PetScan::extract_non_affine_condition: take index expression

[pet.git] / scan.cc

/*
 * Copyright 2011 Leiden University. All rights reserved.
 * Copyright 2012 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 <set>
#include <map>
#include <iostream>
#include <llvm/Support/raw_ostream.h>
#include <clang/AST/ASTContext.h>
#include <clang/AST/ASTDiagnostic.h>
#include <clang/AST/Expr.h>
#include <clang/AST/RecursiveASTVisitor.h>

#include <isl/id.h>
#include <isl/space.h>
#include <isl/aff.h>
#include <isl/set.h>

#include "options.h"
#include "scan.h"
#include "scop.h"
#include "scop_plus.h"

#include "config.h"

using namespace std;
using namespace clang;

#if defined(DECLREFEXPR_CREATE_REQUIRES_BOOL)
static DeclRefExpr *create_DeclRefExpr(VarDecl *var)
{
        return DeclRefExpr::Create(var->getASTContext(), var->getQualifierLoc(),
                SourceLocation(), var, false, var->getInnerLocStart(),
                var->getType(), VK_LValue);
}
#elif defined(DECLREFEXPR_CREATE_REQUIRES_SOURCELOCATION)
static DeclRefExpr *create_DeclRefExpr(VarDecl *var)
{
        return DeclRefExpr::Create(var->getASTContext(), var->getQualifierLoc(),
                SourceLocation(), var, var->getInnerLocStart(), var->getType(),
                VK_LValue);
}
#else
static DeclRefExpr *create_DeclRefExpr(VarDecl *var)
{
        return DeclRefExpr::Create(var->getASTContext(), var->getQualifierLoc(),
                var, var->getInnerLocStart(), var->getType(), VK_LValue);
}
#endif

/* Check if the element type corresponding to the given array type
 * has a const qualifier.
 */
static bool const_base(QualType qt)
{
        const Type *type = qt.getTypePtr();

        if (type->isPointerType())
                return const_base(type->getPointeeType());
        if (type->isArrayType()) {
                const ArrayType *atype;
                type = type->getCanonicalTypeInternal().getTypePtr();
                atype = cast<ArrayType>(type);
                return const_base(atype->getElementType());
        }

        return qt.isConstQualified();
}

/* Mark "decl" as having an unknown value in "assigned_value".
 *
 * If no (known or unknown) value was assigned to "decl" before,
 * then it may have been treated as a parameter before and may
 * therefore appear in a value assigned to another variable.
 * If so, this assignment needs to be turned into an unknown value too.
 */
static void clear_assignment(map<ValueDecl *, isl_pw_aff *> &assigned_value,
        ValueDecl *decl)
{
        map<ValueDecl *, isl_pw_aff *>::iterator it;

        it = assigned_value.find(decl);

        assigned_value[decl] = NULL;

        if (it == assigned_value.end())
                return;

        for (it = assigned_value.begin(); it != assigned_value.end(); ++it) {
                isl_pw_aff *pa = it->second;
                int nparam = isl_pw_aff_dim(pa, isl_dim_param);

                for (int i = 0; i < nparam; ++i) {
                        isl_id *id;

                        if (!isl_pw_aff_has_dim_id(pa, isl_dim_param, i))
                                continue;
                        id = isl_pw_aff_get_dim_id(pa, isl_dim_param, i);
                        if (isl_id_get_user(id) == decl)
                                it->second = NULL;
                        isl_id_free(id);
                }
        }
}

/* Look for any assignments to scalar variables in part of the parse
 * tree and set assigned_value to NULL for each of them.
 * Also reset assigned_value if the address of a scalar variable
 * is being taken.  As an exception, if the address is passed to a function
 * that is declared to receive a const pointer, then assigned_value is
 * not reset.
 *
 * This ensures that we won't use any previously stored value
 * in the current subtree and its parents.
 */
struct clear_assignments : RecursiveASTVisitor<clear_assignments> {
        map<ValueDecl *, isl_pw_aff *> &assigned_value;
        set<UnaryOperator *> skip;

        clear_assignments(map<ValueDecl *, isl_pw_aff *> &assigned_value) :
                assigned_value(assigned_value) {}

        /* Check for "address of" operators whose value is passed
         * to a const pointer argument and add them to "skip", so that
         * we can skip them in VisitUnaryOperator.
         */
        bool VisitCallExpr(CallExpr *expr) {
                FunctionDecl *fd;
                fd = expr->getDirectCallee();
                if (!fd)
                        return true;
                for (int i = 0; i < expr->getNumArgs(); ++i) {
                        Expr *arg = expr->getArg(i);
                        UnaryOperator *op;
                        if (arg->getStmtClass() == Stmt::ImplicitCastExprClass) {
                                ImplicitCastExpr *ice;
                                ice = cast<ImplicitCastExpr>(arg);
                                arg = ice->getSubExpr();
                        }
                        if (arg->getStmtClass() != Stmt::UnaryOperatorClass)
                                continue;
                        op = cast<UnaryOperator>(arg);
                        if (op->getOpcode() != UO_AddrOf)
                                continue;
                        if (const_base(fd->getParamDecl(i)->getType()))
                                skip.insert(op);
                }
                return true;
        }

        bool VisitUnaryOperator(UnaryOperator *expr) {
                Expr *arg;
                DeclRefExpr *ref;
                ValueDecl *decl;

