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 <isl/ctx.h>
#include <isl/hash.h>
#include <isl/id.h>
#include <isl/val.h>
#include <isl/space.h>
#include <isl/local_space.h>
#include <isl/aff.h>
#include <isl/map.h>
#include <isl/union_set.h>
#include <isl/union_map.h>
#include <isl/printer.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"
#include "patch.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_and_assign] = "&=",
	[pet_op_xor_assign] = "^=",
	[pet_op_or_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 index expression.
 * By default, the access is considered to be a read access.
 * The initial depth is set from the index expression and
 * may still be updated by the caller before the access relation
 * is created.
 */
__isl_give pet_expr *pet_expr_from_index(__isl_take isl_multi_pw_aff *index)
{
	isl_ctx *ctx;
	pet_expr *expr;

	if (!index)
		return NULL;
	ctx = isl_multi_pw_aff_get_ctx(index);
	expr = pet_expr_alloc(ctx, pet_expr_access);
	if (!expr)
		goto error;

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

	expr = pet_expr_access_set_index(expr, index);

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

/* 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;
}

/* Does the access expression "expr" have any explicit access relation?
 */
isl_bool pet_expr_access_has_any_access_relation(__isl_keep pet_expr *expr)
{
	enum pet_expr_access_type type;

	if (!expr)
		return isl_bool_error;

	for (type = pet_expr_access_begin; type < pet_expr_access_end; ++type)
		if (expr->acc.access[type])
			return isl_bool_true;

	return isl_bool_false;
}

/* Are all relevant access relations explicitly available in "expr"?
 */
static int has_relevant_access_relations(__isl_keep pet_expr *expr)
{
	if (!expr)
		return -1;

	if (expr->acc.kill && !expr->acc.access[pet_expr_access_fake_killed])
		return 0;
	if (expr->acc.read && !expr->acc.access[pet_expr_access_may_read])
		return 0;
	if (expr->acc.write &&
	    (!expr->acc.access[pet_expr_access_may_write] ||
	     !expr->acc.access[pet_expr_access_must_write]))
		return 0;

	return 1;
}

/* Replace the depth of the access expr "expr" by "depth".
 *
 * To avoid inconsistencies between the depth and the access relation,
 * we currently do not allow the depth to change once the access relation
 * has been set or computed.
 */
__isl_give pet_expr *pet_expr_access_set_depth(__isl_take pet_expr *expr,
	int depth)
{
	if (!expr)
		return NULL;
	if (expr->acc.depth == depth)
		return expr;
	if (pet_expr_access_has_any_access_relation(expr))
		isl_die(pet_expr_get_ctx(expr), isl_error_unsupported,
			"depth cannot be changed after access relation "
			"has been set or computed", return pet_expr_free(expr));

	expr = pet_expr_cow(expr);
	if (!expr)
		return NULL;
	expr->acc.depth = depth;

	return expr;
}

/* 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)
{
	int depth;
	pet_expr *expr;

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

	expr = pet_expr_from_index(index);
	expr = pet_expr_access_set_read(expr, 0);
	expr = pet_expr_access_set_kill(expr, 1);
	depth = isl_map_dim(access, isl_dim_out);
	expr = pet_expr_access_set_depth(expr, depth);
	expr = pet_expr_access_set_access(expr, pet_expr_access_killed,
					isl_union_map_from_map(access));
	return pet_expr_new_unary(0, 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",
 * 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_unary(int type_size, 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->type_size = type_size;
	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->c.name = strdup(name);
	if (!expr->c.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;
}

/* Return an independent duplicate of "expr".
 *
 * In case of an access expression, make sure the depth of the duplicate is set
 * before the access relation (if any) is set and after the index expression
 * is set.
 */
static __isl_give pet_expr *pet_expr_dup(__isl_keep pet_expr *expr)
{
	int i;
	pet_expr *dup;
	enum pet_expr_access_type type;

	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_index(dup,
					isl_multi_pw_aff_copy(expr->acc.index));
		dup = pet_expr_access_set_depth(dup, expr->acc.depth);
		for (type = pet_expr_access_begin;
		     type < pet_expr_access_end; ++type) {
			if (!expr->acc.access[type])
				continue;
			dup = pet_expr_access_set_access(dup, type,
				    isl_union_map_copy(expr->acc.access[type]));
		}
		dup = pet_expr_access_set_read(dup, expr->acc.read);
		dup = pet_expr_access_set_write(dup, expr->acc.write);
		dup = pet_expr_access_set_kill(dup, expr->acc.kill);
		break;
	case pet_expr_call:
		dup = pet_expr_call_set_name(dup, expr->c.name);
		if (expr->c.summary)
			dup = pet_expr_call_set_summary(dup,
				    pet_function_summary_copy(expr->c.summary));
		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;
}

/* Return a pet_expr that is equal to "expr" and that has only
 * a single reference.
 *
 * If "expr" itself only has one reference, then clear its hash value
 * since the returned pet_expr will be modified.
 */
__isl_give pet_expr *pet_expr_cow(__isl_take pet_expr *expr)
{
	if (!expr)
		return NULL;

	if (expr->ref == 1) {
		expr->hash = 0;
		return expr;
	}
	expr->ref--;
	return pet_expr_dup(expr);
}

__isl_null pet_expr *pet_expr_free(__isl_take pet_expr *expr)
{
	enum pet_expr_access_type type;
	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);
		for (type = pet_expr_access_begin;
		     type < pet_expr_access_end; ++type)
			isl_union_map_free(expr->acc.access[type]);
		isl_multi_pw_aff_free(expr->acc.index);
		break;
	case pet_expr_call:
		free(expr->c.name);
		pet_function_summary_free(expr->c.summary);
		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 "expr" by its argument at position "pos".
 */
__isl_give pet_expr *pet_expr_arg(__isl_take pet_expr *expr, int pos)
{
	pet_expr *arg;

	arg = pet_expr_get_arg(expr, pos);
	pet_expr_free(expr);

	return arg;
}

/* 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 address-of operation?
 */
int pet_expr_is_address_of(__isl_keep pet_expr *expr)
{
	if (!expr)
		return -1;
	if (expr->type != pet_expr_op)
		return 0;
	return expr->op == pet_op_address_of;
}

