pet_context_evaluate_expr: plug in affine expressions outside index expressions

[pet.git] / context.c

/*
 * Copyright 2011      Leiden University. All rights reserved.
 * Copyright 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 <isl/aff.h>

#include "aff.h"
#include "array.h"
#include "context.h"
#include "expr.h"
#include "expr_arg.h"
#include "nest.h"
#include "patch.h"
#include "tree.h"
#include "pet_expr_to_isl_pw_aff.h"

/* A pet_context represents the context in which a pet_expr
 * in converted to an affine expression.
 *
 * "domain" prescribes the domain of the affine expressions.
 *
 * "assignments" maps variable names to their currently known values.
 * Internally, the domains of the values may be equal to some prefix
 * of the space of "domain", but the domains are updated to be
 * equal to the space of "domain" before passing them to the user.
 *
 * If "allow_nested" is set, then the affine expression created
 * in this context may involve new parameters that encode a pet_expr.
 *
 * "extracted_affine" caches the results of pet_expr_extract_affine.
 * It may be NULL if no results have been cached so far and
 * it is cleared (in pet_context_cow) whenever the context is changed.
 */
struct pet_context {
        int ref;

        isl_set *domain;
        isl_id_to_pw_aff *assignments;
        int allow_nested;

        pet_expr_to_isl_pw_aff *extracted_affine;
};

/* Create a pet_context with the given domain, assignments,
 * and value for allow_nested.
 */
static __isl_give pet_context *context_alloc(__isl_take isl_set *domain,
        __isl_take isl_id_to_pw_aff *assignments, int allow_nested)
{
        pet_context *pc;

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

        pc = isl_calloc_type(isl_set_get_ctx(domain), struct pet_context);
        if (!pc)
                goto error;

        pc->ref = 1;
        pc->domain = domain;
        pc->assignments = assignments;
        pc->allow_nested = allow_nested;

        return pc;
error:
        isl_set_free(domain);
        isl_id_to_pw_aff_free(assignments);
        return NULL;
}

/* Create a pet_context with the given domain.
 *
 * Initially, there are no assigned values and parameters that
 * encode a pet_expr are not allowed.
 */
__isl_give pet_context *pet_context_alloc(__isl_take isl_set *domain)
{
        isl_id_to_pw_aff *assignments;

        if (!domain)
                return NULL;

        assignments = isl_id_to_pw_aff_alloc(isl_set_get_ctx(domain), 0);
        return context_alloc(domain, assignments, 0);
}

/* Return an independent duplicate of "pc".
 */
static __isl_give pet_context *pet_context_dup(__isl_keep pet_context *pc)
{
        pet_context *dup;

        if (!pc)
                return NULL;

        dup = context_alloc(isl_set_copy(pc->domain),
                            isl_id_to_pw_aff_copy(pc->assignments),
                            pc->allow_nested);

        return dup;
}

/* Return a pet_context that is equal to "pc" and that has only one reference.
 *
 * If "pc" itself only has one reference, then clear the cache of
 * pet_expr_extract_affine results since the returned pet_context
 * will be modified and the cached results may no longer be valid
 * after these modifications.
 */
static __isl_give pet_context *pet_context_cow(__isl_take pet_context *pc)
{
        if (!pc)
                return NULL;

        if (pc->ref == 1) {
                pet_expr_to_isl_pw_aff_free(pc->extracted_affine);
                pc->extracted_affine = NULL;
                return pc;
        }
        pc->ref--;
        return pet_context_dup(pc);
}

/* Return an extra reference to "pc".
 */
__isl_give pet_context *pet_context_copy(__isl_keep pet_context *pc)
{
        if (!pc)
                return NULL;

        pc->ref++;
        return pc;
}

/* Free a reference to "pc" and return NULL.
 */
__isl_null pet_context *pet_context_free(__isl_take pet_context *pc)
{
        if (!pc)
                return NULL;
        if (--pc->ref > 0)
                return NULL;

        isl_set_free(pc->domain);
        isl_id_to_pw_aff_free(pc->assignments);
        pet_expr_to_isl_pw_aff_free(pc->extracted_affine);
        free(pc);
        return NULL;
}

/* If an isl_pw_aff corresponding to "expr" has been cached in "pc",
 * then return a copy of that isl_pw_aff.
 * Otherwise, return (isl_bool_false, NULL).
 */
__isl_give isl_maybe_isl_pw_aff pet_context_get_extracted_affine(
        __isl_keep pet_context *pc, __isl_keep pet_expr *expr)
{
        isl_maybe_isl_pw_aff m = { isl_bool_false, NULL };

        if (!pc)
                goto error;
        if (!pc->extracted_affine)
                return m;
        return pet_expr_to_isl_pw_aff_try_get(pc->extracted_affine, expr);
error:
        m.valid = isl_bool_error;
        return m;
}