                switch (expr->getOpcode()) {
                case UO_AddrOf:
                case UO_PostInc:
                case UO_PostDec:
                case UO_PreInc:
                case UO_PreDec:
                        break;
                default:
                        return true;
                }
                if (skip.find(expr) != skip.end())
                        return true;

                arg = expr->getSubExpr();
                if (arg->getStmtClass() != Stmt::DeclRefExprClass)
                        return true;
                ref = cast<DeclRefExpr>(arg);
                decl = ref->getDecl();
                clear_assignment(assigned_value, decl);
                return true;
        }

        bool VisitBinaryOperator(BinaryOperator *expr) {
                Expr *lhs;
                DeclRefExpr *ref;
                ValueDecl *decl;

                if (!expr->isAssignmentOp())
                        return true;
                lhs = expr->getLHS();
                if (lhs->getStmtClass() != Stmt::DeclRefExprClass)
                        return true;
                ref = cast<DeclRefExpr>(lhs);
                decl = ref->getDecl();
                clear_assignment(assigned_value, decl);
                return true;
        }
};

/* Keep a copy of the currently assigned values.
 *
 * Any variable that is assigned a value inside the current scope
 * is removed again when we leave the scope (either because it wasn't
 * stored in the cache or because it has a different value in the cache).
 */
struct assigned_value_cache {
        map<ValueDecl *, isl_pw_aff *> &assigned_value;
        map<ValueDecl *, isl_pw_aff *> cache;

        assigned_value_cache(map<ValueDecl *, isl_pw_aff *> &assigned_value) :
                assigned_value(assigned_value), cache(assigned_value) {}
        ~assigned_value_cache() {
                map<ValueDecl *, isl_pw_aff *>::iterator it = cache.begin();
                for (it = assigned_value.begin(); it != assigned_value.end();
                     ++it) {
                        if (!it->second ||
                            (cache.find(it->first) != cache.end() &&
                             cache[it->first] != it->second))
                                cache[it->first] = NULL;
                }
                assigned_value = cache;
        }
};

/* Insert an expression into the collection of expressions,
 * provided it is not already in there.
 * The isl_pw_affs are freed in the destructor.
 */
void PetScan::insert_expression(__isl_take isl_pw_aff *expr)
{
        std::set<isl_pw_aff *>::iterator it;

        if (expressions.find(expr) == expressions.end())
                expressions.insert(expr);
        else
                isl_pw_aff_free(expr);
}

PetScan::~PetScan()
{
        std::set<isl_pw_aff *>::iterator it;

        for (it = expressions.begin(); it != expressions.end(); ++it)
                isl_pw_aff_free(*it);

        isl_union_map_free(value_bounds);
}

/* Called if we found something we (currently) cannot handle.
 * We'll provide more informative warnings later.
 *
 * We only actually complain if autodetect is false.
 */
void PetScan::unsupported(Stmt *stmt, const char *msg)
{
        if (options->autodetect)
                return;

        SourceLocation loc = stmt->getLocStart();
        DiagnosticsEngine &diag = PP.getDiagnostics();
        unsigned id = diag.getCustomDiagID(DiagnosticsEngine::Warning,
                                           msg ? msg : "unsupported");
        DiagnosticBuilder B = diag.Report(loc, id) << stmt->getSourceRange();
}

/* Extract an integer from "expr".
 */
__isl_give isl_val *PetScan::extract_int(isl_ctx *ctx, IntegerLiteral *expr)
{
        const Type *type = expr->getType().getTypePtr();
        int is_signed = type->hasSignedIntegerRepresentation();
        llvm::APInt val = expr->getValue();
        int is_negative = is_signed && val.isNegative();
        isl_val *v;

        if (is_negative)
                val = -val;

        v = extract_unsigned(ctx, val);

        if (is_negative)
                v = isl_val_neg(v);
        return v;
}

/* Extract an integer from "val", which assumed to be non-negative.
 */
__isl_give isl_val *PetScan::extract_unsigned(isl_ctx *ctx,
        const llvm::APInt &val)
{
        unsigned n;
        const uint64_t *data;

        data = val.getRawData();
        n = val.getNumWords();
        return isl_val_int_from_chunks(ctx, n, sizeof(uint64_t), data);
}

/* Extract an integer from "expr".
 * Return NULL if "expr" does not (obviously) represent an integer.
 */
__isl_give isl_val *PetScan::extract_int(clang::ParenExpr *expr)
{
        return extract_int(expr->getSubExpr());
}

/* Extract an integer from "expr".
 * Return NULL if "expr" does not (obviously) represent an integer.
 */
__isl_give isl_val *PetScan::extract_int(clang::Expr *expr)
{
        if (expr->getStmtClass() == Stmt::IntegerLiteralClass)
                return extract_int(ctx, cast<IntegerLiteral>(expr));
        if (expr->getStmtClass() == Stmt::ParenExprClass)
                return extract_int(cast<ParenExpr>(expr));

        unsupported(expr);
        return NULL;
}

/* Extract an affine expression from the IntegerLiteral "expr".
 */
__isl_give isl_pw_aff *PetScan::extract_affine(IntegerLiteral *expr)
{
        isl_space *dim = isl_space_params_alloc(ctx, 0);
        isl_local_space *ls = isl_local_space_from_space(isl_space_copy(dim));
        isl_aff *aff = isl_aff_zero_on_domain(ls);
        isl_set *dom = isl_set_universe(dim);
        isl_val *v;

        v = extract_int(expr);
        aff = isl_aff_add_constant_val(aff, v);

