pet_scop_add_boolean_array: allow specification of domain constraints

[pet.git] / nest.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 "expr.h"
#include "expr_arg.h"
#include "nest.h"
#include "scop.h"

/* A wrapper around pet_expr_free to be used as an isl_id free user function.
 */
static void pet_expr_free_wrap(void *user)
{
        pet_expr_free((pet_expr *) user);
}

/* Create an isl_id that refers to the nested access "expr".
 */
__isl_give isl_id *pet_nested_pet_expr(__isl_take pet_expr *expr)
{
        isl_id *id;

        id = isl_id_alloc(pet_expr_get_ctx(expr), "__pet_expr", expr);
        id = isl_id_set_free_user(id, &pet_expr_free_wrap);

        return id;
}

/* Extract a pet_expr from an isl_id created by pet_nested_pet_expr.
 * Such an isl_id has name "__pet_expr" and
 * the user pointer points to a pet_expr object.
 */
__isl_give pet_expr *pet_nested_extract_expr(__isl_keep isl_id *id)
{
        return pet_expr_copy((pet_expr *) isl_id_get_user(id));
}

/* Does "id" refer to a nested access created by pet_nested_pet_expr?
 */
int pet_nested_in_id(__isl_keep isl_id *id)
{
        const char *name;

        if (!id)
                return 0;
        if (!isl_id_get_user(id))
                return 0;

        name = isl_id_get_name(id);
        return !strcmp(name, "__pet_expr");
}

/* Does parameter "pos" of "space" refer to a nested access?
 */
static int pet_nested_in_space(__isl_keep isl_space *space, int pos)
{
        int nested;
        isl_id *id;

        id = isl_space_get_dim_id(space, isl_dim_param, pos);
        nested = pet_nested_in_id(id);
        isl_id_free(id);

        return nested;
}

/* Does parameter "pos" of "set" refer to a nested access?
 */
int pet_nested_in_set(__isl_keep isl_set *set, int pos)
{
        int nested;
        isl_id *id;

        id = isl_set_get_dim_id(set, isl_dim_param, pos);
        nested = pet_nested_in_id(id);
        isl_id_free(id);

        return nested;
}

/* Does parameter "pos" of "map" refer to a nested access?
 */
int pet_nested_in_map(__isl_keep isl_map *map, int pos)
{
        int nested;
        isl_id *id;

        id = isl_map_get_dim_id(map, isl_dim_param, pos);
        nested = pet_nested_in_id(id);
        isl_id_free(id);

        return nested;
}

/* Does "space" involve any parameters that refer to nested accesses?
 */
int pet_nested_any_in_space(__isl_keep isl_space *space)
{
        int i;
        int nparam;

        nparam = isl_space_dim(space, isl_dim_param);
        for (i = 0; i < nparam; ++i)
                if (pet_nested_in_space(space, i))
                        return 1;

        return 0;
}

/* Does "pa" involve any parameters that refer to nested accesses?
 */
int pet_nested_any_in_pw_aff(__isl_keep isl_pw_aff *pa)
{
        isl_space *space;
        int nested;

        space = isl_pw_aff_get_space(pa);
        nested = pet_nested_any_in_space(space);
        isl_space_free(space);

        return nested;
}

/* How many parameters of "space" refer to nested accesses?
 */
int pet_nested_n_in_space(__isl_keep isl_space *space)
{
        int i, n = 0;
        int nparam;

        nparam = isl_space_dim(space, isl_dim_param);
        for (i = 0; i < nparam; ++i)
                if (pet_nested_in_space(space, i))
                        ++n;

        return n;
}

/* How many parameters of "map" refer to nested accesses?
 */
int pet_nested_n_in_map(__isl_keep isl_map *map)
{
        isl_space *space;
        int n;

        space = isl_map_get_space(map);
        n = pet_nested_n_in_space(space);
        isl_space_free(space);

        return n;
}

/* How many parameters of "set" refer to nested accesses?
 */
int pet_nested_n_in_set(__isl_keep isl_set *set)
{
        isl_space *space;
        int n;

        space = isl_set_get_space(set);
        n = pet_nested_n_in_space(space);
        isl_space_free(space);

        return n;
}

/* Remove all parameters from "space" that refer to nested accesses.
 */
__isl_give isl_space *pet_nested_remove_from_space(__isl_take isl_space *space)
{
        int i;
        int nparam;