/* Keep track of the fact that "expr" maps to "pa" in "pc".
 */
isl_stat pet_context_set_extracted_affine(__isl_keep pet_context *pc,
        __isl_keep pet_expr *expr, __isl_keep isl_pw_aff *pa)
{
        if (!pc || !expr)
                return isl_stat_error;

        if (!pc->extracted_affine) {
                isl_ctx *ctx;

                ctx = pet_context_get_ctx(pc);
                pc->extracted_affine = pet_expr_to_isl_pw_aff_alloc(ctx, 1);
        }

        pc->extracted_affine = pet_expr_to_isl_pw_aff_set(pc->extracted_affine,
                                    pet_expr_copy(expr), isl_pw_aff_copy(pa));
        if (!pc->extracted_affine)
                return isl_stat_error;

        return isl_stat_ok;
}

/* Return the isl_ctx in which "pc" was created.
 */
isl_ctx *pet_context_get_ctx(__isl_keep pet_context *pc)
{
        return pc ? isl_set_get_ctx(pc->domain) : NULL;
}

/* Return the domain of "pc".
 */
__isl_give isl_set *pet_context_get_domain(__isl_keep pet_context *pc)
{
        if (!pc)
                return NULL;
        return isl_set_copy(pc->domain);
}

/* Return the domain of "pc" in a form that is suitable
 * for use as a gist context.
 * In particular, remove all references to nested expression parameters
 * so that they do not get introduced in the gisted expression.
 */
__isl_give isl_set *pet_context_get_gist_domain(__isl_keep pet_context *pc)
{
        isl_set *domain;

        domain = pet_context_get_domain(pc);
        domain = pet_nested_remove_from_set(domain);
        return domain;
}

/* Return the domain space of "pc".
 *
 * The domain of "pc" may have constraints involving parameters
 * that encode a pet_expr.  These parameters are not relevant
 * outside this domain.  Furthermore, they need to be resolved
 * from the final result, so we do not want to propagate them needlessly.
 */
__isl_give isl_space *pet_context_get_space(__isl_keep pet_context *pc)
{
        isl_space *space;

        if (!pc)
                return NULL;

        space = isl_set_get_space(pc->domain);
        space = pet_nested_remove_from_space(space);
        return space;
}

/* Return the dimension of the domain space of "pc".
 */
unsigned pet_context_dim(__isl_keep pet_context *pc)
{
        if (!pc)
                return 0;
        return isl_set_dim(pc->domain, isl_dim_set);
}

/* Return the assignments of "pc".
 */
__isl_give isl_id_to_pw_aff *pet_context_get_assignments(
        __isl_keep pet_context *pc)
{
        if (!pc)
                return NULL;
        return isl_id_to_pw_aff_copy(pc->assignments);
}

/* Is "id" assigned any value in "pc"?
 */
int pet_context_is_assigned(__isl_keep pet_context *pc, __isl_keep isl_id *id)
{
        if (!pc || !id)
                return -1;
        return isl_id_to_pw_aff_has(pc->assignments, id);
}

/* Return the value assigned to "id" in "pc".
 *
 * Some dimensions may have been added to pc->domain after the value
 * associated to "id" was added.  We therefore need to adjust the domain
 * of the stored value to match pc->domain by adding the missing
 * dimensions.
 */
__isl_give isl_pw_aff *pet_context_get_value(__isl_keep pet_context *pc,
        __isl_take isl_id *id)
{
        int dim;
        isl_pw_aff *pa;
        isl_multi_aff *ma;

        if (!pc || !id)
                goto error;

        pa = isl_id_to_pw_aff_get(pc->assignments, id);
        dim = isl_pw_aff_dim(pa, isl_dim_in);
        if (dim == isl_set_dim(pc->domain, isl_dim_set))
                return pa;

        ma = pet_prefix_projection(pet_context_get_space(pc), dim);
        pa = isl_pw_aff_pullback_multi_aff(pa, ma);

        return pa;
error:
        isl_id_free(id);
        return NULL;
}

/* Assign the value "value" to "id" in "pc", replacing the previously
 * assigned value, if any.
 */
__isl_give pet_context *pet_context_set_value(__isl_take pet_context *pc,
        __isl_take isl_id *id, isl_pw_aff *value)
{
        pc = pet_context_cow(pc);
        if (!pc)
                goto error;
        pc->assignments = isl_id_to_pw_aff_set(pc->assignments, id, value);
        if (!pc->assignments)
                return pet_context_free(pc);
        return pc;
error:
        isl_id_free(id);
        isl_pw_aff_free(value);
        return NULL;
}

/* Remove any assignment to "id" in "pc".
 */
__isl_give pet_context *pet_context_clear_value(__isl_keep pet_context *pc,
        __isl_take isl_id *id)
{
        pc = pet_context_cow(pc);
        if (!pc)
                goto error;
        pc->assignments = isl_id_to_pw_aff_drop(pc->assignments, id);
        if (!pc->assignments)
                return pet_context_free(pc);
        return pc;
error:
        isl_id_free(id);
        return NULL;
}