        return isl_pw_aff_alloc(dom, aff);
}

/* Extract an affine expression from the APInt "val", which is assumed
 * to be non-negative.
 */
__isl_give isl_pw_aff *PetScan::extract_affine(const llvm::APInt &val)
{
        isl_space *dim = isl_space_params_alloc(ctx, 0);
        isl_local_space *ls = isl_local_space_from_space(isl_space_copy(dim));
        isl_aff *aff = isl_aff_zero_on_domain(ls);
        isl_set *dom = isl_set_universe(dim);
        isl_val *v;

        v = extract_unsigned(ctx, val);
        aff = isl_aff_add_constant_val(aff, v);

        return isl_pw_aff_alloc(dom, aff);
}

__isl_give isl_pw_aff *PetScan::extract_affine(ImplicitCastExpr *expr)
{
        return extract_affine(expr->getSubExpr());
}

static unsigned get_type_size(ValueDecl *decl)
{
        return decl->getASTContext().getIntWidth(decl->getType());
}

/* Bound parameter "pos" of "set" to the possible values of "decl".
 */
static __isl_give isl_set *set_parameter_bounds(__isl_take isl_set *set,
        unsigned pos, ValueDecl *decl)
{
        unsigned width;
        isl_ctx *ctx;
        isl_val *bound;

        ctx = isl_set_get_ctx(set);
        width = get_type_size(decl);
        if (decl->getType()->isUnsignedIntegerType()) {
                set = isl_set_lower_bound_si(set, isl_dim_param, pos, 0);
                bound = isl_val_int_from_ui(ctx, width);
                bound = isl_val_2exp(bound);
                bound = isl_val_sub_ui(bound, 1);
                set = isl_set_upper_bound_val(set, isl_dim_param, pos, bound);
        } else {
                bound = isl_val_int_from_ui(ctx, width - 1);
                bound = isl_val_2exp(bound);
                bound = isl_val_sub_ui(bound, 1);
                set = isl_set_upper_bound_val(set, isl_dim_param, pos,
                                                isl_val_copy(bound));
                bound = isl_val_neg(bound);
                bound = isl_val_sub_ui(bound, 1);
                set = isl_set_lower_bound_val(set, isl_dim_param, pos, bound);
        }

        return set;
}

/* Extract an affine expression from the DeclRefExpr "expr".
 *
 * If the variable has been assigned a value, then we check whether
 * we know what (affine) value was assigned.
 * If so, we return this value.  Otherwise we convert "expr"
 * to an extra parameter (provided nesting_enabled is set).
 *
 * Otherwise, we simply return an expression that is equal
 * to a parameter corresponding to the referenced variable.
 */
__isl_give isl_pw_aff *PetScan::extract_affine(DeclRefExpr *expr)
{
        ValueDecl *decl = expr->getDecl();
        const Type *type = decl->getType().getTypePtr();
        isl_id *id;
        isl_space *dim;
        isl_aff *aff;
        isl_set *dom;

        if (!type->isIntegerType()) {
                unsupported(expr);
                return NULL;
        }

        if (assigned_value.find(decl) != assigned_value.end()) {
                if (assigned_value[decl])
                        return isl_pw_aff_copy(assigned_value[decl]);
                else
                        return nested_access(expr);
        }

        id = isl_id_alloc(ctx, decl->getName().str().c_str(), decl);
        dim = isl_space_params_alloc(ctx, 1);

        dim = isl_space_set_dim_id(dim, isl_dim_param, 0, id);

        dom = isl_set_universe(isl_space_copy(dim));
        aff = isl_aff_zero_on_domain(isl_local_space_from_space(dim));
        aff = isl_aff_add_coefficient_si(aff, isl_dim_param, 0, 1);

        return isl_pw_aff_alloc(dom, aff);
}

/* Extract an affine expression from an integer division operation.
 * In particular, if "expr" is lhs/rhs, then return
 *
 *      lhs >= 0 ? floor(lhs/rhs) : ceil(lhs/rhs)
 *
 * The second argument (rhs) is required to be a (positive) integer constant.
 */
__isl_give isl_pw_aff *PetScan::extract_affine_div(BinaryOperator *expr)
{
        int is_cst;
        isl_pw_aff *rhs, *lhs;

        rhs = extract_affine(expr->getRHS());
        is_cst = isl_pw_aff_is_cst(rhs);
        if (is_cst < 0 || !is_cst) {
                isl_pw_aff_free(rhs);
                if (!is_cst)
                        unsupported(expr);
                return NULL;
        }

        lhs = extract_affine(expr->getLHS());

        return isl_pw_aff_tdiv_q(lhs, rhs);
}

/* Extract an affine expression from a modulo operation.
 * In particular, if "expr" is lhs/rhs, then return
 *
 *      lhs - rhs * (lhs >= 0 ? floor(lhs/rhs) : ceil(lhs/rhs))
 *
 * The second argument (rhs) is required to be a (positive) integer constant.
 */
__isl_give isl_pw_aff *PetScan::extract_affine_mod(BinaryOperator *expr)
{
        int is_cst;
        isl_pw_aff *rhs, *lhs;

        rhs = extract_affine(expr->getRHS());
        is_cst = isl_pw_aff_is_cst(rhs);
        if (is_cst < 0 || !is_cst) {
                isl_pw_aff_free(rhs);
                if (!is_cst)
                        unsupported(expr);
                return NULL;
        }

        lhs = extract_affine(expr->getLHS());

