expr.c: directly include required header

[pet.git] / scop.c

/*
 * Copyright 2011      Leiden University. All rights reserved.
 * Copyright 2012-2014 Ecole Normale Superieure. All rights reserved.
 * 
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 
 *    1. Redistributions of source code must retain the above copyright
 *       notice, this list of conditions and the following disclaimer.
 * 
 *    2. Redistributions in binary form must reproduce the above
 *       copyright notice, this list of conditions and the following
 *       disclaimer in the documentation and/or other materials provided
 *       with the distribution.
 * 
 * THIS SOFTWARE IS PROVIDED BY LEIDEN UNIVERSITY ''AS IS'' AND ANY
 * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL LEIDEN UNIVERSITY OR
 * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
 * OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 * 
 * The views and conclusions contained in the software and documentation
 * are those of the authors and should not be interpreted as
 * representing official policies, either expressed or implied, of
 * Leiden University.
 */ 

#include <string.h>
#include <isl/constraint.h>
#include <isl/union_set.h>
#include <isl/schedule_node.h>

#include "aff.h"
#include "expr.h"
#include "expr_access_type.h"
#include "filter.h"
#include "loc.h"
#include "nest.h"
#include "scop.h"
#include "tree.h"
#include "print.h"
#include "value_bounds.h"

/* pet_scop with extra information that is used during parsing and printing.
 *
 * In particular, we keep track of conditions under which we want
 * to skip the rest of the current loop iteration (skip[pet_skip_now])
 * and of conditions under which we want to skip subsequent
 * loop iterations (skip[pet_skip_later]).
 *
 * The conditions are represented as index expressions defined
 * over the outer loop iterators.  The index expression is either
 * a boolean affine expression or an access to a variable, which
 * is assumed to attain values zero and one.  The condition holds
 * if the variable has value one or if the affine expression
 * has value one (typically for only part of the domain).
 *
 * A missing condition (skip[type] == NULL) means that we don't want
 * to skip anything.
 *
 * Additionally, we keep track of the original input file
 * inside pet_transform_C_source.
 */
struct pet_scop_ext {
        struct pet_scop scop;

        isl_multi_pw_aff *skip[2];
        FILE *input;
};

/* Construct a pet_stmt with given domain and statement number from a pet_tree.
 * The input domain is anonymous and is the same as the domains
 * of the access expressions inside "tree".
 * These domains are modified to include the name of the statement.
 * This name is given by tree->label if it is non-NULL.
 * Otherwise, the name is constructed as S_<id>.
 */
struct pet_stmt *pet_stmt_from_pet_tree(__isl_take isl_set *domain,
        int id, __isl_take pet_tree *tree)
{
        struct pet_stmt *stmt;
        isl_ctx *ctx;
        isl_id *label;
        isl_space *space;
        isl_multi_aff *ma;
        isl_multi_pw_aff *add_name;
        char name[50];

        if (!domain || !tree)
                goto error;

        ctx = pet_tree_get_ctx(tree);
        stmt = isl_calloc_type(ctx, struct pet_stmt);
        if (!stmt)
                goto error;

        if (tree->label) {
                label = isl_id_copy(tree->label);
        } else {
                snprintf(name, sizeof(name), "S_%d", id);
                label = isl_id_alloc(ctx, name, NULL);
        }
        domain = isl_set_set_tuple_id(domain, label);
        space = isl_set_get_space(domain);
        space = pet_nested_remove_from_space(space);
        ma = pet_prefix_projection(space, isl_space_dim(space, isl_dim_set));

        add_name = isl_multi_pw_aff_from_multi_aff(ma);
        tree = pet_tree_update_domain(tree, add_name);

        stmt->loc = pet_tree_get_loc(tree);
        stmt->domain = domain;
        stmt->body = tree;

        if (!stmt->domain || !stmt->body)
                return pet_stmt_free(stmt);

        return stmt;
error:
        isl_set_free(domain);
        pet_tree_free(tree);
        return NULL;
}

void *pet_stmt_free(struct pet_stmt *stmt)
{
        int i;

        if (!stmt)
                return NULL;

        pet_loc_free(stmt->loc);
        isl_set_free(stmt->domain);
        pet_tree_free(stmt->body);

        for (i = 0; i < stmt->n_arg; ++i)
                pet_expr_free(stmt->args[i]);
        free(stmt->args);

        free(stmt);
        return NULL;
}

/* Return the iteration space of "stmt".
 *
 * If the statement has arguments, then stmt->domain is a wrapped map
 * mapping the iteration domain to the values of the arguments
 * for which this statement is executed.
 * In this case, we need to extract the domain space of this wrapped map.
 */
__isl_give isl_space *pet_stmt_get_space(struct pet_stmt *stmt)
{
        isl_space *space;

        if (!stmt)
                return NULL;

        space = isl_set_get_space(stmt->domain);
        if (isl_space_is_wrapping(space))
                space = isl_space_domain(isl_space_unwrap(space));

        return space;
}

static void stmt_dump(struct pet_stmt *stmt, int indent)
{
        int i;

        if (!stmt)
                return;

        fprintf(stderr, "%*s%d\n", indent, "", pet_loc_get_line(stmt->loc));
        fprintf(stderr, "%*s", indent, "");
        isl_set_dump(stmt->domain);
        pet_tree_dump_with_indent(stmt->body, indent);
        for (i = 0; i < stmt->n_arg; ++i)
                pet_expr_dump_with_indent(stmt->args[i], indent + 2);
}

void pet_stmt_dump(struct pet_stmt *stmt)
{
        stmt_dump(stmt, 0);
}

/* Allocate a new pet_type with the given "name" and "definition".
 */
struct pet_type *pet_type_alloc(isl_ctx *ctx, const char *name,
        const char *definition)
{
        struct pet_type *type;

        type = isl_alloc_type(ctx, struct pet_type);
        if (!type)
                return NULL;

        type->name = strdup(name);
        type->definition = strdup(definition);

        if (!type->name || !type->definition)
                return pet_type_free(type);

        return type;
}

/* Free "type" and return NULL.
 */
struct pet_type *pet_type_free(struct pet_type *type)
{
        if (!type)
                return NULL;

        free(type->name);
        free(type->definition);

        free(type);
        return NULL;
}

struct pet_array *pet_array_free(struct pet_array *array)
{
        if (!array)
                return NULL;

        isl_set_free(array->context);
        isl_set_free(array->extent);
        isl_set_free(array->value_bounds);
        free(array->element_type);

        free(array);
        return NULL;
}

void pet_array_dump(struct pet_array *array)
{
        if (!array)
                return;

        isl_set_dump(array->context);
        isl_set_dump(array->extent);
        isl_set_dump(array->value_bounds);
        fprintf(stderr, "%s%s%s\n", array->element_type,
                array->element_is_record ? " element-is-record" : "",
                array->live_out ? " live-out" : "");
}

/* Alloc a pet_scop structure, with extra room for information that
 * is only used during parsing.
 */
struct pet_scop *pet_scop_alloc(isl_ctx *ctx)
{
        return &isl_calloc_type(ctx, struct pet_scop_ext)->scop;
}

/* Construct a pet_scop in the given space, with the given schedule and
 * room for n statements.
 *
 * The context is initialized as a universe set in "space".
 *
 * Since no information on the location is known at this point,
 * scop->loc is initialized with pet_loc_dummy.
 */
static struct pet_scop *scop_alloc(__isl_take isl_space *space, int n,
        __isl_take isl_schedule *schedule)
{
        isl_ctx *ctx;
        struct pet_scop *scop;

        if (!space || !schedule)
                goto error;

        ctx = isl_space_get_ctx(space);
        scop = pet_scop_alloc(ctx);
        if (!scop)
                goto error;

        scop->context = isl_set_universe(isl_space_copy(space));
        scop->context_value = isl_set_universe(isl_space_params(space));
        scop->stmts = isl_calloc_array(ctx, struct pet_stmt *, n);
        scop->schedule = schedule;
        if (!scop->context || !scop->stmts)
                return pet_scop_free(scop);

        scop->loc = &pet_loc_dummy;
        scop->n_stmt = n;

        return scop;
error:
        isl_space_free(space);
        isl_schedule_free(schedule);
        return NULL;
}

/* Construct a pet_scop in the given space containing 0 statements
 * (and therefore an empty iteration domain).
 */
struct pet_scop *pet_scop_empty(__isl_take isl_space *space)
{
        isl_schedule *schedule;

        schedule = isl_schedule_empty(isl_space_copy(space));

        return scop_alloc(space, 0, schedule);
}

/* Given either an iteration domain or a wrapped map with
 * the iteration domain in the domain and some arguments
 * in the range, return the iteration domain.
 * That is, drop the arguments if there are any.
 */
static __isl_give isl_set *drop_arguments(__isl_take isl_set *domain)
{
        if (isl_set_is_wrapping(domain))
                domain = isl_map_domain(isl_set_unwrap(domain));
        return domain;
}

/* Update "context" with the constraints imposed on the outer iteration
 * domain by access expression "expr".
 * "context" lives in an anonymous space, while the domain of the access
 * relation of "expr" refers to a particular statement.
 * This reference therefore needs to be stripped off.
 */
static __isl_give isl_set *access_extract_context(__isl_keep pet_expr *expr,
        __isl_take isl_set *context)
{
        isl_multi_pw_aff *mpa;
        isl_set *domain;

        mpa = pet_expr_access_get_index(expr);
        domain = drop_arguments(isl_multi_pw_aff_domain(mpa));
        domain = isl_set_reset_tuple_id(domain);
        context = isl_set_intersect(context, domain);
        return context;
}

/* Update "context" with the constraints imposed on the outer iteration
 * domain by "expr".
 *
 * "context" lives in an anonymous space, while the domains of
 * the access relations in "expr" refer to a particular statement.
 * This reference therefore needs to be stripped off.
 *
 * If "expr" represents a conditional operator, then a parameter or outer
 * iterator value needs to be valid for the condition and
 * for at least one of the remaining two arguments.
 * If the condition is an affine expression, then we can be a bit more specific.
 * The value then has to be valid for the second argument for
 * non-zero accesses and valid for the third argument for zero accesses.
 *
 * If "expr" represents a kill statement, then its argument is the entire
 * extent of the array being killed.  Do not update "context" based
 * on this argument as that would impose constraints that ensure that
 * the array is non-empty.
 */
static __isl_give isl_set *expr_extract_context(__isl_keep pet_expr *expr,
        __isl_take isl_set *context)
{
        int i;

        if (expr->type == pet_expr_op && expr->op == pet_op_kill)
                return context;

        if (expr->type == pet_expr_op && expr->op == pet_op_cond) {
                int is_aff;
                isl_set *context1, *context2;

                is_aff = pet_expr_is_affine(expr->args[0]);
                if (is_aff < 0)
                        goto error;

                context = expr_extract_context(expr->args[0], context);
                context1 = expr_extract_context(expr->args[1],
                                                isl_set_copy(context));
                context2 = expr_extract_context(expr->args[2], context);

                if (is_aff) {
                        isl_multi_pw_aff *mpa;
                        isl_pw_aff *pa;
                        isl_set *zero_set;

                        mpa = pet_expr_access_get_index(expr->args[0]);
                        pa = isl_multi_pw_aff_get_pw_aff(mpa, 0);
                        isl_multi_pw_aff_free(mpa);
                        zero_set = drop_arguments(isl_pw_aff_zero_set(pa));
                        zero_set = isl_set_reset_tuple_id(zero_set);
                        context1 = isl_set_subtract(context1,
                                                    isl_set_copy(zero_set));
                        context2 = isl_set_intersect(context2, zero_set);
                }

                context = isl_set_union(context1, context2);
                context = isl_set_coalesce(context);

                return context;
        }

        for (i = 0; i < expr->n_arg; ++i)
                context = expr_extract_context(expr->args[i], context);

        if (expr->type == pet_expr_access)
                context = access_extract_context(expr, context);

        return context;
error:
        isl_set_free(context);
        return NULL;
}

/* Is "stmt" an assume statement with an affine assumption?
 */
int pet_stmt_is_affine_assume(struct pet_stmt *stmt)
{
        if (!stmt)
                return 0;
        return pet_tree_is_affine_assume(stmt->body);
}

/* Given an assume statement "stmt" with an access argument,
 * return the index expression of the argument.
 */
__isl_give isl_multi_pw_aff *pet_stmt_assume_get_index(struct pet_stmt *stmt)
{
        if (!stmt)
                return NULL;
        return pet_tree_assume_get_index(stmt->body);
}

