pet_expr_filter: avoid introduction of constraints in index expression

[pet.git] / expr.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 "aff.h"
#include "array.h"
#include "expr.h"
#include "expr_arg.h"
#include "filter.h"
#include "nest.h"
#include "options.h"
#include "value_bounds.h"

#define ARRAY_SIZE(array) (sizeof(array)/sizeof(*array))

static char *type_str[] = {
        [pet_expr_access] = "access",
        [pet_expr_call] = "call",
        [pet_expr_cast] = "cast",
        [pet_expr_double] = "double",
        [pet_expr_int] = "int",
        [pet_expr_op] = "op",
};

static char *op_str[] = {
        [pet_op_add_assign] = "+=",
        [pet_op_sub_assign] = "-=",
        [pet_op_mul_assign] = "*=",
        [pet_op_div_assign] = "/=",
        [pet_op_assign] = "=",
        [pet_op_add] = "+",
        [pet_op_sub] = "-",
        [pet_op_mul] = "*",
        [pet_op_div] = "/",
        [pet_op_mod] = "%",
        [pet_op_shl] = "<<",
        [pet_op_shr] = ">>",
        [pet_op_eq] = "==",
        [pet_op_ne] = "!=",
        [pet_op_le] = "<=",
        [pet_op_ge] = ">=",
        [pet_op_lt] = "<",
        [pet_op_gt] = ">",
        [pet_op_minus] = "-",
        [pet_op_post_inc] = "++",
        [pet_op_post_dec] = "--",
        [pet_op_pre_inc] = "++",
        [pet_op_pre_dec] = "--",
        [pet_op_address_of] = "&",
        [pet_op_and] = "&",
        [pet_op_xor] = "^",
        [pet_op_or] = "|",
        [pet_op_not] = "~",
        [pet_op_land] = "&&",
        [pet_op_lor] = "||",
        [pet_op_lnot] = "!",
        [pet_op_cond] = "?:",
        [pet_op_assume] = "assume",
        [pet_op_kill] = "kill"
};

const char *pet_op_str(enum pet_op_type op)
{
        return op_str[op];
}

int pet_op_is_inc_dec(enum pet_op_type op)
{
        return op == pet_op_post_inc || op == pet_op_post_dec ||
            op == pet_op_pre_inc || op == pet_op_pre_dec;
}

const char *pet_type_str(enum pet_expr_type type)
{
        return type_str[type];
}

enum pet_op_type pet_str_op(const char *str)
{
        int i;

        for (i = 0; i < ARRAY_SIZE(op_str); ++i)
                if (!strcmp(op_str[i], str))
                        return i;

        return -1;
}

enum pet_expr_type pet_str_type(const char *str)
{
        int i;

        for (i = 0; i < ARRAY_SIZE(type_str); ++i)
                if (!strcmp(type_str[i], str))
                        return i;

        return -1;
}

/* Construct a pet_expr of the given type.
 */
__isl_give pet_expr *pet_expr_alloc(isl_ctx *ctx, enum pet_expr_type type)
{
        pet_expr *expr;

        expr = isl_calloc_type(ctx, struct pet_expr);
        if (!expr)
                return NULL;

        expr->ctx = ctx;
        isl_ctx_ref(ctx);
        expr->type = type;
        expr->ref = 1;

        return expr;
}

/* Construct an access pet_expr from an access relation and an index expression.
 * By default, it is considered to be a read access.
 */
__isl_give pet_expr *pet_expr_from_access_and_index( __isl_take isl_map *access,
        __isl_take isl_multi_pw_aff *index)
{
        isl_ctx *ctx = isl_map_get_ctx(access);
        pet_expr *expr;

        if (!index || !access)
                goto error;
        expr = pet_expr_alloc(ctx, pet_expr_access);
        if (!expr)
                goto error;

        expr->acc.access = access;
        expr->acc.index = index;
        expr->acc.read = 1;
        expr->acc.write = 0;

        return expr;
error:
        isl_map_free(access);
        isl_multi_pw_aff_free(index);
        return NULL;
}

/* Construct an access pet_expr from an index expression.
 * By default, the access is considered to be a read access.
 */
__isl_give pet_expr *pet_expr_from_index(__isl_take isl_multi_pw_aff *index)
{
        isl_map *access;

        access = isl_map_from_multi_pw_aff(isl_multi_pw_aff_copy(index));
        return pet_expr_from_access_and_index(access, index);
}

/* Extend the range of "access" with "n" dimensions, retaining
 * the tuple identifier on this range.
 *
 * If "access" represents a member access, then extend the range
 * of the member.
 */
static __isl_give isl_map *extend_range(__isl_take isl_map *access, int n)
{
        isl_id *id;

        id = isl_map_get_tuple_id(access, isl_dim_out);

        if (!isl_map_range_is_wrapping(access)) {
                access = isl_map_add_dims(access, isl_dim_out, n);
        } else {
                isl_map *domain;

                domain = isl_map_copy(access);
                domain = isl_map_range_factor_domain(domain);
                access = isl_map_range_factor_range(access);
                access = extend_range(access, n);
                access = isl_map_range_product(domain, access);
        }

        access = isl_map_set_tuple_id(access, isl_dim_out, id);

        return access;
}

/* Finalize the construction of an access expression by setting
 * the depth of the accessed array.
 *
 * The index expression may have been updated by
 * pet_expr_access_subscript and/or pet_expr_access_member
 * without the access relation having been updated accordingly.
 * We perform this update here, taking into account the depth
 * of the accessed array.
 *
 * If the number of indices is smaller than the depth of the array,
 * then we assume that all elements of the remaining dimensions
 * are accessed.
 */
__isl_give pet_expr *pet_expr_access_set_depth(__isl_take pet_expr *expr,
        int depth)
{
        isl_map *access;
        int dim;

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

        access = isl_map_from_multi_pw_aff(pet_expr_access_get_index(expr));
        if (!access)
                return pet_expr_free(expr);

        dim = isl_map_dim(access, isl_dim_out);
        if (dim > depth)
                isl_die(isl_map_get_ctx(access), isl_error_internal,
                        "number of indices greater than depth",
                        access = isl_map_free(access));

        if (dim != depth)
                access = extend_range(access, depth - dim);

        return pet_expr_access_set_access(expr, access);
}

/* Construct a pet_expr that kills the elements specified by
 * the index expression "index" and the access relation "access".
 */
__isl_give pet_expr *pet_expr_kill_from_access_and_index(
        __isl_take isl_map *access, __isl_take isl_multi_pw_aff *index)
{
        pet_expr *expr;

        if (!access || !index)
                goto error;

        expr = pet_expr_from_access_and_index(access, index);
        expr = pet_expr_access_set_read(expr, 0);
        return pet_expr_new_unary(pet_op_kill, expr);
error:
        isl_map_free(access);
        isl_multi_pw_aff_free(index);
        return NULL;
}

/* Construct a unary pet_expr that performs "op" on "arg".
 */
__isl_give pet_expr *pet_expr_new_unary(enum pet_op_type op,
        __isl_take pet_expr *arg)
{
        isl_ctx *ctx;
        pet_expr *expr;

        if (!arg)
                return NULL;
        ctx = pet_expr_get_ctx(arg);
        expr = pet_expr_alloc(ctx, pet_expr_op);
        expr = pet_expr_set_n_arg(expr, 1);
        if (!expr)
                goto error;

        expr->op = op;
        expr->args[pet_un_arg] = arg;

        return expr;
error:
        pet_expr_free(arg);
        return NULL;
}

/* Construct a binary pet_expr that performs "op" on "lhs" and "rhs",
 * where the result is represented using a type of "type_size" bits
 * (may be zero if unknown or if the type is not an integer).
 */
__isl_give pet_expr *pet_expr_new_binary(int type_size, enum pet_op_type op,
        __isl_take pet_expr *lhs, __isl_take pet_expr *rhs)
{
        isl_ctx *ctx;
        pet_expr *expr;

        if (!lhs || !rhs)
                goto error;
        ctx = pet_expr_get_ctx(lhs);
        expr = pet_expr_alloc(ctx, pet_expr_op);
        expr = pet_expr_set_n_arg(expr, 2);
        if (!expr)
                goto error;

        expr->op = op;
        expr->type_size = type_size;
        expr->args[pet_bin_lhs] = lhs;
        expr->args[pet_bin_rhs] = rhs;

        return expr;
error:
        pet_expr_free(lhs);
        pet_expr_free(rhs);
        return NULL;
}

/* Construct a ternary pet_expr that performs "cond" ? "lhs" : "rhs".
 */
__isl_give pet_expr *pet_expr_new_ternary(__isl_take pet_expr *cond,
        __isl_take pet_expr *lhs, __isl_take pet_expr *rhs)
{
        isl_ctx *ctx;
        pet_expr *expr;

        if (!cond || !lhs || !rhs)
                goto error;
        ctx = pet_expr_get_ctx(cond);
        expr = pet_expr_alloc(ctx, pet_expr_op);
        expr = pet_expr_set_n_arg(expr, 3);
        if (!expr)
                goto error;

        expr->op = pet_op_cond;
        expr->args[pet_ter_cond] = cond;
        expr->args[pet_ter_true] = lhs;
        expr->args[pet_ter_false] = rhs;

        return expr;
error:
        pet_expr_free(cond);
        pet_expr_free(lhs);
        pet_expr_free(rhs);
        return NULL;
}

/* Construct a call pet_expr that calls function "name" with "n_arg"
 * arguments.  The caller is responsible for filling in the arguments.
 */
__isl_give pet_expr *pet_expr_new_call(isl_ctx *ctx, const char *name,
        unsigned n_arg)
{
        pet_expr *expr;

        expr = pet_expr_alloc(ctx, pet_expr_call);
        expr = pet_expr_set_n_arg(expr, n_arg);
        if (!expr)
                return NULL;

        expr->name = strdup(name);
        if (!expr->name)
                return pet_expr_free(expr);

        return expr;
}

/* Construct a pet_expr that represents the cast of "arg" to "type_name".
 */
__isl_give pet_expr *pet_expr_new_cast(const char *type_name,
        __isl_take pet_expr *arg)
{
        isl_ctx *ctx;
        pet_expr *expr;

        if (!arg)
                return NULL;

        ctx = pet_expr_get_ctx(arg);
        expr = pet_expr_alloc(ctx, pet_expr_cast);
        expr = pet_expr_set_n_arg(expr, 1);
        if (!expr)
                goto error;

        expr->type_name = strdup(type_name);
        if (!expr->type_name)
                goto error;

        expr->args[0] = arg;

        return expr;
error:
        pet_expr_free(arg);
        pet_expr_free(expr);
        return NULL;
}