        nparam = isl_space_dim(space, isl_dim_param);
        for (i = nparam - 1; i >= 0; --i)
                if (pet_nested_in_space(space, i))
                        space = isl_space_drop_dims(space, isl_dim_param, i, 1);

        return space;
}

/* Remove all parameters from "set" that refer to nested accesses.
 */
__isl_give isl_set *pet_nested_remove_from_set(__isl_take isl_set *set)
{
        int i;
        int nparam;

        nparam = isl_set_dim(set, isl_dim_param);
        for (i = nparam - 1; i >= 0; --i)
                if (pet_nested_in_set(set, i))
                        set = isl_set_project_out(set, isl_dim_param, i, 1);

        return set;
}

/* Remove all parameters from "map" that refer to nested accesses.
 */
static __isl_give isl_map *pet_nested_remove_from_map(__isl_take isl_map *map)
{
        int i;
        int nparam;

        nparam = isl_map_dim(map, isl_dim_param);
        for (i = nparam - 1; i >= 0; --i)
                if (pet_nested_in_map(map, i))
                        map = isl_map_project_out(map, isl_dim_param, i, 1);

        return map;
}

/* Remove all parameters from "mpa" that refer to nested accesses.
 */
static __isl_give isl_multi_pw_aff *pet_nested_remove_from_multi_pw_aff(
        __isl_take isl_multi_pw_aff *mpa)
{
        int i;
        int nparam;
        isl_space *space;

        space = isl_multi_pw_aff_get_space(mpa);
        nparam = isl_space_dim(space, isl_dim_param);
        for (i = nparam - 1; i >= 0; --i) {
                if (!pet_nested_in_space(space, i))
                        continue;
                mpa = isl_multi_pw_aff_drop_dims(mpa, isl_dim_param, i, 1);
        }
        isl_space_free(space);

        return mpa;
}

/* Remove all parameters from the index expression and access relation of "expr"
 * that refer to nested accesses.
 */
static __isl_give pet_expr *expr_remove_nested_parameters(
        __isl_take pet_expr *expr, void *user)
{
        expr = pet_expr_cow(expr);
        if (!expr)
                return NULL;

        expr->acc.access = pet_nested_remove_from_map(expr->acc.access);
        expr->acc.index = pet_nested_remove_from_multi_pw_aff(expr->acc.index);
        if (!expr->acc.access || !expr->acc.index)
                return pet_expr_free(expr);

        return expr;
}

/* Remove all nested access parameters from the schedule and all
 * accesses of "stmt".
 * There is no need to remove them from the domain as these parameters
 * have already been removed from the domain when this function is called.
 */
struct pet_stmt *pet_stmt_remove_nested_parameters(struct pet_stmt *stmt)
{
        int i;

        if (!stmt)
                return NULL;
        stmt->schedule = pet_nested_remove_from_map(stmt->schedule);
        stmt->body = pet_expr_map_access(stmt->body,
                            &expr_remove_nested_parameters, NULL);
        if (!stmt->schedule || !stmt->body)
                goto error;
        for (i = 0; i < stmt->n_arg; ++i) {
                stmt->args[i] = pet_expr_map_access(stmt->args[i],
                            &expr_remove_nested_parameters, NULL);
                if (!stmt->args[i])
                        goto error;
        }

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

/* For each nested access parameter in "space",
 * construct a corresponding pet_expr, place it in args and
 * record its position in "param2pos".
 * "n_arg" is the number of elements that are already in args.
 * The position recorded in "param2pos" takes this number into account.
 * If the pet_expr corresponding to a parameter is identical to
 * the pet_expr corresponding to an earlier parameter, then these two
 * parameters are made to refer to the same element in args.
 *
 * Return the final number of elements in args or -1 if an error has occurred.
 */
int pet_extract_nested_from_space(__isl_keep isl_space *space,
        int n_arg, __isl_give pet_expr **args, int *param2pos)
{
        int i, nparam;

        nparam = isl_space_dim(space, isl_dim_param);
        for (i = 0; i < nparam; ++i) {
                int j;
                isl_id *id = isl_space_get_dim_id(space, isl_dim_param, i);

                if (!pet_nested_in_id(id)) {
                        isl_id_free(id);
                        continue;
                }

                args[n_arg] = pet_nested_extract_expr(id);
                isl_id_free(id);
                if (!args[n_arg])
                        return -1;