/* Are affine expressions created in this context allowed to involve
 * parameters that encode a pet_expr?
 */
int pet_context_allow_nesting(__isl_keep pet_context *pc)
{
        if (!pc)
                return -1;
        return pc->allow_nested;
}

/* Allow affine expressions created in this context to involve
 * parameters that encode a pet_expr based on the value of "allow_nested".
 */
__isl_give pet_context *pet_context_set_allow_nested(__isl_take pet_context *pc,
        int allow_nested)
{
        if (!pc)
                return NULL;
        if (pc->allow_nested == allow_nested)
                return pc;
        pc = pet_context_cow(pc);
        if (!pc)
                return NULL;
        pc->allow_nested = allow_nested;
        return pc;
}

/* If the access expression "expr" writes to a (non-virtual) scalar,
 * then remove any assignment to the scalar in "pc".
 */
static int clear_write(__isl_keep pet_expr *expr, void *user)
{
        isl_id *id;
        pet_context **pc = (pet_context **) user;

        if (!pet_expr_access_is_write(expr))
                return 0;
        if (!pet_expr_is_scalar_access(expr))
                return 0;

        id = pet_expr_access_get_id(expr);
        if (isl_id_get_user(id))
                *pc = pet_context_clear_value(*pc, id);
        else
                isl_id_free(id);

        return 0;
}

/* Look for any writes to scalar variables in "expr" and
 * remove any assignment to them in "pc".
 */
__isl_give pet_context *pet_context_clear_writes_in_expr(
        __isl_take pet_context *pc, __isl_keep pet_expr *expr)
{
        if (pet_expr_foreach_access_expr(expr, &clear_write, &pc) < 0)
                pc = pet_context_free(pc);

        return pc;
}

/* Look for any writes to scalar variables in "tree" and
 * remove any assignment to them in "pc".
 */
__isl_give pet_context *pet_context_clear_writes_in_tree(
        __isl_take pet_context *pc, __isl_keep pet_tree *tree)
{
        if (pet_tree_foreach_access_expr(tree, &clear_write, &pc) < 0)
                pc = pet_context_free(pc);

        return pc;
}

/* Internal data structure for pet_context_add_parameters.
 *
 * "pc" is the context that is being updated.
 * "get_array_size" is a callback function that can be used to determine
 * the size of the array that is accessed by a given access expression.
 * "user" is the user data for this callback.
 */
struct pet_context_add_parameter_data {
        pet_context *pc;
        __isl_give pet_expr *(*get_array_size)(__isl_keep pet_expr *access,
                void *user);
        void *user;
};

/* Given an access expression "expr", add a parameter assignment to data->pc
 * to the variable being accessed, provided it is a read from an integer
 * scalar variable.
 * If an array is being accesed, then recursively call the function
 * on each of the access expressions in the size expression of the array.
 */
static int add_parameter(__isl_keep pet_expr *expr, void *user)
{
        struct pet_context_add_parameter_data *data = user;
        int pos;
        isl_id *id;
        isl_space *space;
        isl_local_space *ls;
        isl_aff *aff;
        isl_pw_aff *pa;

        if (!pet_expr_is_scalar_access(expr)) {
                pet_expr *size = data->get_array_size(expr, data->user);
                if (pet_expr_foreach_access_expr(size,
                                                &add_parameter, data) < 0)
                        data->pc = pet_context_free(data->pc);
                pet_expr_free(size);
                return 0;
        }
        if (!pet_expr_access_is_read(expr))
                return 0;
        if (pet_expr_get_type_size(expr) == 0)
                return 0;

        id = pet_expr_access_get_id(expr);
        if (pet_context_is_assigned(data->pc, id)) {
                isl_id_free(id);
                return 0;
        }

        space = pet_context_get_space(data->pc);
        pos = isl_space_find_dim_by_id(space, isl_dim_param, id);
        if (pos < 0) {
                pos = isl_space_dim(space, isl_dim_param);
                space = isl_space_add_dims(space, isl_dim_param, 1);
                space = isl_space_set_dim_id(space, isl_dim_param, pos,
                                                isl_id_copy(id));
        }

        ls = isl_local_space_from_space(space);
        aff = isl_aff_var_on_domain(ls, isl_dim_param, pos);
        pa = isl_pw_aff_from_aff(aff);
        data->pc = pet_context_set_value(data->pc, id, pa);

        return 0;
}

/* Add an assignment to "pc" for each parameter in "tree".
 * "get_array_size" is a callback function that can be used to determine
 * the size of the array that is accessed by a given access expression.
 *
 * We initially treat as parameters any integer variable that is read
 * anywhere in "tree" or in any of the size expressions for any of
 * the arrays accessed in "tree".
 * Then we remove from those variables that are written anywhere
 * inside "tree".
 */
__isl_give pet_context *pet_context_add_parameters(__isl_take pet_context *pc,
        __isl_keep pet_tree *tree,
        __isl_give pet_expr *(*get_array_size)(__isl_keep pet_expr *access,
                void *user), void *user)
{
        struct pet_context_add_parameter_data data;