/* Construct a pet_expr that represents the double "d".
 */
__isl_give pet_expr *pet_expr_new_double(isl_ctx *ctx,
        double val, const char *s)
{
        pet_expr *expr;

        expr = pet_expr_alloc(ctx, pet_expr_double);
        if (!expr)
                return NULL;

        expr->d.val = val;
        expr->d.s = strdup(s);
        if (!expr->d.s)
                return pet_expr_free(expr);

        return expr;
}

/* Construct a pet_expr that represents the integer value "v".
 */
__isl_give pet_expr *pet_expr_new_int(__isl_take isl_val *v)
{
        isl_ctx *ctx;
        pet_expr *expr;

        if (!v)
                return NULL;

        ctx = isl_val_get_ctx(v);
        expr = pet_expr_alloc(ctx, pet_expr_int);
        if (!expr)
                goto error;

        expr->i = v;

        return expr;
error:
        isl_val_free(v);
        return NULL;
}

static __isl_give pet_expr *pet_expr_dup(__isl_keep pet_expr *expr)
{
        int i;
        pet_expr *dup;

        if (!expr)
                return NULL;

        dup = pet_expr_alloc(expr->ctx, expr->type);
        dup = pet_expr_set_type_size(dup, expr->type_size);
        dup = pet_expr_set_n_arg(dup, expr->n_arg);
        for (i = 0; i < expr->n_arg; ++i)
                dup = pet_expr_set_arg(dup, i, pet_expr_copy(expr->args[i]));

        switch (expr->type) {
        case pet_expr_access:
                if (expr->acc.ref_id)
                        dup = pet_expr_access_set_ref_id(dup,
                                                isl_id_copy(expr->acc.ref_id));
                dup = pet_expr_access_set_access(dup,
                                                isl_map_copy(expr->acc.access));
                dup = pet_expr_access_set_index(dup,
                                        isl_multi_pw_aff_copy(expr->acc.index));
                dup = pet_expr_access_set_read(dup, expr->acc.read);
                dup = pet_expr_access_set_write(dup, expr->acc.write);
                break;
        case pet_expr_call:
                dup = pet_expr_call_set_name(dup, expr->name);
                break;
        case pet_expr_cast:
                dup = pet_expr_cast_set_type_name(dup, expr->type_name);
                break;
        case pet_expr_double:
                dup = pet_expr_double_set(dup, expr->d.val, expr->d.s);
                break;
        case pet_expr_int:
                dup = pet_expr_int_set_val(dup, isl_val_copy(expr->i));
                break;
        case pet_expr_op:
                dup = pet_expr_op_set_type(dup, expr->op);
                break;
        case pet_expr_error:
                dup = pet_expr_free(dup);
                break;
        }

        return dup;
}

__isl_give pet_expr *pet_expr_cow(__isl_take pet_expr *expr)
{
        if (!expr)
                return NULL;

        if (expr->ref == 1)
                return expr;
        expr->ref--;
        return pet_expr_dup(expr);
}

__isl_null pet_expr *pet_expr_free(__isl_take pet_expr *expr)
{
        int i;

        if (!expr)
                return NULL;
        if (--expr->ref > 0)
                return NULL;

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

        switch (expr->type) {
        case pet_expr_access:
                isl_id_free(expr->acc.ref_id);
                isl_map_free(expr->acc.access);
                isl_multi_pw_aff_free(expr->acc.index);
                break;
        case pet_expr_call:
                free(expr->name);
                break;
        case pet_expr_cast:
                free(expr->type_name);
                break;
        case pet_expr_double:
                free(expr->d.s);
                break;
        case pet_expr_int:
                isl_val_free(expr->i);
                break;
        case pet_expr_op:
        case pet_expr_error:
                break;
        }

        isl_ctx_deref(expr->ctx);
        free(expr);
        return NULL;
}

/* Return an additional reference to "expr".
 */
__isl_give pet_expr *pet_expr_copy(__isl_keep pet_expr *expr)
{
        if (!expr)
                return NULL;

        expr->ref++;
        return expr;
}

/* Return the isl_ctx in which "expr" was created.
 */
isl_ctx *pet_expr_get_ctx(__isl_keep pet_expr *expr)
{
        return expr ? expr->ctx : NULL;
}

/* Return the type of "expr".
 */
enum pet_expr_type pet_expr_get_type(__isl_keep pet_expr *expr)
{
        if (!expr)
                return pet_expr_error;
        return expr->type;
}

/* Return the number of arguments of "expr".
 */
int pet_expr_get_n_arg(__isl_keep pet_expr *expr)
{
        if (!expr)
                return -1;

        return expr->n_arg;
}

/* Set the number of arguments of "expr" to "n".
 *
 * If "expr" originally had more arguments, then remove the extra arguments.
 * If "expr" originally had fewer arguments, then create space for
 * the extra arguments ans initialize them to NULL.
 */
__isl_give pet_expr *pet_expr_set_n_arg(__isl_take pet_expr *expr, int n)
{
        int i;
        pet_expr **args;

        if (!expr)
                return NULL;
        if (expr->n_arg == n)
                return expr;
        expr = pet_expr_cow(expr);
        if (!expr)
                return NULL;

        if (n < expr->n_arg) {
                for (i = n; i < expr->n_arg; ++i)
                        pet_expr_free(expr->args[i]);
                expr->n_arg = n;
                return expr;
        }

        args = isl_realloc_array(expr->ctx, expr->args, pet_expr *, n);
        if (!args)
                return pet_expr_free(expr);
        expr->args = args;
        for (i = expr->n_arg; i < n; ++i)
                expr->args[i] = NULL;
        expr->n_arg = n;

        return expr;
}

/* Return the argument of "expr" at position "pos".
 */
__isl_give pet_expr *pet_expr_get_arg(__isl_keep pet_expr *expr, int pos)
{
        if (!expr)
                return NULL;
        if (pos < 0 || pos >= expr->n_arg)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "position out of bounds", return NULL);

        return pet_expr_copy(expr->args[pos]);
}

/* Replace the argument of "expr" at position "pos" by "arg".
 */
__isl_give pet_expr *pet_expr_set_arg(__isl_take pet_expr *expr, int pos,
        __isl_take pet_expr *arg)
{
        if (!expr || !arg)
                goto error;
        if (pos < 0 || pos >= expr->n_arg)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "position out of bounds", goto error);
        if (expr->args[pos] == arg) {
                pet_expr_free(arg);
                return expr;
        }

        expr = pet_expr_cow(expr);
        if (!expr)
                goto error;

        pet_expr_free(expr->args[pos]);
        expr->args[pos] = arg;

        return expr;
error:
        pet_expr_free(expr);
        pet_expr_free(arg);
        return NULL;
}

/* Does "expr" perform a comparison operation?
 */
int pet_expr_is_comparison(__isl_keep pet_expr *expr)
{
        if (!expr)
                return -1;
        if (expr->type != pet_expr_op)
                return 0;
        switch (expr->op) {
        case pet_op_eq:
        case pet_op_ne:
        case pet_op_le:
        case pet_op_ge:
        case pet_op_lt:
        case pet_op_gt:
                return 1;
        default:
                return 0;
        }
}

/* Does "expr" perform a boolean operation?
 */
int pet_expr_is_boolean(__isl_keep pet_expr *expr)
{
        if (!expr)
                return -1;
        if (expr->type != pet_expr_op)
                return 0;
        switch (expr->op) {
        case pet_op_land:
        case pet_op_lor:
        case pet_op_lnot:
                return 1;
        default:
                return 0;
        }
}

/* Is "expr" an assume statement?
 */
int pet_expr_is_assume(__isl_keep pet_expr *expr)
{
        if (!expr)
                return -1;
        if (expr->type != pet_expr_op)
                return 0;
        return expr->op == pet_op_assume;
}

/* Does "expr" perform a min operation?
 */
int pet_expr_is_min(__isl_keep pet_expr *expr)
{
        if (!expr)
                return -1;
        if (expr->type != pet_expr_call)
                return 0;
        if (expr->n_arg != 2)
                return 0;
        if (strcmp(expr->name, "min") != 0)
                return 0;
        return 1;
}

/* Does "expr" perform a max operation?
 */
int pet_expr_is_max(__isl_keep pet_expr *expr)
{
        if (!expr)
                return -1;
        if (expr->type != pet_expr_call)
                return 0;
        if (expr->n_arg != 2)
                return 0;
        if (strcmp(expr->name, "max") != 0)
                return 0;
        return 1;
}

/* Does "expr" represent an access to an unnamed space, i.e.,
 * does it represent an affine expression?
 */
int pet_expr_is_affine(__isl_keep pet_expr *expr)
{
        int has_id;

        if (!expr)
                return -1;
        if (expr->type != pet_expr_access)
                return 0;

        has_id = isl_map_has_tuple_id(expr->acc.access, isl_dim_out);
        if (has_id < 0)
                return -1;

        return !has_id;
}

/* Does "expr" represent an access to a scalar, i.e., a zero-dimensional array,
 * not part of any struct?
 */
int pet_expr_is_scalar_access(__isl_keep pet_expr *expr)
{
        if (!expr)
                return -1;
        if (expr->type != pet_expr_access)
                return 0;
        if (isl_map_range_is_wrapping(expr->acc.access))
                return 0;

        return isl_map_dim(expr->acc.access, isl_dim_out) == 0;
}

/* Return 1 if the two pet_exprs are equivalent.
 */
int pet_expr_is_equal(__isl_keep pet_expr *expr1, __isl_keep pet_expr *expr2)
{
        int i;

        if (!expr1 || !expr2)
                return 0;