/* Update "context" with the constraints imposed on the outer iteration
 * domain by "stmt".
 *
 * If the statement is an assume statement with an affine expression,
 * then intersect "context" with that expression.
 * Otherwise, if the statement body is an expression tree,
 * then intersect "context" with the context of this expression.
 * Note that we cannot safely extract a context from subtrees
 * of the statement body since we cannot tell when those subtrees
 * are executed, if at all.
 */
static __isl_give isl_set *stmt_extract_context(struct pet_stmt *stmt,
        __isl_take isl_set *context)
{
        int i;
        pet_expr *body;

        if (pet_stmt_is_affine_assume(stmt)) {
                isl_multi_pw_aff *index;
                isl_pw_aff *pa;
                isl_set *cond;

                index = pet_stmt_assume_get_index(stmt);
                pa = isl_multi_pw_aff_get_pw_aff(index, 0);
                isl_multi_pw_aff_free(index);
                cond = isl_pw_aff_non_zero_set(pa);
                cond = isl_set_reset_tuple_id(cond);
                return isl_set_intersect(context, cond);
        }

        for (i = 0; i < stmt->n_arg; ++i)
                context = expr_extract_context(stmt->args[i], context);

        if (pet_tree_get_type(stmt->body) != pet_tree_expr)
                return context;

        body = pet_tree_expr_get_expr(stmt->body);
        context = expr_extract_context(body, context);
        pet_expr_free(body);

        return context;
}

/* Construct a pet_scop in the given space that contains the given pet_stmt.
 * The initial schedule consists of only the iteration domain.
 */
struct pet_scop *pet_scop_from_pet_stmt(__isl_take isl_space *space,
        struct pet_stmt *stmt)
{
        struct pet_scop *scop;
        isl_set *set;
        isl_union_set *domain;
        isl_schedule *schedule;

        if (!stmt)
                space = isl_space_free(space);

        set = pet_nested_remove_from_set(isl_set_copy(stmt->domain));
        domain = isl_union_set_from_set(set);
        schedule = isl_schedule_from_domain(domain);

        scop = scop_alloc(space, 1, schedule);
        if (!scop)
                goto error;

        scop->context = stmt_extract_context(stmt, scop->context);
        if (!scop->context)
                goto error;

        scop->stmts[0] = stmt;
        scop->loc = pet_loc_copy(stmt->loc);

        if (!scop->loc)
                return pet_scop_free(scop);

        return scop;
error:
        pet_stmt_free(stmt);
        pet_scop_free(scop);
        return NULL;
}

/* Does "mpa" represent an access to an element of an unnamed space, i.e.,
 * does it represent an affine expression?
 */
static int multi_pw_aff_is_affine(__isl_keep isl_multi_pw_aff *mpa)
{
        int has_id;

        has_id = isl_multi_pw_aff_has_tuple_id(mpa, isl_dim_out);
        if (has_id < 0)
                return -1;

        return !has_id;
}

/* Return the piecewise affine expression "set ? 1 : 0" defined on "dom".
 */
static __isl_give isl_pw_aff *indicator_function(__isl_take isl_set *set,
        __isl_take isl_set *dom)
{
        isl_pw_aff *pa;
        pa = isl_set_indicator_function(set);
        pa = isl_pw_aff_intersect_domain(pa, dom);
        return pa;
}

/* Return "lhs || rhs", defined on the shared definition domain.
 */
static __isl_give isl_pw_aff *pw_aff_or(__isl_take isl_pw_aff *lhs,
        __isl_take isl_pw_aff *rhs)
{
        isl_set *cond;
        isl_set *dom;

        dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(lhs)),
                                 isl_pw_aff_domain(isl_pw_aff_copy(rhs)));
        cond = isl_set_union(isl_pw_aff_non_zero_set(lhs),
                             isl_pw_aff_non_zero_set(rhs));
        cond = isl_set_coalesce(cond);
        return indicator_function(cond, dom);
}

/* Combine ext1->skip[type] and ext2->skip[type] into ext->skip[type].
 * ext may be equal to either ext1 or ext2.
 *
 * The two skips that need to be combined are assumed to be affine expressions.
 *
 * We need to skip in ext if we need to skip in either ext1 or ext2.
 * We don't need to skip in ext if we don't need to skip in both ext1 and ext2.
 */
static struct pet_scop_ext *combine_skips(struct pet_scop_ext *ext,
        struct pet_scop_ext *ext1, struct pet_scop_ext *ext2,
        enum pet_skip type)
{
        isl_pw_aff *skip, *skip1, *skip2;

        if (!ext)
                return NULL;
        if (!ext1->skip[type] && !ext2->skip[type])
                return ext;
        if (!ext1->skip[type]) {
                if (ext == ext2)
                        return ext;
                ext->skip[type] = ext2->skip[type];
                ext2->skip[type] = NULL;
                return ext;
        }
        if (!ext2->skip[type]) {
                if (ext == ext1)
                        return ext;
                ext->skip[type] = ext1->skip[type];
                ext1->skip[type] = NULL;
                return ext;
        }

        if (!multi_pw_aff_is_affine(ext1->skip[type]) ||
            !multi_pw_aff_is_affine(ext2->skip[type]))
                isl_die(isl_multi_pw_aff_get_ctx(ext1->skip[type]),
                        isl_error_internal, "can only combine affine skips",
                        goto error);

        skip1 = isl_multi_pw_aff_get_pw_aff(ext1->skip[type], 0);
        skip2 = isl_multi_pw_aff_get_pw_aff(ext2->skip[type], 0);
        skip = pw_aff_or(skip1, skip2);
        isl_multi_pw_aff_free(ext1->skip[type]);
        ext1->skip[type] = NULL;
        isl_multi_pw_aff_free(ext2->skip[type]);
        ext2->skip[type] = NULL;
        ext->skip[type] = isl_multi_pw_aff_from_pw_aff(skip);
        if (!ext->skip[type])
                goto error;

        return ext;
error:
        pet_scop_free(&ext->scop);
        return NULL;
}

/* Combine scop1->skip[type] and scop2->skip[type] into scop->skip[type],
 * where type takes on the values pet_skip_now and pet_skip_later.
 * scop may be equal to either scop1 or scop2.
 */
static struct pet_scop *scop_combine_skips(struct pet_scop *scop,
        struct pet_scop *scop1, struct pet_scop *scop2)
{
        struct pet_scop_ext *ext = (struct pet_scop_ext *) scop;
        struct pet_scop_ext *ext1 = (struct pet_scop_ext *) scop1;
        struct pet_scop_ext *ext2 = (struct pet_scop_ext *) scop2;

        ext = combine_skips(ext, ext1, ext2, pet_skip_now);
        ext = combine_skips(ext, ext1, ext2, pet_skip_later);
        return &ext->scop;
}

/* Update start and end of scop->loc to include the region from "start"
 * to "end".  In particular, if scop->loc == &pet_loc_dummy, then "scop"
 * does not have any offset information yet and we simply take the information
 * from "start" and "end".  Otherwise, we update loc using "start" and "end".
 */
struct pet_scop *pet_scop_update_start_end(struct pet_scop *scop,
        unsigned start, unsigned end)
{
        if (!scop)
                return NULL;

        if (scop->loc == &pet_loc_dummy)
                scop->loc = pet_loc_alloc(isl_set_get_ctx(scop->context),
                                            start, end, -1, strdup(""));
        else
                scop->loc = pet_loc_update_start_end(scop->loc, start, end);

        if (!scop->loc)
                return pet_scop_free(scop);

        return scop;
}

/* Update start and end of scop->loc to include the region identified
 * by "loc".
 */
struct pet_scop *pet_scop_update_start_end_from_loc(struct pet_scop *scop,
        __isl_keep pet_loc *loc)
{
        return pet_scop_update_start_end(scop, pet_loc_get_start(loc),
                                                pet_loc_get_end(loc));
}

/* Replace the location of "scop" by "loc".
 */
struct pet_scop *pet_scop_set_loc(struct pet_scop *scop,
        __isl_take pet_loc *loc)
{
        if (!scop || !loc)
                goto error;

        pet_loc_free(scop->loc);
        scop->loc = loc;

        return scop;
error:
        pet_loc_free(loc);
        pet_scop_free(scop);
        return NULL;
}

/* Does "implication" appear in the list of implications of "scop"?
 */
static int is_known_implication(struct pet_scop *scop,
        struct pet_implication *implication)
{
        int i;

        for (i = 0; i < scop->n_implication; ++i) {
                struct pet_implication *pi = scop->implications[i];
                int equal;

                if (pi->satisfied != implication->satisfied)
                        continue;
                equal = isl_map_is_equal(pi->extension, implication->extension);
                if (equal < 0)
                        return -1;
                if (equal)
                        return 1;
        }

        return 0;
}

/* Store the concatenation of the implications of "scop1" and "scop2"
 * in "scop", removing duplicates (i.e., implications in "scop2" that
 * already appear in "scop1").
 */
static struct pet_scop *scop_collect_implications(isl_ctx *ctx,
        struct pet_scop *scop, struct pet_scop *scop1, struct pet_scop *scop2)
{
        int i, j;

        if (!scop)
                return NULL;

        if (scop2->n_implication == 0) {
                scop->n_implication = scop1->n_implication;
                scop->implications = scop1->implications;
                scop1->n_implication = 0;
                scop1->implications = NULL;
                return scop;
        }

        if (scop1->n_implication == 0) {
                scop->n_implication = scop2->n_implication;
                scop->implications = scop2->implications;
                scop2->n_implication = 0;
                scop2->implications = NULL;
                return scop;
        }

        scop->implications = isl_calloc_array(ctx, struct pet_implication *,
                                scop1->n_implication + scop2->n_implication);
        if (!scop->implications)
                return pet_scop_free(scop);

        for (i = 0; i < scop1->n_implication; ++i) {
                scop->implications[i] = scop1->implications[i];
                scop1->implications[i] = NULL;
        }

        scop->n_implication = scop1->n_implication;
        j = scop1->n_implication;
        for (i = 0; i < scop2->n_implication; ++i) {
                int known;

                known = is_known_implication(scop, scop2->implications[i]);
                if (known < 0)
                        return pet_scop_free(scop);
                if (known)
                        continue;
                scop->implications[j++] = scop2->implications[i];
                scop2->implications[i] = NULL;
        }
        scop->n_implication = j;

        return scop;
}

/* Combine the offset information of "scop1" and "scop2" into "scop".
 */
static struct pet_scop *scop_combine_start_end(struct pet_scop *scop,
        struct pet_scop *scop1, struct pet_scop *scop2)
{
        if (scop1->loc != &pet_loc_dummy)
                scop = pet_scop_update_start_end_from_loc(scop, scop1->loc);
        if (scop2->loc != &pet_loc_dummy)
                scop = pet_scop_update_start_end_from_loc(scop, scop2->loc);
        return scop;
}

/* Create and return an independence that filters out the dependences
 * in "filter" with local variables "local".
 */
static struct pet_independence *new_independence(
        __isl_take isl_union_map *filter, __isl_take isl_union_set *local)
{
        isl_ctx *ctx;
        struct pet_independence *independence;

        if (!filter || !local)
                goto error;
        ctx = isl_union_map_get_ctx(filter);
        independence = isl_alloc_type(ctx, struct pet_independence);
        if (!independence)
                goto error;

        independence->filter = filter;
        independence->local = local;

        return independence;
error:
        isl_union_map_free(filter);
        isl_union_set_free(local);
        return NULL;
}

/* Add an independence that filters out the dependences
 * in "filter" with local variables "local" to "scop".
 */
struct pet_scop *pet_scop_add_independence(struct pet_scop *scop,
        __isl_take isl_union_map *filter, __isl_take isl_union_set *local)
{
        isl_ctx *ctx;
        struct pet_independence *independence;
        struct pet_independence **independences;

        ctx = isl_union_map_get_ctx(filter);
        independence = new_independence(filter, local);
        if (!scop || !independence)
                goto error;

        independences = isl_realloc_array(ctx, scop->independences,
                                            struct pet_independence *,
                                            scop->n_independence + 1);
        if (!independences)
                goto error;
        scop->independences = independences;
        scop->independences[scop->n_independence] = independence;
        scop->n_independence++;

        return scop;
error:
        pet_independence_free(independence);
        pet_scop_free(scop);
        return NULL;
}