        return isl_pw_aff_tdiv_r(lhs, rhs);
}

/* Extract an affine expression from a multiplication operation.
 * This is only allowed if at least one of the two arguments
 * is a (piecewise) constant.
 */
__isl_give isl_pw_aff *PetScan::extract_affine_mul(BinaryOperator *expr)
{
        isl_pw_aff *lhs;
        isl_pw_aff *rhs;

        lhs = extract_affine(expr->getLHS());
        rhs = extract_affine(expr->getRHS());

        if (!isl_pw_aff_is_cst(lhs) && !isl_pw_aff_is_cst(rhs)) {
                isl_pw_aff_free(lhs);
                isl_pw_aff_free(rhs);
                unsupported(expr);
                return NULL;
        }

        return isl_pw_aff_mul(lhs, rhs);
}

/* Extract an affine expression from an addition or subtraction operation.
 */
__isl_give isl_pw_aff *PetScan::extract_affine_add(BinaryOperator *expr)
{
        isl_pw_aff *lhs;
        isl_pw_aff *rhs;

        lhs = extract_affine(expr->getLHS());
        rhs = extract_affine(expr->getRHS());

        switch (expr->getOpcode()) {
        case BO_Add:
                return isl_pw_aff_add(lhs, rhs);
        case BO_Sub:
                return isl_pw_aff_sub(lhs, rhs);
        default:
                isl_pw_aff_free(lhs);
                isl_pw_aff_free(rhs);
                return NULL;
        }

}

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

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

        pwaff = isl_pw_aff_mod_val(pwaff, mod);

        return pwaff;
}

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

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

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

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

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

        return pwaff;
}

/* Handle potential overflows on signed computations.
 *
 * If options->signed_overflow is set to PET_OVERFLOW_AVOID,
 * the we adjust the domain of "pa" to avoid overflows.
 */
__isl_give isl_pw_aff *PetScan::signed_overflow(__isl_take isl_pw_aff *pa,
        unsigned width)
{
        if (options->signed_overflow == PET_OVERFLOW_AVOID)
                pa = avoid_overflow(pa, width);

        return pa;
}

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

/* Extract an affine expression from some binary operations.
 * If the result of the expression is unsigned, then we wrap it
 * based on the size of the type.  Otherwise, we ensure that
 * no overflow occurs.
 */
__isl_give isl_pw_aff *PetScan::extract_affine(BinaryOperator *expr)
{
        isl_pw_aff *res;
        unsigned width;

        switch (expr->getOpcode()) {
        case BO_Add:
        case BO_Sub:
                res = extract_affine_add(expr);
                break;
        case BO_Div:
                res = extract_affine_div(expr);
                break;
        case BO_Rem:
                res = extract_affine_mod(expr);
                break;
        case BO_Mul:
                res = extract_affine_mul(expr);
                break;
        case BO_LT:
        case BO_LE:
        case BO_GT:
        case BO_GE:
        case BO_EQ:
        case BO_NE:
        case BO_LAnd:
        case BO_LOr:
                return extract_condition(expr);
        default:
                unsupported(expr);
                return NULL;
        }

        width = ast_context.getIntWidth(expr->getType());
        if (expr->getType()->isUnsignedIntegerType())
                res = wrap(res, width);
        else
                res = signed_overflow(res, width);

        return res;
}

/* Extract an affine expression from a negation operation.
 */
__isl_give isl_pw_aff *PetScan::extract_affine(UnaryOperator *expr)
{
        if (expr->getOpcode() == UO_Minus)
                return isl_pw_aff_neg(extract_affine(expr->getSubExpr()));
        if (expr->getOpcode() == UO_LNot)
                return extract_condition(expr);

        unsupported(expr);
        return NULL;
}

__isl_give isl_pw_aff *PetScan::extract_affine(ParenExpr *expr)
{
        return extract_affine(expr->getSubExpr());
}

/* Extract an affine expression from some special function calls.
 * In particular, we handle "min", "max", "ceild" and "floord".
 * In case of the latter two, the second argument needs to be
 * a (positive) integer constant.
 */
__isl_give isl_pw_aff *PetScan::extract_affine(CallExpr *expr)
{
        FunctionDecl *fd;
        string name;
        isl_pw_aff *aff1, *aff2;

        fd = expr->getDirectCallee();
        if (!fd) {
                unsupported(expr);
                return NULL;
        }

        name = fd->getDeclName().getAsString();
        if (!(expr->getNumArgs() == 2 && name == "min") &&
            !(expr->getNumArgs() == 2 && name == "max") &&
            !(expr->getNumArgs() == 2 && name == "floord") &&
            !(expr->getNumArgs() == 2 && name == "ceild")) {
                unsupported(expr);
                return NULL;
        }

        if (name == "min" || name == "max") {
                aff1 = extract_affine(expr->getArg(0));
                aff2 = extract_affine(expr->getArg(1));

                if (name == "min")
                        aff1 = isl_pw_aff_min(aff1, aff2);
                else
                        aff1 = isl_pw_aff_max(aff1, aff2);
        } else if (name == "floord" || name == "ceild") {
                isl_val *v;
                Expr *arg2 = expr->getArg(1);

                if (arg2->getStmtClass() != Stmt::IntegerLiteralClass) {
                        unsupported(expr);
                        return NULL;
                }
                aff1 = extract_affine(expr->getArg(0));
                v = extract_int(cast<IntegerLiteral>(arg2));
                aff1 = isl_pw_aff_scale_down_val(aff1, v);
                if (name == "floord")
                        aff1 = isl_pw_aff_floor(aff1);
                else
                        aff1 = isl_pw_aff_ceil(aff1);
        } else {
                unsupported(expr);
                return NULL;
        }