        if (expr1->type != expr2->type)
                return 0;
        if (expr1->n_arg != expr2->n_arg)
                return 0;
        for (i = 0; i < expr1->n_arg; ++i)
                if (!pet_expr_is_equal(expr1->args[i], expr2->args[i]))
                        return 0;
        switch (expr1->type) {
        case pet_expr_error:
                return -1;
        case pet_expr_double:
                if (strcmp(expr1->d.s, expr2->d.s))
                        return 0;
                if (expr1->d.val != expr2->d.val)
                        return 0;
                break;
        case pet_expr_int:
                if (!isl_val_eq(expr1->i, expr2->i))
                        return 0;
                break;
        case pet_expr_access:
                if (expr1->acc.read != expr2->acc.read)
                        return 0;
                if (expr1->acc.write != expr2->acc.write)
                        return 0;
                if (expr1->acc.ref_id != expr2->acc.ref_id)
                        return 0;
                if (!expr1->acc.access || !expr2->acc.access)
                        return 0;
                if (!isl_map_is_equal(expr1->acc.access, expr2->acc.access))
                        return 0;
                if (!expr1->acc.index || !expr2->acc.index)
                        return 0;
                if (!isl_multi_pw_aff_plain_is_equal(expr1->acc.index,
                                                        expr2->acc.index))
                        return 0;
                break;
        case pet_expr_op:
                if (expr1->op != expr2->op)
                        return 0;
                break;
        case pet_expr_call:
                if (strcmp(expr1->name, expr2->name))
                        return 0;
                break;
        case pet_expr_cast:
                if (strcmp(expr1->type_name, expr2->type_name))
                        return 0;
                break;
        }

        return 1;
}

/* Does the access expression "expr" read the accessed elements?
 */
int pet_expr_access_is_read(__isl_keep pet_expr *expr)
{
        if (!expr)
                return -1;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", return -1);

        return expr->acc.read;
}

/* Does the access expression "expr" write to the accessed elements?
 */
int pet_expr_access_is_write(__isl_keep pet_expr *expr)
{
        if (!expr)
                return -1;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", return -1);

        return expr->acc.write;
}

/* Return the identifier of the array accessed by "expr".
 *
 * If "expr" represents a member access, then return the identifier
 * of the outer structure array.
 */
__isl_give isl_id *pet_expr_access_get_id(__isl_keep pet_expr *expr)
{
        if (!expr)
                return NULL;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", return NULL);

        if (isl_map_range_is_wrapping(expr->acc.access)) {
                isl_space *space;
                isl_id *id;

                space = isl_map_get_space(expr->acc.access);
                space = isl_space_range(space);
                while (space && isl_space_is_wrapping(space))
                        space = isl_space_domain(isl_space_unwrap(space));
                id = isl_space_get_tuple_id(space, isl_dim_set);
                isl_space_free(space);

                return id;
        }

        return isl_map_get_tuple_id(expr->acc.access, isl_dim_out);
}

/* Return the parameter space of "expr".
 */
__isl_give isl_space *pet_expr_access_get_parameter_space(
        __isl_keep pet_expr *expr)
{
        isl_space *space;

        if (!expr)
                return NULL;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", return NULL);

        space = isl_multi_pw_aff_get_space(expr->acc.index);
        space = isl_space_params(space);

        return space;
}

/* Return the domain space of "expr", without the arguments (if any).
 */
__isl_give isl_space *pet_expr_access_get_domain_space(
        __isl_keep pet_expr *expr)
{
        isl_space *space;

        if (!expr)
                return NULL;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", return NULL);

        space = isl_multi_pw_aff_get_space(expr->acc.index);
        space = isl_space_domain(space);
        if (isl_space_is_wrapping(space))
                space = isl_space_domain(isl_space_unwrap(space));

        return space;
}

/* Return the space of the data accessed by "expr".
 */
__isl_give isl_space *pet_expr_access_get_data_space(__isl_keep pet_expr *expr)
{
        isl_space *space;

        if (!expr)
                return NULL;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", return NULL);

        space = isl_multi_pw_aff_get_space(expr->acc.index);
        space = isl_space_range(space);

        return space;
}

/* Modify all expressions of type pet_expr_access in "expr"
 * by calling "fn" on them.
 */
__isl_give pet_expr *pet_expr_map_access(__isl_take pet_expr *expr,
        __isl_give pet_expr *(*fn)(__isl_take pet_expr *expr, void *user),
        void *user)
{
        int i, n;

        n = pet_expr_get_n_arg(expr);
        for (i = 0; i < n; ++i) {
                pet_expr *arg = pet_expr_get_arg(expr, i);
                arg = pet_expr_map_access(arg, fn, user);
                expr = pet_expr_set_arg(expr, i, arg);
        }

        if (!expr)
                return NULL;

        if (expr->type == pet_expr_access)
                expr = fn(expr, user);

        return expr;
}

/* Call "fn" on each of the subexpressions of "expr" of type "type".
 *
 * Return -1 on error (where fn returning a negative value is treated as
 * an error).
 * Otherwise return 0.
 */
int pet_expr_foreach_expr_of_type(__isl_keep pet_expr *expr,
        enum pet_expr_type type,
        int (*fn)(__isl_keep pet_expr *expr, void *user), void *user)
{
        int i;

        if (!expr)
                return -1;

        for (i = 0; i < expr->n_arg; ++i)
                if (pet_expr_foreach_expr_of_type(expr->args[i],
                                                    type, fn, user) < 0)
                        return -1;

        if (expr->type == type)
                return fn(expr, user);

        return 0;
}

/* Call "fn" on each of the subexpressions of "expr" of type pet_expr_access.
 *
 * Return -1 on error (where fn returning a negative value is treated as
 * an error).
 * Otherwise return 0.
 */
int pet_expr_foreach_access_expr(__isl_keep pet_expr *expr,
        int (*fn)(__isl_keep pet_expr *expr, void *user), void *user)
{
        return pet_expr_foreach_expr_of_type(expr, pet_expr_access, fn, user);
}

/* Call "fn" on each of the subexpressions of "expr" of type pet_expr_call.
 *
 * Return -1 on error (where fn returning a negative value is treated as
 * an error).
 * Otherwise return 0.
 */
int pet_expr_foreach_call_expr(__isl_keep pet_expr *expr,
        int (*fn)(__isl_keep pet_expr *expr, void *user), void *user)
{
        return pet_expr_foreach_expr_of_type(expr, pet_expr_call, fn, user);
}

/* Internal data structure for pet_expr_writes.
 * "id" is the identifier that we are looking for.
 * "found" is set if we have found the identifier being written to.
 */
struct pet_expr_writes_data {
        isl_id *id;
        int found;
};

/* Given an access expression, check if it writes to data->id.
 * If so, set data->found and abort the search.
 */
static int writes(__isl_keep pet_expr *expr, void *user)
{
        struct pet_expr_writes_data *data = user;
        isl_id *write_id;

        if (!expr->acc.write)
                return 0;
        if (pet_expr_is_affine(expr))
                return 0;

        write_id = pet_expr_access_get_id(expr);
        isl_id_free(write_id);

        if (!write_id)
                return -1;

        if (write_id != data->id)
                return 0;

        data->found = 1;
        return -1;
}

/* Does expression "expr" write to "id"?
 */
int pet_expr_writes(__isl_keep pet_expr *expr, __isl_keep isl_id *id)
{
        struct pet_expr_writes_data data;

        data.id = id;
        data.found = 0;
        if (pet_expr_foreach_access_expr(expr, &writes, &data) < 0 &&
            !data.found)
                return -1;

        return data.found;
}

/* Move the "n" dimensions of "src_type" starting at "src_pos" of
 * index expression and access relation of "expr"
 * to dimensions of "dst_type" at "dst_pos".
 */
__isl_give pet_expr *pet_expr_access_move_dims(__isl_take pet_expr *expr,
        enum isl_dim_type dst_type, unsigned dst_pos,
        enum isl_dim_type src_type, unsigned src_pos, unsigned n)
{
        expr = pet_expr_cow(expr);
        if (!expr)
                return NULL;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access pet_expr", return pet_expr_free(expr));

        expr->acc.access = isl_map_move_dims(expr->acc.access,
                                dst_type, dst_pos, src_type, src_pos, n);
        expr->acc.index = isl_multi_pw_aff_move_dims(expr->acc.index,
                                dst_type, dst_pos, src_type, src_pos, n);
        if (!expr->acc.access || !expr->acc.index)
                return pet_expr_free(expr);

        return expr;
}

/* Replace the index expression and access relation of "expr"
 * by their preimages under the function represented by "ma".
 */
__isl_give pet_expr *pet_expr_access_pullback_multi_aff(
        __isl_take pet_expr *expr, __isl_take isl_multi_aff *ma)
{
        expr = pet_expr_cow(expr);
        if (!expr || !ma)
                goto error;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access pet_expr", goto error);

        expr->acc.access = isl_map_preimage_domain_multi_aff(expr->acc.access,
                                                isl_multi_aff_copy(ma));
        expr->acc.index = isl_multi_pw_aff_pullback_multi_aff(expr->acc.index,
                                                ma);
        if (!expr->acc.access || !expr->acc.index)
                return pet_expr_free(expr);

        return expr;
error:
        isl_multi_aff_free(ma);
        pet_expr_free(expr);
        return NULL;
}

/* Replace the index expression and access relation of "expr"
 * by their preimages under the function represented by "mpa".
 */
__isl_give pet_expr *pet_expr_access_pullback_multi_pw_aff(
        __isl_take pet_expr *expr, __isl_take isl_multi_pw_aff *mpa)
{
        expr = pet_expr_cow(expr);
        if (!expr || !mpa)
                goto error;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access pet_expr", goto error);

        expr->acc.access = isl_map_preimage_domain_multi_pw_aff(
                                expr->acc.access, isl_multi_pw_aff_copy(mpa));
        expr->acc.index = isl_multi_pw_aff_pullback_multi_pw_aff(
                                expr->acc.index, mpa);
        if (!expr->acc.access || !expr->acc.index)
                return pet_expr_free(expr);

        return expr;
error:
        isl_multi_pw_aff_free(mpa);
        pet_expr_free(expr);
        return NULL;
}