/* Store the concatenation of the independences of "scop1" and "scop2"
 * in "scop".
 */
static struct pet_scop *scop_collect_independences(isl_ctx *ctx,
        struct pet_scop *scop, struct pet_scop *scop1, struct pet_scop *scop2)
{
        int i, off;

        if (!scop)
                return NULL;

        if (scop2->n_independence == 0) {
                scop->n_independence = scop1->n_independence;
                scop->independences = scop1->independences;
                scop1->n_independence = 0;
                scop1->independences = NULL;
                return scop;
        }

        if (scop1->n_independence == 0) {
                scop->n_independence = scop2->n_independence;
                scop->independences = scop2->independences;
                scop2->n_independence = 0;
                scop2->independences = NULL;
                return scop;
        }

        scop->independences = isl_calloc_array(ctx, struct pet_independence *,
                                scop1->n_independence + scop2->n_independence);
        if (!scop->independences)
                return pet_scop_free(scop);

        for (i = 0; i < scop1->n_independence; ++i) {
                scop->independences[i] = scop1->independences[i];
                scop1->independences[i] = NULL;
        }

        off = scop1->n_independence;
        for (i = 0; i < scop2->n_independence; ++i) {
                scop->independences[off + i] = scop2->independences[i];
                scop2->independences[i] = NULL;
        }
        scop->n_independence = scop1->n_independence + scop2->n_independence;

        return scop;
}

/* Construct a pet_scop with the given schedule
 * that contains the offset information,
 * arrays, statements and skip information in "scop1" and "scop2".
 */
static struct pet_scop *pet_scop_add(isl_ctx *ctx,
        __isl_take isl_schedule *schedule, struct pet_scop *scop1,
        struct pet_scop *scop2)
{
        int i;
        isl_space *space;
        struct pet_scop *scop = NULL;

        if (!scop1 || !scop2)
                goto error;

        if (scop1->n_stmt == 0) {
                scop2 = scop_combine_skips(scop2, scop1, scop2);
                pet_scop_free(scop1);
                isl_schedule_free(schedule);
                return scop2;
        }

        if (scop2->n_stmt == 0) {
                scop1 = scop_combine_skips(scop1, scop1, scop2);
                pet_scop_free(scop2);
                isl_schedule_free(schedule);
                return scop1;
        }

        space = isl_set_get_space(scop1->context);
        scop = scop_alloc(space, scop1->n_stmt + scop2->n_stmt,
                        isl_schedule_copy(schedule));
        if (!scop)
                goto error;

        scop->arrays = isl_calloc_array(ctx, struct pet_array *,
                                        scop1->n_array + scop2->n_array);
        if (!scop->arrays)
                goto error;
        scop->n_array = scop1->n_array + scop2->n_array;

        for (i = 0; i < scop1->n_stmt; ++i) {
                scop->stmts[i] = scop1->stmts[i];
                scop1->stmts[i] = NULL;
        }

        for (i = 0; i < scop2->n_stmt; ++i) {
                scop->stmts[scop1->n_stmt + i] = scop2->stmts[i];
                scop2->stmts[i] = NULL;
        }

        for (i = 0; i < scop1->n_array; ++i) {
                scop->arrays[i] = scop1->arrays[i];
                scop1->arrays[i] = NULL;
        }

        for (i = 0; i < scop2->n_array; ++i) {
                scop->arrays[scop1->n_array + i] = scop2->arrays[i];
                scop2->arrays[i] = NULL;
        }

        scop = scop_collect_implications(ctx, scop, scop1, scop2);
        scop = pet_scop_restrict_context(scop, isl_set_copy(scop1->context));
        scop = pet_scop_restrict_context(scop, isl_set_copy(scop2->context));
        scop = scop_combine_skips(scop, scop1, scop2);
        scop = scop_combine_start_end(scop, scop1, scop2);
        scop = scop_collect_independences(ctx, scop, scop1, scop2);

        pet_scop_free(scop1);
        pet_scop_free(scop2);
        isl_schedule_free(schedule);
        return scop;
error:
        pet_scop_free(scop1);
        pet_scop_free(scop2);
        pet_scop_free(scop);
        isl_schedule_free(schedule);
        return NULL;
}

/* Apply the skip condition "skip" to "scop".
 * That is, make sure "scop" is not executed when the condition holds.
 *
 * If "skip" is an affine expression, we add the conditions under
 * which the expression is zero to the context and the skip conditions
 * of "scop".
 * Otherwise, we add a filter on the variable attaining the value zero.
 */
static struct pet_scop *restrict_skip(struct pet_scop *scop,
        __isl_take isl_multi_pw_aff *skip)
{
        isl_set *zero;
        isl_pw_aff *pa;
        int is_aff;

        if (!scop || !skip)
                goto error;

        is_aff = multi_pw_aff_is_affine(skip);
        if (is_aff < 0)
                goto error;

        if (!is_aff)
                return pet_scop_filter(scop, skip, 0);

        pa = isl_multi_pw_aff_get_pw_aff(skip, 0);
        isl_multi_pw_aff_free(skip);
        zero = isl_pw_aff_zero_set(pa);
        scop = pet_scop_restrict(scop, zero);

        return scop;
error:
        isl_multi_pw_aff_free(skip);
        return pet_scop_free(scop);
}

/* Construct a pet_scop that contains the arrays, statements and
 * skip information in "scop1" and "scop2", where the two scops
 * are executed "in sequence".  That is, breaks and continues
 * in scop1 have an effect on scop2 and the schedule of the result
 * is the sequence of the schedules of "scop1" and "scop2".
 */
struct pet_scop *pet_scop_add_seq(isl_ctx *ctx, struct pet_scop *scop1,
        struct pet_scop *scop2)
{
        isl_schedule *schedule;

        if (!scop1 || !scop2)
                goto error;

        if (scop1 && pet_scop_has_skip(scop1, pet_skip_now))
                scop2 = restrict_skip(scop2,
                                        pet_scop_get_skip(scop1, pet_skip_now));
        schedule = isl_schedule_sequence(isl_schedule_copy(scop1->schedule),
                                        isl_schedule_copy(scop2->schedule));
        return pet_scop_add(ctx, schedule, scop1, scop2);
error:
        pet_scop_free(scop1);
        pet_scop_free(scop2);
        return NULL;
}

/* Construct a pet_scop that contains the arrays, statements and
 * skip information in "scop1" and "scop2", where the two scops
 * are executed "in parallel".  That is, any break or continue
 * in scop1 has no effect on scop2 and the schedule of the result
 * is the set of the schedules of "scop1" and "scop2".
 */
struct pet_scop *pet_scop_add_par(isl_ctx *ctx, struct pet_scop *scop1,
        struct pet_scop *scop2)
{
        isl_schedule *schedule;

        if (!scop1 || !scop2)
                goto error;

        schedule = isl_schedule_set(isl_schedule_copy(scop1->schedule),
                                        isl_schedule_copy(scop2->schedule));
        return pet_scop_add(ctx, schedule, scop1, scop2);
error:
        pet_scop_free(scop1);
        pet_scop_free(scop2);
        return NULL;
}

void *pet_implication_free(struct pet_implication *implication)
{
        int i;

        if (!implication)
                return NULL;

        isl_map_free(implication->extension);

        free(implication);
        return NULL;
}

void *pet_independence_free(struct pet_independence *independence)
{
        if (!independence)
                return NULL;

        isl_union_map_free(independence->filter);
        isl_union_set_free(independence->local);

        free(independence);
        return NULL;
}

struct pet_scop *pet_scop_free(struct pet_scop *scop)
{
        int i;
        struct pet_scop_ext *ext = (struct pet_scop_ext *) scop;

        if (!scop)
                return NULL;
        pet_loc_free(scop->loc);
        isl_set_free(scop->context);
        isl_set_free(scop->context_value);
        isl_schedule_free(scop->schedule);
        if (scop->types)
                for (i = 0; i < scop->n_type; ++i)
                        pet_type_free(scop->types[i]);
        free(scop->types);
        if (scop->arrays)
                for (i = 0; i < scop->n_array; ++i)
                        pet_array_free(scop->arrays[i]);
        free(scop->arrays);
        if (scop->stmts)
                for (i = 0; i < scop->n_stmt; ++i)
                        pet_stmt_free(scop->stmts[i]);
        free(scop->stmts);
        if (scop->implications)
                for (i = 0; i < scop->n_implication; ++i)
                        pet_implication_free(scop->implications[i]);
        free(scop->implications);
        if (scop->independences)
                for (i = 0; i < scop->n_independence; ++i)
                        pet_independence_free(scop->independences[i]);
        free(scop->independences);
        isl_multi_pw_aff_free(ext->skip[pet_skip_now]);
        isl_multi_pw_aff_free(ext->skip[pet_skip_later]);
        free(scop);
        return NULL;
}

void pet_type_dump(struct pet_type *type)
{
        if (!type)
                return;

        fprintf(stderr, "%s -> %s\n", type->name, type->definition);
}

void pet_implication_dump(struct pet_implication *implication)
{
        if (!implication)
                return;

        fprintf(stderr, "%d\n", implication->satisfied);
        isl_map_dump(implication->extension);
}

void pet_scop_dump(struct pet_scop *scop)
{
        int i;
        struct pet_scop_ext *ext = (struct pet_scop_ext *) scop;

        if (!scop)
                return;
        
        isl_set_dump(scop->context);
        isl_set_dump(scop->context_value);
        isl_schedule_dump(scop->schedule);
        for (i = 0; i < scop->n_type; ++i)
                pet_type_dump(scop->types[i]);
        for (i = 0; i < scop->n_array; ++i)
                pet_array_dump(scop->arrays[i]);
        for (i = 0; i < scop->n_stmt; ++i)
                pet_stmt_dump(scop->stmts[i]);
        for (i = 0; i < scop->n_implication; ++i)
                pet_implication_dump(scop->implications[i]);

        if (ext->skip[0]) {
                fprintf(stderr, "skip\n");
                isl_multi_pw_aff_dump(ext->skip[0]);
                isl_multi_pw_aff_dump(ext->skip[1]);
        }
}

/* Return 1 if the two pet_arrays are equivalent.
 *
 * We don't compare element_size as this may be target dependent.
 */
int pet_array_is_equal(struct pet_array *array1, struct pet_array *array2)
{
        if (!array1 || !array2)
                return 0;

        if (!isl_set_is_equal(array1->context, array2->context))
                return 0;
        if (!isl_set_is_equal(array1->extent, array2->extent))
                return 0;
        if (!!array1->value_bounds != !!array2->value_bounds)
                return 0;
        if (array1->value_bounds &&
            !isl_set_is_equal(array1->value_bounds, array2->value_bounds))
                return 0;
        if (strcmp(array1->element_type, array2->element_type))
                return 0;
        if (array1->element_is_record != array2->element_is_record)
                return 0;
        if (array1->live_out != array2->live_out)
                return 0;
        if (array1->uniquely_defined != array2->uniquely_defined)
                return 0;
        if (array1->declared != array2->declared)
                return 0;
        if (array1->exposed != array2->exposed)
                return 0;

        return 1;
}

/* Return 1 if the two pet_stmts are equivalent.
 */
int pet_stmt_is_equal(struct pet_stmt *stmt1, struct pet_stmt *stmt2)
{
        int i;

        if (!stmt1 || !stmt2)
                return 0;
        
        if (pet_loc_get_line(stmt1->loc) != pet_loc_get_line(stmt2->loc))
                return 0;
        if (!isl_set_is_equal(stmt1->domain, stmt2->domain))
                return 0;
        if (!pet_tree_is_equal(stmt1->body, stmt2->body))
                return 0;
        if (stmt1->n_arg != stmt2->n_arg)
                return 0;
        for (i = 0; i < stmt1->n_arg; ++i) {
                if (!pet_expr_is_equal(stmt1->args[i], stmt2->args[i]))
                        return 0;
        }

        return 1;
}

/* Return 1 if the two pet_types are equivalent.
 *
 * We only compare the names of the types since the exact representation
 * of the definition may depend on the version of clang being used.
 */
int pet_type_is_equal(struct pet_type *type1, struct pet_type *type2)
{
        if (!type1 || !type2)
                return 0;

        if (strcmp(type1->name, type2->name))
                return 0;

        return 1;
}

/* Return 1 if the two pet_implications are equivalent.
 */
int pet_implication_is_equal(struct pet_implication *implication1,
        struct pet_implication *implication2)
{
        if (!implication1 || !implication2)
                return 0;

        if (implication1->satisfied != implication2->satisfied)
                return 0;
        if (!isl_map_is_equal(implication1->extension, implication2->extension))
                return 0;

        return 1;
}

/* Return 1 if the two pet_independences are equivalent.
 */
int pet_independence_is_equal(struct pet_independence *independence1,
        struct pet_independence *independence2)
{
        if (!independence1 || !independence2)
                return 0;

        if (!isl_union_map_is_equal(independence1->filter,
                                        independence2->filter))
                return 0;
        if (!isl_union_set_is_equal(independence1->local, independence2->local))
                return 0;

        return 1;
}

/* Return 1 if the two pet_scops are equivalent.
 */
int pet_scop_is_equal(struct pet_scop *scop1, struct pet_scop *scop2)
{
        int i;
        int equal;

        if (!scop1 || !scop2)
                return 0;

        if (!isl_set_is_equal(scop1->context, scop2->context))
                return 0;
        if (!isl_set_is_equal(scop1->context_value, scop2->context_value))
                return 0;
        equal = isl_schedule_plain_is_equal(scop1->schedule, scop2->schedule);
        if (equal < 0)
                return -1;
        if (!equal)
                return 0;

        if (scop1->n_type != scop2->n_type)
                return 0;
        for (i = 0; i < scop1->n_type; ++i)
                if (!pet_type_is_equal(scop1->types[i], scop2->types[i]))
                        return 0;

        if (scop1->n_array != scop2->n_array)
                return 0;
        for (i = 0; i < scop1->n_array; ++i)
                if (!pet_array_is_equal(scop1->arrays[i], scop2->arrays[i]))
                        return 0;

        if (scop1->n_stmt != scop2->n_stmt)
                return 0;
        for (i = 0; i < scop1->n_stmt; ++i)
                if (!pet_stmt_is_equal(scop1->stmts[i], scop2->stmts[i]))
                        return 0;