                for (j = 0; j < n_arg; ++j)
                        if (pet_expr_is_equal(args[j], args[n_arg]))
                                break;

                if (j < n_arg) {
                        pet_expr_free(args[n_arg]);
                        args[n_arg] = NULL;
                        param2pos[i] = j;
                } else
                        param2pos[i] = n_arg++;
        }

        return n_arg;
}

/* For each nested access parameter in the access relations in "expr",
 * construct a corresponding pet_expr, append it to the arguments of "expr"
 * and record its position in "param2pos" (relative to the initial
 * number of arguments).
 * n is the number of nested access parameters.
 */
__isl_give pet_expr *pet_expr_extract_nested(__isl_take pet_expr *expr, int n,
        int *param2pos)
{
        isl_ctx *ctx;
        isl_space *space;
        int i, n_arg;
        pet_expr **args;

        ctx = pet_expr_get_ctx(expr);
        args = isl_calloc_array(ctx, pet_expr *, n);
        if (!args)
                return pet_expr_free(expr);

        n_arg = pet_expr_get_n_arg(expr);
        space = pet_expr_access_get_parameter_space(expr);
        n = pet_extract_nested_from_space(space, 0, args, param2pos);
        isl_space_free(space);

        if (n < 0)
                expr = pet_expr_free(expr);
        else
                expr = pet_expr_set_n_arg(expr, n_arg + n);

        for (i = 0; i < n; ++i)
                expr = pet_expr_set_arg(expr, n_arg + i, args[i]);
        free(args);

        return expr;
}

/* Are "expr1" and "expr2" both array accesses such that
 * the access relation of "expr1" is a subset of that of "expr2"?
 * Only take into account the first "n_arg" arguments.
 */
static int is_sub_access(__isl_keep pet_expr *expr1, __isl_keep pet_expr *expr2,
        int n_arg)
{
        isl_id *id1, *id2;
        isl_map *access1, *access2;
        int is_subset;
        int i, n1, n2;

        if (!expr1 || !expr2)
                return 0;
        if (pet_expr_get_type(expr1) != pet_expr_access)
                return 0;
        if (pet_expr_get_type(expr2) != pet_expr_access)
                return 0;
        if (pet_expr_is_affine(expr1))
                return 0;
        if (pet_expr_is_affine(expr2))
                return 0;
        n1 = pet_expr_get_n_arg(expr1);
        if (n1 > n_arg)
                n1 = n_arg;
        n2 = pet_expr_get_n_arg(expr2);
        if (n2 > n_arg)
                n2 = n_arg;
        if (n1 != n2)
                return 0;
        for (i = 0; i < n1; ++i) {
                pet_expr *arg1, *arg2;
                int equal;
                arg1 = pet_expr_get_arg(expr1, i);
                arg2 = pet_expr_get_arg(expr2, i);
                equal = pet_expr_is_equal(arg1, arg2);
                pet_expr_free(arg1);
                pet_expr_free(arg2);
                if (equal < 0 || !equal)
                        return equal;
        }
        id1 = pet_expr_access_get_id(expr1);
        id2 = pet_expr_access_get_id(expr2);
        isl_id_free(id1);
        isl_id_free(id2);
        if (!id1 || !id2)
                return 0;
        if (id1 != id2)
                return 0;

        access1 = pet_expr_access_get_access(expr1);
        access2 = pet_expr_access_get_access(expr2);
        is_subset = isl_map_is_subset(access1, access2);
        isl_map_free(access1);
        isl_map_free(access2);

        return is_subset;
}

/* Mark self dependences among the arguments of "expr" starting at "first".
 * These arguments have already been added to the list of arguments
 * but are not yet referenced directly from the index expression.
 * Instead, they are still referenced through parameters encoding
 * nested accesses.
 *
 * In particular, if "expr" is a read access, then check the arguments
 * starting at "first" to see if "expr" accesses a subset of
 * the elements accessed by the argument, or under more restrictive conditions.
 * If so, then this nested access can be removed from the constraints
 * governing the outer access.  There is no point in restricting
 * accesses to an array if in order to evaluate the restriction,
 * we have to access the same elements (or more).
 *
 * Rather than removing the argument at this point (which would
 * complicate the resolution of the other nested accesses), we simply
 * mark it here by replacing it by a NaN pet_expr.
 * These NaNs are then later removed in remove_marked_self_dependences.
 */
static __isl_give pet_expr *mark_self_dependences(__isl_take pet_expr *expr,
        int first)
{
        int i, n;

