0)
                        return NULL;
                guard = isl_set_copy(graft_0->guard);
                if (!equal)
                        guard = hoist_guard(guard, build);
                isl_ast_graft_free(graft_0);
                return guard;
        }

        ctx = isl_ast_build_get_ctx(build);
        set_list = isl_set_list_alloc(ctx, n);
        guard = isl_set_empty(isl_ast_build_get_space(build, 1));
        for (i = 0; i < n; ++i) {
                isl_ast_graft *graft;
                isl_basic_set *enforced;
                isl_set *guard_i;

                graft = isl_ast_graft_list_get_ast_graft(list, i);
                enforced = isl_ast_graft_get_enforced(graft);
                guard_i = isl_set_copy(graft->guard);
                isl_ast_graft_free(graft);
                set_list = isl_set_list_add(set_list, isl_set_copy(guard_i));
                guard_i = isl_set_intersect(guard_i,
                                            isl_set_from_basic_set(enforced));
                guard_i = isl_set_intersect(guard_i,
                                            isl_ast_build_get_domain(build));
                guard = isl_set_union(guard, guard_i);
        }
        hull = isl_set_unshifted_simple_hull_from_set_list(guard, set_list);
        guard = isl_set_from_basic_set(hull);
        return hoist_guard(guard, build);
}

/* Internal data structure used inside insert_if.
 *
 * list is the list of guarded nodes created by each call to insert_if.
 * node is the original node that is guarded by insert_if.
 * build is the build in which the AST is constructed.
 */
struct isl_insert_if_data {
        isl_ast_node_list *list;
        isl_ast_node *node;
        isl_ast_build *build;
};

static isl_stat insert_if(__isl_take isl_basic_set *bset, void *user);

/* Insert an if node around "node" testing the condition encoded
 * in guard "guard".
 *
 * If the user does not want any disjunctions in the if conditions
 * and if "guard" does involve a disjunction, then we make the different
 * disjuncts disjoint and insert an if node corresponding to each disjunct
 * around a copy of "node".  The result is then a block node containing
 * this sequence of guarded copies of "node".
 */
static __isl_give isl_ast_node *ast_node_insert_if(
        __isl_take isl_ast_node *node, __isl_take isl_set *guard,
        __isl_keep isl_ast_build *build)
{
        struct isl_insert_if_data data;
        isl_ctx *ctx;
        isl_size n;

        n = isl_set_n_basic_set(guard);
        if (n < 0)
                goto error;
        ctx = isl_ast_build_get_ctx(build);
        if (isl_options_get_ast_build_allow_or(ctx) || n <= 1) {
                isl_ast_node *if_node;
                isl_ast_expr *expr;

                expr = isl_ast_build_expr_from_set_internal(build, guard);

                if_node = isl_ast_node_alloc_if(expr);
                return isl_ast_node_if_set_then(if_node, node);
        }

        guard = isl_set_make_disjoint(guard);

        data.list = isl_ast_node_list_alloc(ctx, 0);
        data.node = node;
        data.build = build;
        if (isl_set_foreach_basic_set(guard, &insert_if, &data) < 0)
                data.list = isl_ast_node_list_free(data.list);

        isl_set_free(guard);
        isl_ast_node_free(data.node);
        return isl_ast_node_alloc_block(data.list);
error:
        isl_set_free(guard);
        isl_ast_node_free(node);
        return NULL;
}

/* Insert an if node around a copy of "data->node" testing the condition
 * encoded in guard "bset" and add the result to data->list.
 */
static isl_stat insert_if(__isl_take isl_basic_set *bset, void *user)
{
        struct isl_insert_if_data *data = user;
        isl_ast_node *node;
        isl_set *set;

        set = isl_set_from_basic_set(bset);
        node = isl_ast_node_copy(data->node);
        node = ast_node_insert_if(node, set, data->build);
        data->list = isl_ast_node_list_add(data->list, node);

        return isl_stat_ok;
}

/* Insert an if node around graft->node testing the condition encoded
 * in guard "guard", assuming guard involves any conditions.
 */
static __isl_give isl_ast_graft *insert_if_node(
        __isl_take isl_ast_graft *graft, __isl_take isl_set *guard,
        __isl_keep isl_ast_build *build)
{
        int univ;

        if (!graft)
                goto error;

        univ = isl_set_plain_is_universe(guard);
        if (univ < 0)
                goto error;
        if (univ) {
                isl_set_free(guard);
                return graft;
        }

        graft->node = ast_node_insert_if(graft->node, guard, build);

        if (!graft->node)
                return isl_ast_graft_free(graft);

        return graft;
error:
        isl_set_free(guard);
        return isl_ast_graft_free(graft);
}

/* Insert an if node around graft->node testing the condition encoded
 * in graft->guard, assuming graft->guard involves any conditions.
 */
static __isl_give isl_ast_graft *insert_pending_guard_node(
        __isl_take isl_ast_graft *graft, __isl_keep isl_ast_build *build)
{
        if (!graft)
                return NULL;

        return insert_if_node(graft, isl_set_copy(graft->guard), build);
}

/* Replace graft->enforced by "enforced".
 */
__isl_give isl_ast_graft *isl_ast_graft_set_enforced(
        __isl_take isl_ast_graft *graft, __isl_take isl_basic_set *enforced)
{
        if (!graft || !enforced)
                goto error;

        isl_basic_set_free(graft->enforced);
        graft->enforced = enforced;

        return graft;
error:
        isl_basic_set_free(enforced);
        return isl_ast_graft_free(graft);
}