        data.pc = pc;
        data.get_array_size = get_array_size;
        data.user = user;
        if (pet_tree_foreach_access_expr(tree, &add_parameter, &data) < 0)
                data.pc = pet_context_free(data.pc);

        data.pc = pet_context_clear_writes_in_tree(data.pc, tree);

        return data.pc;
}

/* Given an access expression, check if it reads a scalar variable
 * that has a known value in "pc".
 * If so, then replace the access by an access to that value.
 */
static __isl_give pet_expr *access_plug_in_affine_read(
        __isl_take pet_expr *expr, void *user)
{
        pet_context *pc = user;
        isl_pw_aff *pa;

        if (pet_expr_access_is_write(expr))
                return expr;
        if (!pet_expr_is_scalar_access(expr))
                return expr;

        pa = pet_expr_extract_affine(expr, pc);
        if (!pa)
                return pet_expr_free(expr);
        if (isl_pw_aff_involves_nan(pa)) {
                isl_pw_aff_free(pa);
                return expr;
        }

        pet_expr_free(expr);
        expr = pet_expr_from_index(isl_multi_pw_aff_from_pw_aff(pa));

        return expr;
}

/* Replace every read access in "expr" to a scalar variable
 * that has a known value in "pc" by that known value.
 */
static __isl_give pet_expr *plug_in_affine_read(__isl_take pet_expr *expr,
        __isl_keep pet_context *pc)
{
        return pet_expr_map_access(expr, &access_plug_in_affine_read, pc);
}

/* Add an extra affine expression to "mpa" that is equal to
 * an extra dimension in the range of the wrapped relation in the domain
 * of "mpa".  "n_arg" is the original number of dimensions in this range.
 *
 * That is, if "n_arg" is 0, then the input has the form
 *
 *      D(i) -> [f(i)]
 *
 * and the output has the form
 *
 *      [D(i) -> [y]] -> [f(i), y]
 *
 * If "n_arg" is different from 0, then the input has the form
 *
 *      [D(i) -> [x]] -> [f(i,x)]
 *
 * with x consisting of "n_arg" dimensions, and the output has the form
 *
 *      [D(i) -> [x,y]] -> [f(i,x), y]
 *
 *
 * We first adjust the domain of "mpa" and then add the extra
 * affine expression (y).
 */
static __isl_give isl_multi_pw_aff *add_arg(__isl_take isl_multi_pw_aff *mpa,
        int n_arg)
{
        int dim;
        isl_space *space;
        isl_multi_aff *ma;
        isl_multi_pw_aff *mpa2;

        if (n_arg == 0) {
                space = isl_space_domain(isl_multi_pw_aff_get_space(mpa));
                dim = isl_space_dim(space, isl_dim_set);
                space = isl_space_from_domain(space);
                space = isl_space_add_dims(space, isl_dim_set, 1);
                ma = isl_multi_aff_domain_map(space);
        } else {
                isl_multi_aff *ma2;
                isl_space *dom, *ran;

                space = isl_space_domain(isl_multi_pw_aff_get_space(mpa));
                space = isl_space_unwrap(space);
                dom = isl_space_domain(isl_space_copy(space));
                dim = isl_space_dim(dom, isl_dim_set);
                ran = isl_space_range(space);
                ran = isl_space_add_dims(ran, isl_dim_set, 1);
                space = isl_space_map_from_set(dom);
                ma = isl_multi_aff_identity(space);
                ma2 = isl_multi_aff_project_out_map(ran, isl_dim_set, n_arg, 1);
                ma = isl_multi_aff_product(ma, ma2);
        }

        mpa = isl_multi_pw_aff_pullback_multi_aff(mpa, ma);
        space = isl_space_domain(isl_multi_pw_aff_get_space(mpa));
        ma = isl_multi_aff_project_out_map(space, isl_dim_set, 0, dim + n_arg);
        mpa2 = isl_multi_pw_aff_from_multi_aff(ma);
        mpa = isl_multi_pw_aff_flat_range_product(mpa, mpa2);

        return mpa;
}

/* Add the integer value from "arg" to "mpa".
 */
static __isl_give isl_multi_pw_aff *add_int(__isl_take isl_multi_pw_aff *mpa,
        __isl_take pet_expr *arg)
{
        isl_space *space;
        isl_val *v;
        isl_aff *aff;
        isl_multi_pw_aff *mpa_arg;

        v = pet_expr_int_get_val(arg);
        pet_expr_free(arg);

        space = isl_space_domain(isl_multi_pw_aff_get_space(mpa));
        aff = isl_aff_val_on_domain(isl_local_space_from_space(space), v);
        mpa_arg = isl_multi_pw_aff_from_pw_aff(isl_pw_aff_from_aff(aff));

        mpa = isl_multi_pw_aff_flat_range_product(mpa, mpa_arg);