        if (pet_expr_access_is_write(expr))
                return expr;

        n = pet_expr_get_n_arg(expr);
        for (i = first; i < n; ++i) {
                int mark;
                pet_expr *arg;

                arg = pet_expr_get_arg(expr, i);
                mark = is_sub_access(expr, arg, first);
                pet_expr_free(arg);
                if (mark < 0)
                        return pet_expr_free(expr);
                if (!mark)
                        continue;

                arg = pet_expr_new_int(isl_val_nan(pet_expr_get_ctx(expr)));
                expr = pet_expr_set_arg(expr, i, arg);
        }

        return expr;
}

/* Is "expr" a NaN integer expression?
 */
static int expr_is_nan(__isl_keep pet_expr *expr)
{
        isl_val *v;
        int is_nan;

        if (pet_expr_get_type(expr) != pet_expr_int)
                return 0;

        v = pet_expr_int_get_val(expr);
        is_nan = isl_val_is_nan(v);
        isl_val_free(v);

        return is_nan;
}

/* Check if we have marked any self dependences (as NaNs)
 * in mark_self_dependences and remove them here.
 * It is safe to project them out since these arguments
 * can at most be referenced from the condition of the access relation,
 * but do not appear in the index expression.
 * "dim" is the dimension of the iteration domain.
 */
static __isl_give pet_expr *remove_marked_self_dependences(
        __isl_take pet_expr *expr, int dim, int first)
{
        int i, n;

        n = pet_expr_get_n_arg(expr);
        for (i = n - 1; i >= first; --i) {
                int is_nan;
                pet_expr *arg;

                arg = pet_expr_get_arg(expr, i);
                is_nan = expr_is_nan(arg);
                pet_expr_free(arg);
                if (!is_nan)
                        continue;
                expr = pet_expr_access_project_out_arg(expr, dim, i);
        }

        return expr;
}

/* Look for parameters in any access relation in "expr" that
 * refer to nested accesses.  In particular, these are
 * parameters with name "__pet_expr".
 *
 * If there are any such parameters, then the domain of the index
 * expression and the access relation, which is either [] or
 * [[] -> [a_1,...,a_m]] at this point, is replaced by [[] -> [t_1,...,t_n]] or
 * [[] -> [a_1,...,a_m,t_1,...,t_n]], with m the original number of arguments
 * (n_arg) and n the number of these parameters
 * (after identifying identical nested accesses).
 *
 * This transformation is performed in several steps.
 * We first extract the arguments in pet_expr_extract_nested.
 * param2pos maps the original parameter position to the position
 * of the argument beyond the initial (n_arg) number of arguments.
 * Then we move these parameters to input dimensions.
 * t2pos maps the positions of these temporary input dimensions
 * to the positions of the corresponding arguments.
 * Finally, we express these temporary dimensions in terms of the domain
 * [[] -> [a_1,...,a_m,t_1,...,t_n]] and precompose index expression and access
 * relations with this function.
 */
__isl_give pet_expr *pet_expr_resolve_nested(__isl_take pet_expr *expr)
{
        int i, n, n_arg;
        int nparam;
        isl_ctx *ctx;
        isl_space *space;
        isl_local_space *ls;
        isl_aff *aff;
        isl_multi_aff *ma;
        int *param2pos;
        int *t2pos;

        if (!expr)
                return expr;

        n_arg = pet_expr_get_n_arg(expr);
        for (i = 0; i < n_arg; ++i) {
                pet_expr *arg;
                arg = pet_expr_get_arg(expr, i);
                arg = pet_expr_resolve_nested(arg);
                expr = pet_expr_set_arg(expr, i, arg);
        }

        if (pet_expr_get_type(expr) != pet_expr_access)
                return expr;

        space = pet_expr_access_get_parameter_space(expr);
        n = pet_nested_n_in_space(space);
        isl_space_free(space);
        if (n == 0)
                return expr;

        expr = pet_expr_access_align_params(expr);
        if (!expr)
                return NULL;

        space = pet_expr_access_get_parameter_space(expr);
        nparam = isl_space_dim(space, isl_dim_param);
        isl_space_free(space);

        ctx = pet_expr_get_ctx(expr);