/* 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->c.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->c.name, "max") != 0)
		return 0;
	return 1;
}

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

	if (!expr)
		return isl_bool_error;
	if (expr->type != pet_expr_access)
		return isl_bool_false;

	has_id = isl_multi_pw_aff_has_tuple_id(expr->acc.index, isl_dim_out);
	if (has_id < 0)
		return isl_bool_error;

	return !has_id;
}

/* Given that "expr" represents an affine expression, i.e., that
 * it is an access to an unnamed (1D) space, return this affine expression.
 */
__isl_give isl_pw_aff *pet_expr_get_affine(__isl_keep pet_expr *expr)
{
	isl_bool is_affine;
	isl_pw_aff *pa;
	isl_multi_pw_aff *mpa;

	is_affine = pet_expr_is_affine(expr);
	if (is_affine < 0)
		return NULL;
	if (!is_affine)
		isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
			"not an affine expression", return NULL);

	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;
}

/* 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_multi_pw_aff_range_is_wrapping(expr->acc.index))
		return 0;

	return expr->acc.depth == 0;
}

/* Construct an access relation from the index expression and
 * the array depth of the access expression "expr".
 *
 * 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.
 */
static __isl_give isl_union_map *construct_access_relation(
	__isl_keep pet_expr *expr)
{
	isl_map *access;
	int dim;

	if (!expr)
		return NULL;

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

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

	if (dim != expr->acc.depth)
		access = extend_range(access, expr->acc.depth - dim);

	return isl_union_map_from_map(access);
}

/* Ensure that all relevant access relations are explicitly
 * available in "expr".
 *
 * If "expr" does not already have the relevant access relations, then create
 * them based on the index expression and the array depth.
 *
 * We do not cow since adding an explicit access relation
 * does not change the meaning of the expression.
 * However, the explicit access relations may modify the hash value,
 * so the cached value is reset.
 */
static __isl_give pet_expr *introduce_access_relations(
	__isl_take pet_expr *expr)
{
	isl_union_map *access;
	int kill, read, write;

	if (!expr)
		return NULL;
	if (has_relevant_access_relations(expr))
		return expr;

	access = construct_access_relation(expr);
	if (!access)
		return pet_expr_free(expr);

	expr->hash = 0;
	kill = expr->acc.kill;
	read = expr->acc.read;
	write = expr->acc.write;
	if (kill && !expr->acc.access[pet_expr_access_fake_killed])
		expr->acc.access[pet_expr_access_fake_killed] =
						isl_union_map_copy(access);
	if (read && !expr->acc.access[pet_expr_access_may_read])
		expr->acc.access[pet_expr_access_may_read] =
						isl_union_map_copy(access);
	if (write && !expr->acc.access[pet_expr_access_may_write])
		expr->acc.access[pet_expr_access_may_write] =
						isl_union_map_copy(access);
	if (write && !expr->acc.access[pet_expr_access_must_write])
		expr->acc.access[pet_expr_access_must_write] =
						isl_union_map_copy(access);

	isl_union_map_free(access);

	if (!has_relevant_access_relations(expr))
		return pet_expr_free(expr);

	return expr;
}

/* Return a hash value that digests "expr".
 * If a hash value was computed already, then return that value.
 * Otherwise, compute the hash value and store a copy in expr->hash.
 */
uint32_t pet_expr_get_hash(__isl_keep pet_expr *expr)
{
	int i;
	enum pet_expr_access_type type;
	uint32_t hash, hash_f;

	if (!expr)
		return 0;
	if (expr->hash)
		return expr->hash;

	hash = isl_hash_init();
	isl_hash_byte(hash, expr->type & 0xFF);
	isl_hash_byte(hash, expr->n_arg & 0xFF);
	for (i = 0; i < expr->n_arg; ++i) {
		uint32_t hash_i;
		hash_i = pet_expr_get_hash(expr->args[i]);
		isl_hash_hash(hash, hash_i);
	}
	switch (expr->type) {
	case pet_expr_error:
		return 0;
	case pet_expr_double:
		hash = isl_hash_string(hash, expr->d.s);
		break;
	case pet_expr_int:
		hash_f = isl_val_get_hash(expr->i);
		isl_hash_hash(hash, hash_f);
		break;
	case pet_expr_access:
		isl_hash_byte(hash, expr->acc.read & 0xFF);
		isl_hash_byte(hash, expr->acc.write & 0xFF);
		isl_hash_byte(hash, expr->acc.kill & 0xFF);
		hash_f = isl_id_get_hash(expr->acc.ref_id);
		isl_hash_hash(hash, hash_f);
		hash_f = isl_multi_pw_aff_get_hash(expr->acc.index);
		isl_hash_hash(hash, hash_f);
		isl_hash_byte(hash, expr->acc.depth & 0xFF);
		for (type = pet_expr_access_begin;
		     type < pet_expr_access_end; ++type) {
			hash_f = isl_union_map_get_hash(expr->acc.access[type]);
			isl_hash_hash(hash, hash_f);
		}
		break;
	case pet_expr_op:
		isl_hash_byte(hash, expr->op & 0xFF);
		break;
	case pet_expr_call:
		hash = isl_hash_string(hash, expr->c.name);
		break;
	case pet_expr_cast:
		hash = isl_hash_string(hash, expr->type_name);
		break;
	}
	expr->hash = hash;
	return hash;
}

/* 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;
	enum pet_expr_access_type type;