/* Update "enforced" such that it only involves constraints that are
 * also enforced by "graft".
 */
static __isl_give isl_basic_set *update_enforced(
        __isl_take isl_basic_set *enforced, __isl_keep isl_ast_graft *graft,
        int depth)
{
        isl_size dim;
        isl_basic_set *enforced_g;

        enforced_g = isl_ast_graft_get_enforced(graft);
        dim = isl_basic_set_dim(enforced_g, isl_dim_set);
        if (dim < 0)
                enforced_g = isl_basic_set_free(enforced_g);
        if (depth < dim)
                enforced_g = isl_basic_set_eliminate(enforced_g,
                                                        isl_dim_set, depth, 1);
        enforced_g = isl_basic_set_remove_unknown_divs(enforced_g);
        enforced_g = isl_basic_set_align_params(enforced_g,
                                isl_basic_set_get_space(enforced));
        enforced = isl_basic_set_align_params(enforced,
                                isl_basic_set_get_space(enforced_g));
        enforced = isl_set_simple_hull(isl_basic_set_union(enforced,
                                                enforced_g));

        return enforced;
}

/* Extend the node at *body with node.
 *
 * If body points to the else branch, then *body may still be NULL.
 * If so, we simply attach node to this else branch.
 * Otherwise, we attach a list containing the statements already
 * attached at *body followed by node.
 */
static void extend_body(__isl_keep isl_ast_node **body,
        __isl_take isl_ast_node *node)
{
        isl_ast_node_list *list;

        if  (!*body) {
                *body = node;
                return;
        }

        if ((*body)->type == isl_ast_node_block) {
                list = isl_ast_node_block_get_children(*body);
                isl_ast_node_free(*body);
        } else
                list = isl_ast_node_list_from_ast_node(*body);
        list = isl_ast_node_list_add(list, node);
        *body = isl_ast_node_alloc_block(list);
}

/* Merge "graft" into the last graft of "list".
 * body points to the then or else branch of an if node in that last graft.
 *
 * We attach graft->node to this branch and update the enforced
 * set of the last graft of "list" to take into account the enforced
 * set of "graft".
 */
static __isl_give isl_ast_graft_list *graft_extend_body(
        __isl_take isl_ast_graft_list *list,
        __isl_keep isl_ast_node **body, __isl_take isl_ast_graft *graft,
        __isl_keep isl_ast_build *build)
{
        isl_size n;
        isl_size depth;
        isl_ast_graft *last;
        isl_space *space;
        isl_basic_set *enforced;

        n = isl_ast_graft_list_n_ast_graft(list);
        depth = isl_ast_build_get_depth(build);
        if (n < 0 || depth < 0 || !graft)
                goto error;
        extend_body(body, isl_ast_node_copy(graft->node));
        if (!*body)
                goto error;

        last = isl_ast_graft_list_get_ast_graft(list, n - 1);

        space = isl_ast_build_get_space(build, 1);
        enforced = isl_basic_set_empty(space);
        enforced = update_enforced(enforced, last, depth);
        enforced = update_enforced(enforced, graft, depth);
        last = isl_ast_graft_set_enforced(last, enforced);

        list = isl_ast_graft_list_set_ast_graft(list, n - 1, last);
        isl_ast_graft_free(graft);
        return list;
error:
        isl_ast_graft_free(graft);
        return isl_ast_graft_list_free(list);
}

/* Merge "graft" into the last graft of "list", attaching graft->node
 * to the then branch of "last_if".
 */
static __isl_give isl_ast_graft_list *extend_then(
        __isl_take isl_ast_graft_list *list,
        __isl_keep isl_ast_node *last_if, __isl_take isl_ast_graft *graft,
        __isl_keep isl_ast_build *build)
{
        return graft_extend_body(list, &last_if->u.i.then, graft, build);
}

/* Merge "graft" into the last graft of "list", attaching graft->node
 * to the else branch of "last_if".
 */
static __isl_give isl_ast_graft_list *extend_else(
        __isl_take isl_ast_graft_list *list,
        __isl_keep isl_ast_node *last_if, __isl_take isl_ast_graft *graft,
        __isl_keep isl_ast_build *build)
{
        return graft_extend_body(list, &last_if->u.i.else_node, graft, build);
}

/* This data structure keeps track of an if node.
 *
 * "node" is the actual if-node
 * "guard" is the original, non-simplified guard of the node
 * "complement" is the complement of "guard" in the context of outer if nodes
 */
struct isl_if_node {
        isl_ast_node *node;
        isl_set *guard;
        isl_set *complement;
};