/* Return the access relation of access expression "expr".
 */
__isl_give isl_map *pet_expr_access_get_access(__isl_keep pet_expr *expr)
{
        if (!expr)
                return NULL;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", return NULL);

        return isl_map_copy(expr->acc.access);
}

/* Return the index expression of access expression "expr".
 */
__isl_give isl_multi_pw_aff *pet_expr_access_get_index(
        __isl_keep pet_expr *expr)
{
        if (!expr)
                return NULL;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", return NULL);

        return isl_multi_pw_aff_copy(expr->acc.index);
}

/* Align the parameters of expr->acc.index and expr->acc.access.
 */
__isl_give pet_expr *pet_expr_access_align_params(__isl_take pet_expr *expr)
{
        expr = pet_expr_cow(expr);
        if (!expr)
                return NULL;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", return pet_expr_free(expr));

        expr->acc.access = isl_map_align_params(expr->acc.access,
                                isl_multi_pw_aff_get_space(expr->acc.index));
        expr->acc.index = isl_multi_pw_aff_align_params(expr->acc.index,
                                isl_map_get_space(expr->acc.access));
        if (!expr->acc.access || !expr->acc.index)
                return pet_expr_free(expr);

        return expr;
}

/* Add extra conditions on the parameters to all access relations in "expr".
 *
 * The conditions are not added to the index expression.  Instead, they
 * are used to try and simplify the index expression.
 */
__isl_give pet_expr *pet_expr_restrict(__isl_take pet_expr *expr,
        __isl_take isl_set *cond)
{
        int i;

        expr = pet_expr_cow(expr);
        if (!expr)
                goto error;

        for (i = 0; i < expr->n_arg; ++i) {
                expr->args[i] = pet_expr_restrict(expr->args[i],
                                                        isl_set_copy(cond));
                if (!expr->args[i])
                        goto error;
        }

        if (expr->type == pet_expr_access) {
                expr->acc.access = isl_map_intersect_params(expr->acc.access,
                                                            isl_set_copy(cond));
                expr->acc.index = isl_multi_pw_aff_gist_params(
                                        expr->acc.index, isl_set_copy(cond));
                if (!expr->acc.access || !expr->acc.index)
                        goto error;
        }

        isl_set_free(cond);
        return expr;
error:
        isl_set_free(cond);
        return pet_expr_free(expr);
}

/* Modify the access relation and index expression
 * of the given access expression
 * based on the given iteration space transformation.
 * In particular, precompose the access relation and index expression
 * with the update function.
 *
 * If the access has any arguments then the domain of the access relation
 * is a wrapped mapping from the iteration space to the space of
 * argument values.  We only need to change the domain of this wrapped
 * mapping, so we extend the input transformation with an identity mapping
 * on the space of argument values.
 */
__isl_give pet_expr *pet_expr_access_update_domain(__isl_take pet_expr *expr,
        __isl_keep isl_multi_pw_aff *update)
{
        isl_space *space;

        expr = pet_expr_cow(expr);
        if (!expr)
                return NULL;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", return pet_expr_free(expr));

        update = isl_multi_pw_aff_copy(update);

        space = isl_map_get_space(expr->acc.access);
        space = isl_space_domain(space);
        if (!isl_space_is_wrapping(space))
                isl_space_free(space);
        else {
                isl_multi_pw_aff *id;
                space = isl_space_unwrap(space);
                space = isl_space_range(space);
                space = isl_space_map_from_set(space);
                id = isl_multi_pw_aff_identity(space);
                update = isl_multi_pw_aff_product(update, id);
        }

        expr->acc.access = isl_map_preimage_domain_multi_pw_aff(
                                            expr->acc.access,
                                            isl_multi_pw_aff_copy(update));
        expr->acc.index = isl_multi_pw_aff_pullback_multi_pw_aff(
                                            expr->acc.index, update);
        if (!expr->acc.access || !expr->acc.index)
                return pet_expr_free(expr);

        return expr;
}

static __isl_give pet_expr *update_domain(__isl_take pet_expr *expr, void *user)
{
        isl_multi_pw_aff *update = user;

        return pet_expr_access_update_domain(expr, update);
}

/* Modify all access relations in "expr" by precomposing them with
 * the given iteration space transformation.
 */
__isl_give pet_expr *pet_expr_update_domain(__isl_take pet_expr *expr,
        __isl_take isl_multi_pw_aff *update)
{
        expr = pet_expr_map_access(expr, &update_domain, update);
        isl_multi_pw_aff_free(update);
        return expr;
}

/* Add all parameters in "space" to the access relation and index expression
 * of "expr".
 */
static __isl_give pet_expr *align_params(__isl_take pet_expr *expr, void *user)
{
        isl_space *space = user;

        expr = pet_expr_cow(expr);
        if (!expr)
                return NULL;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", return pet_expr_free(expr));

        expr->acc.access = isl_map_align_params(expr->acc.access,
                                                isl_space_copy(space));
        expr->acc.index = isl_multi_pw_aff_align_params(expr->acc.index,
                                                isl_space_copy(space));
        if (!expr->acc.access || !expr->acc.index)
                return pet_expr_free(expr);

        return expr;
}

/* Add all parameters in "space" to all access relations and index expressions
 * in "expr".
 */
__isl_give pet_expr *pet_expr_align_params(__isl_take pet_expr *expr,
        __isl_take isl_space *space)
{
        expr = pet_expr_map_access(expr, &align_params, space);
        isl_space_free(space);
        return expr;
}

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

        if (!test)
                return pet_expr_free(expr);
        expr = pet_expr_cow(expr);
        if (!expr)
                return NULL;

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

        return expr;
}

/* Make the expression "expr" depend on the value of "test"
 * being equal to "satisfied".
 *
 * If "test" is an affine expression, we simply add the conditions
 * on the expression having the value "satisfied" to all access relations
 * and index expressions.
 *
 * Otherwise, we add a filter to "expr" (which is then assumed to be
 * an access expression) corresponding to "test" being equal to "satisfied".
 */
__isl_give pet_expr *pet_expr_filter(__isl_take pet_expr *expr,
        __isl_take isl_multi_pw_aff *test, int satisfied)
{
        isl_id *id;
        isl_ctx *ctx;
        isl_space *space;
        isl_pw_multi_aff *pma;

        expr = pet_expr_cow(expr);
        if (!expr || !test)
                goto error;

        if (!isl_multi_pw_aff_has_tuple_id(test, isl_dim_out)) {
                isl_pw_aff *pa;
                isl_set *cond;

                pa = isl_multi_pw_aff_get_pw_aff(test, 0);
                isl_multi_pw_aff_free(test);
                if (satisfied)
                        cond = isl_pw_aff_non_zero_set(pa);
                else
                        cond = isl_pw_aff_zero_set(pa);
                return pet_expr_restrict(expr, isl_set_params(cond));
        }

        ctx = isl_multi_pw_aff_get_ctx(test);
        if (expr->type != pet_expr_access)
                isl_die(ctx, isl_error_invalid,
                        "can only filter access expressions", goto error);

        space = isl_space_domain(isl_map_get_space(expr->acc.access));
        id = isl_multi_pw_aff_get_tuple_id(test, isl_dim_out);
        pma = pet_filter_insert_pma(space, id, satisfied);

        expr->acc.access = isl_map_preimage_domain_pw_multi_aff(
                                                expr->acc.access,
                                                isl_pw_multi_aff_copy(pma));
        pma = isl_pw_multi_aff_gist(pma,
                        isl_pw_multi_aff_domain(isl_pw_multi_aff_copy(pma)));
        expr->acc.index = isl_multi_pw_aff_pullback_pw_multi_aff(
                                                        expr->acc.index, pma);
        if (!expr->acc.access || !expr->acc.index)
                goto error;

        expr = insert_access_arg(expr, test);

        isl_multi_pw_aff_free(test);
        return expr;
error:
        isl_multi_pw_aff_free(test);
        return pet_expr_free(expr);
}

/* Check if the given index expression accesses a (0D) array that corresponds
 * to one of the parameters in "space".  If so, replace the array access
 * by an access to the set of integers with as index (and value)
 * that parameter.
 */
static __isl_give isl_multi_pw_aff *index_detect_parameter(
        __isl_take isl_multi_pw_aff *index, __isl_take isl_space *space)
{
        isl_local_space *ls;
        isl_id *array_id = NULL;
        isl_aff *aff;
        int pos = -1;

        if (isl_multi_pw_aff_has_tuple_id(index, isl_dim_out)) {
                array_id = isl_multi_pw_aff_get_tuple_id(index, isl_dim_out);
                pos = isl_space_find_dim_by_id(space, isl_dim_param, array_id);
        }
        isl_space_free(space);

        if (pos < 0) {
                isl_id_free(array_id);
                return index;
        }

        space = isl_multi_pw_aff_get_domain_space(index);
        isl_multi_pw_aff_free(index);

        pos = isl_space_find_dim_by_id(space, isl_dim_param, array_id);
        if (pos < 0) {
                space = isl_space_insert_dims(space, isl_dim_param, 0, 1);
                space = isl_space_set_dim_id(space, isl_dim_param, 0, array_id);
                pos = 0;
        } else
                isl_id_free(array_id);

        ls = isl_local_space_from_space(space);
        aff = isl_aff_var_on_domain(ls, isl_dim_param, pos);
        index = isl_multi_pw_aff_from_pw_aff(isl_pw_aff_from_aff(aff));

        return index;
}

/* Check if the given access relation accesses a (0D) array that corresponds
 * to one of the parameters in "space".  If so, replace the array access
 * by an access to the set of integers with as index (and value)
 * that parameter.
 */
static __isl_give isl_map *access_detect_parameter(__isl_take isl_map *access,
        __isl_take isl_space *space)
{
        isl_id *array_id = NULL;
        int pos = -1;

        if (isl_map_has_tuple_id(access, isl_dim_out)) {
                array_id = isl_map_get_tuple_id(access, isl_dim_out);
                pos = isl_space_find_dim_by_id(space, isl_dim_param, array_id);
        }
        isl_space_free(space);

        if (pos < 0) {
                isl_id_free(array_id);
                return access;
        }

        pos = isl_map_find_dim_by_id(access, isl_dim_param, array_id);
        if (pos < 0) {
                access = isl_map_insert_dims(access, isl_dim_param, 0, 1);
                access = isl_map_set_dim_id(access, isl_dim_param, 0, array_id);
                pos = 0;
        } else
                isl_id_free(array_id);

        access = isl_map_insert_dims(access, isl_dim_out, 0, 1);
        access = isl_map_equate(access, isl_dim_param, pos, isl_dim_out, 0);

        return access;
}

/* If "expr" accesses a (0D) array that corresponds to one of the parameters
 * in "space" then replace it by a value equal to the corresponding parameter.
 */
static __isl_give pet_expr *detect_parameter_accesses(__isl_take pet_expr *expr,
        void *user)
{
        isl_space *space = user;

        expr = pet_expr_cow(expr);
        if (!expr)
                return NULL;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", return pet_expr_free(expr));

        expr->acc.access = access_detect_parameter(expr->acc.access,
                                                isl_space_copy(space));
        expr->acc.index = index_detect_parameter(expr->acc.index,
                                                isl_space_copy(space));
        if (!expr->acc.access || !expr->acc.index)
                return pet_expr_free(expr);

        return expr;
}

/* Replace all accesses to (0D) arrays that correspond to one of the parameters
 * in "space" by a value equal to the corresponding parameter.
 */
__isl_give pet_expr *pet_expr_detect_parameter_accesses(
        __isl_take pet_expr *expr, __isl_take isl_space *space)
{
        expr = pet_expr_map_access(expr, &detect_parameter_accesses, space);
        isl_space_free(space);
        return expr;
}