	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.kill != expr2->acc.kill)
			return 0;
		if (expr1->acc.ref_id != expr2->acc.ref_id)
			return 0;
		if (!expr1->acc.index || !expr2->acc.index)
			return 0;
		if (!isl_multi_pw_aff_is_equal(expr1->acc.index,
						expr2->acc.index))
			return 0;
		if (expr1->acc.depth != expr2->acc.depth)
			return 0;
		if (has_relevant_access_relations(expr1) !=
		    has_relevant_access_relations(expr2)) {
			int equal;
			expr1 = pet_expr_copy(expr1);
			expr2 = pet_expr_copy(expr2);
			expr1 = introduce_access_relations(expr1);
			expr2 = introduce_access_relations(expr2);
			equal = pet_expr_is_equal(expr1, expr2);
			pet_expr_free(expr1);
			pet_expr_free(expr2);
			return equal;
		}
		for (type = pet_expr_access_begin;
		     type < pet_expr_access_end; ++type) {
			if (!expr1->acc.access[type] !=
						    !expr2->acc.access[type])
				return 0;
			if (!expr1->acc.access[type])
				continue;
			if (!isl_union_map_is_equal(expr1->acc.access[type],
						    expr2->acc.access[type]))
				return 0;
		}
		break;
	case pet_expr_op:
		if (expr1->op != expr2->op)
			return 0;
		break;
	case pet_expr_call:
		if (strcmp(expr1->c.name, expr2->c.name))
			return 0;
		break;
	case pet_expr_cast:
		if (strcmp(expr1->type_name, expr2->type_name))
			return 0;
		break;
	}

	return 1;
}

/* Do "expr1" and "expr2" represent two accesses to the same array
 * that are also of the same type?  That is, can these two accesses
 * be replaced by a single access?
 */
isl_bool pet_expr_is_same_access(__isl_keep pet_expr *expr1,
	__isl_keep pet_expr *expr2)
{
	isl_space *space1, *space2;
	isl_bool same;

	if (!expr1 || !expr2)
		return isl_bool_error;
	if (pet_expr_get_type(expr1) != pet_expr_access)
		return isl_bool_false;
	if (pet_expr_get_type(expr2) != pet_expr_access)
		return isl_bool_false;
	if (expr1->acc.read != expr2->acc.read)
		return isl_bool_false;
	if (expr1->acc.write != expr2->acc.write)
		return isl_bool_false;
	if (expr1->acc.kill != expr2->acc.kill)
		return isl_bool_false;
	if (expr1->acc.depth != expr2->acc.depth)
		return isl_bool_false;

	space1 = isl_multi_pw_aff_get_space(expr1->acc.index);
	space2 = isl_multi_pw_aff_get_space(expr2->acc.index);
	same = isl_space_tuple_is_equal(space1, isl_dim_out,
					space2, isl_dim_out);
	if (same >= 0 && same)
		same = isl_space_tuple_is_equal(space1, isl_dim_in,
						space2, isl_dim_in);
	isl_space_free(space1);
	isl_space_free(space2);

	return same;
}

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

	return expr->acc.read;
}

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

	return expr->acc.write;
}

/* Does the access expression "expr" kill the accessed elements?
 */
isl_bool pet_expr_access_is_kill(__isl_keep pet_expr *expr)
{
	if (!expr)
		return isl_bool_error;
	if (expr->type != pet_expr_access)
		isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
			"not an access expression", return isl_bool_error);

	return expr->acc.kill;
}

/* 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_multi_pw_aff_range_is_wrapping(expr->acc.index)) {
		isl_space *space;
		isl_id *id;

		space = isl_multi_pw_aff_get_space(expr->acc.index);
		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_multi_pw_aff_get_tuple_id(expr->acc.index, 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", including the arguments (if any).
 */
__isl_give isl_space *pet_expr_access_get_augmented_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);

	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;

	space = pet_expr_access_get_augmented_domain_space(expr);
	if (isl_space_is_wrapping(space))
		space = isl_space_domain(isl_space_unwrap(space));

	return space;
}

/* Internal data structure for pet_expr_access_foreach_data_space.
 */
struct pet_foreach_data_space_data {
	isl_stat (*fn)(__isl_take isl_space *space, void *user);
	void *user;
};

/* Given a piece of an access relation, call data->fn on the data
 * (i.e., range) space.
 */
static isl_stat foreach_data_space(__isl_take isl_map *map, void *user)
{
	struct pet_foreach_data_space_data *data = user;
	isl_space *space;

	space = isl_map_get_space(map);
	space = isl_space_range(space);
	isl_map_free(map);

	return data->fn(space, data->user);
}

/* Call "fn" on the data spaces accessed by "expr".
 * In particular, call "fn" on the range space of the index expression,
 * but if "expr" keeps track of any explicit access relations,
 * then also call "fn" on the corresponding range spaces.
 */
isl_stat pet_expr_access_foreach_data_space(__isl_keep pet_expr *expr,
	isl_stat (*fn)(__isl_take isl_space *space, void *user), void *user)
{
	struct pet_foreach_data_space_data data = { fn, user };
	enum pet_expr_access_type type;
	isl_space *space;

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

	for (type = pet_expr_access_begin; type < pet_expr_access_end; ++type) {
		if (!expr->acc.access[type])
			continue;
		if (isl_union_map_foreach_map(expr->acc.access[type],
					&foreach_data_space, &data) < 0)
			return isl_stat_error;
	}

	space = isl_multi_pw_aff_get_space(expr->acc.index);
	space = isl_space_range(space);
	return fn(space, user);
}

/* Modify all subexpressions of "expr" by calling "fn" on them.
 * The subexpressions are traversed in depth first preorder.
 */
__isl_give pet_expr *pet_expr_map_top_down(__isl_take pet_expr *expr,
	__isl_give pet_expr *(*fn)(__isl_take pet_expr *expr, void *user),
	void *user)
{
	int i, n;

	if (!expr)
		return NULL;

	expr = fn(expr, user);

	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_top_down(arg, fn, user);
		expr = pet_expr_set_arg(expr, i, arg);
	}

	return expr;
}

/* Modify all expressions of type "type" in "expr" by calling "fn" on them.
 */
static __isl_give pet_expr *pet_expr_map_expr_of_type(__isl_take pet_expr *expr,
	enum pet_expr_type type,
	__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_expr_of_type(arg, type, fn, user);
		expr = pet_expr_set_arg(expr, i, arg);
	}

	if (!expr)
		return NULL;

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

	return expr;
}

/* 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)
{
	return pet_expr_map_expr_of_type(expr, pet_expr_access, fn, user);
}

/* Modify all expressions of type pet_expr_call in "expr"
 * by calling "fn" on them.
 */
__isl_give pet_expr *pet_expr_map_call(__isl_take pet_expr *expr,
	__isl_give pet_expr *(*fn)(__isl_take pet_expr *expr, void *user),
	void *user)
{
	return pet_expr_map_expr_of_type(expr, pet_expr_call, fn, user);
}