/* Given a list of "n" if nodes, clear those starting at "first"
 * and return "first" (i.e., the updated size of the array).
 */
static int clear_if_nodes(struct isl_if_node *if_node, int first, int n)
{
        int i;

        for (i = first; i < n; ++i) {
                isl_set_free(if_node[i].guard);
                isl_set_free(if_node[i].complement);
        }

        return first;
}

/* For each graft in "list",
 * insert an if node around graft->node testing the condition encoded
 * in graft->guard, assuming graft->guard involves any conditions.
 *
 * We keep track of a list of generated if nodes that can be extended
 * without changing the order of the elements in "list".
 * If the guard of a graft is a subset of either the guard or its complement
 * of one of those if nodes, then the node
 * of the new graft is inserted into the then or else branch of the last graft
 * and the current graft is discarded.
 * The guard of the node is then simplified based on the conditions
 * enforced at that then or else branch.
 * Otherwise, the current graft is appended to the list.
 *
 * We only construct else branches if allowed by the user.
 */
static __isl_give isl_ast_graft_list *insert_pending_guard_nodes(
        __isl_take isl_ast_graft_list *list,
        __isl_keep isl_ast_build *build)
{
        int i, j, n_if;
        isl_size n;
        int allow_else;
        isl_ctx *ctx;
        isl_ast_graft_list *res;
        struct isl_if_node *if_node = NULL;

        n = isl_ast_graft_list_n_ast_graft(list);
        if (!build || n < 0)
                return isl_ast_graft_list_free(list);

        ctx = isl_ast_build_get_ctx(build);

        allow_else = isl_options_get_ast_build_allow_else(ctx);

        n_if = 0;
        if (n > 1) {
                if_node = isl_alloc_array(ctx, struct isl_if_node, n - 1);
                if (!if_node)
                        return isl_ast_graft_list_free(list);
        }

        res = isl_ast_graft_list_alloc(ctx, n);

        for (i = 0; i < n; ++i) {
                isl_set *guard;
                isl_ast_graft *graft;
                int subset, found_then, found_else;
                isl_ast_node *node;

                graft = isl_ast_graft_list_get_ast_graft(list, i);
                if (!graft)
                        break;
                subset = 0;
                found_then = found_else = -1;
                if (n_if > 0) {
                        isl_set *test;
                        test = isl_set_copy(graft->guard);
                        test = isl_set_intersect(test,
                                                isl_set_copy(build->domain));
                        for (j = n_if - 1; j >= 0; --j) {
                                subset = isl_set_is_subset(test,
                                                        if_node[j].guard);
                                if (subset < 0 || subset) {
                                        found_then = j;
                                        break;
                                }
                                if (!allow_else)
                                        continue;
                                subset = isl_set_is_subset(test,
                                                        if_node[j].complement);
                                if (subset < 0 || subset) {
                                        found_else = j;
                                        break;
                                }
                        }
                        n_if = clear_if_nodes(if_node, j + 1, n_if);
                        isl_set_free(test);
                }
                if (subset < 0) {
                        graft = isl_ast_graft_free(graft);
                        break;
                }

                guard = isl_set_copy(graft->guard);
                if (found_then >= 0)
                        graft->guard = isl_set_gist(graft->guard,
                                isl_set_copy(if_node[found_then].guard));
                else if (found_else >= 0)
                        graft->guard = isl_set_gist(graft->guard,
                                isl_set_copy(if_node[found_else].complement));

                node = graft->node;
                if (!graft->guard)
                        graft = isl_ast_graft_free(graft);
                graft = insert_pending_guard_node(graft, build);
                if (graft && graft->node != node && i != n - 1) {
                        isl_set *set;
                        if_node[n_if].node = graft->node;
                        if_node[n_if].guard = guard;
                        if (found_then >= 0)
                                set = if_node[found_then].guard;
                        else if (found_else >= 0)
                                set = if_node[found_else].complement;
                        else
                                set = build->domain;
                        set = isl_set_copy(set);
                        set = isl_set_subtract(set, isl_set_copy(guard));
                        if_node[n_if].complement = set;
                        n_if++;
                } else
                        isl_set_free(guard);
                if (!graft)
                        break;

                if (found_then >= 0)
                        res = extend_then(res, if_node[found_then].node,
                                                graft, build);
                else if (found_else >= 0)
                        res = extend_else(res, if_node[found_else].node,
                                                graft, build);
                else
                        res = isl_ast_graft_list_add(res, graft);
        }
        if (i < n)
                res = isl_ast_graft_list_free(res);

        isl_ast_graft_list_free(list);
        clear_if_nodes(if_node, 0, n_if);
        free(if_node);
        return res;
}

/* For each graft in "list",
 * insert an if node around graft->node testing the condition encoded
 * in graft->guard, assuming graft->guard involves any conditions.
 * Subsequently remove the guards from the grafts.
 */
__isl_give isl_ast_graft_list *isl_ast_graft_list_insert_pending_guard_nodes(
        __isl_take isl_ast_graft_list *list, __isl_keep isl_ast_build *build)
{
        int i;
        isl_size n;
        isl_set *universe;

        list = insert_pending_guard_nodes(list, build);
        n = isl_ast_graft_list_n_ast_graft(list);
        if (n < 0)
                return isl_ast_graft_list_free(list);

        universe = isl_set_universe(isl_ast_build_get_space(build, 1));
        for (i = 0; i < n; ++i) {
                isl_ast_graft *graft;

                graft = isl_ast_graft_list_get_ast_graft(list, i);
                if (!graft)
                        break;
                isl_set_free(graft->guard);
                graft->guard = isl_set_copy(universe);
                if (!graft->guard)
                        graft = isl_ast_graft_free(graft);
                list = isl_ast_graft_list_set_ast_graft(list, i, graft);
        }
        isl_set_free(universe);
        if (i < n)
                return isl_ast_graft_list_free(list);

        return list;
}

/* Collect the nodes contained in the grafts in "list" in a node list.
 */
static __isl_give isl_ast_node_list *extract_node_list(
        __isl_keep isl_ast_graft_list *list)
{
        int i;
        isl_size n;
        isl_ctx *ctx;
        isl_ast_node_list *node_list;