        return aff1;
}

/* This method is called when we come across an access that is
 * nested in what is supposed to be an affine expression.
 * If nesting is allowed, we return a new parameter that corresponds
 * to this nested access.  Otherwise, we simply complain.
 *
 * Note that we currently don't allow nested accesses themselves
 * to contain any nested accesses, so we check if we can extract
 * the access without any nesting and complain if we can't.
 *
 * The new parameter is resolved in resolve_nested.
 */
isl_pw_aff *PetScan::nested_access(Expr *expr)
{
        isl_id *id;
        isl_space *dim;
        isl_aff *aff;
        isl_set *dom;
        isl_multi_pw_aff *index;

        if (!nesting_enabled) {
                unsupported(expr);
                return NULL;
        }

        allow_nested = false;
        index = extract_index(expr);
        allow_nested = true;
        if (!index) {
                unsupported(expr);
                return NULL;
        }
        isl_multi_pw_aff_free(index);

        id = isl_id_alloc(ctx, NULL, expr);
        dim = isl_space_params_alloc(ctx, 1);

        dim = isl_space_set_dim_id(dim, isl_dim_param, 0, id);

        dom = isl_set_universe(isl_space_copy(dim));
        aff = isl_aff_zero_on_domain(isl_local_space_from_space(dim));
        aff = isl_aff_add_coefficient_si(aff, isl_dim_param, 0, 1);

        return isl_pw_aff_alloc(dom, aff);
}

/* Affine expressions are not supposed to contain array accesses,
 * but if nesting is allowed, we return a parameter corresponding
 * to the array access.
 */
__isl_give isl_pw_aff *PetScan::extract_affine(ArraySubscriptExpr *expr)
{
        return nested_access(expr);
}

/* Extract an affine expression from a conditional operation.
 */
__isl_give isl_pw_aff *PetScan::extract_affine(ConditionalOperator *expr)
{
        isl_pw_aff *cond, *lhs, *rhs, *res;

        cond = extract_condition(expr->getCond());
        lhs = extract_affine(expr->getTrueExpr());
        rhs = extract_affine(expr->getFalseExpr());

        return isl_pw_aff_cond(cond, lhs, rhs);
}

/* Extract an affine expression, if possible, from "expr".
 * Otherwise return NULL.
 */
__isl_give isl_pw_aff *PetScan::extract_affine(Expr *expr)
{
        switch (expr->getStmtClass()) {
        case Stmt::ImplicitCastExprClass:
                return extract_affine(cast<ImplicitCastExpr>(expr));
        case Stmt::IntegerLiteralClass:
                return extract_affine(cast<IntegerLiteral>(expr));
        case Stmt::DeclRefExprClass:
                return extract_affine(cast<DeclRefExpr>(expr));
        case Stmt::BinaryOperatorClass:
                return extract_affine(cast<BinaryOperator>(expr));
        case Stmt::UnaryOperatorClass:
                return extract_affine(cast<UnaryOperator>(expr));
        case Stmt::ParenExprClass:
                return extract_affine(cast<ParenExpr>(expr));
        case Stmt::CallExprClass:
                return extract_affine(cast<CallExpr>(expr));
        case Stmt::ArraySubscriptExprClass:
                return extract_affine(cast<ArraySubscriptExpr>(expr));
        case Stmt::ConditionalOperatorClass:
                return extract_affine(cast<ConditionalOperator>(expr));
        default:
                unsupported(expr);
        }
        return NULL;
}

__isl_give isl_multi_pw_aff *PetScan::extract_index(ImplicitCastExpr *expr)
{
        return extract_index(expr->getSubExpr());
}

/* Return the depth of an array of the given type.
 */
static int array_depth(const Type *type)
{
        if (type->isPointerType())
                return 1 + array_depth(type->getPointeeType().getTypePtr());
        if (type->isArrayType()) {
                const ArrayType *atype;
                type = type->getCanonicalTypeInternal().getTypePtr();
                atype = cast<ArrayType>(type);
                return 1 + array_depth(atype->getElementType().getTypePtr());
        }
        return 0;
}

/* Return the depth of the array accessed by the index expression "index".
 * If "index" is an affine expression, i.e., if it does not access
 * any array, then return 1.
 */
static int extract_depth(__isl_keep isl_multi_pw_aff *index)
{
        isl_id *id;
        ValueDecl *decl;

        if (!index)
                return -1;

        if (!isl_multi_pw_aff_has_tuple_id(index, isl_dim_set))
                return 1;

        id = isl_multi_pw_aff_get_tuple_id(index, isl_dim_set);
        if (!id)
                return -1;
        decl = (ValueDecl *) isl_id_get_user(id);
        isl_id_free(id);

        return array_depth(decl->getType().getTypePtr());
}

/* Return the element type of the given array type.
 */
static QualType base_type(QualType qt)
{
        const Type *type = qt.getTypePtr();

        if (type->isPointerType())
                return base_type(type->getPointeeType());
        if (type->isArrayType()) {
                const ArrayType *atype;
                type = type->getCanonicalTypeInternal().getTypePtr();
                atype = cast<ArrayType>(type);
                return base_type(atype->getElementType());
        }
        return qt;
}