        param2pos = isl_alloc_array(ctx, int, nparam);
        t2pos = isl_alloc_array(ctx, int, n);
        if (!param2pos)
                goto error;
        expr = pet_expr_extract_nested(expr, n, param2pos);
        expr = mark_self_dependences(expr, n_arg);
        if (!expr)
                goto error;

        n = 0;
        space = pet_expr_access_get_parameter_space(expr);
        nparam = isl_space_dim(space, isl_dim_param);
        for (i = nparam - 1; i >= 0; --i) {
                isl_id *id = isl_space_get_dim_id(space, isl_dim_param, i);
                if (!pet_nested_in_id(id)) {
                        isl_id_free(id);
                        continue;
                }

                expr = pet_expr_access_move_dims(expr,
                                    isl_dim_in, n_arg + n, isl_dim_param, i, 1);
                t2pos[n] = n_arg + param2pos[i];
                n++;

                isl_id_free(id);
        }
        isl_space_free(space);

        space = pet_expr_access_get_parameter_space(expr);
        space = isl_space_set_from_params(space);
        space = isl_space_add_dims(space, isl_dim_set,
                                        pet_expr_get_n_arg(expr));
        space = isl_space_wrap(isl_space_from_range(space));
        ls = isl_local_space_from_space(isl_space_copy(space));
        space = isl_space_from_domain(space);
        space = isl_space_add_dims(space, isl_dim_out, n_arg + n);
        ma = isl_multi_aff_zero(space);

        for (i = 0; i < n_arg; ++i) {
                aff = isl_aff_var_on_domain(isl_local_space_copy(ls),
                                            isl_dim_set, i);
                ma = isl_multi_aff_set_aff(ma, i, aff);
        }
        for (i = 0; i < n; ++i) {
                aff = isl_aff_var_on_domain(isl_local_space_copy(ls),
                                            isl_dim_set, t2pos[i]);
                ma = isl_multi_aff_set_aff(ma, n_arg + i, aff);
        }
        isl_local_space_free(ls);

        expr = pet_expr_access_pullback_multi_aff(expr, ma);

        expr = remove_marked_self_dependences(expr, 0, n_arg);

        free(t2pos);
        free(param2pos);
        return expr;
error:
        free(t2pos);
        free(param2pos);
        return pet_expr_free(expr);
}

/* Precompose the access relation and the index expression associated
 * to "expr" with the function pointed to by "user",
 * thereby embedding the access relation in the domain of this function.
 * The initial domain of the access relation and the index expression
 * is the zero-dimensional domain.
 */
static __isl_give pet_expr *embed_access(__isl_take pet_expr *expr, void *user)
{
        isl_multi_aff *ma = (isl_multi_aff *) user;

        return pet_expr_access_pullback_multi_aff(expr, isl_multi_aff_copy(ma));
}

/* Precompose all access relations in "expr" with "ma", thereby
 * embedding them in the domain of "ma".
 */
static __isl_give pet_expr *embed(__isl_take pet_expr *expr,
        __isl_keep isl_multi_aff *ma)
{
        return pet_expr_map_access(expr, &embed_access, ma);
}

/* For each nested access parameter in the domain of "stmt",
 * construct a corresponding pet_expr, place it before the original
 * elements in stmt->args and record its position in "param2pos".
 * n is the number of nested access parameters.
 */
struct pet_stmt *pet_stmt_extract_nested(struct pet_stmt *stmt, int n,
        int *param2pos)
{
        int i;
        isl_ctx *ctx;
        isl_space *space;
        int n_arg;
        pet_expr **args;

        ctx = isl_set_get_ctx(stmt->domain);

        n_arg = stmt->n_arg;
        args = isl_calloc_array(ctx, pet_expr *, n + n_arg);
        if (!args)
                goto error;

        space = isl_set_get_space(stmt->domain);
        n_arg = pet_extract_nested_from_space(space, 0, args, param2pos);
        isl_space_free(space);

        if (n_arg < 0)
                goto error;

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

        return stmt;
error:
        if (args) {
                for (i = 0; i < n; ++i)
                        pet_expr_free(args[i]);
                free(args);
        }
        pet_stmt_free(stmt);
        return NULL;
}