/* Modify all expressions of type pet_expr_op in "expr"
 * by calling "fn" on them.
 */
__isl_give pet_expr *pet_expr_map_op(__isl_take pet_expr *expr,
	__isl_give pet_expr *(*fn)(__isl_take pet_expr *expr, void *user),
	void *user)
{
	return pet_expr_map_expr_of_type(expr, pet_expr_op, fn, user);
}

/* 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 relations of "expr" (if any)
 * 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)
{
	enum pet_expr_access_type type;

	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));

	for (type = pet_expr_access_begin; type < pet_expr_access_end; ++type) {
		if (!expr->acc.access[type])
			continue;
		expr->acc.access[type] =
			pet_union_map_move_dims(expr->acc.access[type],
				dst_type, dst_pos, src_type, src_pos, n);
		if (!expr->acc.access[type])
			break;
	}
	expr->acc.index = isl_multi_pw_aff_move_dims(expr->acc.index,
				dst_type, dst_pos, src_type, src_pos, n);
	if (!expr->acc.index || type < pet_expr_access_end)
		return pet_expr_free(expr);

	return expr;
}

/* Replace the index expression and access relations (if any) 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)
{
	enum pet_expr_access_type type;

	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);

	for (type = pet_expr_access_begin; type < pet_expr_access_end; ++type) {
		if (!expr->acc.access[type])
			continue;
		expr->acc.access[type] =
		    isl_union_map_preimage_domain_multi_aff(
			expr->acc.access[type], isl_multi_aff_copy(ma));
		if (!expr->acc.access[type])
			break;
	}
	expr->acc.index = isl_multi_pw_aff_pullback_multi_aff(expr->acc.index,
						ma);
	if (!expr->acc.index || type < pet_expr_access_end)
		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 relations (if any) 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)
{
	enum pet_expr_access_type type;

	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);

	for (type = pet_expr_access_begin; type < pet_expr_access_end; ++type) {
		if (!expr->acc.access[type])
			continue;
		expr->acc.access[type] =
		    isl_union_map_preimage_domain_multi_pw_aff(
			expr->acc.access[type], isl_multi_pw_aff_copy(mpa));
		if (!expr->acc.access[type])
			break;
	}
	expr->acc.index = isl_multi_pw_aff_pullback_multi_pw_aff(
				expr->acc.index, mpa);
	if (!expr->acc.index || type < pet_expr_access_end)
		return pet_expr_free(expr);

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

/* 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[*] (if set).
 */
__isl_give pet_expr *pet_expr_access_align_params(__isl_take pet_expr *expr)
{
	isl_space *space;
	enum pet_expr_access_type type;

	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));

	if (!pet_expr_access_has_any_access_relation(expr))
		return expr;

	space = isl_multi_pw_aff_get_space(expr->acc.index);
	for (type = pet_expr_access_begin; type < pet_expr_access_end; ++type) {
		if (!expr->acc.access[type])
			continue;
		space = isl_space_align_params(space,
			    isl_union_map_get_space(expr->acc.access[type]));
	}
	expr->acc.index = isl_multi_pw_aff_align_params(expr->acc.index,
							isl_space_copy(space));
	for (type = pet_expr_access_begin; type < pet_expr_access_end; ++type) {
		if (!expr->acc.access[type])
			continue;
		expr->acc.access[type] =
		    isl_union_map_align_params(expr->acc.access[type],
							isl_space_copy(space));
		if (!expr->acc.access[type])
			break;
	}
	isl_space_free(space);
	if (!expr->acc.index || type < pet_expr_access_end)
		return pet_expr_free(expr);

	return expr;
}

/* Are "expr1" and "expr2" both array accesses such that
 * the access relation of "expr1" is a subset of that of "expr2"?
 * Only take into account the first "n_arg" arguments.
 *
 * This function is tailored for use by mark_self_dependences in nest.c.
 * In particular, the input expressions may have more than "n_arg"
 * elements in their arguments arrays, while only the first "n_arg"
 * elements are referenced from the access relations.
 */
int pet_expr_is_sub_access(__isl_keep pet_expr *expr1,
	__isl_keep pet_expr *expr2, int n_arg)
{
	isl_id *id1, *id2;
	int i, n1, n2;
	int is_subset;

	if (!expr1 || !expr2)
		return 0;
	if (pet_expr_get_type(expr1) != pet_expr_access)
		return 0;
	if (pet_expr_get_type(expr2) != pet_expr_access)
		return 0;
	if (pet_expr_is_affine(expr1))
		return 0;
	if (pet_expr_is_affine(expr2))
		return 0;
	n1 = pet_expr_get_n_arg(expr1);
	if (n1 > n_arg)
		n1 = n_arg;
	n2 = pet_expr_get_n_arg(expr2);
	if (n2 > n_arg)
		n2 = n_arg;
	if (n1 != n2)
		return 0;
	for (i = 0; i < n1; ++i) {
		int equal;
		equal = pet_expr_is_equal(expr1->args[i], expr2->args[i]);
		if (equal < 0 || !equal)
			return equal;
	}
	id1 = pet_expr_access_get_id(expr1);
	id2 = pet_expr_access_get_id(expr2);
	isl_id_free(id1);
	isl_id_free(id2);
	if (!id1 || !id2)
		return 0;
	if (id1 != id2)
		return 0;

	expr1 = pet_expr_copy(expr1);
	expr2 = pet_expr_copy(expr2);
	expr1 = introduce_access_relations(expr1);
	expr2 = introduce_access_relations(expr2);
	if (!expr1 || !expr2)
		goto error;

	is_subset = isl_union_map_is_subset(
			expr1->acc.access[pet_expr_access_may_read],
			expr2->acc.access[pet_expr_access_may_read]);

	pet_expr_free(expr1);
	pet_expr_free(expr2);

	return is_subset;
error:
	pet_expr_free(expr1);
	pet_expr_free(expr2);
	return -1;
}

/* Given a set in the iteration space "domain", extend it to live in the space
 * of the domain of access relations.
 *
 * That, is the number of arguments "n" is 0, then simply return domain.
 * Otherwise, return [domain -> [a_1,...,a_n]].
 */
static __isl_give isl_set *add_arguments(__isl_take isl_set *domain, int n)
{
	isl_map *map;

	if (n == 0)
		return domain;

	map = isl_map_from_domain(domain);
	map = isl_map_add_dims(map, isl_dim_out, n);
	return isl_map_wrap(map);
}