        n = isl_ast_graft_list_n_ast_graft(list);
        if (n < 0)
                return NULL;
        ctx = isl_ast_graft_list_get_ctx(list);
        node_list = isl_ast_node_list_alloc(ctx, n);
        for (i = 0; i < n; ++i) {
                isl_ast_node *node;
                isl_ast_graft *graft;

                graft = isl_ast_graft_list_get_ast_graft(list, i);
                node = isl_ast_graft_get_node(graft);
                node_list = isl_ast_node_list_add(node_list, node);
                isl_ast_graft_free(graft);
        }

        return node_list;
}

/* Look for shared enforced constraints by all the elements in "list"
 * on outer loops (with respect to the current depth) and return the result.
 *
 * If there are no elements in "list", then return the empty set.
 */
__isl_give isl_basic_set *isl_ast_graft_list_extract_shared_enforced(
        __isl_keep isl_ast_graft_list *list,
        __isl_keep isl_ast_build *build)
{
        int i;
        isl_size n;
        isl_size depth;
        isl_space *space;
        isl_basic_set *enforced;

        n = isl_ast_graft_list_n_ast_graft(list);
        depth = isl_ast_build_get_depth(build);
        if (n < 0 || depth < 0)
                return NULL;

        space = isl_ast_build_get_space(build, 1);
        enforced = isl_basic_set_empty(space);

        for (i = 0; i < n; ++i) {
                isl_ast_graft *graft;

                graft = isl_ast_graft_list_get_ast_graft(list, i);
                enforced = update_enforced(enforced, graft, depth);
                isl_ast_graft_free(graft);
        }

        return enforced;
}

/* Record "guard" in "graft" so that it will be enforced somewhere
 * up the tree.  If the graft already has a guard, then it may be partially
 * redundant in combination with the new guard and in the context
 * the generated constraints of "build".  In fact, the new guard
 * may in itself have some redundant constraints.
 * We therefore (re)compute the gist of the intersection
 * and coalesce the result.
 */
static __isl_give isl_ast_graft *store_guard(__isl_take isl_ast_graft *graft,
        __isl_take isl_set *guard, __isl_keep isl_ast_build *build)
{
        int is_universe;

        if (!graft)
                goto error;

        is_universe = isl_set_plain_is_universe(guard);
        if (is_universe < 0)
                goto error;
        if (is_universe) {
                isl_set_free(guard);
                return graft;
        }

        graft->guard = isl_set_intersect(graft->guard, guard);
        graft->guard = isl_set_gist(graft->guard,
                                    isl_ast_build_get_generated(build));
        graft->guard = isl_set_coalesce(graft->guard);
        if (!graft->guard)
                return isl_ast_graft_free(graft);

        return graft;
error:
        isl_set_free(guard);
        return isl_ast_graft_free(graft);
}

/* For each graft in "list", replace its guard with the gist with
 * respect to "context".
 */
static __isl_give isl_ast_graft_list *gist_guards(
        __isl_take isl_ast_graft_list *list, __isl_keep isl_set *context)
{
        int i;
        isl_size n;

        n = isl_ast_graft_list_n_ast_graft(list);
        if (!list)
                return isl_ast_graft_list_free(list);

        for (i = 0; i < n; ++i) {
                isl_ast_graft *graft;

                graft = isl_ast_graft_list_get_ast_graft(list, i);
                if (!graft)
                        break;
                graft->guard = isl_set_gist(graft->guard,
                                                isl_set_copy(context));
                if (!graft->guard)
                        graft = isl_ast_graft_free(graft);
                list = isl_ast_graft_list_set_ast_graft(list, i, graft);
        }
        if (i < n)
                return isl_ast_graft_list_free(list);

        return list;
}

/* For each graft in "list", replace its guard with the gist with
 * respect to "context".
 */
__isl_give isl_ast_graft_list *isl_ast_graft_list_gist_guards(
        __isl_take isl_ast_graft_list *list, __isl_take isl_set *context)
{
        list = gist_guards(list, context);
        isl_set_free(context);

        return list;
}

/* Allocate a graft in "build" based on the list of grafts in "sub_build".
 * "guard" and "enforced" are the guard and enforced constraints
 * of the allocated graft.  The guard is used to simplify the guards
 * of the elements in "list".
 *
 * The node is initialized to either a block containing the nodes of "children"
 * or, if there is only a single child, the node of that child.
 * If the current level requires a for node, it should be inserted by
 * a subsequent call to isl_ast_graft_insert_for.
 */
__isl_give isl_ast_graft *isl_ast_graft_alloc_from_children(
        __isl_take isl_ast_graft_list *list, __isl_take isl_set *guard,
        __isl_take isl_basic_set *enforced, __isl_keep isl_ast_build *build,
        __isl_keep isl_ast_build *sub_build)
{
        isl_ast_build *guard_build;
        isl_ast_node *node;
        isl_ast_node_list *node_list;
        isl_ast_graft *graft;

        guard_build = isl_ast_build_copy(sub_build);
        guard_build = isl_ast_build_replace_pending_by_guard(guard_build,
                                                isl_set_copy(guard));
        list = gist_guards(list, guard);
        list = insert_pending_guard_nodes(list, guard_build);
        isl_ast_build_free(guard_build);