        return mpa;
}

/* Add the affine expression from "arg" to "mpa".
 * "n_arg" is the number of dimensions in the range of the wrapped
 * relation in the domain of "mpa".
 */
static __isl_give isl_multi_pw_aff *add_aff(__isl_take isl_multi_pw_aff *mpa,
        int n_arg, __isl_take pet_expr *arg)
{
        isl_multi_pw_aff *mpa_arg;

        mpa_arg = pet_expr_access_get_index(arg);
        pet_expr_free(arg);

        if (n_arg > 0) {
                isl_space *space;
                isl_multi_aff *ma;

                space = isl_space_domain(isl_multi_pw_aff_get_space(mpa));
                space = isl_space_unwrap(space);
                ma = isl_multi_aff_domain_map(space);
                mpa_arg = isl_multi_pw_aff_pullback_multi_aff(mpa_arg, ma);
        }

        mpa = isl_multi_pw_aff_flat_range_product(mpa, mpa_arg);

        return mpa;
}

/* Combine the index expression of "expr" with the subaccess relation "access".
 * If "add" is set, then it is not the index expression of "expr" itself
 * that is passed to the function, but its address.
 *
 * We call patch_map on each map in "access" and return the combined results.
 */
static __isl_give isl_union_map *patch(__isl_take isl_union_map *access,
        __isl_keep pet_expr *expr, int add)
{
        isl_multi_pw_aff *prefix;

        prefix = pet_expr_access_get_index(expr);
        return pet_patch_union_map(prefix, access, add, 1);
}

/* Set the access relations of "expr", which appears in the argument
 * at position "pos" in a call expression by composing the access
 * relations in "summary" with the expression "int_arg" of the integer
 * arguments in terms of the domain and expression arguments of "expr" and
 * combining the result with the index expression passed to the function.
 * If "add" is set, then it is not "expr" itself that is passed
 * to the function, but the address of "expr".
 *
 * We reset the read an write flag of "expr" and rely on
 * pet_expr_access_set_access setting the flags based on
 * the access relations.
 *
 * After relating each access relation of the called function
 * to the domain and expression arguments at the call site,
 * the result is combined with the index expression by the function patch
 * and then stored in the access expression.
 */
static __isl_give pet_expr *set_access_relations(__isl_take pet_expr *expr,
        __isl_keep pet_function_summary *summary, int pos,
        __isl_take isl_multi_pw_aff *int_arg, int add)
{
        enum pet_expr_access_type type;

        expr = pet_expr_access_set_read(expr, 0);
        expr = pet_expr_access_set_write(expr, 0);
        for (type = pet_expr_access_begin; type < pet_expr_access_end; ++type) {
                isl_union_map *access;

                access = pet_function_summary_arg_get_access(summary,
                                                                pos, type);
                access = isl_union_map_preimage_domain_multi_pw_aff(access,
                                                isl_multi_pw_aff_copy(int_arg));
                access = patch(access, expr, add);
                expr = pet_expr_access_set_access(expr, type, access);
        }
        isl_multi_pw_aff_free(int_arg);

        return expr;
}

/* Set the access relations of "arg", which appears in the argument
 * at position "pos" in the call expression "call" based on the
 * information in "summary".
 * If "add" is set, then it is not "arg" itself that is passed
 * to the function, but the address of "arg".
 *
 * We create an affine function "int_arg" that expresses
 * the integer function call arguments in terms of the domain of "arg"
 * (i.e., the outer loop iterators) and the expression arguments.
 * If the actual argument is not an affine expression or if it itself
 * has expression arguments, then it is added as an argument to "arg" and
 * "int_arg" is made to reference this additional expression argument.
 *
 * Finally, we call set_access_relations to plug in the actual arguments
 * (expressed in "int_arg") into the access relations in "summary" and
 * to add the resulting access relations to "arg".
 */
static __isl_give pet_expr *access_plug_in_summary(__isl_take pet_expr *arg,
        __isl_keep pet_expr *call, __isl_keep pet_function_summary *summary,
        int pos, int add)
{
        int j, n;
        isl_space *space;
        isl_multi_pw_aff *int_arg;
        int arg_n_arg;

        space = pet_expr_access_get_augmented_domain_space(arg);
        space = isl_space_from_domain(space);
        arg_n_arg = pet_expr_get_n_arg(arg);
        int_arg = isl_multi_pw_aff_zero(space);
        n = pet_function_summary_get_n_arg(summary);
        for (j = 0; j < n; ++j) {
                pet_expr *arg_j;
                int arg_j_n_arg;

                if (!pet_function_summary_arg_is_int(summary, j))
                        continue;

                arg_j = pet_expr_get_arg(call, j);
                arg_j_n_arg = pet_expr_get_n_arg(arg_j);
                if (pet_expr_get_type(arg_j) == pet_expr_int) {
                        int_arg = add_int(int_arg, arg_j);
                } else if (arg_j_n_arg != 0 || !pet_expr_is_affine(arg_j)) {
                        arg = pet_expr_insert_arg(arg, arg_n_arg,
                                                        arg_j);
                        int_arg = add_arg(int_arg, arg_n_arg);
                        arg_n_arg++;
                } else {
                        int_arg = add_aff(int_arg, arg_n_arg, arg_j);
                }
        }
        arg = set_access_relations(arg, summary, pos, int_arg, add);