/* Add extra conditions to the domains of all access relations in "expr",
 * introducing access relations if they are not already present.
 *
 * 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;
	isl_union_set *uset;
	enum pet_expr_access_type type;

	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) {
		isl_set_free(cond);
		return expr;
	}

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

	cond = add_arguments(cond, expr->n_arg);
	uset = isl_union_set_from_set(isl_set_copy(cond));
	for (type = pet_expr_access_begin; type < pet_expr_access_end; ++type) {
		if (!expr->acc.access[type])
			continue;
		expr->acc.access[type] =
		    isl_union_map_intersect_domain(expr->acc.access[type],
						    isl_union_set_copy(uset));
		if (!expr->acc.access[type])
			break;
	}
	isl_union_set_free(uset);
	expr->acc.index = isl_multi_pw_aff_gist(expr->acc.index, cond);
	if (type < pet_expr_access_end || !expr->acc.index)
		return pet_expr_free(expr);

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

/* Modify the access relations (if any) 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)
{
	enum pet_expr_access_type type;

	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);

	if (expr->n_arg > 0) {
		isl_space *space;
		isl_multi_pw_aff *id;

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

	for (type = pet_expr_access_begin; type < pet_expr_access_end; ++type) {
		if (!expr->acc.access[type])
			continue;
		expr->acc.access[type] =
		    isl_union_map_preimage_domain_multi_pw_aff(
					    expr->acc.access[type],
					    isl_multi_pw_aff_copy(update));
		if (!expr->acc.access[type])
			break;
	}
	expr->acc.index = isl_multi_pw_aff_pullback_multi_pw_aff(
					    expr->acc.index, update);
	if (type < pet_expr_access_end || !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;
}

/* Given an expression with accesses that have a 0D anonymous domain,
 * replace those domains by "space".
 */
__isl_give pet_expr *pet_expr_insert_domain(__isl_take pet_expr *expr,
	__isl_take isl_space *space)
{
	isl_multi_pw_aff *mpa;

	space = isl_space_from_domain(space);
	mpa = isl_multi_pw_aff_zero(space);
	return pet_expr_update_domain(expr, mpa);
}

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

	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));

	for (type = pet_expr_access_begin; type < pet_expr_access_end; ++type) {
		if (!expr->acc.access[type])
			continue;
		expr->acc.access[type] =
		    isl_union_map_align_params(expr->acc.access[type],
						isl_space_copy(space));
		if (!expr->acc.access[type])
			break;
	}
	expr->acc.index = isl_multi_pw_aff_align_params(expr->acc.index,
						isl_space_copy(space));
	if (type < pet_expr_access_end || !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
 * (introducing access relations if they are missing) 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;
	enum pet_expr_access_type type;

	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, 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);

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

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

	for (type = pet_expr_access_begin; type < pet_expr_access_end; ++type) {
		if (!expr->acc.access[type])
			continue;
		expr->acc.access[type] =
		    isl_union_map_preimage_domain_pw_multi_aff(
						expr->acc.access[type],
						isl_pw_multi_aff_copy(pma));
		if (!expr->acc.access[type])
			break;
	}
	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 (type < pet_expr_access_end || !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);
}

/* 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 = pet_expr_get_ctx(expr);
	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 relations (if any) and the index expression
 * of the access expression "expr".
 */
static __isl_give pet_expr *access_anonymize(__isl_take pet_expr *expr,
	void *user)
{
	enum pet_expr_access_type type;

	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));

	for (type = pet_expr_access_begin; type < pet_expr_access_end; ++type) {
		if (!expr->acc.access[type])
			continue;
		expr->acc.access[type] =
			isl_union_map_reset_user(expr->acc.access[type]);
		if (!expr->acc.access[type])
			break;
	}
	expr->acc.index = isl_multi_pw_aff_reset_user(expr->acc.index);
	if (type < pet_expr_access_end || !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 relations (if any) 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;
	isl_union_set *uset;
	enum pet_expr_access_type type;

	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);

	uset = isl_union_set_from_set(isl_set_copy(domain));
	for (type = pet_expr_access_begin; type < pet_expr_access_end; ++type) {
		if (!expr->acc.access[type])
			continue;
		expr->acc.access[type] =
		    isl_union_map_gist_domain(expr->acc.access[type],
						isl_union_set_copy(uset));
		if (!expr->acc.access[type])
			break;
	}
	isl_union_set_free(uset);
	expr->acc.index = isl_multi_pw_aff_gist(expr->acc.index, domain);
	if (type < pet_expr_access_end || !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;
}

/* Mark "expr" as a kill dependening on "kill".
 */
__isl_give pet_expr *pet_expr_access_set_kill(__isl_take pet_expr *expr,
	int kill)
{
	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.kill == kill)
		return expr;
	expr = pet_expr_cow(expr);
	if (!expr)
		return NULL;
	expr->acc.kill = kill;

	return expr;
}

/* Map the access type "type" to the corresponding location
 * in the access array.
 * In particular, the access relation of type pet_expr_access_killed is
 * stored in the element at position pet_expr_access_fake_killed.
 */
static enum pet_expr_access_type internalize_type(
	enum pet_expr_access_type type)
{
	if (type == pet_expr_access_killed)
		return pet_expr_access_fake_killed;
	return type;
}

/* Replace the access relation of the given "type" of "expr" by "access".
 * If the access relation is non-empty and the type is a read or a write,
 * then also mark the access expression itself as a read or a write.
 */
__isl_give pet_expr *pet_expr_access_set_access(__isl_take pet_expr *expr,
	enum pet_expr_access_type type, __isl_take isl_union_map *access)
{
	int empty;

	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);
	type = internalize_type(type);
	isl_union_map_free(expr->acc.access[type]);
	expr->acc.access[type] = access;

	if (expr->acc.kill)
		return expr;

	empty = isl_union_map_is_empty(access);
	if (empty < 0)
		return pet_expr_free(expr);
	if (empty)
		return expr;

	if (type == pet_expr_access_may_read)
		expr = pet_expr_access_set_read(expr, 1);
	else
		expr = pet_expr_access_set_write(expr, 1);