        node_list = extract_node_list(list);
        node = isl_ast_node_from_ast_node_list(node_list);
        isl_ast_graft_list_free(list);

        graft = isl_ast_graft_alloc(node, build);
        graft = store_guard(graft, guard, build);
        graft = isl_ast_graft_enforce(graft, enforced);

        return graft;
}

/* Combine the grafts in the list into a single graft.
 *
 * The guard is initialized to the shared guard of the list elements (if any),
 * provided it does not depend on the current dimension.
 * The guards in the elements are then simplified with respect to the
 * hoisted guard and materialized as if nodes around the contained AST nodes
 * in the context of "sub_build".
 *
 * The enforced set is initialized to the simple hull of the enforced sets
 * of the elements, provided the ast_build_exploit_nested_bounds option is set
 * or the new graft will be used at the same level.
 *
 * The node is initialized to either a block containing the nodes of "list"
 * or, if there is only a single element, the node of that element.
 */
static __isl_give isl_ast_graft *ast_graft_list_fuse(
        __isl_take isl_ast_graft_list *list, __isl_keep isl_ast_build *build)
{
        isl_ast_graft *graft;
        isl_basic_set *enforced;
        isl_set *guard;

        if (!list)
                return NULL;

        enforced = isl_ast_graft_list_extract_shared_enforced(list, build);
        guard = isl_ast_graft_list_extract_hoistable_guard(list, build);
        graft = isl_ast_graft_alloc_from_children(list, guard, enforced,
                                                    build, build);

        return graft;
}

/* Combine the grafts in the list into a single graft.
 * Return a list containing this single graft.
 * If the original list is empty, then return an empty list.
 */
__isl_give isl_ast_graft_list *isl_ast_graft_list_fuse(
        __isl_take isl_ast_graft_list *list,
        __isl_keep isl_ast_build *build)
{
        isl_size n;
        isl_ast_graft *graft;

        n = isl_ast_graft_list_n_ast_graft(list);
        if (n < 0)
                return isl_ast_graft_list_free(list);
        if (n <= 1)
                return list;
        graft = ast_graft_list_fuse(list, build);
        return isl_ast_graft_list_from_ast_graft(graft);
}

/* Combine the two grafts into a single graft.
 * Return a list containing this single graft.
 */
static __isl_give isl_ast_graft *isl_ast_graft_fuse(
        __isl_take isl_ast_graft *graft1, __isl_take isl_ast_graft *graft2,
        __isl_keep isl_ast_build *build)
{
        isl_ctx *ctx;
        isl_ast_graft_list *list;

        ctx = isl_ast_build_get_ctx(build);

        list = isl_ast_graft_list_alloc(ctx, 2);
        list = isl_ast_graft_list_add(list, graft1);
        list = isl_ast_graft_list_add(list, graft2);

        return ast_graft_list_fuse(list, build);
}

/* Insert a for node enclosing the current graft->node.
 */
__isl_give isl_ast_graft *isl_ast_graft_insert_for(
        __isl_take isl_ast_graft *graft, __isl_take isl_ast_node *node)
{
        if (!graft)
                goto error;

        graft->node = isl_ast_node_for_set_body(node, graft->node);
        if (!graft->node)
                return isl_ast_graft_free(graft);

        return graft;
error:
        isl_ast_node_free(node);
        isl_ast_graft_free(graft);
        return NULL;
}

/* Insert a mark governing the current graft->node.
 */
__isl_give isl_ast_graft *isl_ast_graft_insert_mark(
        __isl_take isl_ast_graft *graft, __isl_take isl_id *mark)
{
        if (!graft)
                goto error;

        graft->node = isl_ast_node_alloc_mark(mark, graft->node);
        if (!graft->node)
                return isl_ast_graft_free(graft);

        return graft;
error:
        isl_id_free(mark);
        isl_ast_graft_free(graft);
        return NULL;
}

/* Represent the graft list as an AST node.
 * This operation drops the information about guards in the grafts, so
 * if there are any pending guards, then they are materialized as if nodes.
 */
__isl_give isl_ast_node *isl_ast_node_from_graft_list(
        __isl_take isl_ast_graft_list *list,
        __isl_keep isl_ast_build *build)
{
        isl_ast_node_list *node_list;

        list = insert_pending_guard_nodes(list, build);
        node_list = extract_node_list(list);
        isl_ast_graft_list_free(list);

        return isl_ast_node_from_ast_node_list(node_list);
}

__isl_null isl_ast_graft *isl_ast_graft_free(__isl_take isl_ast_graft *graft)
{
        if (!graft)
                return NULL;

        if (--graft->ref > 0)
                return NULL;

        isl_ast_node_free(graft->node);
        isl_set_free(graft->guard);
        isl_basic_set_free(graft->enforced);
        free(graft);

        return NULL;
}

/* Record that the grafted tree enforces
 * "enforced" by intersecting graft->enforced with "enforced".
 */
__isl_give isl_ast_graft *isl_ast_graft_enforce(
        __isl_take isl_ast_graft *graft, __isl_take isl_basic_set *enforced)
{
        if (!graft || !enforced)
                goto error;

        enforced = isl_basic_set_align_params(enforced,
                                isl_basic_set_get_space(graft->enforced));
        graft->enforced = isl_basic_set_align_params(graft->enforced,
                                isl_basic_set_get_space(enforced));
        graft->enforced = isl_basic_set_intersect(graft->enforced, enforced);
        if (!graft->enforced)
                return isl_ast_graft_free(graft);

        return graft;
error:
        isl_basic_set_free(enforced);
        return isl_ast_graft_free(graft);
}