        return arg;
}

/* Given the argument "arg" at position "pos" of "call",
 * check if it is either an access expression or the address
 * of an access expression.  If so, use the information in "summary"
 * to set the access relations of the access expression.
 */
static __isl_give pet_expr *arg_plug_in_summary(__isl_take pet_expr *arg,
        __isl_keep pet_expr *call, __isl_keep pet_function_summary *summary,
        int pos)
{
        enum pet_expr_type type;
        pet_expr *arg2;

        type = pet_expr_get_type(arg);
        if (type == pet_expr_access)
                return access_plug_in_summary(arg, call, summary, pos, 0);
        if (!pet_expr_is_address_of(arg))
                return arg;

        arg2 = pet_expr_get_arg(arg, 0);
        if (pet_expr_get_type(arg2) == pet_expr_access)
                arg2 = access_plug_in_summary(arg2, call, summary, pos, 1);
        arg = pet_expr_set_arg(arg, 0, arg2);

        return arg;
}

/* Given a call expression, check if the integer arguments can
 * be represented by affine expressions in the context "pc"
 * (assuming they are not already affine expressions).
 * If so, replace these arguments by the corresponding affine expressions.
 */
static __isl_give pet_expr *call_plug_in_affine_args(__isl_take pet_expr *call,
        __isl_keep pet_context *pc)
{
        int i, n;

        n = pet_expr_get_n_arg(call);
        for (i = 0; i < n; ++i) {
                pet_expr *arg;
                isl_pw_aff *pa;

                arg = pet_expr_get_arg(call, i);
                if (!arg)
                        return pet_expr_free(call);
                if (pet_expr_get_type_size(arg) == 0 ||
                    pet_expr_is_affine(arg)) {
                        pet_expr_free(arg);
                        continue;
                }

                pa = pet_expr_extract_affine(arg, pc);
                pet_expr_free(arg);
                if (!pa)
                        return pet_expr_free(call);
                if (isl_pw_aff_involves_nan(pa)) {
                        isl_pw_aff_free(pa);
                        continue;
                }

                arg = pet_expr_from_index(isl_multi_pw_aff_from_pw_aff(pa));
                call = pet_expr_set_arg(call, i, arg);
        }

        return call;
}

/* If "call" has an associated function summary, then use it
 * to set the access relations of the array arguments of the function call.
 *
 * We first plug in affine expressions for the integer arguments
 * whenever possible as these arguments will be plugged in
 * in the access relations of the array arguments.
 */
static __isl_give pet_expr *call_plug_in_summary(__isl_take pet_expr *call,
        void *user)
{
        pet_context *pc = user;
        pet_function_summary *summary;
        int i, n;

        if (!pet_expr_call_has_summary(call))
                return call;

        call = call_plug_in_affine_args(call, pc);

        summary = pet_expr_call_get_summary(call);
        if (!summary)
                return pet_expr_free(call);

        n = pet_expr_get_n_arg(call);
        for (i = 0; i < n; ++i) {
                pet_expr *arg_i;

                if (!pet_function_summary_arg_is_array(summary, i))
                        continue;

                arg_i = pet_expr_get_arg(call, i);
                arg_i = arg_plug_in_summary(arg_i, call, summary, i);
                call = pet_expr_set_arg(call, i, arg_i);
        }

        pet_function_summary_free(summary);
        return call;
}

/* For each call subexpression of "expr", plug in the access relations
 * from the associated function summary (if any).
 */
static __isl_give pet_expr *plug_in_summaries(__isl_take pet_expr *expr,
        __isl_keep pet_context *pc)
{
        return pet_expr_map_call(expr, &call_plug_in_summary, pc);
}

/* Given an access expression "expr", check that it is an affine
 * access expression and set *only_affine to 1.
 * If "expr" is not an affine access expression, then set *only_affine to 0
 * and abort.
 */
static int check_only_affine(__isl_keep pet_expr *expr, void *user)
{
        int *only_affine = user;
        int is_affine;

        is_affine = pet_expr_is_affine(expr);
        if (is_affine < 0)
                return -1;
        if (!is_affine) {
                *only_affine = 0;
                return -1;
        }
        *only_affine = 1;

        return 0;
}

/* Does "expr" have any affine access subexpression and no other
 * access subexpressions?
 *
 * only_affine is initialized to -1 and set to 1 as soon as one affine
 * access subexpression has been found and to 0 if some other access
 * subexpression has been found.  In this latter case, the search is
 * aborted.
 */
static isl_bool has_only_affine_access_sub_expr(__isl_keep pet_expr *expr)
{
        int only_affine = -1;

        if (pet_expr_foreach_access_expr(expr, &check_only_affine,
                                        &only_affine) < 0 &&
            only_affine != 0)
                return isl_bool_error;