/* Extract an index expression from a reference to a variable.
 * If the variable has name "A", then the returned index expression
 * is of the form
 *
 *      { [] -> A[] }
 */
__isl_give isl_multi_pw_aff *PetScan::extract_index(DeclRefExpr *expr)
{
        return extract_index(expr->getDecl());
}

/* Extract an index expression from a variable.
 * If the variable has name "A", then the returned index expression
 * is of the form
 *
 *      { [] -> A[] }
 */
__isl_give isl_multi_pw_aff *PetScan::extract_index(ValueDecl *decl)
{
        isl_id *id = isl_id_alloc(ctx, decl->getName().str().c_str(), decl);
        isl_space *space = isl_space_alloc(ctx, 0, 0, 0);

        space = isl_space_set_tuple_id(space, isl_dim_out, id);

        return isl_multi_pw_aff_zero(space);
}

/* Extract an index expression from an integer contant.
 * If the value of the constant is "v", then the returned access relation
 * is
 *
 *      { [] -> [v] }
 */
__isl_give isl_multi_pw_aff *PetScan::extract_index(IntegerLiteral *expr)
{
        isl_multi_pw_aff *mpa;

        mpa = isl_multi_pw_aff_from_pw_aff(extract_affine(expr));
        mpa = isl_multi_pw_aff_from_range(mpa);
        return mpa;
}

/* Try and extract an index expression from the given Expr.
 * Return NULL if it doesn't work out.
 */
__isl_give isl_multi_pw_aff *PetScan::extract_index(Expr *expr)
{
        switch (expr->getStmtClass()) {
        case Stmt::ImplicitCastExprClass:
                return extract_index(cast<ImplicitCastExpr>(expr));
        case Stmt::DeclRefExprClass:
                return extract_index(cast<DeclRefExpr>(expr));
        case Stmt::ArraySubscriptExprClass:
                return extract_index(cast<ArraySubscriptExpr>(expr));
        case Stmt::IntegerLiteralClass:
                return extract_index(cast<IntegerLiteral>(expr));
        default:
                unsupported(expr);
        }
        return NULL;
}

/* Extract an index expression from the given array subscript expression.
 * If nesting is allowed in general, then we turn it on while
 * examining the index expression.
 *
 * We first extract an index expression from the base.
 * This will result in an index expression with a range that corresponds
 * to the earlier indices.
 * We then extract the current index, restrict its domain
 * to those values that result in a non-negative index and
 * append the index to the base index expression.
 */
__isl_give isl_multi_pw_aff *PetScan::extract_index(ArraySubscriptExpr *expr)
{
        Expr *base = expr->getBase();
        Expr *idx = expr->getIdx();
        isl_pw_aff *index;
        isl_set *domain;
        isl_multi_pw_aff *base_access;
        isl_multi_pw_aff *access;
        isl_id *id;
        bool save_nesting = nesting_enabled;

        nesting_enabled = allow_nested;

        base_access = extract_index(base);
        index = extract_affine(idx);

        nesting_enabled = save_nesting;

        id = isl_multi_pw_aff_get_tuple_id(base_access, isl_dim_set);
        index = isl_pw_aff_from_range(index);
        domain = isl_pw_aff_nonneg_set(isl_pw_aff_copy(index));
        index = isl_pw_aff_intersect_domain(index, domain);
        access = isl_multi_pw_aff_from_pw_aff(index);
        access = isl_multi_pw_aff_flat_range_product(base_access, access);
        access = isl_multi_pw_aff_set_tuple_id(access, isl_dim_set, id);

        return access;
}

/* Check if "expr" calls function "minmax" with two arguments and if so
 * make lhs and rhs refer to these two arguments.
 */
static bool is_minmax(Expr *expr, const char *minmax, Expr *&lhs, Expr *&rhs)
{
        CallExpr *call;
        FunctionDecl *fd;
        string name;

        if (expr->getStmtClass() != Stmt::CallExprClass)
                return false;

        call = cast<CallExpr>(expr);
        fd = call->getDirectCallee();
        if (!fd)
                return false;

        if (call->getNumArgs() != 2)
                return false;

        name = fd->getDeclName().getAsString();
        if (name != minmax)
                return false;

        lhs = call->getArg(0);
        rhs = call->getArg(1);

        return true;
}

/* Check if "expr" is of the form min(lhs, rhs) and if so make
 * lhs and rhs refer to the two arguments.
 */
static bool is_min(Expr *expr, Expr *&lhs, Expr *&rhs)
{
        return is_minmax(expr, "min", lhs, rhs);
}

/* Check if "expr" is of the form max(lhs, rhs) and if so make
 * lhs and rhs refer to the two arguments.
 */
static bool is_max(Expr *expr, Expr *&lhs, Expr *&rhs)
{
        return is_minmax(expr, "max", lhs, rhs);
}

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

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

/* Return "lhs && rhs", with shortcut semantics.
 * That is, if lhs is false, then the result is defined even if rhs is not.
 * In practice, we compute lhs ? rhs : lhs.
 */
static __isl_give isl_pw_aff *pw_aff_and_then(__isl_take isl_pw_aff *lhs,
        __isl_take isl_pw_aff *rhs)
{
        return isl_pw_aff_cond(isl_pw_aff_copy(lhs), rhs, lhs);
}