__isl_give isl_basic_set *isl_ast_graft_get_enforced(
        __isl_keep isl_ast_graft *graft)
{
        return graft ? isl_basic_set_copy(graft->enforced) : NULL;
}

__isl_give isl_set *isl_ast_graft_get_guard(__isl_keep isl_ast_graft *graft)
{
        return graft ? isl_set_copy(graft->guard) : NULL;
}

/* Record that "guard" needs to be inserted in "graft".
 */
__isl_give isl_ast_graft *isl_ast_graft_add_guard(
        __isl_take isl_ast_graft *graft,
        __isl_take isl_set *guard, __isl_keep isl_ast_build *build)
{
        return store_guard(graft, guard, build);
}

/* Reformulate the "graft", which was generated in the context
 * of an inner code generation, in terms of the outer code generation
 * AST build.
 *
 * If "product" is set, then the domain of the inner code generation build is
 *
 *      [O -> S]
 *
 * with O the domain of the outer code generation build.
 * We essentially need to project out S.
 *
 * If "product" is not set, then we need to project the domains onto
 * their parameter spaces.
 */
__isl_give isl_ast_graft *isl_ast_graft_unembed(__isl_take isl_ast_graft *graft,
        int product)
{
        isl_basic_set *enforced;

        if (!graft)
                return NULL;

        if (product) {
                enforced = graft->enforced;
                enforced = isl_basic_map_domain(isl_basic_set_unwrap(enforced));
                graft->enforced = enforced;
                graft->guard = isl_map_domain(isl_set_unwrap(graft->guard));
        } else {
                graft->enforced = isl_basic_set_params(graft->enforced);
                graft->guard = isl_set_params(graft->guard);
        }
        graft->guard = isl_set_compute_divs(graft->guard);

        if (!graft->enforced || !graft->guard)
                return isl_ast_graft_free(graft);

        return graft;
}

/* Reformulate the grafts in "list", which were generated in the context
 * of an inner code generation, in terms of the outer code generation
 * AST build.
 */
__isl_give isl_ast_graft_list *isl_ast_graft_list_unembed(
        __isl_take isl_ast_graft_list *list, int product)
{
        int i;
        isl_size n;

        n = isl_ast_graft_list_n_ast_graft(list);
        if (n < 0)
                return isl_ast_graft_list_free(list);
        for (i = 0; i < n; ++i) {
                isl_ast_graft *graft;

                graft = isl_ast_graft_list_get_ast_graft(list, i);
                graft = isl_ast_graft_unembed(graft, product);
                list = isl_ast_graft_list_set_ast_graft(list, i, graft);
        }

        return list;
}

/* Compute the preimage of "graft" under the function represented by "ma".
 * In other words, plug in "ma" in "enforced" and "guard" fields of "graft".
 */
__isl_give isl_ast_graft *isl_ast_graft_preimage_multi_aff(
        __isl_take isl_ast_graft *graft, __isl_take isl_multi_aff *ma)
{
        isl_basic_set *enforced;

        if (!graft)
                return NULL;

        enforced = graft->enforced;
        graft->enforced = isl_basic_set_preimage_multi_aff(enforced,
                                                isl_multi_aff_copy(ma));
        graft->guard = isl_set_preimage_multi_aff(graft->guard, ma);

        if (!graft->enforced || !graft->guard)
                return isl_ast_graft_free(graft);

        return graft;
}

/* Compute the preimage of all the grafts in "list" under
 * the function represented by "ma".
 */
__isl_give isl_ast_graft_list *isl_ast_graft_list_preimage_multi_aff(
        __isl_take isl_ast_graft_list *list, __isl_take isl_multi_aff *ma)
{
        int i;
        isl_size n;

        n = isl_ast_graft_list_n_ast_graft(list);
        if (n < 0)
                list = isl_ast_graft_list_free(list);
        for (i = 0; i < n; ++i) {
                isl_ast_graft *graft;

                graft = isl_ast_graft_list_get_ast_graft(list, i);
                graft = isl_ast_graft_preimage_multi_aff(graft,
                                                    isl_multi_aff_copy(ma));
                list = isl_ast_graft_list_set_ast_graft(list, i, graft);
        }

        isl_multi_aff_free(ma);
        return list;
}

/* Compare two grafts based on their guards.
 */
static int cmp_graft(__isl_keep isl_ast_graft *a, __isl_keep isl_ast_graft *b,
        void *user)
{
        return isl_set_plain_cmp(a->guard, b->guard);
}

/* Order the elements in "list" based on their guards.
 */
__isl_give isl_ast_graft_list *isl_ast_graft_list_sort_guard(
        __isl_take isl_ast_graft_list *list)
{
        return isl_ast_graft_list_sort(list, &cmp_graft, NULL);
}