        if (scop1->n_implication != scop2->n_implication)
                return 0;
        for (i = 0; i < scop1->n_implication; ++i)
                if (!pet_implication_is_equal(scop1->implications[i],
                                                scop2->implications[i]))
                        return 0;

        if (scop1->n_independence != scop2->n_independence)
                return 0;
        for (i = 0; i < scop1->n_independence; ++i)
                if (!pet_independence_is_equal(scop1->independences[i],
                                                scop2->independences[i]))
                        return 0;

        return 1;
}

/* Does the set "extent" reference a virtual array, i.e.,
 * one with user pointer equal to NULL?
 * A virtual array does not have any members.
 */
static int extent_is_virtual_array(__isl_keep isl_set *extent)
{
        isl_id *id;
        int is_virtual;

        if (!isl_set_has_tuple_id(extent))
                return 0;
        if (isl_set_is_wrapping(extent))
                return 0;
        id = isl_set_get_tuple_id(extent);
        is_virtual = !isl_id_get_user(id);
        isl_id_free(id);

        return is_virtual;
}

/* Intersect the initial dimensions of "array" with "domain", provided
 * that "array" represents a virtual array.
 *
 * If "array" is virtual, then We take the preimage of "domain"
 * over the projection of the extent of "array" onto its initial dimensions
 * and intersect this extent with the result.
 */
static struct pet_array *virtual_array_intersect_domain_prefix(
        struct pet_array *array, __isl_take isl_set *domain)
{
        int n;
        isl_space *space;
        isl_multi_aff *ma;

        if (!array || !extent_is_virtual_array(array->extent)) {
                isl_set_free(domain);
                return array;
        }

        space = isl_set_get_space(array->extent);
        n = isl_set_dim(domain, isl_dim_set);
        ma = pet_prefix_projection(space, n);
        domain = isl_set_preimage_multi_aff(domain, ma);

        array->extent = isl_set_intersect(array->extent, domain);
        if (!array->extent)
                return pet_array_free(array);

        return array;
}

/* Intersect the initial dimensions of the domain of "stmt"
 * with "domain".
 *
 * We take the preimage of "domain" over the projection of the
 * domain of "stmt" onto its initial dimensions and intersect
 * the domain of "stmt" with the result.
 */
static struct pet_stmt *stmt_intersect_domain_prefix(struct pet_stmt *stmt,
        __isl_take isl_set *domain)
{
        int n;
        isl_space *space;
        isl_multi_aff *ma;

        if (!stmt)
                goto error;

        space = isl_set_get_space(stmt->domain);
        n = isl_set_dim(domain, isl_dim_set);
        ma = pet_prefix_projection(space, n);
        domain = isl_set_preimage_multi_aff(domain, ma);

        stmt->domain = isl_set_intersect(stmt->domain, domain);
        if (!stmt->domain)
                return pet_stmt_free(stmt);

        return stmt;
error:
        isl_set_free(domain);
        return pet_stmt_free(stmt);
}

/* Intersect the initial dimensions of the domain of "implication"
 * with "domain".
 *
 * We take the preimage of "domain" over the projection of the
 * domain of "implication" onto its initial dimensions and intersect
 * the domain of "implication" with the result.
 */
static struct pet_implication *implication_intersect_domain_prefix(
        struct pet_implication *implication, __isl_take isl_set *domain)
{
        int n;
        isl_space *space;
        isl_multi_aff *ma;

        if (!implication)
                goto error;

        space = isl_map_get_space(implication->extension);
        n = isl_set_dim(domain, isl_dim_set);
        ma = pet_prefix_projection(isl_space_domain(space), n);
        domain = isl_set_preimage_multi_aff(domain, ma);

        implication->extension =
                isl_map_intersect_domain(implication->extension, domain);
        if (!implication->extension)
                return pet_implication_free(implication);

        return implication;
error:
        isl_set_free(domain);
        return pet_implication_free(implication);
}

/* Intersect the initial dimensions of the domains in "scop" with "domain".
 *
 * The extents of the virtual arrays match the iteration domains,
 * so if the iteration domain changes, we need to change those extents too.
 *
 * The domain of the schedule is intersected with (i.e., replaced by)
 * the union of the updated iteration domains.
 */
struct pet_scop *pet_scop_intersect_domain_prefix(struct pet_scop *scop,
        __isl_take isl_set *domain)
{
        int i;

        if (!scop)
                goto error;

        for (i = 0; i < scop->n_array; ++i) {
                scop->arrays[i] = virtual_array_intersect_domain_prefix(
                                        scop->arrays[i], isl_set_copy(domain));
                if (!scop->arrays[i])
                        goto error;
        }

        for (i = 0; i < scop->n_stmt; ++i) {
                scop->stmts[i] = stmt_intersect_domain_prefix(scop->stmts[i],
                                                    isl_set_copy(domain));
                if (!scop->stmts[i])
                        goto error;
        }

        for (i = 0; i < scop->n_implication; ++i) {
                scop->implications[i] =
                    implication_intersect_domain_prefix(scop->implications[i],
                                                    isl_set_copy(domain));
                if (!scop->implications[i])
                        return pet_scop_free(scop);
        }

        scop->schedule = isl_schedule_intersect_domain(scop->schedule,
                                            pet_scop_collect_domains(scop));
        if (!scop->schedule)
                goto error;

        isl_set_free(domain);
        return scop;
error:
        isl_set_free(domain);
        return pet_scop_free(scop);
}

/* Update the context with respect to an embedding into a loop
 * with iteration domain "dom".
 * The input context lives in the same space as "dom".
 * The output context has the inner dimension removed.
 *
 * An outer loop iterator value is invalid for the embedding if
 * any of the corresponding inner iterator values is invalid.
 * That is, an outer loop iterator value is valid only if all the corresponding
 * inner iterator values are valid.
 * We therefore compute the set of outer loop iterators l
 *
 *      forall i: dom(l,i) => valid(l,i)
 *
 * or
 *
 *      forall i: not dom(l,i) or valid(l,i)
 *
 * or
 *
 *      not exists i: dom(l,i) and not valid(l,i)
 *
 * i.e.,
 *
 *      not exists i: (dom \ valid)(l,i)
 *
 * If there are any unnamed parameters in "dom", then we consider
 * a parameter value to be valid if it is valid for any value of those
 * unnamed parameters.  They are therefore projected out at the end.
 */
static __isl_give isl_set *context_embed(__isl_take isl_set *context,
        __isl_keep isl_set *dom)
{
        int pos;

        pos = isl_set_dim(context, isl_dim_set) - 1;
        context = isl_set_subtract(isl_set_copy(dom), context);
        context = isl_set_project_out(context, isl_dim_set, pos, 1);
        context = isl_set_complement(context);
        context = pet_nested_remove_from_set(context);

        return context;
}

/* Update the implication with respect to an embedding into a loop
 * with iteration domain "dom".
 *
 * Since embed_access extends virtual arrays along with the domain
 * of the access, we need to do the same with domain and range
 * of the implication.  Since the original implication is only valid
 * within a given iteration of the loop, the extended implication
 * maps the extra array dimension corresponding to the extra loop
 * to itself.
 */
static struct pet_implication *pet_implication_embed(
        struct pet_implication *implication, __isl_take isl_set *dom)
{
        isl_id *id;
        isl_map *map;

        if (!implication)
                goto error;

        map = isl_set_identity(dom);
        id = isl_map_get_tuple_id(implication->extension, isl_dim_in);
        map = isl_map_flat_product(map, implication->extension);
        map = isl_map_set_tuple_id(map, isl_dim_in, isl_id_copy(id));
        map = isl_map_set_tuple_id(map, isl_dim_out, id);
        implication->extension = map;
        if (!implication->extension)
                return pet_implication_free(implication);

        return implication;
error:
        isl_set_free(dom);
        return NULL;
}

/* Internal data structure for outer_projection_mupa.
 *
 * "n" is the number of outer dimensions onto which to project.
 * "res" collects the result.
 */
struct pet_outer_projection_data {
        int n;
        isl_union_pw_multi_aff *res;
};

/* Create a function that maps "set" onto its outer data->n dimensions and
 * add it to data->res.
 */
static int add_outer_projection(__isl_take isl_set *set, void *user)
{
        struct pet_outer_projection_data *data = user;
        int dim;
        isl_space *space;
        isl_pw_multi_aff *pma;

        dim = isl_set_dim(set, isl_dim_set);
        space = isl_set_get_space(set);
        pma = isl_pw_multi_aff_project_out_map(space,
                                        isl_dim_set, data->n, dim - data->n);
        data->res = isl_union_pw_multi_aff_add_pw_multi_aff(data->res, pma);

        isl_set_free(set);

        return 0;
}

/* Create and return a function that maps the sets in "domain"
 * onto their outer "n" dimensions.
 */
static __isl_give isl_multi_union_pw_aff *outer_projection_mupa(
        __isl_take isl_union_set *domain, int n)
{
        struct pet_outer_projection_data data;
        isl_space *space;

        space = isl_union_set_get_space(domain);
        data.n = n;
        data.res = isl_union_pw_multi_aff_empty(space);
        if (isl_union_set_foreach_set(domain, &add_outer_projection, &data) < 0)
                data.res = isl_union_pw_multi_aff_free(data.res);

        isl_union_set_free(domain);
        return isl_multi_union_pw_aff_from_union_pw_multi_aff(data.res);
}

/* Embed "schedule" in a loop with schedule "prefix".
 * The domain of "prefix" corresponds to the outer dimensions
 * of the iteration domains.
 * We therefore construct a projection onto these outer dimensions,
 * compose it with "prefix" and then add the result as a band schedule.
 *
 * If the domain of the schedule is empty, then there is no need
 * to insert any node.
 */
static __isl_give isl_schedule *schedule_embed(
        __isl_take isl_schedule *schedule, __isl_keep isl_multi_aff *prefix)
{
        int n;
        int empty;
        isl_union_set *domain;
        isl_multi_aff *ma;
        isl_multi_union_pw_aff *mupa;

        domain = isl_schedule_get_domain(schedule);
        empty = isl_union_set_is_empty(domain);
        if (empty < 0 || empty) {
                isl_union_set_free(domain);
                return empty < 0 ? isl_schedule_free(schedule) : schedule;
        }

        n = isl_multi_aff_dim(prefix, isl_dim_in);
        mupa = outer_projection_mupa(domain, n);
        ma = isl_multi_aff_copy(prefix);
        mupa = isl_multi_union_pw_aff_apply_multi_aff(mupa, ma);
        schedule = isl_schedule_insert_partial_schedule(schedule, mupa);

        return schedule;
}

/* Adjust the context and the schedule according to an embedding
 * in a loop with iteration domain "dom" and schedule "sched".
 */
struct pet_scop *pet_scop_embed(struct pet_scop *scop, __isl_take isl_set *dom,
        __isl_take isl_multi_aff *sched)
{
        int i;

        if (!scop)
                goto error;

        scop->context = context_embed(scop->context, dom);
        if (!scop->context)
                goto error;

        scop->schedule = schedule_embed(scop->schedule, sched);
        if (!scop->schedule)
                goto error;

        isl_set_free(dom);
        isl_multi_aff_free(sched);
        return scop;
error:
        isl_set_free(dom);
        isl_multi_aff_free(sched);
        return pet_scop_free(scop);
}

/* Add extra conditions to scop->skip[type].
 *
 * The new skip condition only holds if it held before
 * and the condition is true.  It does not hold if it did not hold
 * before or the condition is false.
 *
 * The skip condition is assumed to be an affine expression.
 */
static struct pet_scop *pet_scop_restrict_skip(struct pet_scop *scop,
        enum pet_skip type, __isl_keep isl_set *cond)
{
        struct pet_scop_ext *ext = (struct pet_scop_ext *) scop;
        isl_pw_aff *skip;
        isl_set *dom;

        if (!scop)
                return NULL;
        if (!ext->skip[type])
                return scop;

        if (!multi_pw_aff_is_affine(ext->skip[type]))
                isl_die(isl_multi_pw_aff_get_ctx(ext->skip[type]),
                        isl_error_internal, "can only restrict affine skips",
                        return pet_scop_free(scop));

        skip = isl_multi_pw_aff_get_pw_aff(ext->skip[type], 0);
        dom = isl_pw_aff_domain(isl_pw_aff_copy(skip));
        cond = isl_set_copy(cond);
        cond = isl_set_intersect(cond, isl_pw_aff_non_zero_set(skip));
        skip = indicator_function(cond, dom);
        isl_multi_pw_aff_free(ext->skip[type]);
        ext->skip[type] = isl_multi_pw_aff_from_pw_aff(skip);
        if (!ext->skip[type])
                return pet_scop_free(scop);

        return scop;
}

/* Adjust the context and the skip conditions to the fact that
 * the scop was created in a context where "cond" holds.
 *
 * An outer loop iterator or parameter value is valid for the result
 * if it was valid for the original scop and satisfies "cond" or if it does
 * not satisfy "cond" as in this case the scop is not executed
 * and the original constraints on these values are irrelevant.
 */
struct pet_scop *pet_scop_restrict(struct pet_scop *scop,
        __isl_take isl_set *cond)
{
        int i;

        scop = pet_scop_restrict_skip(scop, pet_skip_now, cond);
        scop = pet_scop_restrict_skip(scop, pet_skip_later, cond);

        if (!scop)
                goto error;

        scop->context = isl_set_intersect(scop->context, isl_set_copy(cond));
        scop->context = isl_set_union(scop->context,
                                isl_set_complement(isl_set_copy(cond)));
        scop->context = isl_set_coalesce(scop->context);
        scop->context = pet_nested_remove_from_set(scop->context);
        if (!scop->context)
                goto error;

        isl_set_free(cond);
        return scop;
error:
        isl_set_free(cond);
        return pet_scop_free(scop);
}