        return only_affine > 0;
}

/* Try and replace "expr" by an affine access expression by essentially
 * evaluating operations and/or special calls on affine access expressions.
 * It therefore only makes sense to do this if "expr" is a call or an operation
 * and if it has at least one affine access subexpression and no other
 * access subexpressions.
 */
static __isl_give pet_expr *expr_plug_in_affine(__isl_take pet_expr *expr,
        void *user)
{
        enum pet_expr_type type;
        pet_context *pc = user;
        isl_pw_aff *pa;
        isl_bool contains_access;

        type = pet_expr_get_type(expr);
        if (type != pet_expr_call && type != pet_expr_op)
                return expr;
        contains_access = has_only_affine_access_sub_expr(expr);
        if (contains_access < 0)
                return pet_expr_free(expr);
        if (!contains_access)
                return expr;

        pa = pet_expr_extract_affine(expr, pc);
        if (!pa)
                return pet_expr_free(expr);
        if (isl_pw_aff_involves_nan(pa)) {
                isl_pw_aff_free(pa);
                return expr;
        }

        pet_expr_free(expr);
        expr = pet_expr_from_index(isl_multi_pw_aff_from_pw_aff(pa));

        return expr;
}

/* Detect affine subexpressions in "expr".
 *
 * The detection is performed top-down in order to be able
 * to exploit the min/max optimization in comparisons.
 * That is, if some subexpression is of the form max(a,b) <= min(c,d)
 * and if the affine expressions were being detected bottom-up, then
 * affine expressions for max(a,b) and min(c,d) would be constructed
 * first and it would no longer be possible to optimize the extraction
 * of the comparison as a <= c && a <= d && b <= c && b <= d.
 */
static __isl_give pet_expr *plug_in_affine(__isl_take pet_expr *expr,
        __isl_keep pet_context *pc)
{
        return pet_expr_map_top_down(expr, &expr_plug_in_affine, pc);
}

/* Evaluate "expr" in the context of "pc".
 *
 * In particular, we first make sure that all the access expressions
 * inside "expr" have the same domain as "pc".
 * Then, we plug in affine expressions for scalar reads,
 * plug in the arguments of all access expressions in "expr" as well
 * as any other affine expressions that may appear inside "expr" and
 * plug in the access relations from the summary functions associated
 * to call expressions.
 */
__isl_give pet_expr *pet_context_evaluate_expr(__isl_keep pet_context *pc,
        __isl_take pet_expr *expr)
{
        expr = pet_expr_insert_domain(expr, pet_context_get_space(pc));
        expr = plug_in_affine_read(expr, pc);
        expr = pet_expr_plug_in_args(expr, pc);
        expr = plug_in_affine(expr, pc);
        expr = plug_in_summaries(expr, pc);
        return expr;
}

/* Wrapper around pet_context_evaluate_expr
 * for use as a callback to pet_tree_map_expr.
 */
static __isl_give pet_expr *evaluate_expr(__isl_take pet_expr *expr,
        void *user)
{
        pet_context *pc = user;

        return pet_context_evaluate_expr(pc, expr);
}

/* Evaluate "tree" in the context of "pc".
 * That is, evaluate all the expressions of "tree" in the context of "pc".
 */
__isl_give pet_tree *pet_context_evaluate_tree(__isl_keep pet_context *pc,
        __isl_take pet_tree *tree)
{
        return pet_tree_map_expr(tree, &evaluate_expr, pc);
}

/* Add an unbounded inner dimension "id" to pc->domain.
 *
 * The assignments are not adjusted here and therefore keep
 * their original domain.  These domains need to be adjusted before
 * these assigned values can be used.  This is taken care of by
 * pet_context_get_value.
 */
static __isl_give pet_context *extend_domain(__isl_take pet_context *pc,
        __isl_take isl_id *id)
{
        int pos;

        pc = pet_context_cow(pc);
        if (!pc || !id)
                goto error;

        pos = pet_context_dim(pc);
        pc->domain = isl_set_add_dims(pc->domain, isl_dim_set, 1);
        pc->domain = isl_set_set_dim_id(pc->domain, isl_dim_set, pos, id);
        if (!pc->domain)
                return pet_context_free(pc);

        return pc;
error:
        pet_context_free(pc);
        isl_id_free(id);
        return NULL;
}

/* Add an unbounded inner iterator "id" to pc->domain.
 * Additionally, mark the variable "id" as having the value of this
 * new inner iterator.
 */
__isl_give pet_context *pet_context_add_inner_iterator(
        __isl_take pet_context *pc, __isl_take isl_id *id)
{
        int pos;
        isl_space *space;
        isl_local_space *ls;
        isl_aff *aff;
        isl_pw_aff *pa;

        if (!pc || !id)
                goto error;

        pos = pet_context_dim(pc);
        pc = extend_domain(pc, isl_id_copy(id));
        if (!pc)
                goto error;

        space = pet_context_get_space(pc);
        ls = isl_local_space_from_space(space);
        aff = isl_aff_var_on_domain(ls, isl_dim_set, pos);
        pa = isl_pw_aff_from_aff(aff);

        pc = pet_context_set_value(pc, id, pa);

        return pc;
error:
        pet_context_free(pc);
        isl_id_free(id);
        return NULL;
}