/* Merge the given two lists into a single list of grafts,
 * merging grafts with the same guard into a single graft.
 *
 * "list2" has been sorted using isl_ast_graft_list_sort.
 * "list1" may be the result of a previous call to isl_ast_graft_list_merge
 * and may therefore not be completely sorted.
 *
 * The elements in "list2" need to be executed after those in "list1",
 * but if the guard of a graft in "list2" is disjoint from the guards
 * of some final elements in "list1", then it can be moved up to before
 * those final elements.
 *
 * In particular, we look at each element g of "list2" in turn
 * and move it up beyond elements of "list1" that would be sorted
 * after g as long as each of these elements has a guard that is disjoint
 * from that of g.
 *
 * We do not allow the second or any later element of "list2" to be moved
 * before a previous elements of "list2" even if the reason that
 * that element didn't move up further was that its guard was not disjoint
 * from that of the previous element in "list1".
 */
__isl_give isl_ast_graft_list *isl_ast_graft_list_merge(
        __isl_take isl_ast_graft_list *list1,
        __isl_take isl_ast_graft_list *list2,
        __isl_keep isl_ast_build *build)
{
        int i, j, first;

        if (!list1 || !list2 || !build)
                goto error;
        if (list2->n == 0) {
                isl_ast_graft_list_free(list2);
                return list1;
        }
        if (list1->n == 0) {
                isl_ast_graft_list_free(list1);
                return list2;
        }

        first = 0;
        for (i = 0; i < list2->n; ++i) {
                isl_ast_graft *graft;
                graft = isl_ast_graft_list_get_ast_graft(list2, i);
                if (!graft)
                        break;

                for (j = list1->n; j >= 0; --j) {
                        int cmp, disjoint;
                        isl_ast_graft *graft_j;

                        if (j == first)
                                cmp = -1;
                        else
                                cmp = isl_set_plain_cmp(list1->p[j - 1]->guard,
                                                        graft->guard);
                        if (cmp > 0) {
                                disjoint = isl_set_is_disjoint(graft->guard,
                                                        list1->p[j - 1]->guard);
                                if (disjoint < 0) {
                                        isl_ast_graft_free(graft);
                                        list1 = isl_ast_graft_list_free(list1);
                                        break;
                                }
                                if (!disjoint)
                                        cmp = -1;
                        }
                        if (cmp > 0)
                                continue;
                        if (cmp < 0) {
                                list1 = isl_ast_graft_list_insert(list1, j,
                                                                graft);
                                break;
                        }

                        --j;

                        graft_j = isl_ast_graft_list_get_ast_graft(list1, j);
                        graft_j = isl_ast_graft_fuse(graft_j, graft, build);
                        list1 = isl_ast_graft_list_set_ast_graft(list1, j,
                                                                graft_j);
                        break;
                }

                if (j < 0) {
                        isl_ast_graft_free(graft);
                        isl_die(isl_ast_build_get_ctx(build),
                                isl_error_internal,
                                "element failed to get inserted", break);
                }

                first = j + 1;
                if (!list1)
                        break;
        }
        if (i < list2->n)
                list1 = isl_ast_graft_list_free(list1);
        isl_ast_graft_list_free(list2);

        return list1;
error:
        isl_ast_graft_list_free(list1);
        isl_ast_graft_list_free(list2);
        return NULL;
}

/* Internal data structure for split_on_guard.
 *
 * "guard2list" is the constructed associative array.
 * "any_match" gets set if any guard was seen more than once.
 */
struct isl_split_on_guard_data {
        isl_set_to_ast_graft_list *guard2list;
        int *any_match;
};

/* Add "graft" to the list associated to its guard in data->guard2list.
 * If some other graft was already associated to this guard,
 * then set data->any_match.
 */
static isl_stat add_to_guard_list(__isl_take isl_ast_graft *graft, void *user)
{
        struct isl_split_on_guard_data *data = user;
        isl_set *guard;
        isl_maybe_isl_ast_graft_list m;

        if (!graft)
                return isl_stat_error;
        m = isl_set_to_ast_graft_list_try_get(data->guard2list, graft->guard);
        if (m.valid < 0)
                return isl_stat_non_null(isl_ast_graft_free(graft));

        if (m.valid) {
                *data->any_match = 1;
                m.value = isl_ast_graft_list_add(m.value, graft);
        } else {
                m.value = isl_ast_graft_list_from_ast_graft(graft);
        }
        guard = isl_set_copy(graft->guard);
        data->guard2list =
                isl_set_to_ast_graft_list_set(data->guard2list, guard, m.value);

        return isl_stat_non_null(data->guard2list);
}

/* Construct an associative array that groups the elements
 * of "list" based on their guards.
 * If any guard appears more than once, then set "any_match".
 */
static __isl_give isl_set_to_ast_graft_list *split_on_guard(
        __isl_keep isl_ast_graft_list *list, int *any_match)
{
        struct isl_split_on_guard_data data = { NULL, any_match };
        isl_size n;
        isl_ctx *ctx;

        n = isl_ast_graft_list_size(list);
        if (n < 0)
                return NULL;

        ctx = isl_ast_graft_list_get_ctx(list);
        data.guard2list = isl_set_to_ast_graft_list_alloc(ctx, n);

        if (isl_ast_graft_list_foreach(list, &add_to_guard_list, &data) < 0)
                return isl_set_to_ast_graft_list_free(data.guard2list);

        return data.guard2list;
}

/* Add the elements of "guard_list" to "list".
 */
static isl_stat add_same_guard(__isl_take isl_set *guard,
        __isl_take isl_ast_graft_list *guard_list, void *user)
{
        isl_ast_graft_list **list = user;

        isl_set_free(guard);
        *list = isl_ast_graft_list_concat(*list, guard_list);