/* Insert an argument expression corresponding to "test" in front
 * of the list of arguments described by *n_arg and *args.
 */
static int args_insert_access(unsigned *n_arg, pet_expr ***args,
        __isl_keep isl_multi_pw_aff *test)
{
        int i;
        isl_ctx *ctx = isl_multi_pw_aff_get_ctx(test);

        if (!test)
                return -1;

        if (!*args) {
                *args = isl_calloc_array(ctx, pet_expr *, 1);
                if (!*args)
                        return -1;
        } else {
                pet_expr **ext;
                ext = isl_calloc_array(ctx, pet_expr *, 1 + *n_arg);
                if (!ext)
                        return -1;
                for (i = 0; i < *n_arg; ++i)
                        ext[1 + i] = (*args)[i];
                free(*args);
                *args = ext;
        }
        (*n_arg)++;
        (*args)[0] = pet_expr_from_index(isl_multi_pw_aff_copy(test));
        if (!(*args)[0])
                return -1;

        return 0;
}

/* Look through the applications in "scop" for any that can be
 * applied to the filter expressed by "map" and "satisified".
 * If there is any, then apply it to "map" and return the result.
 * Otherwise, return "map".
 * "id" is the identifier of the virtual array.
 *
 * We only introduce at most one implication for any given virtual array,
 * so we can apply the implication and return as soon as we find one.
 */
static __isl_give isl_map *apply_implications(struct pet_scop *scop,
        __isl_take isl_map *map, __isl_keep isl_id *id, int satisfied)
{
        int i;

        for (i = 0; i < scop->n_implication; ++i) {
                struct pet_implication *pi = scop->implications[i];
                isl_id *pi_id;

                if (pi->satisfied != satisfied)
                        continue;
                pi_id = isl_map_get_tuple_id(pi->extension, isl_dim_in);
                isl_id_free(pi_id);
                if (pi_id != id)
                        continue;

                return isl_map_apply_range(map, isl_map_copy(pi->extension));
        }

        return map;
}

/* Is the filter expressed by "test" and "satisfied" implied
 * by filter "pos" on "domain", with filter "expr", taking into
 * account the implications of "scop"?
 *
 * For filter on domain implying that expressed by "test" and "satisfied",
 * the filter needs to be an access to the same (virtual) array as "test" and
 * the filter value needs to be equal to "satisfied".
 * Moreover, the filter access relation, possibly extended by
 * the implications in "scop" needs to contain "test".
 */
static int implies_filter(struct pet_scop *scop,
        __isl_keep isl_map *domain, int pos, __isl_keep pet_expr *expr,
        __isl_keep isl_map *test, int satisfied)
{
        isl_id *test_id, *arg_id;
        isl_val *val;
        int is_int;
        int s;
        int is_subset;
        isl_map *implied;

        if (expr->type != pet_expr_access)
                return 0;
        test_id = isl_map_get_tuple_id(test, isl_dim_out);
        arg_id = pet_expr_access_get_id(expr);
        isl_id_free(arg_id);
        isl_id_free(test_id);
        if (test_id != arg_id)
                return 0;
        val = isl_map_plain_get_val_if_fixed(domain, isl_dim_out, pos);
        is_int = isl_val_is_int(val);
        if (is_int)
                s = isl_val_get_num_si(val);
        isl_val_free(val);
        if (!val)
                return -1;
        if (!is_int)
                return 0;
        if (s != satisfied)
                return 0;

        implied = isl_map_from_multi_pw_aff(pet_expr_access_get_index(expr));
        implied = apply_implications(scop, implied, test_id, satisfied);
        is_subset = isl_map_is_subset(test, implied);
        isl_map_free(implied);

        return is_subset;
}

/* Is the filter expressed by "test" and "satisfied" implied
 * by any of the filters on the domain of "stmt", taking into
 * account the implications of "scop"?
 */
static int filter_implied(struct pet_scop *scop,
        struct pet_stmt *stmt, __isl_keep isl_multi_pw_aff *test, int satisfied)
{
        int i;
        int implied;
        isl_id *test_id;
        isl_map *domain;
        isl_map *test_map;

        if (!scop || !stmt || !test)
                return -1;
        if (scop->n_implication == 0)
                return 0;
        if (stmt->n_arg == 0)
                return 0;

        domain = isl_set_unwrap(isl_set_copy(stmt->domain));
        test_map = isl_map_from_multi_pw_aff(isl_multi_pw_aff_copy(test));

        implied = 0;
        for (i = 0; i < stmt->n_arg; ++i) {
                implied = implies_filter(scop, domain, i, stmt->args[i],
                                         test_map, satisfied);
                if (implied < 0 || implied)
                        break;
        }

        isl_map_free(test_map);
        isl_map_free(domain);
        return implied;
}

/* Make the statement "stmt" depend on the value of "test"
 * being equal to "satisfied" by adjusting stmt->domain.
 *
 * The domain of "test" corresponds to the (zero or more) outer dimensions
 * of the iteration domain.
 *
 * We first extend "test" to apply to the entire iteration domain and
 * then check if the filter that we are about to add is implied
 * by any of the current filters, possibly taking into account
 * the implications in "scop".  If so, we leave "stmt" untouched and return.
 *
 * Otherwise, we insert an argument corresponding to a read to "test"
 * from the iteration domain of "stmt" in front of the list of arguments.
 * We also insert a corresponding output dimension in the wrapped
 * map contained in stmt->domain, with value set to "satisfied".
 */
static struct pet_stmt *stmt_filter(struct pet_scop *scop,
        struct pet_stmt *stmt, __isl_take isl_multi_pw_aff *test, int satisfied)
{
        int i;
        int implied;
        isl_id *id;
        isl_ctx *ctx;
        isl_pw_multi_aff *pma;
        isl_multi_aff *add_dom;
        isl_space *space;
        isl_local_space *ls;
        int n_test_dom;

        if (!stmt || !test)
                goto error;

        space = pet_stmt_get_space(stmt);
        n_test_dom = isl_multi_pw_aff_dim(test, isl_dim_in);
        space = isl_space_from_domain(space);
        space = isl_space_add_dims(space, isl_dim_out, n_test_dom);
        add_dom = isl_multi_aff_zero(isl_space_copy(space));
        ls = isl_local_space_from_space(isl_space_domain(space));
        for (i = 0; i < n_test_dom; ++i) {
                isl_aff *aff;
                aff = isl_aff_var_on_domain(isl_local_space_copy(ls),
                                            isl_dim_set, i);
                add_dom = isl_multi_aff_set_aff(add_dom, i, aff);
        }
        isl_local_space_free(ls);
        test = isl_multi_pw_aff_pullback_multi_aff(test, add_dom);

        implied = filter_implied(scop, stmt, test, satisfied);
        if (implied < 0)
                goto error;
        if (implied) {
                isl_multi_pw_aff_free(test);
                return stmt;
        }

        id = isl_multi_pw_aff_get_tuple_id(test, isl_dim_out);
        pma = pet_filter_insert_pma(isl_set_get_space(stmt->domain),
                                        id, satisfied);
        stmt->domain = isl_set_preimage_pw_multi_aff(stmt->domain, pma);

        if (args_insert_access(&stmt->n_arg, &stmt->args, test) < 0)
                goto error;

        isl_multi_pw_aff_free(test);
        return stmt;
error:
        isl_multi_pw_aff_free(test);
        return pet_stmt_free(stmt);
}

/* Does "scop" have a skip condition of the given "type"?
 */
int pet_scop_has_skip(struct pet_scop *scop, enum pet_skip type)
{
        struct pet_scop_ext *ext = (struct pet_scop_ext *) scop;

        if (!scop)
                return -1;
        return ext->skip[type] != NULL;
}

/* Does "scop" have a skip condition of the given "type" that
 * is an affine expression?
 */
int pet_scop_has_affine_skip(struct pet_scop *scop, enum pet_skip type)
{
        struct pet_scop_ext *ext = (struct pet_scop_ext *) scop;

        if (!scop)
                return -1;
        if (!ext->skip[type])
                return 0;
        return multi_pw_aff_is_affine(ext->skip[type]);
}

/* Does "scop" have a skip condition of the given "type" that
 * is not an affine expression?
 */
int pet_scop_has_var_skip(struct pet_scop *scop, enum pet_skip type)
{
        struct pet_scop_ext *ext = (struct pet_scop_ext *) scop;
        int aff;

        if (!scop)
                return -1;
        if (!ext->skip[type])
                return 0;
        aff = multi_pw_aff_is_affine(ext->skip[type]);
        if (aff < 0)
                return -1;
        return !aff;
}

/* Does "scop" have a skip condition of the given "type" that
 * is affine and holds on the entire domain?
 */
int pet_scop_has_universal_skip(struct pet_scop *scop, enum pet_skip type)
{
        struct pet_scop_ext *ext = (struct pet_scop_ext *) scop;
        isl_pw_aff *pa;
        isl_set *set;
        int is_aff;
        int is_univ;

        is_aff = pet_scop_has_affine_skip(scop, type);
        if (is_aff < 0 || !is_aff)
                return is_aff;

        pa = isl_multi_pw_aff_get_pw_aff(ext->skip[type], 0);
        set = isl_pw_aff_non_zero_set(pa);
        is_univ = isl_set_plain_is_universe(set);
        isl_set_free(set);

        return is_univ;
}

/* Replace scop->skip[type] by "skip".
 */
struct pet_scop *pet_scop_set_skip(struct pet_scop *scop,
        enum pet_skip type, __isl_take isl_multi_pw_aff *skip)
{
        struct pet_scop_ext *ext = (struct pet_scop_ext *) scop;

        if (!scop || !skip)
                goto error;

        isl_multi_pw_aff_free(ext->skip[type]);
        ext->skip[type] = skip;

        return scop;
error:
        isl_multi_pw_aff_free(skip);
        return pet_scop_free(scop);
}

/* Return a copy of scop->skip[type].
 */
__isl_give isl_multi_pw_aff *pet_scop_get_skip(struct pet_scop *scop,
        enum pet_skip type)
{
        struct pet_scop_ext *ext = (struct pet_scop_ext *) scop;

        if (!scop)
                return NULL;

        return isl_multi_pw_aff_copy(ext->skip[type]);
}

/* Assuming scop->skip[type] is an affine expression,
 * return the constraints on the outer loop domain for which the skip condition
 * holds.
 */
__isl_give isl_set *pet_scop_get_affine_skip_domain(struct pet_scop *scop,
        enum pet_skip type)
{
        isl_multi_pw_aff *skip;
        isl_pw_aff *pa;

        skip = pet_scop_get_skip(scop, type);
        pa = isl_multi_pw_aff_get_pw_aff(skip, 0);
        isl_multi_pw_aff_free(skip);
        return isl_pw_aff_non_zero_set(pa);
}

/* Return the identifier of the variable that is accessed by
 * the skip condition of the given type.
 *
 * The skip condition is assumed not to be an affine condition.
 */
__isl_give isl_id *pet_scop_get_skip_id(struct pet_scop *scop,
        enum pet_skip type)
{
        struct pet_scop_ext *ext = (struct pet_scop_ext *) scop;

        if (!scop)
                return NULL;

        return isl_multi_pw_aff_get_tuple_id(ext->skip[type], isl_dim_out);
}

/* Return an access pet_expr corresponding to the skip condition
 * of the given type.
 */
__isl_give pet_expr *pet_scop_get_skip_expr(struct pet_scop *scop,
        enum pet_skip type)
{
        return pet_expr_from_index(pet_scop_get_skip(scop, type));
}