/* Check whether any of the arguments i of "stmt" starting at position "n"
 * is equal to one of the first "n" arguments j.
 * If so, combine the constraints on arguments i and j and remove
 * argument i.
 */
static struct pet_stmt *remove_duplicate_arguments(struct pet_stmt *stmt, int n)
{
        int i, j;
        isl_map *map;

        if (!stmt)
                return NULL;
        if (n == 0)
                return stmt;
        if (n == stmt->n_arg)
                return stmt;

        map = isl_set_unwrap(stmt->domain);

        for (i = stmt->n_arg - 1; i >= n; --i) {
                for (j = 0; j < n; ++j)
                        if (pet_expr_is_equal(stmt->args[i], stmt->args[j]))
                                break;
                if (j >= n)
                        continue;

                map = isl_map_equate(map, isl_dim_out, i, isl_dim_out, j);
                map = isl_map_project_out(map, isl_dim_out, i, 1);

                pet_expr_free(stmt->args[i]);
                for (j = i; j + 1 < stmt->n_arg; ++j)
                        stmt->args[j] = stmt->args[j + 1];
                stmt->n_arg--;
        }

        stmt->domain = isl_map_wrap(map);
        if (!stmt->domain)
                goto error;
        return stmt;
error:
        pet_stmt_free(stmt);
        return NULL;
}

/* Look for parameters in the iteration domain of "stmt" that
 * refer to nested accesses.  In particular, these are
 * parameters with name "__pet_expr".
 *
 * If there are any such parameters, then as many extra variables
 * (after identifying identical nested accesses) are inserted in the
 * range of the map wrapped inside the domain, before the original variables.
 * If the original domain is not a wrapped map, then a new wrapped
 * map is created with zero output dimensions.
 * The parameters are then equated to the corresponding output dimensions
 * and subsequently projected out, from the iteration domain,
 * the schedule and the access relations.
 * For each of the output dimensions, a corresponding argument
 * expression is inserted.  Initially they are created with
 * a zero-dimensional domain, so they have to be embedded
 * in the current iteration domain.
 * param2pos maps the position of the parameter to the position
 * of the corresponding output dimension in the wrapped map.
 */
struct pet_stmt *pet_stmt_resolve_nested(struct pet_stmt *stmt)
{
        int i, n;
        int pos;
        int nparam;
        unsigned n_arg;
        isl_ctx *ctx;
        isl_map *map;
        isl_space *space;
        isl_multi_aff *ma;
        int *param2pos;

        if (!stmt)
                return NULL;

        n = pet_nested_n_in_set(stmt->domain);
        if (n == 0)
                return stmt;

        ctx = isl_set_get_ctx(stmt->domain);

        n_arg = stmt->n_arg;
        nparam = isl_set_dim(stmt->domain, isl_dim_param);
        param2pos = isl_alloc_array(ctx, int, nparam);
        stmt = pet_stmt_extract_nested(stmt, n, param2pos);
        if (!stmt) {
                free(param2pos);
                return NULL;
        }

        n = stmt->n_arg - n_arg;
        if (isl_set_is_wrapping(stmt->domain))
                map = isl_set_unwrap(stmt->domain);
        else
                map = isl_map_from_domain(stmt->domain);
        map = isl_map_insert_dims(map, isl_dim_out, 0, n);

        for (i = nparam - 1; i >= 0; --i) {
                isl_id *id;

                if (!pet_nested_in_map(map, i))
                        continue;

                id = pet_expr_access_get_id(stmt->args[param2pos[i]]);
                map = isl_map_set_dim_id(map, isl_dim_out, param2pos[i], id);
                map = isl_map_equate(map, isl_dim_param, i, isl_dim_out,
                                        param2pos[i]);
                map = isl_map_project_out(map, isl_dim_param, i, 1);
        }

        stmt->domain = isl_map_wrap(map);

        space = isl_space_unwrap(isl_set_get_space(stmt->domain));
        space = isl_space_from_domain(isl_space_domain(space));
        ma = isl_multi_aff_zero(space);
        for (pos = 0; pos < n; ++pos)
                stmt->args[pos] = embed(stmt->args[pos], ma);
        isl_multi_aff_free(ma);

        stmt = pet_stmt_remove_nested_parameters(stmt);
        stmt = remove_duplicate_arguments(stmt, n);

        free(param2pos);
        return stmt;
}

/* For each statement in "scop", move the parameters that correspond
 * to nested access into the ranges of the domains and create
 * corresponding argument expressions.
 */
struct pet_scop *pet_scop_resolve_nested(struct pet_scop *scop)
{
        int i;

        if (!scop)
                return NULL;

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

        return scop;
}