/* Add an inner iterator to pc->domain.
 * In particular, extend the domain with an inner loop { [t] : t >= 0 }.
 */
__isl_give pet_context *pet_context_add_infinite_loop(
        __isl_take pet_context *pc)
{
        int dim;
        isl_ctx *ctx;
        isl_id *id;

        if (!pc)
                return NULL;

        dim = pet_context_dim(pc);
        ctx = pet_context_get_ctx(pc);
        id = isl_id_alloc(ctx, "t", NULL);
        pc = extend_domain(pc, id);
        pc = pet_context_cow(pc);
        if (!pc)
                return NULL;
        pc->domain = isl_set_lower_bound_si(pc->domain, isl_dim_set, dim, 0);
        if (!pc->domain)
                return pet_context_free(pc);

        return pc;
}

/* Internal data structure for preimage_domain.
 *
 * "ma" is the function under which the preimage should be computed.
 * "assignments" collects the results.
 */
struct pet_preimage_domain_data {
        isl_multi_aff *ma;
        isl_id_to_pw_aff *assignments;
};

/* Add the assignment to "key" of the preimage of "val" under data->ma
 * to data->assignments.
 *
 * Some dimensions may have been added to the domain of the enclosing
 * pet_context after the value "val" was added.  We therefore need to
 * adjust the domain of "val" to match the range of data->ma (which
 * in turn matches the domain of the pet_context), by adding the missing
 * dimensions.
 */
static isl_stat preimage_domain_pair(__isl_take isl_id *key,
        __isl_take isl_pw_aff *val, void *user)
{
        struct pet_preimage_domain_data *data = user;
        int dim;
        isl_multi_aff *ma;

        ma = isl_multi_aff_copy(data->ma);

        dim = isl_pw_aff_dim(val, isl_dim_in);
        if (dim != isl_multi_aff_dim(data->ma, isl_dim_out)) {
                isl_space *space;
                isl_multi_aff *proj;
                space = isl_multi_aff_get_space(data->ma);
                space = isl_space_range(space);
                proj = pet_prefix_projection(space, dim);
                ma = isl_multi_aff_pullback_multi_aff(proj, ma);
        }

        val = isl_pw_aff_pullback_multi_aff(val, ma);
        data->assignments = isl_id_to_pw_aff_set(data->assignments, key, val);

        return isl_stat_ok;
}

/* Compute the preimage of "assignments" under the function represented by "ma".
 * In other words, plug in "ma" in the domains of the assigned values.
 */
static __isl_give isl_id_to_pw_aff *preimage_domain(
        __isl_take isl_id_to_pw_aff *assignments, __isl_keep isl_multi_aff *ma)
{
        struct pet_preimage_domain_data data = { ma };
        isl_ctx *ctx;

        ctx = isl_id_to_pw_aff_get_ctx(assignments);
        data.assignments = isl_id_to_pw_aff_alloc(ctx, 0);
        if (isl_id_to_pw_aff_foreach(assignments, &preimage_domain_pair,
                                        &data) < 0)
                data.assignments = isl_id_to_pw_aff_free(data.assignments);
        isl_id_to_pw_aff_free(assignments);

        return data.assignments;
}

/* Compute the preimage of "pc" under the function represented by "ma".
 * In other words, plug in "ma" in the domain of "pc".
 */
__isl_give pet_context *pet_context_preimage_domain(__isl_take pet_context *pc,
        __isl_keep isl_multi_aff *ma)
{
        pc = pet_context_cow(pc);
        if (!pc)
                return NULL;
        pc->domain = isl_set_preimage_multi_aff(pc->domain,
                                                isl_multi_aff_copy(ma));
        pc->assignments = preimage_domain(pc->assignments, ma);
        if (!pc->domain || !pc->assignments)
                return pet_context_free(pc);
        return pc;
}

/* Add the constraints of "set" to the domain of "pc".
 */
__isl_give pet_context *pet_context_intersect_domain(__isl_take pet_context *pc,
        __isl_take isl_set *set)
{
        pc = pet_context_cow(pc);
        if (!pc)
                goto error;
        pc->domain = isl_set_intersect(pc->domain, set);
        if (!pc->domain)
                return pet_context_free(pc);
        return pc;
error:
        pet_context_free(pc);
        isl_set_free(set);
        return NULL;
}

void pet_context_dump(__isl_keep pet_context *pc)
{
        if (!pc)
                return;
        fprintf(stderr, "domain: ");
        isl_set_dump(pc->domain);
        fprintf(stderr, "assignments: ");
        isl_id_to_pw_aff_dump(pc->assignments);
        fprintf(stderr, "nesting allowed: %d\n", pc->allow_nested);
}