/* Drop the skip condition scop->skip[type].
 */
void pet_scop_reset_skip(struct pet_scop *scop, enum pet_skip type)
{
        struct pet_scop_ext *ext = (struct pet_scop_ext *) scop;

        if (!scop)
                return;

        isl_multi_pw_aff_free(ext->skip[type]);
        ext->skip[type] = NULL;
}

/* Drop all skip conditions on "scop".
 */
struct pet_scop *pet_scop_reset_skips(struct pet_scop *scop)
{
        pet_scop_reset_skip(scop, pet_skip_now);
        pet_scop_reset_skip(scop, pet_skip_later);

        return scop;
}

/* Make the skip condition (if any) depend on the value of "test" being
 * equal to "satisfied".
 *
 * We only support the case where the original skip condition is universal,
 * i.e., where skipping is unconditional, and where satisfied == 1.
 * In this case, the skip condition is changed to skip only when 
 * "test" is equal to one.
 */
static struct pet_scop *pet_scop_filter_skip(struct pet_scop *scop,
        enum pet_skip type, __isl_keep isl_multi_pw_aff *test, int satisfied)
{
        int is_univ = 0;

        if (!scop)
                return NULL;
        if (!pet_scop_has_skip(scop, type))
                return scop;

        if (satisfied)
                is_univ = pet_scop_has_universal_skip(scop, type);
        if (is_univ < 0)
                return pet_scop_free(scop);
        if (satisfied && is_univ) {
                isl_multi_pw_aff *skip;
                skip = isl_multi_pw_aff_copy(test);
                scop = pet_scop_set_skip(scop, type, skip);
                if (!scop)
                        return NULL;
        } else {
                isl_die(isl_multi_pw_aff_get_ctx(test), isl_error_internal,
                        "skip expression cannot be filtered",
                        return pet_scop_free(scop));
        }

        return scop;
}

/* Make all statements in "scop" depend on the value of "test"
 * being equal to "satisfied" by adjusting their domains.
 */
struct pet_scop *pet_scop_filter(struct pet_scop *scop,
        __isl_take isl_multi_pw_aff *test, int satisfied)
{
        int i;

        scop = pet_scop_filter_skip(scop, pet_skip_now, test, satisfied);
        scop = pet_scop_filter_skip(scop, pet_skip_later, test, satisfied);

        if (!scop || !test)
                goto error;

        for (i = 0; i < scop->n_stmt; ++i) {
                scop->stmts[i] = stmt_filter(scop, scop->stmts[i],
                                        isl_multi_pw_aff_copy(test), satisfied);
                if (!scop->stmts[i])
                        goto error;
        }

        isl_multi_pw_aff_free(test);
        return scop;
error:
        isl_multi_pw_aff_free(test);
        return pet_scop_free(scop);
}

/* Add the parameters of the access expression "expr" to "space".
 */
static int access_collect_params(__isl_keep pet_expr *expr, void *user)
{
        int i;
        isl_space *expr_space;
        isl_space **space = user;

        expr_space = pet_expr_access_get_parameter_space(expr);
        *space = isl_space_align_params(*space, expr_space);

        return *space ? 0 : -1;
}

/* Add all parameters in "stmt" to "space" and return the result.
 */
static __isl_give isl_space *stmt_collect_params(struct pet_stmt *stmt,
        __isl_take isl_space *space)
{
        int i;

        if (!stmt)
                return isl_space_free(space);

        space = isl_space_align_params(space, isl_set_get_space(stmt->domain));
        for (i = 0; i < stmt->n_arg; ++i)
                if (pet_expr_foreach_access_expr(stmt->args[i],
                                        &access_collect_params, &space) < 0)
                        space = isl_space_free(space);
        if (pet_tree_foreach_access_expr(stmt->body, &access_collect_params,
                                        &space) < 0)
                space = isl_space_free(space);

        return space;
}

/* Add all parameters in "array" to "space" and return the result.
 */
static __isl_give isl_space *array_collect_params(struct pet_array *array,
        __isl_take isl_space *space)
{
        if (!array)
                return isl_space_free(space);

        space = isl_space_align_params(space,
                                        isl_set_get_space(array->context));
        space = isl_space_align_params(space, isl_set_get_space(array->extent));

        return space;
}

/* Add all parameters in "independence" to "space" and return the result.
 */
static __isl_give isl_space *independence_collect_params(
        struct pet_independence *independence, __isl_take isl_space *space)
{
        if (!independence)
                return isl_space_free(space);

        space = isl_space_align_params(space,
                                isl_union_map_get_space(independence->filter));
        space = isl_space_align_params(space,
                                isl_union_set_get_space(independence->local));

        return space;
}

/* Collect all parameters in "scop" in a parameter space and return the result.
 */
static __isl_give isl_space *scop_collect_params(struct pet_scop *scop)
{
        isl_space *space;
        int i;

        if (!scop)
                return NULL;

        space = isl_set_get_space(scop->context);

        for (i = 0; i < scop->n_array; ++i)
                space = array_collect_params(scop->arrays[i], space);

        for (i = 0; i < scop->n_stmt; ++i)
                space = stmt_collect_params(scop->stmts[i], space);

        for (i = 0; i < scop->n_independence; ++i)
                space = independence_collect_params(scop->independences[i],
                                                        space);

        return space;
}

/* Add all parameters in "space" to the domain and
 * all access relations in "stmt".
 */
static struct pet_stmt *stmt_propagate_params(struct pet_stmt *stmt,
        __isl_take isl_space *space)
{
        int i;

        if (!stmt)
                goto error;

        stmt->domain = isl_set_align_params(stmt->domain,
                                                isl_space_copy(space));

        for (i = 0; i < stmt->n_arg; ++i) {
                stmt->args[i] = pet_expr_align_params(stmt->args[i],
                                                isl_space_copy(space));
                if (!stmt->args[i])
                        goto error;
        }
        stmt->body = pet_tree_align_params(stmt->body, isl_space_copy(space));

        if (!stmt->domain || !stmt->body)
                goto error;

        isl_space_free(space);
        return stmt;
error:
        isl_space_free(space);
        return pet_stmt_free(stmt);
}

/* Add all parameters in "space" to "array".
 */
static struct pet_array *array_propagate_params(struct pet_array *array,
        __isl_take isl_space *space)
{
        if (!array)
                goto error;

        array->context = isl_set_align_params(array->context,
                                                isl_space_copy(space));
        array->extent = isl_set_align_params(array->extent,
                                                isl_space_copy(space));
        if (array->value_bounds) {
                array->value_bounds = isl_set_align_params(array->value_bounds,
                                                        isl_space_copy(space));
                if (!array->value_bounds)
                        goto error;
        }

        if (!array->context || !array->extent)
                goto error;

        isl_space_free(space);
        return array;
error:
        isl_space_free(space);
        return pet_array_free(array);
}

/* Add all parameters in "space" to "independence".
 */
static struct pet_independence *independence_propagate_params(
        struct pet_independence *independence, __isl_take isl_space *space)
{
        if (!independence)
                goto error;

        independence->filter = isl_union_map_align_params(independence->filter,
                                                isl_space_copy(space));
        independence->local = isl_union_set_align_params(independence->local,
                                                isl_space_copy(space));
        if (!independence->filter || !independence->local)
                goto error;

        isl_space_free(space);
        return independence;
error:
        isl_space_free(space);
        return pet_independence_free(independence);
}

/* Add all parameters in "space" to "scop".
 */
static struct pet_scop *scop_propagate_params(struct pet_scop *scop,
        __isl_take isl_space *space)
{
        int i;

        if (!scop)
                goto error;

        scop->context = isl_set_align_params(scop->context,
                                                isl_space_copy(space));
        scop->schedule = isl_schedule_align_params(scop->schedule,
                                                isl_space_copy(space));
        if (!scop->context || !scop->schedule)
                goto error;

        for (i = 0; i < scop->n_array; ++i) {
                scop->arrays[i] = array_propagate_params(scop->arrays[i],
                                                        isl_space_copy(space));
                if (!scop->arrays[i])
                        goto error;
        }

        for (i = 0; i < scop->n_stmt; ++i) {
                scop->stmts[i] = stmt_propagate_params(scop->stmts[i],
                                                        isl_space_copy(space));
                if (!scop->stmts[i])
                        goto error;
        }

        for (i = 0; i < scop->n_independence; ++i) {
                scop->independences[i] = independence_propagate_params(
                                scop->independences[i], isl_space_copy(space));
                if (!scop->independences[i])
                        goto error;
        }

        isl_space_free(space);
        return scop;
error:
        isl_space_free(space);
        return pet_scop_free(scop);
}

/* Update all isl_sets and isl_maps in "scop" such that they all
 * have the same parameters.
 */
struct pet_scop *pet_scop_align_params(struct pet_scop *scop)
{
        isl_space *space;

        if (!scop)
                return NULL;

        space = scop_collect_params(scop);

        scop = scop_propagate_params(scop, space);

        return scop;
}

/* Add the access relation of the give "type" of the access expression "expr"
 * to "accesses" and return the result.
 * The domain of the access relation is intersected with "domain".
 * If "tag" is set, then the access relation is tagged with
 * the corresponding reference identifier.
 */
static __isl_give isl_union_map *expr_collect_access(__isl_keep pet_expr *expr,
        enum pet_expr_access_type type, int tag,
        __isl_take isl_union_map *accesses, __isl_keep isl_union_set *domain)
{
        isl_union_map *access;

        access = pet_expr_access_get_access(expr, type);
        access = isl_union_map_intersect_domain(access,
                                                isl_union_set_copy(domain));
        if (tag)
                access = pet_expr_tag_access(expr, access);
        return isl_union_map_union(accesses, access);
}

/* Internal data structure for expr_collect_accesses.
 *
 * "type" is the type of accesses we want to collect.
 * "tag" is set if the access relations should be tagged with
 * the corresponding reference identifiers.
 * "domain" are constraints on the domain of the access relations.
 * "accesses" collects the results.
 */
struct pet_expr_collect_accesses_data {
        enum pet_expr_access_type type;
        int tag;
        isl_union_set *domain;

        isl_union_map *accesses;
};

/* Add the access relation of the access expression "expr"
 * to data->accesses if the access expression is a read and we are collecting
 * reads and/or it is a write and we are collecting writes.
 * The domains of the access relations are intersected with data->domain.
 * If data->tag is set, then the access relations are tagged with
 * the corresponding reference identifiers.
 *
 * If data->type is pet_expr_access_must_write, then we only add
 * the accesses that are definitely performed.  Otherwise, we add
 * all potential accesses.
 * In particular, if the access has any arguments, then in case of
 * pet_expr_access_must_write we currently skip the access completely.
 * In other cases, we project out the values of the access arguments.
 */
static int expr_collect_accesses(__isl_keep pet_expr *expr, void *user)
{
        struct pet_expr_collect_accesses_data *data = user;
        int i;
        isl_id *id;
        isl_space *dim;

        if (!expr)
                return -1;

        if (pet_expr_is_affine(expr))
                return 0;
        if (data->type == pet_expr_access_must_write && expr->n_arg != 0)
                return 0;

        if ((data->type == pet_expr_access_may_read && expr->acc.read) ||
            ((data->type == pet_expr_access_may_write ||
              data->type == pet_expr_access_must_write) && expr->acc.write))
                data->accesses = expr_collect_access(expr,
                                                data->type, data->tag,
                                                data->accesses, data->domain);

        return data->accesses ? 0 : -1;
}

/* Collect and return all access relations of the given "type" in "stmt".
 * If "tag" is set, then the access relations are tagged with
 * the corresponding reference identifiers.
 * If "type" is pet_expr_access_killed, then "stmt" is a kill statement and
 * we simply add the argument of the kill operation.
 *
 * If we are looking for definite accesses (pet_expr_access_must_write
 * or pet_expr_access_killed), then we only add the accesses that are
 * definitely performed.  Otherwise, we add all potential accesses.
 * In particular, if the statement has any arguments, then if we are looking
 * for definite accesses we currently skip the statement completely.  Othewise,
 * we project out the values of the statement arguments.
 * If the statement body is not an expression tree, then we cannot
 * know for sure if/when the accesses inside the tree are performed.
 * We therefore ignore such statements when we are looking for
 * definite accesses.
 */
static __isl_give isl_union_map *stmt_collect_accesses(struct pet_stmt *stmt,
        enum pet_expr_access_type type, int tag, __isl_take isl_space *dim)
{
        struct pet_expr_collect_accesses_data data = { type, tag };
        int must;
        isl_set *domain;

        if (!stmt)
                return NULL;

        data.accesses = isl_union_map_empty(dim);

        if (type == pet_expr_access_must_write ||
            type == pet_expr_access_killed)
                must = 1;
        else
                must = 0;

        if (must && stmt->n_arg > 0)
                return data.accesses;
        if (must && pet_tree_get_type(stmt->body) != pet_tree_expr)
                return data.accesses;

        domain = drop_arguments(isl_set_copy(stmt->domain));
        data.domain = isl_union_set_from_set(domain);

        if (type == pet_expr_access_killed) {
                pet_expr *body, *arg;

                body = pet_tree_expr_get_expr(stmt->body);
                arg = pet_expr_get_arg(body, 0);
                data.accesses = expr_collect_access(arg,
                                                pet_expr_access_killed, tag,
                                                data.accesses, data.domain);
                pet_expr_free(arg);
                pet_expr_free(body);
        } else if (pet_tree_foreach_access_expr(stmt->body,
                                        &expr_collect_accesses, &data) < 0)
                data.accesses = isl_union_map_free(data.accesses);

        isl_union_set_free(data.domain);

        return data.accesses;
}

/* Is "stmt" an assignment statement?
 */
int pet_stmt_is_assign(struct pet_stmt *stmt)
{
        if (!stmt)
                return 0;
        return pet_tree_is_assign(stmt->body);
}