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

/* Replace the index expression of "expr" by "index" and
 * set the array depth accordingly.
 */
__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;
	expr->acc.depth = isl_multi_pw_aff_dim(index, isl_dim_out);

	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_union_map *pet_expr_tag_access(__isl_keep pet_expr *expr,
	__isl_take isl_union_map *access)
{
	isl_space *space;
	isl_multi_aff *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_union_map_free(access));

	id = isl_id_copy(expr->acc.ref_id);
	space = pet_expr_access_get_domain_space(expr);
	space = isl_space_from_domain(space);
	space = isl_space_set_tuple_id(space, isl_dim_out, id);
	add_tag = isl_multi_aff_domain_map(space);
	access = isl_union_map_preimage_domain_multi_aff(access, add_tag);

	return access;
}

/* Return the access relation of the given "type" associated to "expr"
 * that maps pairs of domain iterations and argument values
 * to the corresponding accessed data elements.
 *
 * If the requested access relation is explicitly available,
 * then return a copy.  Otherwise, check if it is irrelevant for
 * the access expression and return an empty relation if this is the case.
 * Otherwise, introduce the requested access relation in "expr" and
 * return a copy.
 */
__isl_give isl_union_map *pet_expr_access_get_dependent_access(
	__isl_keep pet_expr *expr, enum pet_expr_access_type type)
{
	isl_union_map *access;
	int empty;

	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);

	type = internalize_type(type);
	if (expr->acc.access[type])
		return isl_union_map_copy(expr->acc.access[type]);

	if (type == pet_expr_access_may_read)
		empty = !expr->acc.read;
	else
		empty = !expr->acc.write;

	if (!empty) {
		expr = pet_expr_copy(expr);
		expr = introduce_access_relations(expr);
		if (!expr)
			return NULL;
		access = isl_union_map_copy(expr->acc.access[type]);
		pet_expr_free(expr);

		return access;
	}

	return isl_union_map_empty(pet_expr_access_get_parameter_space(expr));
}

/* Return the may read access relation associated to "expr"
 * that maps pairs of domain iterations and argument values
 * to the corresponding accessed data elements.
 */
__isl_give isl_union_map *pet_expr_access_get_dependent_may_read(
	__isl_keep pet_expr *expr)
{
	return pet_expr_access_get_dependent_access(expr,
						    pet_expr_access_may_read);
}

/* Return the may write access relation associated to "expr"
 * that maps pairs of domain iterations and argument values
 * to the corresponding accessed data elements.
 */
__isl_give isl_union_map *pet_expr_access_get_dependent_may_write(
	__isl_keep pet_expr *expr)
{
	return pet_expr_access_get_dependent_access(expr,
						    pet_expr_access_may_write);
}

/* Return the must write access relation associated to "expr"
 * that maps pairs of domain iterations and argument values
 * to the corresponding accessed data elements.
 */
__isl_give isl_union_map *pet_expr_access_get_dependent_must_write(
	__isl_keep pet_expr *expr)
{
	return pet_expr_access_get_dependent_access(expr,
						    pet_expr_access_must_write);
}

/* Return the relation of the given "type" mapping domain iterations
 * to the accessed data elements.
 * In particular, take the access relation and, in case of may_read
 * or may_write, project out the values of the arguments, if any.
 * In case of must_write, return the empty relation if there are
 * any arguments.
 */
__isl_give isl_union_map *pet_expr_access_get_access(__isl_keep pet_expr *expr,
	enum pet_expr_access_type type)
{
	isl_union_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);

	if (expr->n_arg != 0 && type == pet_expr_access_must_write) {
		space = pet_expr_access_get_parameter_space(expr);
		return isl_union_map_empty(space);
	}

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

	space = isl_multi_pw_aff_get_space(expr->acc.index);
	space = isl_space_domain(space);
	map = isl_map_universe(isl_space_unwrap(space));
	map = isl_map_domain_map(map);
	access = isl_union_map_apply_domain(access,
						isl_union_map_from_map(map));

	return access;
}

/* Return the relation mapping domain iterations to all possibly
 * read data elements.
 */
__isl_give isl_union_map *pet_expr_access_get_may_read(
	__isl_keep pet_expr *expr)
{
	return pet_expr_access_get_access(expr, pet_expr_access_may_read);
}

/* Return the relation mapping domain iterations to all possibly
 * written data elements.
 */
__isl_give isl_union_map *pet_expr_access_get_may_write(
	__isl_keep pet_expr *expr)
{
	return pet_expr_access_get_access(expr, pet_expr_access_may_write);
}

/* Return a relation mapping domain iterations to definitely
 * written data elements, assuming the statement containing
 * the expression is executed.
 */
__isl_give isl_union_map *pet_expr_access_get_must_write(
	__isl_keep pet_expr *expr)
{
	return pet_expr_access_get_access(expr, pet_expr_access_must_write);
}

/* Return the relation of the given "type" mapping domain iterations to
 * accessed data elements, with its domain tagged with the reference
 * identifier.
 */
static __isl_give isl_union_map *pet_expr_access_get_tagged_access(
	__isl_keep pet_expr *expr, enum pet_expr_access_type type)
{
	isl_union_map *access;

	if (!expr)
		return NULL;

	access = pet_expr_access_get_access(expr, type);
	access = pet_expr_tag_access(expr, access);

	return access;
}

/* Return the relation mapping domain iterations to all possibly
 * read data elements, with its domain tagged with the reference
 * identifier.
 */
__isl_give isl_union_map *pet_expr_access_get_tagged_may_read(
	__isl_keep pet_expr *expr)
{
	return pet_expr_access_get_tagged_access(expr,
						pet_expr_access_may_read);
}

/* Return the relation mapping domain iterations to all possibly
 * written data elements, with its domain tagged with the reference
 * identifier.
 */
__isl_give isl_union_map *pet_expr_access_get_tagged_may_write(
	__isl_keep pet_expr *expr)
{
	return pet_expr_access_get_tagged_access(expr,
						pet_expr_access_may_write);
}

/* 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->c.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->c.name);
	expr->c.name = strdup(name);
	if (!expr->c.name)
		return pet_expr_free(expr);
	return expr;
}