/* Add a reference identifier to access expression "expr".
 * "user" points to an integer that contains the sequence number
 * of the next reference.
 */
static __isl_give pet_expr *access_add_ref_id(__isl_take pet_expr *expr,
        void *user)
{
        isl_ctx *ctx;
        char name[50];
        int *n_ref = user;

        expr = pet_expr_cow(expr);
        if (!expr)
                return expr;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", return pet_expr_free(expr));

        ctx = isl_map_get_ctx(expr->acc.access);
        snprintf(name, sizeof(name), "__pet_ref_%d", (*n_ref)++);
        expr->acc.ref_id = isl_id_alloc(ctx, name, NULL);
        if (!expr->acc.ref_id)
                return pet_expr_free(expr);

        return expr;
}

__isl_give pet_expr *pet_expr_add_ref_ids(__isl_take pet_expr *expr, int *n_ref)
{
        return pet_expr_map_access(expr, &access_add_ref_id, n_ref);
}

/* Reset the user pointer on all parameter and tuple ids in
 * the access relation and the index expressions
 * of the access expression "expr".
 */
static __isl_give pet_expr *access_anonymize(__isl_take pet_expr *expr,
        void *user)
{
        expr = pet_expr_cow(expr);
        if (!expr)
                return expr;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", return pet_expr_free(expr));

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

        return expr;
}

__isl_give pet_expr *pet_expr_anonymize(__isl_take pet_expr *expr)
{
        return pet_expr_map_access(expr, &access_anonymize, NULL);
}

/* Data used in access_gist() callback.
 */
struct pet_access_gist_data {
        isl_set *domain;
        isl_union_map *value_bounds;
};

/* Given an expression "expr" of type pet_expr_access, compute
 * the gist of the associated access relation and index expression
 * with respect to data->domain and the bounds on the values of the arguments
 * of the expression.
 *
 * The arguments of "expr" have been gisted right before "expr" itself
 * is gisted.  The gisted arguments may have become equal where before
 * they may not have been (obviously) equal.  We therefore take
 * the opportunity to remove duplicate arguments here.
 */
static __isl_give pet_expr *access_gist(__isl_take pet_expr *expr, void *user)
{
        struct pet_access_gist_data *data = user;
        isl_set *domain;

        expr = pet_expr_remove_duplicate_args(expr);
        expr = pet_expr_cow(expr);
        if (!expr)
                return expr;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", return pet_expr_free(expr));

        domain = isl_set_copy(data->domain);
        if (expr->n_arg > 0)
                domain = pet_value_bounds_apply(domain, expr->n_arg, expr->args,
                                                data->value_bounds);

        expr->acc.access = isl_map_gist_domain(expr->acc.access,
                                                isl_set_copy(domain));
        expr->acc.index = isl_multi_pw_aff_gist(expr->acc.index, domain);
        if (!expr->acc.access || !expr->acc.index)
                return pet_expr_free(expr);

        return expr;
}

__isl_give pet_expr *pet_expr_gist(__isl_take pet_expr *expr,
        __isl_keep isl_set *context, __isl_keep isl_union_map *value_bounds)
{
        struct pet_access_gist_data data = { context, value_bounds };

        return pet_expr_map_access(expr, &access_gist, &data);
}

/* Mark "expr" as a read dependening on "read".
 */
__isl_give pet_expr *pet_expr_access_set_read(__isl_take pet_expr *expr,
        int read)
{
        if (!expr)
                return pet_expr_free(expr);
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", return pet_expr_free(expr));
        if (expr->acc.read == read)
                return expr;
        expr = pet_expr_cow(expr);
        if (!expr)
                return NULL;
        expr->acc.read = read;

        return expr;
}

/* Mark "expr" as a write dependening on "write".
 */
__isl_give pet_expr *pet_expr_access_set_write(__isl_take pet_expr *expr,
        int write)
{
        if (!expr)
                return pet_expr_free(expr);
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", return pet_expr_free(expr));
        if (expr->acc.write == write)
                return expr;
        expr = pet_expr_cow(expr);
        if (!expr)
                return NULL;
        expr->acc.write = write;

        return expr;
}

/* Replace the access relation of "expr" by "access".
 */
__isl_give pet_expr *pet_expr_access_set_access(__isl_take pet_expr *expr,
        __isl_take isl_map *access)
{
        expr = pet_expr_cow(expr);
        if (!expr || !access)
                goto error;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", goto error);
        isl_map_free(expr->acc.access);
        expr->acc.access = access;

        return expr;
error:
        isl_map_free(access);
        pet_expr_free(expr);
        return NULL;
}

/* Replace the index expression of "expr" by "index".
 */
__isl_give pet_expr *pet_expr_access_set_index(__isl_take pet_expr *expr,
        __isl_take isl_multi_pw_aff *index)
{
        expr = pet_expr_cow(expr);
        if (!expr || !index)
                goto error;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", goto error);
        isl_multi_pw_aff_free(expr->acc.index);
        expr->acc.index = index;

        return expr;
error:
        isl_multi_pw_aff_free(index);
        pet_expr_free(expr);
        return NULL;
}

/* Return the reference identifier of access expression "expr".
 */
__isl_give isl_id *pet_expr_access_get_ref_id(__isl_keep pet_expr *expr)
{
        if (!expr)
                return NULL;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", return NULL);

        return isl_id_copy(expr->acc.ref_id);
}

/* Replace the reference identifier of access expression "expr" by "ref_id".
 */
__isl_give pet_expr *pet_expr_access_set_ref_id(__isl_take pet_expr *expr,
        __isl_take isl_id *ref_id)
{
        expr = pet_expr_cow(expr);
        if (!expr || !ref_id)
                goto error;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", goto error);
        isl_id_free(expr->acc.ref_id);
        expr->acc.ref_id = ref_id;

        return expr;
error:
        isl_id_free(ref_id);
        pet_expr_free(expr);
        return NULL;
}

/* Tag the access relation "access" with "id".
 * That is, insert the id as the range of a wrapped relation
 * in the domain of "access".
 *
 * If "access" is of the form
 *
 *      D[i] -> A[a]
 *
 * then the result is of the form
 *
 *      [D[i] -> id[]] -> A[a]
 */
__isl_give isl_map *pet_expr_tag_access(__isl_keep pet_expr *expr,
        __isl_take isl_map *access)
{
        isl_space *space;
        isl_map *add_tag;
        isl_id *id;

        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression",
                        return isl_map_free(access));

        id = isl_id_copy(expr->acc.ref_id);
        space = isl_space_range(isl_map_get_space(access));
        space = isl_space_from_range(space);
        space = isl_space_set_tuple_id(space, isl_dim_in, id);
        add_tag = isl_map_universe(space);
        access = isl_map_domain_product(access, add_tag);

        return access;
}

/* Return the relation mapping pairs of domain iterations and argument
 * values to the corresponding accessed data elements.
 */
__isl_give isl_map *pet_expr_access_get_dependent_access(
        __isl_keep pet_expr *expr)
{
        if (!expr)
                return NULL;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", return NULL);

        return isl_map_copy(expr->acc.access);
}

/* Return the relation mapping domain iterations to all possibly
 * accessed data elements.
 * In particular, take the access relation and project out the values
 * of the arguments, if any.
 */
__isl_give isl_map *pet_expr_access_get_may_access(__isl_keep pet_expr *expr)
{
        isl_map *access;
        isl_space *space;
        isl_map *map;

        if (!expr)
                return NULL;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", return NULL);

        access = pet_expr_access_get_dependent_access(expr);
        if (expr->n_arg == 0)
                return access;

        space = isl_space_domain(isl_map_get_space(access));
        map = isl_map_universe(isl_space_unwrap(space));
        map = isl_map_domain_map(map);
        access = isl_map_apply_domain(access, map);

        return access;
}

/* Return a relation mapping domain iterations to definitely
 * accessed data elements, assuming the statement containing
 * the expression is executed.
 *
 * If there are no arguments, then all elements are accessed.
 * Otherwise, we conservatively return an empty relation.
 */
__isl_give isl_map *pet_expr_access_get_must_access(__isl_keep pet_expr *expr)
{
        isl_space *space;

        if (!expr)
                return NULL;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access expression", return NULL);

        if (expr->n_arg == 0)
                return pet_expr_access_get_dependent_access(expr);

        space = isl_map_get_space(expr->acc.access);
        space = isl_space_domain_factor_domain(space);

        return isl_map_empty(space);
}

/* Return the relation mapping domain iterations to all possibly
 * accessed data elements, with its domain tagged with the reference
 * identifier.
 */
__isl_give isl_map *pet_expr_access_get_tagged_may_access(
        __isl_keep pet_expr *expr)
{
        isl_map *access;

        if (!expr)
                return NULL;

        access = pet_expr_access_get_may_access(expr);
        access = pet_expr_tag_access(expr, access);

        return access;
}

/* Return the operation type of operation expression "expr".
 */
enum pet_op_type pet_expr_op_get_type(__isl_keep pet_expr *expr)
{
        if (!expr)
                return pet_op_last;
        if (expr->type != pet_expr_op)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an operation expression", return pet_op_last);

        return expr->op;
}

/* Replace the operation type of operation expression "expr" by "type".
 */
__isl_give pet_expr *pet_expr_op_set_type(__isl_take pet_expr *expr,
        enum pet_op_type type)
{
        if (!expr)
                return pet_expr_free(expr);
        if (expr->type != pet_expr_op)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an operation expression",
                        return pet_expr_free(expr));
        if (expr->op == type)
                return expr;
        expr = pet_expr_cow(expr);
        if (!expr)
                return NULL;
        expr->op = type;

        return expr;
}

/* Return the name of the function called by "expr".
 */
__isl_keep const char *pet_expr_call_get_name(__isl_keep pet_expr *expr)
{
        if (!expr)
                return NULL;
        if (expr->type != pet_expr_call)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not a call expression", return NULL);
        return expr->name;
}

/* Replace the name of the function called by "expr" by "name".
 */
__isl_give pet_expr *pet_expr_call_set_name(__isl_take pet_expr *expr,
        __isl_keep const char *name)
{
        expr = pet_expr_cow(expr);
        if (!expr || !name)
                return pet_expr_free(expr);
        if (expr->type != pet_expr_call)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not a call expression", return pet_expr_free(expr));
        free(expr->name);
        expr->name = strdup(name);
        if (!expr->name)
                return pet_expr_free(expr);
        return expr;
}