/* Is "stmt" a kill statement?
 */
int pet_stmt_is_kill(struct pet_stmt *stmt)
{
        if (!stmt)
                return 0;
        return pet_tree_is_kill(stmt->body);
}

/* Is "stmt" an assume statement?
 */
int pet_stmt_is_assume(struct pet_stmt *stmt)
{
        if (!stmt)
                return 0;
        return pet_tree_is_assume(stmt->body);
}

/* Helper function to add a domain gisted copy of "map" (wrt "set") to "umap".
 */
static __isl_give isl_union_map *add_gisted(__isl_take isl_union_map *umap,
        __isl_keep isl_map *map, __isl_keep isl_set *set)
{
        isl_map *gist;

        gist = isl_map_copy(map);
        gist = isl_map_gist_domain(gist, isl_set_copy(set));
        return isl_union_map_add_map(umap, gist);
}

/* Compute a mapping from all arrays (of structs) in scop
 * to their members.
 *
 * If "from_outermost" is set, then the domain only consists
 * of outermost arrays.
 * If "to_innermost" is set, then the range only consists
 * of innermost arrays.
 */
static __isl_give isl_union_map *compute_to_inner(struct pet_scop *scop,
        int from_outermost, int to_innermost)
{
        int i;
        isl_union_map *to_inner;

        if (!scop)
                return NULL;

        to_inner = isl_union_map_empty(isl_set_get_space(scop->context));

        for (i = 0; i < scop->n_array; ++i) {
                struct pet_array *array = scop->arrays[i];
                isl_set *set;
                isl_map *map;

                if (to_innermost && array->element_is_record)
                        continue;

                set = isl_set_copy(array->extent);
                map = isl_set_identity(isl_set_copy(set));

                while (set && isl_set_is_wrapping(set)) {
                        isl_id *id;
                        isl_map *wrapped;

                        if (!from_outermost)
                                to_inner = add_gisted(to_inner, map, set);

                        id = isl_set_get_tuple_id(set);
                        wrapped = isl_set_unwrap(set);
                        wrapped = isl_map_domain_map(wrapped);
                        wrapped = isl_map_set_tuple_id(wrapped, isl_dim_in, id);
                        map = isl_map_apply_domain(map, wrapped);
                        set = isl_map_domain(isl_map_copy(map));
                }

                map = isl_map_gist_domain(map, set);
                to_inner = isl_union_map_add_map(to_inner, map);
        }

        return to_inner;
}

/* Compute a mapping from all arrays (of structs) in scop
 * to their innermost arrays.
 *
 * In particular, for each array of a primitive type, the result
 * contains the identity mapping on that array.
 * For each array involving member accesses, the result
 * contains a mapping from the elements of any intermediate array of structs
 * to all corresponding elements of the innermost nested arrays.
 */
static __isl_give isl_union_map *pet_scop_compute_any_to_inner(
        struct pet_scop *scop)
{
        return compute_to_inner(scop, 0, 1);
}

/* Compute a mapping from all outermost arrays (of structs) in scop
 * to their innermost members.
 */
__isl_give isl_union_map *pet_scop_compute_outer_to_inner(struct pet_scop *scop)
{
        return compute_to_inner(scop, 1, 1);
}

/* Compute a mapping from all outermost arrays (of structs) in scop
 * to their members, including the outermost arrays themselves.
 */
__isl_give isl_union_map *pet_scop_compute_outer_to_any(struct pet_scop *scop)
{
        return compute_to_inner(scop, 1, 0);
}

/* Collect and return all access relations of the given "type" in "scop".
 * If "type" is pet_expr_access_killed, then we only add the arguments of
 * kill operations.
 * If we are looking for definite accesses (pet_expr_access_must_write
 * or pet_expr_access_killed), then we only add the accesses that are
 * definitely performed.  Otherwise, we add all potential accesses.
 * If "tag" is set, then the access relations are tagged with
 * the corresponding reference identifiers.
 * For accesses to structures, the returned access relation accesses
 * all individual fields in the structures.
 */
static __isl_give isl_union_map *scop_collect_accesses(struct pet_scop *scop,
        enum pet_expr_access_type type, int tag)
{
        int i;
        isl_union_map *accesses;
        isl_union_set *arrays;
        isl_union_map *to_inner;

        if (!scop)
                return NULL;

        accesses = isl_union_map_empty(isl_set_get_space(scop->context));

        for (i = 0; i < scop->n_stmt; ++i) {
                struct pet_stmt *stmt = scop->stmts[i];
                isl_union_map *accesses_i;
                isl_space *space;

                if (type == pet_expr_access_killed && !pet_stmt_is_kill(stmt))
                        continue;

                space = isl_set_get_space(scop->context);
                accesses_i = stmt_collect_accesses(stmt, type, tag, space);
                accesses = isl_union_map_union(accesses, accesses_i);
        }

        arrays = isl_union_set_empty(isl_union_map_get_space(accesses));
        for (i = 0; i < scop->n_array; ++i) {
                isl_set *extent = isl_set_copy(scop->arrays[i]->extent);
                arrays = isl_union_set_add_set(arrays, extent);
        }
        accesses = isl_union_map_intersect_range(accesses, arrays);

        to_inner = pet_scop_compute_any_to_inner(scop);
        accesses = isl_union_map_apply_range(accesses, to_inner);

        return accesses;
}

/* Collect all potential read access relations.
 */
__isl_give isl_union_map *pet_scop_collect_may_reads(struct pet_scop *scop)
{
        return scop_collect_accesses(scop, pet_expr_access_may_read, 0);
}

/* Collect all potential write access relations.
 */
__isl_give isl_union_map *pet_scop_collect_may_writes(struct pet_scop *scop)
{
        return scop_collect_accesses(scop, pet_expr_access_may_write, 0);
}

/* Collect all definite write access relations.
 */
__isl_give isl_union_map *pet_scop_collect_must_writes(struct pet_scop *scop)
{
        return scop_collect_accesses(scop, pet_expr_access_must_write, 0);
}

/* Collect all definite kill access relations.
 */
__isl_give isl_union_map *pet_scop_collect_must_kills(struct pet_scop *scop)
{
        return scop_collect_accesses(scop, pet_expr_access_killed, 0);
}

/* Collect all tagged potential read access relations.
 */
__isl_give isl_union_map *pet_scop_collect_tagged_may_reads(
        struct pet_scop *scop)
{
        return scop_collect_accesses(scop, pet_expr_access_may_read, 1);
}

/* Collect all tagged potential write access relations.
 */
__isl_give isl_union_map *pet_scop_collect_tagged_may_writes(
        struct pet_scop *scop)
{
        return scop_collect_accesses(scop, pet_expr_access_may_write, 1);
}

/* Collect all tagged definite write access relations.
 */
__isl_give isl_union_map *pet_scop_collect_tagged_must_writes(
        struct pet_scop *scop)
{
        return scop_collect_accesses(scop, pet_expr_access_must_write, 1);
}

/* Collect all tagged definite kill access relations.
 */
__isl_give isl_union_map *pet_scop_collect_tagged_must_kills(
        struct pet_scop *scop)
{
        return scop_collect_accesses(scop, pet_expr_access_killed, 1);
}

/* Collect and return the union of iteration domains in "scop".
 */
__isl_give isl_union_set *pet_scop_collect_domains(struct pet_scop *scop)
{
        int i;
        isl_set *domain_i;
        isl_union_set *domain;

        if (!scop)
                return NULL;

        domain = isl_union_set_empty(isl_set_get_space(scop->context));

        for (i = 0; i < scop->n_stmt; ++i) {
                domain_i = isl_set_copy(scop->stmts[i]->domain);
                if (scop->stmts[i]->n_arg > 0)
                        domain_i = isl_map_domain(isl_set_unwrap(domain_i));
                domain = isl_union_set_add_set(domain, domain_i);
        }

        return domain;
}

/* Add a reference identifier to all access expressions in "stmt".
 * "n_ref" points to an integer that contains the sequence number
 * of the next reference.
 */
static struct pet_stmt *stmt_add_ref_ids(struct pet_stmt *stmt, int *n_ref)
{
        int i;

        if (!stmt)
                return NULL;

        for (i = 0; i < stmt->n_arg; ++i) {
                stmt->args[i] = pet_expr_add_ref_ids(stmt->args[i], n_ref);
                if (!stmt->args[i])
                        return pet_stmt_free(stmt);
        }

        stmt->body = pet_tree_add_ref_ids(stmt->body, n_ref);
        if (!stmt->body)
                return pet_stmt_free(stmt);

        return stmt;
}

/* Add a reference identifier to all access expressions in "scop".
 */
struct pet_scop *pet_scop_add_ref_ids(struct pet_scop *scop)
{
        int i;
        int n_ref;

        if (!scop)
                return NULL;

        n_ref = 0;
        for (i = 0; i < scop->n_stmt; ++i) {
                scop->stmts[i] = stmt_add_ref_ids(scop->stmts[i], &n_ref);
                if (!scop->stmts[i])
                        return pet_scop_free(scop);
        }

        return scop;
}

/* Reset the user pointer on all parameter ids in "array".
 */
static struct pet_array *array_anonymize(struct pet_array *array)
{
        if (!array)
                return NULL;

        array->context = isl_set_reset_user(array->context);
        array->extent = isl_set_reset_user(array->extent);
        if (!array->context || !array->extent)
                return pet_array_free(array);

        return array;
}

/* Reset the user pointer on all parameter and tuple ids in "stmt".
 */
static struct pet_stmt *stmt_anonymize(struct pet_stmt *stmt)
{
        int i;
        isl_space *space;
        isl_set *domain;

        if (!stmt)
                return NULL;

        stmt->domain = isl_set_reset_user(stmt->domain);
        if (!stmt->domain)
                return pet_stmt_free(stmt);

        for (i = 0; i < stmt->n_arg; ++i) {
                stmt->args[i] = pet_expr_anonymize(stmt->args[i]);
                if (!stmt->args[i])
                        return pet_stmt_free(stmt);
        }

        stmt->body = pet_tree_anonymize(stmt->body);
        if (!stmt->body)
                return pet_stmt_free(stmt);

        return stmt;
}

/* Reset the user pointer on the tuple ids and all parameter ids
 * in "implication".
 */
static struct pet_implication *implication_anonymize(
        struct pet_implication *implication)
{
        if (!implication)
                return NULL;

        implication->extension = isl_map_reset_user(implication->extension);
        if (!implication->extension)
                return pet_implication_free(implication);

        return implication;
}

/* Reset the user pointer on the tuple ids and all parameter ids
 * in "independence".
 */
static struct pet_independence *independence_anonymize(
        struct pet_independence *independence)
{
        if (!independence)
                return NULL;

        independence->filter = isl_union_map_reset_user(independence->filter);
        independence->local = isl_union_set_reset_user(independence->local);
        if (!independence->filter || !independence->local)
                return pet_independence_free(independence);

        return independence;
}

/* Reset the user pointer on all parameter and tuple ids in "scop".
 */
struct pet_scop *pet_scop_anonymize(struct pet_scop *scop)
{
        int i;

        if (!scop)
                return NULL;

        scop->context = isl_set_reset_user(scop->context);
        scop->context_value = isl_set_reset_user(scop->context_value);
        scop->schedule = isl_schedule_reset_user(scop->schedule);
        if (!scop->context || !scop->context_value || !scop->schedule)
                return pet_scop_free(scop);

        for (i = 0; i < scop->n_array; ++i) {
                scop->arrays[i] = array_anonymize(scop->arrays[i]);
                if (!scop->arrays[i])
                        return pet_scop_free(scop);
        }

        for (i = 0; i < scop->n_stmt; ++i) {
                scop->stmts[i] = stmt_anonymize(scop->stmts[i]);
                if (!scop->stmts[i])
                        return pet_scop_free(scop);
        }

        for (i = 0; i < scop->n_implication; ++i) {
                scop->implications[i] =
                                implication_anonymize(scop->implications[i]);
                if (!scop->implications[i])
                        return pet_scop_free(scop);
        }

        for (i = 0; i < scop->n_independence; ++i) {
                scop->independences[i] =
                                independence_anonymize(scop->independences[i]);
                if (!scop->independences[i])
                        return pet_scop_free(scop);
        }

        return scop;
}

/* Compute the gist of the iteration domain and all access relations
 * of "stmt" based on the constraints on the parameters specified by "context"
 * and the constraints on the values of nested accesses specified
 * by "value_bounds".
 */
static struct pet_stmt *stmt_gist(struct pet_stmt *stmt,
        __isl_keep isl_set *context, __isl_keep isl_union_map *value_bounds)
{
        int i;
        isl_set *domain;

        if (!stmt)
                return NULL;

        domain = isl_set_copy(stmt->domain);
        if (stmt->n_arg > 0)
                domain = isl_map_domain(isl_set_unwrap(domain));

        domain = isl_set_intersect_params(domain, isl_set_copy(context));

        for (i = 0; i < stmt->n_arg; ++i) {
                stmt->args[i] = pet_expr_gist(stmt->args[i],
                                                        domain, value_bounds);
                if (!stmt->args[i])
                        goto error;
        }

        stmt->body = pet_tree_gist(stmt->body, domain, value_bounds);
        if (!stmt->body)
                goto error;

        isl_set_free(domain);

        domain = isl_set_universe(pet_stmt_get_space(stmt));
        domain = isl_set_intersect_params(domain, isl_set_copy(context));
        if (stmt->n_arg > 0)
                domain = pet_value_bounds_apply(domain, stmt->n_arg, stmt->args,
                                                value_bounds);
        stmt->domain = isl_set_gist(stmt->domain, domain);
        if (!stmt->domain)
                return pet_stmt_free(stmt);

        return stmt;
error:
        isl_set_free(domain);
        return pet_stmt_free(stmt);
}