/* Does the call expression "expr" have an associated function summary?
 */
int pet_expr_call_has_summary(__isl_keep pet_expr *expr)
{
	if (!expr)
		return -1;
	if (expr->type != pet_expr_call)
		isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
			"not a call expression", return -1);

	return expr->c.summary != NULL;
}

/* Return a copy of the function summary associated to
 * the call expression "expr".
 */
__isl_give pet_function_summary *pet_expr_call_get_summary(
	__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 pet_function_summary_copy(expr->c.summary);
}

/* Replace the function summary associated to the call expression "expr"
 * by "summary".
 */
__isl_give pet_expr *pet_expr_call_set_summary(__isl_take pet_expr *expr,
	__isl_take pet_function_summary *summary)
{
	expr = pet_expr_cow(expr);
	if (!expr || !summary)
		goto error;
	if (expr->type != pet_expr_call)
		isl_die(pet_expr_get_ctx(expr), isl_error_invalid,
			"not a call expression", goto error);
	pet_function_summary_free(expr->c.summary);
	expr->c.summary = summary;
	return expr;
error:
	pet_function_summary_free(summary);
	return pet_expr_free(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 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)
{
	isl_id *id;

	if (pet_expr_is_affine(expr))
		return pet_expr_get_affine(expr);

	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))
		return pet_context_get_value(pc, id);

	isl_id_free(id);
	return nested_access(expr, pc);
}

/* 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.
 *
 * We simplify the result in the context of the domain of "pc" in case
 * this domain implies that lhs >= 0 (or < 0).
 */
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;
	isl_pw_aff *res;

	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:
		res = isl_pw_aff_tdiv_q(lhs, rhs);
		break;
	case pet_op_mod:
		res = isl_pw_aff_tdiv_r(lhs, rhs);
		break;
	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);
	}

	return isl_pw_aff_gist(res, pet_context_get_gist_domain(pc));
}

/* 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))
		return isl_pw_aff_mul(lhs, rhs);

	isl_pw_aff_free(lhs);
	isl_pw_aff_free(rhs);

	if (lhs_cst < 0 || rhs_cst < 0)
		return NULL;

	return non_affine(pet_context_get_space(pc));
}

/* 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);
}

/* 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 = pet_wrap_pw_aff(res, type_size);
	else
		res = signed_overflow(res, -type_size);

	return res;
}

/* Internal data structure for affine builtin function declarations.
 *
 * "pencil" is set if the builtin is pencil specific.
 * "n_args" is the number of arguments the function takes.
 * "name" is the function name.
 */
struct affine_builtin_decl {
	int pencil;
	int n_args;
	const char *name;
};

static struct affine_builtin_decl affine_builtins[] = {
	{ 0, 2, "min" },
	{ 1, 2, "imin" },
	{ 1, 2, "umin" },
	{ 0, 2, "max" },
	{ 1, 2, "imax" },
	{ 1, 2, "umax" },
	{ 0, 2, "intMod" },
	{ 0, 2, "intFloor" },
	{ 0, 2, "intCeil" },
	{ 0, 2, "floord" },
	{ 0, 2, "ceild" }
};

/* List of min and max builtin functions.
 */
static const char *min_max_builtins[] = {
	"min", "imin", "umin",
	"max", "imax", "umax"
};

/* Is a function call to "name" with "n_args" arguments a call to a
 * builtin function for which we can construct an affine expression?
 * pencil specific builtins are only recognized if "pencil" is set.
 */
static int is_affine_builtin(int pencil, int n_args, const char *name)
{
	int i;

	for (i = 0; i < ARRAY_SIZE(affine_builtins); ++i) {
		struct affine_builtin_decl *decl = &affine_builtins[i];

		if (decl->pencil && !pencil)
			continue;
		if (decl->n_args == n_args && !strcmp(decl->name, name))
			return 1;
	}

	return 0;
}

/* Is function "name" a known min or max builtin function?
 */
static int is_min_or_max_builtin(const char *name)
{
	int i;

	for (i = 0; i < ARRAY_SIZE(min_max_builtins); ++i)
		if (!strcmp(min_max_builtins[i], name))
			return 1;

	return 0;
}

/* 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.
 * If the pencil option is set, then we also handle "{i,u}min" and
 * "{i,u}max".
 *
 * "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_ctx *ctx;
	isl_pw_aff *aff1, *aff2;
	int n;
	const char *name;
	struct pet_options *options;

	if (!expr)
		return NULL;
	ctx = pet_expr_get_ctx(expr);
	options = isl_ctx_peek_pet_options(ctx);

	n = pet_expr_get_n_arg(expr);
	name = pet_expr_call_get_name(expr);
	if (!is_affine_builtin(options->pencil, n, name))
		return non_affine(pet_context_get_space(pc));

	if (is_min_or_max_builtin(name)) {
		aff1 = pet_expr_extract_affine(expr->args[0], pc);
		aff2 = pet_expr_extract_affine(expr->args[1], pc);

		if (strstr(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.
 *
 * Store the result in "pc" such that it can be reused in case
 * pet_expr_extract_affine is called again on the same pair of
 * "expr" and "pc".
 */
__isl_give isl_pw_aff *pet_expr_extract_affine(__isl_keep pet_expr *expr,
	__isl_keep pet_context *pc)
{
	isl_maybe_isl_pw_aff m;
	isl_pw_aff *pa;

	if (!expr)
		return NULL;

	m = pet_context_get_extracted_affine(pc, expr);
	if (m.valid < 0 || m.valid)
		return m.value;

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

	if (pet_context_set_extracted_affine(pc, expr, pa) < 0)
		return isl_pw_aff_free(pa);

	return pa;
}

/* 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;
}

/* Prefix the access expression "expr" with "prefix".
 * If "add" is set, then it is not the index expression "prefix" itself
 * that was passed to the function, but its address.
 */
__isl_give pet_expr *pet_expr_access_patch(__isl_take pet_expr *expr,
	__isl_take isl_multi_pw_aff *prefix, int add)
{
	enum pet_expr_access_type type;

	expr = pet_expr_cow(expr);
	if (!expr || !prefix)
		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.depth += isl_multi_pw_aff_dim(prefix, isl_dim_out) - add;
	for (type = pet_expr_access_begin; type < pet_expr_access_end; ++type) {
		if (!expr->acc.access[type])
			continue;
		expr->acc.access[type] = pet_patch_union_map(
			isl_multi_pw_aff_copy(prefix), expr->acc.access[type],
			add, 0);
		if (!expr->acc.access[type])
			break;
	}
	expr->acc.index = pet_patch_multi_pw_aff(prefix, expr->acc.index, add);
	if (!expr->acc.index || type < pet_expr_access_end)
		return pet_expr_free(expr);