/* Replace the type of the cast performed by "expr" by "name".
 */
__isl_give pet_expr *pet_expr_cast_set_type_name(__isl_take pet_expr *expr,
        __isl_keep const char *name)
{
        expr = pet_expr_cow(expr);
        if (!expr || !name)
                return pet_expr_free(expr);
        if (expr->type != pet_expr_cast)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not a cast expression", return pet_expr_free(expr));
        free(expr->type_name);
        expr->type_name = strdup(name);
        if (!expr->type_name)
                return pet_expr_free(expr);
        return expr;
}

/* Return the value of the integer represented by "expr".
 */
__isl_give isl_val *pet_expr_int_get_val(__isl_keep pet_expr *expr)
{
        if (!expr)
                return NULL;
        if (expr->type != pet_expr_int)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an int expression", return NULL);

        return isl_val_copy(expr->i);
}

/* Replace the value of the integer represented by "expr" by "v".
 */
__isl_give pet_expr *pet_expr_int_set_val(__isl_take pet_expr *expr,
        __isl_take isl_val *v)
{
        expr = pet_expr_cow(expr);
        if (!expr || !v)
                goto error;
        if (expr->type != pet_expr_int)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an int expression", goto error);
        isl_val_free(expr->i);
        expr->i = v;

        return expr;
error:
        isl_val_free(v);
        pet_expr_free(expr);
        return NULL;
}

/* Replace the value and string representation of the double
 * represented by "expr" by "d" and "s".
 */
__isl_give pet_expr *pet_expr_double_set(__isl_take pet_expr *expr,
        double d, __isl_keep const char *s)
{
        expr = pet_expr_cow(expr);
        if (!expr || !s)
                return pet_expr_free(expr);
        if (expr->type != pet_expr_double)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not a double expression", return pet_expr_free(expr));
        expr->d.val = d;
        free(expr->d.s);
        expr->d.s = strdup(s);
        if (!expr->d.s)
                return pet_expr_free(expr);
        return expr;
}

/* Return a string representation of the double expression "expr".
 */
__isl_give char *pet_expr_double_get_str(__isl_keep pet_expr *expr)
{
        if (!expr)
                return NULL;
        if (expr->type != pet_expr_double)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not a double expression", return NULL);
        return strdup(expr->d.s);
}

/* Return a piecewise affine expression defined on the specified domain
 * that represents NaN.
 */
static __isl_give isl_pw_aff *non_affine(__isl_take isl_space *space)
{
        return isl_pw_aff_nan_on_domain(isl_local_space_from_space(space));
}

/* This function is called when we come across an access that is
 * nested in what is supposed to be an affine expression.
 * "pc" is the context in which the affine expression is created.
 * If nesting is allowed in "pc", we return an affine expression that is
 * equal to a new parameter corresponding to this nested access.
 * Otherwise, we return NaN.
 *
 * Note that we currently don't allow nested accesses themselves
 * to contain any nested accesses, so we check if "expr" itself
 * involves any nested accesses (either explicitly as arguments
 * or implicitly through parameters) and return NaN if it does.
 *
 * The new parameter is resolved in resolve_nested.
 */
static __isl_give isl_pw_aff *nested_access(__isl_keep pet_expr *expr,
        __isl_keep pet_context *pc)
{
        isl_ctx *ctx;
        isl_id *id;
        isl_space *space;
        isl_local_space *ls;
        isl_aff *aff;
        int nested;

        if (!expr || !pc)
                return NULL;
        if (!pet_context_allow_nesting(pc))
                return non_affine(pet_context_get_space(pc));

        if (pet_expr_get_type(expr) != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_internal,
                        "not an access expression", return NULL);

        if (expr->n_arg > 0)
                return non_affine(pet_context_get_space(pc));

        space = pet_expr_access_get_parameter_space(expr);
        nested = pet_nested_any_in_space(space);
        isl_space_free(space);
        if (nested)
                return non_affine(pet_context_get_space(pc));

        ctx = pet_expr_get_ctx(expr);
        id = pet_nested_pet_expr(pet_expr_copy(expr));
        space = pet_context_get_space(pc);
        space = isl_space_insert_dims(space, isl_dim_param, 0, 1);

        space = isl_space_set_dim_id(space, isl_dim_param, 0, id);
        ls = isl_local_space_from_space(space);
        aff = isl_aff_var_on_domain(ls, isl_dim_param, 0);

        return isl_pw_aff_from_aff(aff);
}

/* Extract an affine expression from the access pet_expr "expr".
 * "pc" is the context in which the affine expression is created.
 *
 * If "expr" is actually an affine expression rather than
 * a real access, then we return that expression.
 * Otherwise, we require that "expr" is of an integral type.
 * If not, we return NaN.
 *
 * If we are accessing a scalar (i.e., not an array and not a member)
 * and if that scalar can be treated as a parameter (because it is
 * not assigned a known or unknown value in the relevant part of the AST),
 * then we return an affine expression equal to that parameter.
 *
 * If the variable has been assigned a known affine expression,
 * then we return that expression.
 *
 * Otherwise, we return an expression that is equal to a parameter
 * representing "expr" (if "allow_nested" is set).
 */
static __isl_give isl_pw_aff *extract_affine_from_access(
        __isl_keep pet_expr *expr, __isl_keep pet_context *pc)
{
        int pos;
        isl_id *id;
        isl_space *space;
        isl_local_space *ls;
        isl_aff *aff;

        if (pet_expr_is_affine(expr)) {
                isl_pw_aff *pa;
                isl_multi_pw_aff *mpa;

                mpa = pet_expr_access_get_index(expr);
                pa = isl_multi_pw_aff_get_pw_aff(mpa, 0);
                isl_multi_pw_aff_free(mpa);
                return pa;
        }

        if (pet_expr_get_type_size(expr) == 0)
                return non_affine(pet_context_get_space(pc));

        if (!pet_expr_is_scalar_access(expr))
                return nested_access(expr, pc);

        id = pet_expr_access_get_id(expr);
        if (pet_context_is_assigned(pc, id)) {
                isl_pw_aff *pa;

                pa = pet_context_get_value(pc, id);
                if (!pa)
                        return NULL;
                if (!isl_pw_aff_involves_nan(pa))
                        return pa;
                isl_pw_aff_free(pa);
                return nested_access(expr, pc);
        }

        space = pet_context_get_space(pc);

        pos = isl_space_find_dim_by_id(space, isl_dim_param, id);
        if (pos >= 0) {
                isl_id_free(id);
        } else {
                pos = isl_space_dim(space, isl_dim_param);
                space = isl_space_add_dims(space, isl_dim_param, 1);
                space = isl_space_set_dim_id(space, isl_dim_param, pos, id);
        }

        ls = isl_local_space_from_space(space);
        aff = isl_aff_var_on_domain(ls, isl_dim_param, pos);

        return isl_pw_aff_from_aff(aff);
}

/* Construct an affine expression from the integer constant "expr".
 * "pc" is the context in which the affine expression is created.
 */
static __isl_give isl_pw_aff *extract_affine_from_int(__isl_keep pet_expr *expr,
        __isl_keep pet_context *pc)
{
        isl_local_space *ls;
        isl_aff *aff;

        if (!expr)
                return NULL;

        ls = isl_local_space_from_space(pet_context_get_space(pc));
        aff = isl_aff_val_on_domain(ls, pet_expr_int_get_val(expr));

        return isl_pw_aff_from_aff(aff);
}

/* Extract an affine expression from an addition or subtraction operation.
 * Return NaN if we are unable to extract an affine expression.
 *
 * "pc" is the context in which the affine expression is created.
 */
static __isl_give isl_pw_aff *extract_affine_add_sub(__isl_keep pet_expr *expr,
        __isl_keep pet_context *pc)
{
        isl_pw_aff *lhs;
        isl_pw_aff *rhs;

        if (!expr)
                return NULL;
        if (expr->n_arg != 2)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "expecting two arguments", return NULL);

        lhs = pet_expr_extract_affine(expr->args[0], pc);
        rhs = pet_expr_extract_affine(expr->args[1], pc);

        switch (pet_expr_op_get_type(expr)) {
        case pet_op_add:
                return isl_pw_aff_add(lhs, rhs);
        case pet_op_sub:
                return isl_pw_aff_sub(lhs, rhs);
        default:
                isl_pw_aff_free(lhs);
                isl_pw_aff_free(rhs);
                isl_die(pet_expr_get_ctx(expr), isl_error_internal,
                        "not an addition or subtraction operation",
                        return NULL);
        }

}

/* Extract an affine expression from an integer division or a modulo operation.
 * Return NaN if we are unable to extract an affine expression.
 *
 * "pc" is the context in which the affine expression is created.
 *
 * In particular, if "expr" is lhs/rhs, then return
 *
 *      lhs >= 0 ? floor(lhs/rhs) : ceil(lhs/rhs)
 *
 * If "expr" is lhs%rhs, then return
 *
 *      lhs - rhs * (lhs >= 0 ? floor(lhs/rhs) : ceil(lhs/rhs))
 *
 * If the second argument (rhs) is not a (positive) integer constant,
 * then we fail to extract an affine expression.
 */
static __isl_give isl_pw_aff *extract_affine_div_mod(__isl_keep pet_expr *expr,
        __isl_keep pet_context *pc)
{
        int is_cst;
        isl_pw_aff *lhs;
        isl_pw_aff *rhs;

        if (!expr)
                return NULL;
        if (expr->n_arg != 2)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "expecting two arguments", return NULL);

        rhs = pet_expr_extract_affine(expr->args[1], pc);

        is_cst = isl_pw_aff_is_cst(rhs);
        if (is_cst < 0 || !is_cst) {
                isl_pw_aff_free(rhs);
                return non_affine(pet_context_get_space(pc));
        }

        lhs = pet_expr_extract_affine(expr->args[0], pc);

        switch (pet_expr_op_get_type(expr)) {
        case pet_op_div:
                return isl_pw_aff_tdiv_q(lhs, rhs);
        case pet_op_mod:
                return isl_pw_aff_tdiv_r(lhs, rhs);
        default:
                isl_pw_aff_free(lhs);
                isl_pw_aff_free(rhs);
                isl_die(pet_expr_get_ctx(expr), isl_error_internal,
                        "not a div or mod operator", return NULL);
        }