/* Compute the gist of the extent of the array
 * based on the constraints on the parameters specified by "context".
 */
static struct pet_array *array_gist(struct pet_array *array,
        __isl_keep isl_set *context)
{
        if (!array)
                return NULL;

        array->extent = isl_set_gist_params(array->extent,
                                                isl_set_copy(context));
        if (!array->extent)
                return pet_array_free(array);

        return array;
}

/* Compute the gist of all sets and relations in "scop"
 * based on the constraints on the parameters specified by "scop->context"
 * and the constraints on the values of nested accesses specified
 * by "value_bounds".
 */
struct pet_scop *pet_scop_gist(struct pet_scop *scop,
        __isl_keep isl_union_map *value_bounds)
{
        int i;

        if (!scop)
                return NULL;

        scop->context = isl_set_coalesce(scop->context);
        if (!scop->context)
                return pet_scop_free(scop);

        for (i = 0; i < scop->n_array; ++i) {
                scop->arrays[i] = array_gist(scop->arrays[i], scop->context);
                if (!scop->arrays[i])
                        return pet_scop_free(scop);
        }

        for (i = 0; i < scop->n_stmt; ++i) {
                scop->stmts[i] = stmt_gist(scop->stmts[i], scop->context,
                                            value_bounds);
                if (!scop->stmts[i])
                        return pet_scop_free(scop);
        }

        return scop;
}

/* Intersect the context of "scop" with "context".
 * To ensure that we don't introduce any unnamed parameters in
 * the context of "scop", we first remove the unnamed parameters
 * from "context".
 */
struct pet_scop *pet_scop_restrict_context(struct pet_scop *scop,
        __isl_take isl_set *context)
{
        if (!scop)
                goto error;

        context = pet_nested_remove_from_set(context);
        scop->context = isl_set_intersect(scop->context, context);
        if (!scop->context)
                return pet_scop_free(scop);

        return scop;
error:
        isl_set_free(context);
        return pet_scop_free(scop);
}

/* Drop the current context of "scop".  That is, replace the context
 * by a universal set.
 */
struct pet_scop *pet_scop_reset_context(struct pet_scop *scop)
{
        isl_space *space;

        if (!scop)
                return NULL;

        space = isl_set_get_space(scop->context);
        isl_set_free(scop->context);
        scop->context = isl_set_universe(space);
        if (!scop->context)
                return pet_scop_free(scop);

        return scop;
}

/* Append "array" to the arrays of "scop".
 */
struct pet_scop *pet_scop_add_array(struct pet_scop *scop,
        struct pet_array *array)
{
        isl_ctx *ctx;
        struct pet_array **arrays;

        if (!array || !scop)
                goto error;

        ctx = isl_set_get_ctx(scop->context);
        arrays = isl_realloc_array(ctx, scop->arrays, struct pet_array *,
                                    scop->n_array + 1);
        if (!arrays)
                goto error;
        scop->arrays = arrays;
        scop->arrays[scop->n_array] = array;
        scop->n_array++;

        return scop;
error:
        pet_array_free(array);
        return pet_scop_free(scop);
}

/* Create an index expression for an access to a virtual array
 * representing the result of a condition.
 * Unlike other accessed data, the id of the array is NULL as
 * there is no ValueDecl in the program corresponding to the virtual
 * array.
 * The index expression is created as an identity mapping on "space".
 * That is, the dimension of the array is the same as that of "space".
 */
__isl_give isl_multi_pw_aff *pet_create_test_index(__isl_take isl_space *space,
        int test_nr)
{
        isl_id *id;
        char name[50];

        snprintf(name, sizeof(name), "__pet_test_%d", test_nr);
        id = isl_id_alloc(isl_space_get_ctx(space), name, NULL);
        space = isl_space_map_from_set(space);
        space = isl_space_set_tuple_id(space, isl_dim_out, id);
        return isl_multi_pw_aff_identity(space);
}

/* Add an array with the given extent to the list
 * of arrays in "scop" and return the extended pet_scop.
 * Specifically, the extent is determined by the image of "domain"
 * under "index".
 * "int_size" is the number of bytes needed to represent values of type "int".
 * The array is marked as attaining values 0 and 1 only and
 * as each element being assigned at most once.
 */
struct pet_scop *pet_scop_add_boolean_array(struct pet_scop *scop,
        __isl_take isl_set *domain, __isl_take isl_multi_pw_aff *index,
        int int_size)
{
        isl_ctx *ctx;
        isl_space *space;
        struct pet_array *array;
        isl_map *access;

        if (!scop || !domain || !index)
                goto error;

        ctx = isl_multi_pw_aff_get_ctx(index);
        array = isl_calloc_type(ctx, struct pet_array);
        if (!array)
                goto error;

        access = isl_map_from_multi_pw_aff(index);
        access = isl_map_intersect_domain(access, domain);
        array->extent = isl_map_range(access);
        space = isl_space_params_alloc(ctx, 0);
        array->context = isl_set_universe(space);
        space = isl_space_set_alloc(ctx, 0, 1);
        array->value_bounds = isl_set_universe(space);
        array->value_bounds = isl_set_lower_bound_si(array->value_bounds,
                                                isl_dim_set, 0, 0);
        array->value_bounds = isl_set_upper_bound_si(array->value_bounds,
                                                isl_dim_set, 0, 1);
        array->element_type = strdup("int");
        array->element_size = int_size;
        array->uniquely_defined = 1;

        if (!array->extent || !array->context)
                array = pet_array_free(array);

        scop = pet_scop_add_array(scop, array);

        return scop;
error:
        isl_set_free(domain);
        isl_multi_pw_aff_free(index);
        return pet_scop_free(scop);
}

/* Create and return an implication on filter values equal to "satisfied"
 * with extension "map".
 */
static struct pet_implication *new_implication(__isl_take isl_map *map,
        int satisfied)
{
        isl_ctx *ctx;
        struct pet_implication *implication;

        if (!map)
                return NULL;
        ctx = isl_map_get_ctx(map);
        implication = isl_alloc_type(ctx, struct pet_implication);
        if (!implication)
                goto error;

        implication->extension = map;
        implication->satisfied = satisfied;

        return implication;
error:
        isl_map_free(map);
        return NULL;
}

/* Add an implication on filter values equal to "satisfied"
 * with extension "map" to "scop".
 */
struct pet_scop *pet_scop_add_implication(struct pet_scop *scop,
        __isl_take isl_map *map, int satisfied)
{
        isl_ctx *ctx;
        struct pet_implication *implication;
        struct pet_implication **implications;

        implication = new_implication(map, satisfied);
        if (!scop || !implication)
                goto error;

        ctx = isl_set_get_ctx(scop->context);
        implications = isl_realloc_array(ctx, scop->implications,
                                            struct pet_implication *,
                                            scop->n_implication + 1);
        if (!implications)
                goto error;
        scop->implications = implications;
        scop->implications[scop->n_implication] = implication;
        scop->n_implication++;

        return scop;
error:
        pet_implication_free(implication);
        return pet_scop_free(scop);
}

/* Create and return a function that maps the iteration domains
 * of the statements in "scop" onto their outer "n" dimensions.
 * "space" is the parameters space of the created function.
 */
static __isl_give isl_union_pw_multi_aff *outer_projection(
        struct pet_scop *scop, __isl_take isl_space *space, int n)
{
        int i;
        isl_union_pw_multi_aff *res;

        res = isl_union_pw_multi_aff_empty(space);

        if (!scop)
                return isl_union_pw_multi_aff_free(res);

        for (i = 0; i < scop->n_stmt; ++i) {
                struct pet_stmt *stmt = scop->stmts[i];
                isl_space *space;
                isl_multi_aff *ma;
                isl_pw_multi_aff *pma;

                space = pet_stmt_get_space(stmt);
                ma = pet_prefix_projection(space, n);
                pma = isl_pw_multi_aff_from_multi_aff(ma);
                res = isl_union_pw_multi_aff_add_pw_multi_aff(res, pma);
        }

        return res;
}

/* Add an independence to "scop" for the inner iterator of "domain"
 * with local variables "local", where "domain" represents the outer
 * loop iterators of all statements in "scop".
 * If "sign" is positive, then the inner iterator increases.
 * Otherwise it decreases.
 *
 * The independence is supposed to filter out any dependence of
 * an iteration of domain on a previous iteration along the inner dimension.
 * We therefore create a mapping from an iteration to later iterations and
 * then plug in the projection of the iterations domains of "scop"
 * onto the outer loop iterators.
 */
struct pet_scop *pet_scop_set_independent(struct pet_scop *scop,
        __isl_keep isl_set *domain, __isl_take isl_union_set *local, int sign)
{
        int i, dim;
        isl_space *space;
        isl_map *map;
        isl_union_map *independence;
        isl_union_pw_multi_aff *proj;

        if (!scop || !domain || !local)
                goto error;

        dim = isl_set_dim(domain, isl_dim_set);
        space = isl_space_map_from_set(isl_set_get_space(domain));
        map = isl_map_universe(space);
        for (i = 0; i + 1 < dim; ++i)
                map = isl_map_equate(map, isl_dim_in, i, isl_dim_out, i);
        if (sign > 0)
                map = isl_map_order_lt(map,
                                    isl_dim_in, dim - 1, isl_dim_out, dim - 1);
        else
                map = isl_map_order_gt(map,
                                    isl_dim_in, dim - 1, isl_dim_out, dim - 1);

        independence = isl_union_map_from_map(map);
        space = isl_space_params(isl_set_get_space(domain));
        proj = outer_projection(scop, space, dim);
        independence = isl_union_map_preimage_domain_union_pw_multi_aff(
                            independence, isl_union_pw_multi_aff_copy(proj));
        independence = isl_union_map_preimage_range_union_pw_multi_aff(
                            independence, proj);

        scop = pet_scop_add_independence(scop, independence, local);

        return scop;
error:
        isl_union_set_free(local);
        return pet_scop_free(scop);
}

/* Given an access expression, check if it is data dependent.
 * If so, set *found and abort the search.
 */
static int is_data_dependent(__isl_keep pet_expr *expr, void *user)
{
        int *found = user;

        if (pet_expr_get_n_arg(expr) > 0) {
                *found = 1;
                return -1;
        }

        return 0;
}

/* Does "scop" contain any data dependent accesses?
 *
 * Check the body of each statement for such accesses.
 */
int pet_scop_has_data_dependent_accesses(struct pet_scop *scop)
{
        int i;
        int found = 0;

        if (!scop)
                return -1;

        for (i = 0; i < scop->n_stmt; ++i) {
                int r = pet_tree_foreach_access_expr(scop->stmts[i]->body,
                                        &is_data_dependent, &found);
                if (r < 0 && !found)
                        return -1;
                if (found)
                        return found;
        }

        return found;
}

/* Does "scop" contain and data dependent conditions?
 */
int pet_scop_has_data_dependent_conditions(struct pet_scop *scop)
{
        int i;

        if (!scop)
                return -1;

        for (i = 0; i < scop->n_stmt; ++i)
                if (scop->stmts[i]->n_arg > 0)
                        return 1;

        return 0;
}

/* Keep track of the "input" file inside the (extended) "scop".
 */
struct pet_scop *pet_scop_set_input_file(struct pet_scop *scop, FILE *input)
{
        struct pet_scop_ext *ext = (struct pet_scop_ext *) scop;

        if (!scop)
                return NULL;

        ext->input = input;

        return scop;
}

/* Print the original code corresponding to "scop" to printer "p".
 *
 * pet_scop_print_original can only be called from
 * a pet_transform_C_source callback.  This means that the input
 * file is stored in the extended scop and that the printer prints
 * to a file.
 */
__isl_give isl_printer *pet_scop_print_original(struct pet_scop *scop,
        __isl_take isl_printer *p)
{
        struct pet_scop_ext *ext = (struct pet_scop_ext *) scop;
        FILE *output;
        unsigned start, end;

        if (!scop || !p)
                return isl_printer_free(p);

        if (!ext->input)
                isl_die(isl_printer_get_ctx(p), isl_error_invalid,
                        "no input file stored in scop",
                        return isl_printer_free(p));

        output = isl_printer_get_file(p);
        if (!output)
                return isl_printer_free(p);

        start = pet_loc_get_start(scop->loc);
        end = pet_loc_get_end(scop->loc);
        if (copy(ext->input, output, start, end) < 0)
                return isl_printer_free(p);

        return p;
}