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

/* Dump the arguments of "expr" to "p" as a YAML sequence keyed
 * by "args", if there are any such arguments.
 */
static __isl_give isl_printer *dump_arguments(__isl_keep pet_expr *expr,
	__isl_take isl_printer *p)
{
	int i;

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

	p = isl_printer_print_str(p, "args");
	p = isl_printer_yaml_next(p);
	p = isl_printer_yaml_start_sequence(p);
	for (i = 0; i < expr->n_arg; ++i) {
		p = pet_expr_print(expr->args[i], p);
		p = isl_printer_yaml_next(p);
	}
	p = isl_printer_yaml_end_sequence(p);

	return p;
}

/* Print "expr" to "p" in YAML format.
 */
__isl_give isl_printer *pet_expr_print(__isl_keep pet_expr *expr,
	__isl_take isl_printer *p)
{
	if (!expr || !p)
		return isl_printer_free(p);

	switch (expr->type) {
	case pet_expr_double:
		p = isl_printer_print_str(p, expr->d.s);
		break;
	case pet_expr_int:
		p = isl_printer_print_val(p, expr->i);
		break;
	case pet_expr_access:
		p = isl_printer_yaml_start_mapping(p);
		if (expr->acc.ref_id) {
			p = isl_printer_print_str(p, "ref_id");
			p = isl_printer_yaml_next(p);
			p = isl_printer_print_id(p, expr->acc.ref_id);
			p = isl_printer_yaml_next(p);
		}
		p = isl_printer_print_str(p, "index");
		p = isl_printer_yaml_next(p);
		p = isl_printer_print_multi_pw_aff(p, expr->acc.index);
		p = isl_printer_yaml_next(p);
		p = isl_printer_print_str(p, "depth");
		p = isl_printer_yaml_next(p);
		p = isl_printer_print_int(p, expr->acc.depth);
		p = isl_printer_yaml_next(p);
		if (expr->acc.kill) {
			p = isl_printer_print_str(p, "kill");
			p = isl_printer_yaml_next(p);
			p = isl_printer_print_int(p, 1);
			p = isl_printer_yaml_next(p);
		} else {
			p = isl_printer_print_str(p, "read");
			p = isl_printer_yaml_next(p);
			p = isl_printer_print_int(p, expr->acc.read);
			p = isl_printer_yaml_next(p);
			p = isl_printer_print_str(p, "write");
			p = isl_printer_yaml_next(p);
			p = isl_printer_print_int(p, expr->acc.write);
			p = isl_printer_yaml_next(p);
		}
		if (expr->acc.access[pet_expr_access_may_read]) {
			p = isl_printer_print_str(p, "may_read");
			p = isl_printer_yaml_next(p);
			p = isl_printer_print_union_map(p,
				expr->acc.access[pet_expr_access_may_read]);
			p = isl_printer_yaml_next(p);
		}
		if (expr->acc.access[pet_expr_access_may_write]) {
			p = isl_printer_print_str(p, "may_write");
			p = isl_printer_yaml_next(p);
			p = isl_printer_print_union_map(p,
				expr->acc.access[pet_expr_access_may_write]);
			p = isl_printer_yaml_next(p);
		}
		if (expr->acc.access[pet_expr_access_must_write]) {
			p = isl_printer_print_str(p, "must_write");
			p = isl_printer_yaml_next(p);
			p = isl_printer_print_union_map(p,
				expr->acc.access[pet_expr_access_must_write]);
			p = isl_printer_yaml_next(p);
		}
		p = dump_arguments(expr, p);
		p = isl_printer_yaml_end_mapping(p);
		break;
	case pet_expr_op:
		p = isl_printer_yaml_start_mapping(p);
		p = isl_printer_print_str(p, "op");
		p = isl_printer_yaml_next(p);
		p = isl_printer_print_str(p, op_str[expr->op]);
		p = isl_printer_yaml_next(p);
		p = dump_arguments(expr, p);
		p = isl_printer_yaml_end_mapping(p);
		break;
	case pet_expr_call:
		p = isl_printer_yaml_start_mapping(p);
		p = isl_printer_print_str(p, "call");
		p = isl_printer_yaml_next(p);
		p = isl_printer_print_str(p, expr->c.name);
		p = isl_printer_print_str(p, "/");
		p = isl_printer_print_int(p, expr->n_arg);
		p = isl_printer_yaml_next(p);
		p = dump_arguments(expr, p);
		if (expr->c.summary) {
			p = isl_printer_print_str(p, "summary");
			p = isl_printer_yaml_next(p);
			p = pet_function_summary_print(expr->c.summary, p);
		}
		p = isl_printer_yaml_end_mapping(p);
		break;
	case pet_expr_cast:
		p = isl_printer_yaml_start_mapping(p);
		p = isl_printer_print_str(p, "cast");
		p = isl_printer_yaml_next(p);
		p = isl_printer_print_str(p, expr->type_name);
		p = isl_printer_yaml_next(p);
		p = dump_arguments(expr, p);
		p = isl_printer_yaml_end_mapping(p);
		break;
	case pet_expr_error:
		p = isl_printer_print_str(p, "ERROR");
		break;
	}

	return p;
}

/* Dump "expr" to stderr with indentation "indent".
 */
void pet_expr_dump_with_indent(__isl_keep pet_expr *expr, int indent)
{
	isl_printer *p;

	if (!expr)
		return;

	p = isl_printer_to_file(pet_expr_get_ctx(expr), stderr);
	p = isl_printer_set_indent(p, indent);
	p = isl_printer_set_yaml_style(p, ISL_YAML_STYLE_BLOCK);
	p = isl_printer_start_line(p);
	p = pet_expr_print(expr, p);

	isl_printer_free(p);
}

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