}

/* Extract an affine expression from a multiplication operation.
 * Return NaN if we are unable to extract an affine expression.
 * In particular, if neither of the arguments is a (piecewise) constant
 * then we return NaN.
 *
 * "pc" is the context in which the affine expression is created.
 */
static __isl_give isl_pw_aff *extract_affine_mul(__isl_keep pet_expr *expr,
        __isl_keep pet_context *pc)
{
        int lhs_cst, rhs_cst;
        isl_pw_aff *lhs;
        isl_pw_aff *rhs;

        if (!expr)
                return NULL;
        if (expr->n_arg != 2)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "expecting two arguments", return NULL);

        lhs = pet_expr_extract_affine(expr->args[0], pc);
        rhs = pet_expr_extract_affine(expr->args[1], pc);

        lhs_cst = isl_pw_aff_is_cst(lhs);
        rhs_cst = isl_pw_aff_is_cst(rhs);
        if (lhs_cst < 0 || rhs_cst < 0 || (!lhs_cst && !rhs_cst)) {
                isl_pw_aff_free(lhs);
                isl_pw_aff_free(rhs);
                return non_affine(pet_context_get_space(pc));
        }

        return isl_pw_aff_mul(lhs, rhs);
}

/* Extract an affine expression from a negation operation.
 * Return NaN if we are unable to extract an affine expression.
 *
 * "pc" is the context in which the affine expression is created.
 */
static __isl_give isl_pw_aff *extract_affine_neg(__isl_keep pet_expr *expr,
        __isl_keep pet_context *pc)
{
        isl_pw_aff *res;

        if (!expr)
                return NULL;
        if (expr->n_arg != 1)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "expecting one argument", return NULL);

        res = pet_expr_extract_affine(expr->args[0], pc);
        return isl_pw_aff_neg(res);
}

/* Extract an affine expression from a conditional operation.
 * Return NaN if we are unable to extract an affine expression.
 *
 * "pc" is the context in which the affine expression is created.
 */
static __isl_give isl_pw_aff *extract_affine_cond(__isl_keep pet_expr *expr,
        __isl_keep pet_context *pc)
{
        isl_pw_aff *cond, *lhs, *rhs;

        if (!expr)
                return NULL;
        if (expr->n_arg != 3)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "expecting three arguments", return NULL);

        cond = pet_expr_extract_affine_condition(expr->args[0], pc);
        lhs = pet_expr_extract_affine(expr->args[1], pc);
        rhs = pet_expr_extract_affine(expr->args[2], pc);

        return isl_pw_aff_cond(cond, lhs, rhs);
}

/* Compute
 *
 *      pwaff mod 2^width
 */
static __isl_give isl_pw_aff *wrap(__isl_take isl_pw_aff *pwaff, unsigned width)
{
        isl_ctx *ctx;
        isl_val *mod;

        ctx = isl_pw_aff_get_ctx(pwaff);
        mod = isl_val_int_from_ui(ctx, width);
        mod = isl_val_2exp(mod);

        pwaff = isl_pw_aff_mod_val(pwaff, mod);

        return pwaff;
}

/* Limit the domain of "pwaff" to those elements where the function
 * value satisfies
 *
 *      2^{width-1} <= pwaff < 2^{width-1}
 */
static __isl_give isl_pw_aff *avoid_overflow(__isl_take isl_pw_aff *pwaff,
        unsigned width)
{
        isl_ctx *ctx;
        isl_val *v;
        isl_space *space = isl_pw_aff_get_domain_space(pwaff);
        isl_local_space *ls = isl_local_space_from_space(space);
        isl_aff *bound;
        isl_set *dom;
        isl_pw_aff *b;

        ctx = isl_pw_aff_get_ctx(pwaff);
        v = isl_val_int_from_ui(ctx, width - 1);
        v = isl_val_2exp(v);

        bound = isl_aff_zero_on_domain(ls);
        bound = isl_aff_add_constant_val(bound, v);
        b = isl_pw_aff_from_aff(bound);

        dom = isl_pw_aff_lt_set(isl_pw_aff_copy(pwaff), isl_pw_aff_copy(b));
        pwaff = isl_pw_aff_intersect_domain(pwaff, dom);

        b = isl_pw_aff_neg(b);
        dom = isl_pw_aff_ge_set(isl_pw_aff_copy(pwaff), b);
        pwaff = isl_pw_aff_intersect_domain(pwaff, dom);

        return pwaff;
}

/* Handle potential overflows on signed computations.
 *
 * If options->signed_overflow is set to PET_OVERFLOW_AVOID,
 * then we adjust the domain of "pa" to avoid overflows.
 */
static __isl_give isl_pw_aff *signed_overflow(__isl_take isl_pw_aff *pa,
        unsigned width)
{
        isl_ctx *ctx;
        struct pet_options *options;

        if (!pa)
                return NULL;

        ctx = isl_pw_aff_get_ctx(pa);
        options = isl_ctx_peek_pet_options(ctx);
        if (!options || options->signed_overflow == PET_OVERFLOW_AVOID)
                pa = avoid_overflow(pa, width);

        return pa;
}

/* Extract an affine expression from some an operation.
 * Return NaN if we are unable to extract an affine expression.
 * If the result of a binary (non boolean) operation is unsigned,
 * then we wrap it based on the size of the type.  If the result is signed,
 * then we ensure that no overflow occurs.
 *
 * "pc" is the context in which the affine expression is created.
 */
static __isl_give isl_pw_aff *extract_affine_from_op(__isl_keep pet_expr *expr,
        __isl_keep pet_context *pc)
{
        isl_pw_aff *res;
        int type_size;

        switch (pet_expr_op_get_type(expr)) {
        case pet_op_add:
        case pet_op_sub:
                res = extract_affine_add_sub(expr, pc);
                break;
        case pet_op_div:
        case pet_op_mod:
                res = extract_affine_div_mod(expr, pc);
                break;
        case pet_op_mul:
                res = extract_affine_mul(expr, pc);
                break;
        case pet_op_minus:
                return extract_affine_neg(expr, pc);
        case pet_op_cond:
                return extract_affine_cond(expr, pc);
        case pet_op_eq:
        case pet_op_ne:
        case pet_op_le:
        case pet_op_ge:
        case pet_op_lt:
        case pet_op_gt:
        case pet_op_land:
        case pet_op_lor:
        case pet_op_lnot:
                return pet_expr_extract_affine_condition(expr, pc);
        default:
                return non_affine(pet_context_get_space(pc));
        }

        if (!res)
                return NULL;
        if (isl_pw_aff_involves_nan(res)) {
                isl_space *space = isl_pw_aff_get_domain_space(res);
                isl_pw_aff_free(res);
                return non_affine(space);
        }

        type_size = pet_expr_get_type_size(expr);
        if (type_size > 0)
                res = wrap(res, type_size);
        else
                res = signed_overflow(res, -type_size);

        return res;
}

/* Extract an affine expression from some special function calls.
 * Return NaN if we are unable to extract an affine expression.
 * In particular, we handle "min", "max", "ceild", "floord",
 * "intMod", "intFloor" and "intCeil".
 * In case of the latter five, the second argument needs to be
 * a (positive) integer constant.
 *
 * "pc" is the context in which the affine expression is created.
 */
static __isl_give isl_pw_aff *extract_affine_from_call(
        __isl_keep pet_expr *expr, __isl_keep pet_context *pc)
{
        isl_pw_aff *aff1, *aff2;
        int n;
        const char *name;

        n = pet_expr_get_n_arg(expr);
        name = pet_expr_call_get_name(expr);
        if (!(n == 2 && !strcmp(name, "min")) &&
            !(n == 2 && !strcmp(name, "max")) &&
            !(n == 2 && !strcmp(name, "intMod")) &&
            !(n == 2 && !strcmp(name, "intFloor")) &&
            !(n == 2 && !strcmp(name, "intCeil")) &&
            !(n == 2 && !strcmp(name, "floord")) &&
            !(n == 2 && !strcmp(name, "ceild")))
                return non_affine(pet_context_get_space(pc));

        if (!strcmp(name, "min") || !strcmp(name, "max")) {
                aff1 = pet_expr_extract_affine(expr->args[0], pc);
                aff2 = pet_expr_extract_affine(expr->args[1], pc);

                if (!strcmp(name, "min"))
                        aff1 = isl_pw_aff_min(aff1, aff2);
                else
                        aff1 = isl_pw_aff_max(aff1, aff2);
        } else if (!strcmp(name, "intMod")) {
                isl_val *v;

                if (pet_expr_get_type(expr->args[1]) != pet_expr_int)
                        return non_affine(pet_context_get_space(pc));
                v = pet_expr_int_get_val(expr->args[1]);
                aff1 = pet_expr_extract_affine(expr->args[0], pc);
                aff1 = isl_pw_aff_mod_val(aff1, v);
        } else {
                isl_val *v;

                if (pet_expr_get_type(expr->args[1]) != pet_expr_int)
                        return non_affine(pet_context_get_space(pc));
                v = pet_expr_int_get_val(expr->args[1]);
                aff1 = pet_expr_extract_affine(expr->args[0], pc);
                aff1 = isl_pw_aff_scale_down_val(aff1, v);
                if (!strcmp(name, "floord") || !strcmp(name, "intFloor"))
                        aff1 = isl_pw_aff_floor(aff1);
                else
                        aff1 = isl_pw_aff_ceil(aff1);
        }

        return aff1;
}

/* Extract an affine expression from "expr", if possible.
 * Otherwise return NaN.
 *
 * "pc" is the context in which the affine expression is created.
 */
__isl_give isl_pw_aff *pet_expr_extract_affine(__isl_keep pet_expr *expr,
        __isl_keep pet_context *pc)
{
        if (!expr)
                return NULL;

        switch (pet_expr_get_type(expr)) {
        case pet_expr_access:
                return extract_affine_from_access(expr, pc);
        case pet_expr_int:
                return extract_affine_from_int(expr, pc);
        case pet_expr_op:
                return extract_affine_from_op(expr, pc);
        case pet_expr_call:
                return extract_affine_from_call(expr, pc);
        case pet_expr_cast:
        case pet_expr_double:
        case pet_expr_error:
                return non_affine(pet_context_get_space(pc));
        }
}