        return isl_stat_non_null(*list);
}

/* Given an associative array "guard2list" containing the elements
 * of "list" grouped on common guards, reconstruct "list"
 * by placing elements with the same guard consecutively.
 */
static __isl_give isl_ast_graft_list *reconstruct(
        __isl_take isl_ast_graft_list *list,
        __isl_keep isl_set_to_ast_graft_list *guard2list,
        __isl_keep isl_ast_build *build)
{
        list = isl_ast_graft_list_clear(list);
        if (isl_set_to_ast_graft_list_foreach(guard2list,
                                                &add_same_guard, &list) < 0)
                list = isl_ast_graft_list_free(list);

        return list;
}

/* Group the grafts in "list" based on identical guards.
 *
 * Note that there need to be a least three elements in the list
 * for the elements not to be grouped already.
 *
 * Group the elements in an associative array based on their guards.
 * If any guard was seen more than once, then reconstruct the list
 * from the associative array.  Otherwise, simply return the original list.
 */
__isl_give isl_ast_graft_list *isl_ast_graft_list_group_on_guard(
        __isl_take isl_ast_graft_list *list, __isl_keep isl_ast_build *build)
{
        int any_match = 0;
        isl_size n;
        isl_set_to_ast_graft_list *guard2list;

        n = isl_ast_graft_list_size(list);
        if (n < 0)
                return isl_ast_graft_list_free(list);
        if (n <= 2)
                return list;

        guard2list = split_on_guard(list, &any_match);
        if (any_match)
                list = reconstruct(list, guard2list, build);

        isl_set_to_ast_graft_list_free(guard2list);

        return list;
}

/* An enumeration of the keys that appear in the textual representation
 * of an isl_sat_graft object.
 */
enum isl_graft_key {
        isl_graft_key_error = -1,
        isl_graft_key_guard,
        isl_graft_key_enforced,
        isl_graft_key_node,
        isl_graft_key_end
};

/* Textual representations of the keys for an isl_sat_graft object.
 */
static char *key_str[] = {
        [isl_graft_key_guard] = "guard",
        [isl_graft_key_enforced] = "enforced",
        [isl_graft_key_node] = "node",
};

__isl_give isl_printer *isl_printer_print_ast_graft(__isl_take isl_printer *p,
        __isl_keep isl_ast_graft *graft)
{
        if (!p)
                return NULL;
        if (!graft)
                return isl_printer_free(p);

        p = isl_printer_print_str(p, "(");
        p = isl_printer_print_str(p, key_str[isl_graft_key_guard]);
        p = isl_printer_print_str(p, ": ");
        p = isl_printer_print_set(p, graft->guard);
        p = isl_printer_print_str(p, ", ");
        p = isl_printer_print_str(p, key_str[isl_graft_key_enforced]);
        p = isl_printer_print_str(p, ": ");
        p = isl_printer_print_basic_set(p, graft->enforced);
        p = isl_printer_print_str(p, ", ");
        p = isl_printer_print_str(p, key_str[isl_graft_key_node]);
        p = isl_printer_print_str(p, ": ");
        p = isl_printer_print_ast_node(p, graft->node);
        p = isl_printer_print_str(p, ")");

        return p;
}

#undef KEY
#define KEY enum isl_graft_key
#undef KEY_ERROR
#define KEY_ERROR isl_graft_key_error
#undef KEY_END
#define KEY_END isl_graft_key_end
#undef KEY_STR
#define KEY_STR key_str
#undef KEY_EXTRACT
#define KEY_EXTRACT extract_key
#undef KEY_GET
#define KEY_GET get_key
#include "extract_key.c"

/* Read the key "key" from "s", along with the subsequent colon.
 */
static isl_stat read_key(__isl_keep isl_stream *s, enum isl_graft_key key)
{
        enum isl_graft_key extracted;

        extracted = get_key(s);
        if (extracted < 0)
                return isl_stat_error;
        if (extracted != key)
                isl_die(isl_stream_get_ctx(s), isl_error_invalid,
                        "expecting different field", return isl_stat_error);
        if (isl_stream_eat(s, ':') < 0)
                return isl_stat_error;
        return isl_stat_ok;
}

/* Read an isl_ast_graft object from "s".
 *
 * Read the pieces in the way they are printed in isl_printer_print_ast_graft.
 */
static __isl_give isl_ast_graft *isl_stream_read_ast_graft(
        __isl_keep isl_stream *s)
{
        isl_set *guard;
        isl_basic_set *enforced = NULL;
        isl_ast_node *node = NULL;

        if (isl_stream_eat(s, '(') < 0)
                return NULL;
        if (read_key(s, isl_graft_key_guard) < 0)
                return NULL;
        guard = isl_stream_read_set(s);
        if (!guard)
                goto error;
        if (isl_stream_eat(s, ',') < 0)
                goto error;
        if (read_key(s, isl_graft_key_enforced) < 0)
                goto error;
        enforced = isl_stream_read_basic_set(s);
        if (!enforced)
                goto error;
        if (isl_stream_eat(s, ',') < 0)
                goto error;
        if (read_key(s, isl_graft_key_node) < 0)
                goto error;
        node = isl_stream_read_ast_node(s);
        if (!node)
                goto error;
        if (isl_stream_eat(s, ')') < 0)
                goto error;
        return graft_alloc(node, guard, enforced);
error:
        isl_set_free(guard);
        isl_basic_set_free(enforced);
        isl_ast_node_free(node);
        return NULL;
}