/* Return "lhs || rhs", with shortcut semantics.
 * That is, if lhs is true, then the result is defined even if rhs is not.
 * In practice, we compute lhs ? lhs : rhs.
 */
static __isl_give isl_pw_aff *pw_aff_or_else(__isl_take isl_pw_aff *lhs,
        __isl_take isl_pw_aff *rhs)
{
        return isl_pw_aff_cond(isl_pw_aff_copy(lhs), lhs, rhs);
}

/* Extract an affine expressions representing the comparison "LHS op RHS"
 * "comp" is the original statement that "LHS op RHS" is derived from
 * and is used for diagnostics.
 *
 * 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 *PetScan::extract_comparison(BinaryOperatorKind op,
        Expr *LHS, Expr *RHS, Stmt *comp)
{
        isl_pw_aff *lhs;
        isl_pw_aff *rhs;
        isl_pw_aff *res;
        isl_set *cond;
        isl_set *dom;

        if (op == BO_GT)
                return extract_comparison(BO_LT, RHS, LHS, comp);
        if (op == BO_GE)
                return extract_comparison(BO_LE, RHS, LHS, comp);

        if (op == BO_LT || op == BO_LE) {
                Expr *expr1, *expr2;
                if (is_min(RHS, expr1, expr2)) {
                        lhs = extract_comparison(op, LHS, expr1, comp);
                        rhs = extract_comparison(op, LHS, expr2, comp);
                        return pw_aff_and(lhs, rhs);
                }
                if (is_max(LHS, expr1, expr2)) {
                        lhs = extract_comparison(op, expr1, RHS, comp);
                        rhs = extract_comparison(op, expr2, RHS, comp);
                        return pw_aff_and(lhs, rhs);
                }
        }

        lhs = extract_affine(LHS);
        rhs = extract_affine(RHS);

        dom = isl_pw_aff_domain(isl_pw_aff_copy(lhs));
        dom = isl_set_intersect(dom, isl_pw_aff_domain(isl_pw_aff_copy(rhs)));

        switch (op) {
        case BO_LT:
                cond = isl_pw_aff_lt_set(lhs, rhs);
                break;
        case BO_LE:
                cond = isl_pw_aff_le_set(lhs, rhs);
                break;
        case BO_EQ:
                cond = isl_pw_aff_eq_set(lhs, rhs);
                break;
        case BO_NE:
                cond = isl_pw_aff_ne_set(lhs, rhs);
                break;
        default:
                isl_pw_aff_free(lhs);
                isl_pw_aff_free(rhs);
                isl_set_free(dom);
                unsupported(comp);
                return NULL;
        }

        cond = isl_set_coalesce(cond);
        res = indicator_function(cond, dom);

        return res;
}

__isl_give isl_pw_aff *PetScan::extract_comparison(BinaryOperator *comp)
{
        return extract_comparison(comp->getOpcode(), comp->getLHS(),
                                comp->getRHS(), comp);
}

/* Extract an affine expression representing the negation (logical not)
 * of a subexpression.
 */
__isl_give isl_pw_aff *PetScan::extract_boolean(UnaryOperator *op)
{
        isl_set *set_cond, *dom;
        isl_pw_aff *cond, *res;

        cond = extract_condition(op->getSubExpr());

        dom = isl_pw_aff_domain(isl_pw_aff_copy(cond));

        set_cond = isl_pw_aff_zero_set(cond);

        res = indicator_function(set_cond, dom);

        return res;
}

/* Extract an affine expression representing the disjunction (logical or)
 * or conjunction (logical and) of two subexpressions.
 */
__isl_give isl_pw_aff *PetScan::extract_boolean(BinaryOperator *comp)
{
        isl_pw_aff *lhs, *rhs;

        lhs = extract_condition(comp->getLHS());
        rhs = extract_condition(comp->getRHS());

        switch (comp->getOpcode()) {
        case BO_LAnd:
                return pw_aff_and_then(lhs, rhs);
        case BO_LOr:
                return pw_aff_or_else(lhs, rhs);
        default:
                isl_pw_aff_free(lhs);
                isl_pw_aff_free(rhs);
        }

        unsupported(comp);
        return NULL;
}

__isl_give isl_pw_aff *PetScan::extract_condition(UnaryOperator *expr)
{
        switch (expr->getOpcode()) {
        case UO_LNot:
                return extract_boolean(expr);
        default:
                unsupported(expr);
                return NULL;
        }
}

/* Extract the affine expression "expr != 0 ? 1 : 0".
 */
__isl_give isl_pw_aff *PetScan::extract_implicit_condition(Expr *expr)
{
        isl_pw_aff *res;
        isl_set *set, *dom;

        res = extract_affine(expr);

        dom = isl_pw_aff_domain(isl_pw_aff_copy(res));
        set = isl_pw_aff_non_zero_set(res);

        res = indicator_function(set, dom);

        return res;
}

/* Extract an affine expression from a boolean expression.
 * In particular, return the expression "expr ? 1 : 0".
 *
 * If the expression doesn't look like a condition, we assume it
 * is an affine expression and return the condition "expr != 0 ? 1 : 0".
 */
__isl_give isl_pw_aff *PetScan::extract_condition(Expr *expr)
{
        BinaryOperator *comp;

        if (!expr) {
                isl_set *u = isl_set_universe(isl_space_params_alloc(ctx, 0));
                return indicator_function(u, isl_set_copy(u));
        }

        if (expr->getStmtClass() == Stmt::ParenExprClass)
                return extract_condition(cast<ParenExpr>(expr)->getSubExpr());