/* Extract an affine expressions representing the comparison "LHS op RHS"
 * Return NaN if we are unable to extract such an affine expression.
 *
 * "pc" is the context in which the affine expression is created.
 *
 * If the comparison is of the form
 *
 *      a <= min(b,c)
 *
 * then the expression is constructed as the conjunction of
 * the comparisons
 *
 *      a <= b          and             a <= c
 *
 * A similar optimization is performed for max(a,b) <= c.
 * We do this because that will lead to simpler representations
 * of the expression.
 * If isl is ever enhanced to explicitly deal with min and max expressions,
 * this optimization can be removed.
 */
__isl_give isl_pw_aff *pet_expr_extract_comparison(enum pet_op_type op,
        __isl_keep pet_expr *lhs, __isl_keep pet_expr *rhs,
        __isl_keep pet_context *pc)
{
        isl_pw_aff *lhs_pa, *rhs_pa;

        if (op == pet_op_gt)
                return pet_expr_extract_comparison(pet_op_lt, rhs, lhs, pc);
        if (op == pet_op_ge)
                return pet_expr_extract_comparison(pet_op_le, rhs, lhs, pc);

        if (op == pet_op_lt || op == pet_op_le) {
                if (pet_expr_is_min(rhs)) {
                        lhs_pa = pet_expr_extract_comparison(op, lhs,
                                                rhs->args[0], pc);
                        rhs_pa = pet_expr_extract_comparison(op, lhs,
                                                rhs->args[1], pc);
                        return pet_and(lhs_pa, rhs_pa);
                }
                if (pet_expr_is_max(lhs)) {
                        lhs_pa = pet_expr_extract_comparison(op, lhs->args[0],
                                                rhs, pc);
                        rhs_pa = pet_expr_extract_comparison(op, lhs->args[1],
                                                rhs, pc);
                        return pet_and(lhs_pa, rhs_pa);
                }
        }

        lhs_pa = pet_expr_extract_affine(lhs, pc);
        rhs_pa = pet_expr_extract_affine(rhs, pc);

        return pet_comparison(op, lhs_pa, rhs_pa);
}

/* Extract an affine expressions from the comparison "expr".
 * Return NaN if we are unable to extract such an affine expression.
 *
 * "pc" is the context in which the affine expression is created.
 */
static __isl_give isl_pw_aff *extract_comparison(__isl_keep pet_expr *expr,
        __isl_keep pet_context *pc)
{
        enum pet_op_type type;

        if (!expr)
                return NULL;
        if (expr->n_arg != 2)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "expecting two arguments", return NULL);

        type = pet_expr_op_get_type(expr);
        return pet_expr_extract_comparison(type, expr->args[0], expr->args[1],
                                                pc);
}

/* Extract an affine expression representing the boolean operation
 * expressed by "expr".
 * Return NaN if we are unable to extract an affine expression.
 *
 * "pc" is the context in which the affine expression is created.
 */
static __isl_give isl_pw_aff *extract_boolean(__isl_keep pet_expr *expr,
        __isl_keep pet_context *pc)
{
        isl_pw_aff *lhs, *rhs;
        int n;

        if (!expr)
                return NULL;

        n = pet_expr_get_n_arg(expr);
        lhs = pet_expr_extract_affine_condition(expr->args[0], pc);
        if (n == 1)
                return pet_not(lhs);

        rhs = pet_expr_extract_affine_condition(expr->args[1], pc);
        return pet_boolean(pet_expr_op_get_type(expr), lhs, rhs);
}

/* Extract the affine expression "expr != 0 ? 1 : 0".
 * Return NaN if we are unable to extract an affine expression.
 *
 * "pc" is the context in which the affine expression is created.
 */
static __isl_give isl_pw_aff *extract_implicit_condition(
        __isl_keep pet_expr *expr, __isl_keep pet_context *pc)
{
        isl_pw_aff *res;

        res = pet_expr_extract_affine(expr, pc);
        return pet_to_bool(res);
}

/* Extract a boolean affine expression from "expr".
 * Return NaN if we are unable to extract an affine expression.
 *
 * "pc" is the context in which the affine expression is created.
 *
 * If "expr" is neither a comparison nor a boolean operation,
 * then we assume it is an affine expression and return the
 * boolean expression "expr != 0 ? 1 : 0".
 */
__isl_give isl_pw_aff *pet_expr_extract_affine_condition(
        __isl_keep pet_expr *expr, __isl_keep pet_context *pc)
{
        if (!expr)
                return NULL;

        if (pet_expr_is_comparison(expr))
                return extract_comparison(expr, pc);
        if (pet_expr_is_boolean(expr))
                return extract_boolean(expr, pc);

        return extract_implicit_condition(expr, pc);
}

/* Check if "expr" is an assume expression and if its single argument
 * can be converted to an affine expression in the context of "pc".
 * If so, replace the argument by the affine expression.
 */
__isl_give pet_expr *pet_expr_resolve_assume(__isl_take pet_expr *expr,
        __isl_keep pet_context *pc)
{
        isl_pw_aff *cond;
        isl_multi_pw_aff *index;

        if (!expr)
                return NULL;
        if (!pet_expr_is_assume(expr))
                return expr;
        if (expr->n_arg != 1)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "expecting one argument", return pet_expr_free(expr));

        cond = pet_expr_extract_affine_condition(expr->args[0], pc);
        if (!cond)
                return pet_expr_free(expr);
        if (isl_pw_aff_involves_nan(cond)) {
                isl_pw_aff_free(cond);
                return expr;
        }

        index = isl_multi_pw_aff_from_pw_aff(cond);
        expr = pet_expr_set_arg(expr, 0, pet_expr_from_index(index));

        return expr;
}

/* Return the number of bits needed to represent the type of "expr".
 * See the description of the type_size field of pet_expr.
 */
int pet_expr_get_type_size(__isl_keep pet_expr *expr)
{
        return expr ? expr->type_size : 0;
}

/* Replace the number of bits needed to represent the type of "expr"
 * by "type_size".
 * See the description of the type_size field of pet_expr.
 */
__isl_give pet_expr *pet_expr_set_type_size(__isl_take pet_expr *expr,
        int type_size)
{
        expr = pet_expr_cow(expr);
        if (!expr)
                return NULL;

        expr->type_size = type_size;

        return expr;
}

/* Extend an access expression "expr" with an additional index "index".
 * In particular, add "index" as an extra argument to "expr" and
 * adjust the index expression of "expr" to refer to this extra argument.
 * The caller is responsible for calling pet_expr_access_set_depth
 * to update the corresponding access relation.
 *
 * Note that we only collect the individual index expressions as
 * arguments of "expr" here.
 * An attempt to integrate them into the index expression of "expr"
 * is performed in pet_expr_access_plug_in_args.
 */
__isl_give pet_expr *pet_expr_access_subscript(__isl_take pet_expr *expr,
        __isl_take pet_expr *index)
{
        int n;
        isl_space *space;
        isl_local_space *ls;
        isl_pw_aff *pa;

        expr = pet_expr_cow(expr);
        if (!expr || !index)
                goto error;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access pet_expr", goto error);

        n = pet_expr_get_n_arg(expr);
        expr = pet_expr_insert_arg(expr, n, index);
        if (!expr)
                return NULL;

        space = isl_multi_pw_aff_get_domain_space(expr->acc.index);
        ls = isl_local_space_from_space(space);
        pa = isl_pw_aff_from_aff(isl_aff_var_on_domain(ls, isl_dim_set, n));
        expr->acc.index = pet_array_subscript(expr->acc.index, pa);
        if (!expr->acc.index)
                return pet_expr_free(expr);

        return expr;
error:
        pet_expr_free(expr);
        pet_expr_free(index);
        return NULL;
}

/* Extend an access expression "expr" with an additional member acces to "id".
 * In particular, extend the index expression of "expr" to include
 * the additional member access.
 * The caller is responsible for calling pet_expr_access_set_depth
 * to update the corresponding access relation.
 */
__isl_give pet_expr *pet_expr_access_member(__isl_take pet_expr *expr,
        __isl_take isl_id *id)
{
        isl_space *space;
        isl_multi_pw_aff *field_access;

        expr = pet_expr_cow(expr);
        if (!expr || !id)
                goto error;
        if (expr->type != pet_expr_access)
                isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
                        "not an access pet_expr", goto error);

        space = isl_multi_pw_aff_get_domain_space(expr->acc.index);
        space = isl_space_from_domain(space);
        space = isl_space_set_tuple_id(space, isl_dim_out, id);
        field_access = isl_multi_pw_aff_zero(space);
        expr->acc.index = pet_array_member(expr->acc.index, field_access);
        if (!expr->acc.index)
                return pet_expr_free(expr);

        return expr;
error:
        pet_expr_free(expr);
        isl_id_free(id);
        return NULL;
}

void pet_expr_dump_with_indent(__isl_keep pet_expr *expr, int indent)
{
        int i;

        if (!expr)
                return;

        fprintf(stderr, "%*s", indent, "");

        switch (expr->type) {
        case pet_expr_double:
                fprintf(stderr, "%s\n", expr->d.s);
                break;
        case pet_expr_int:
                isl_val_dump(expr->i);
                break;
        case pet_expr_access:
                if (expr->acc.ref_id) {
                        isl_id_dump(expr->acc.ref_id);
                        fprintf(stderr, "%*s", indent, "");
                }
                isl_map_dump(expr->acc.access);
                fprintf(stderr, "%*s", indent, "");
                isl_multi_pw_aff_dump(expr->acc.index);
                fprintf(stderr, "%*sread: %d\n", indent + 2,
                                "", expr->acc.read);
                fprintf(stderr, "%*swrite: %d\n", indent + 2,
                                "", expr->acc.write);
                for (i = 0; i < expr->n_arg; ++i)
                        pet_expr_dump_with_indent(expr->args[i], indent + 2);
                break;
        case pet_expr_op:
                fprintf(stderr, "%s\n", op_str[expr->op]);
                for (i = 0; i < expr->n_arg; ++i)
                        pet_expr_dump_with_indent(expr->args[i], indent + 2);
                break;
        case pet_expr_call:
                fprintf(stderr, "%s/%d\n", expr->name, expr->n_arg);
                for (i = 0; i < expr->n_arg; ++i)
                        pet_expr_dump_with_indent(expr->args[i], indent + 2);
                break;
        case pet_expr_cast:
                fprintf(stderr, "(%s)\n", expr->type_name);
                for (i = 0; i < expr->n_arg; ++i)
                        pet_expr_dump_with_indent(expr->args[i], indent + 2);
                break;
        case pet_expr_error:
                fprintf(stderr, "ERROR\n");
                break;
        }
}

void pet_expr_dump(__isl_keep pet_expr *expr)
{
        pet_expr_dump_with_indent(expr, 0);
}