        if (expr->getStmtClass() == Stmt::UnaryOperatorClass)
                return extract_condition(cast<UnaryOperator>(expr));

        if (expr->getStmtClass() != Stmt::BinaryOperatorClass)
                return extract_implicit_condition(expr);

        comp = cast<BinaryOperator>(expr);
        switch (comp->getOpcode()) {
        case BO_LT:
        case BO_LE:
        case BO_GT:
        case BO_GE:
        case BO_EQ:
        case BO_NE:
                return extract_comparison(comp);
        case BO_LAnd:
        case BO_LOr:
                return extract_boolean(comp);
        default:
                return extract_implicit_condition(expr);
        }
}

static enum pet_op_type UnaryOperatorKind2pet_op_type(UnaryOperatorKind kind)
{
        switch (kind) {
        case UO_Minus:
                return pet_op_minus;
        case UO_PostInc:
                return pet_op_post_inc;
        case UO_PostDec:
                return pet_op_post_dec;
        case UO_PreInc:
                return pet_op_pre_inc;
        case UO_PreDec:
                return pet_op_pre_dec;
        default:
                return pet_op_last;
        }
}

static enum pet_op_type BinaryOperatorKind2pet_op_type(BinaryOperatorKind kind)
{
        switch (kind) {
        case BO_AddAssign:
                return pet_op_add_assign;
        case BO_SubAssign:
                return pet_op_sub_assign;
        case BO_MulAssign:
                return pet_op_mul_assign;
        case BO_DivAssign:
                return pet_op_div_assign;
        case BO_Assign:
                return pet_op_assign;
        case BO_Add:
                return pet_op_add;
        case BO_Sub:
                return pet_op_sub;
        case BO_Mul:
                return pet_op_mul;
        case BO_Div:
                return pet_op_div;
        case BO_Rem:
                return pet_op_mod;
        case BO_EQ:
                return pet_op_eq;
        case BO_LE:
                return pet_op_le;
        case BO_LT:
                return pet_op_lt;
        case BO_GT:
                return pet_op_gt;
        default:
                return pet_op_last;
        }
}

/* Construct a pet_expr representing a unary operator expression.
 */
struct pet_expr *PetScan::extract_expr(UnaryOperator *expr)
{
        struct pet_expr *arg;
        enum pet_op_type op;

        op = UnaryOperatorKind2pet_op_type(expr->getOpcode());
        if (op == pet_op_last) {
                unsupported(expr);
                return NULL;
        }

        arg = extract_expr(expr->getSubExpr());

        if (expr->isIncrementDecrementOp() &&
            arg && arg->type == pet_expr_access) {
                mark_write(arg);
                arg->acc.read = 1;
        }

        return pet_expr_new_unary(ctx, op, arg);
}

/* Mark the given access pet_expr as a write.
 * If a scalar is being accessed, then mark its value
 * as unknown in assigned_value.
 */
void PetScan::mark_write(struct pet_expr *access)
{
        isl_id *id;
        ValueDecl *decl;

        if (!access)
                return;

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

        if (!pet_expr_is_scalar_access(access))
                return;

        id = pet_expr_access_get_id(access);
        decl = (ValueDecl *) isl_id_get_user(id);
        clear_assignment(assigned_value, decl);
        isl_id_free(id);
}

/* Assign "rhs" to "lhs".
 *
 * In particular, if "lhs" is a scalar variable, then mark
 * the variable as having been assigned.  If, furthermore, "rhs"
 * is an affine expression, then keep track of this value in assigned_value
 * so that we can plug it in when we later come across the same variable.
 */
void PetScan::assign(struct pet_expr *lhs, Expr *rhs)
{
        isl_id *id;
        ValueDecl *decl;
        isl_pw_aff *pa;

        if (!lhs)
                return;
        if (!pet_expr_is_scalar_access(lhs))
                return;

        id = pet_expr_access_get_id(lhs);
        decl = (ValueDecl *) isl_id_get_user(id);
        isl_id_free(id);

        pa = try_extract_affine(rhs);
        clear_assignment(assigned_value, decl);
        if (!pa)
                return;
        assigned_value[decl] = pa;
        insert_expression(pa);
}

/* Construct a pet_expr representing a binary operator expression.
 *
 * If the top level operator is an assignment and the LHS is an access,
 * then we mark that access as a write.  If the operator is a compound
 * assignment, the access is marked as both a read and a write.
 *
 * If "expr" assigns something to a scalar variable, then we mark
 * the variable as having been assigned.  If, furthermore, the expression
 * is affine, then keep track of this value in assigned_value
 * so that we can plug it in when we later come across the same variable.
 */
struct pet_expr *PetScan::extract_expr(BinaryOperator *expr)
{
        struct pet_expr *lhs, *rhs;
        enum pet_op_type op;

        op = BinaryOperatorKind2pet_op_type(expr->getOpcode());
        if (op == pet_op_last) {
                unsupported(expr);
                return NULL;
        }

        lhs = extract_expr(expr->getLHS());
        rhs = extract_expr(expr->getRHS());

        if (expr->isAssignmentOp() && lhs && lhs->type == pet_expr_access) {
                mark_write(lhs);
                if (expr->isCompoundAssignmentOp())
                        lhs->acc.read = 1;
        }

        if (expr->getOpcode() == BO_Assign)
                assign(lhs, expr->getRHS());

        return pet_expr_new_binary(ctx, op, lhs, rhs);
}

/* Construct a pet_scop with a single statement killing the entire
 * array "array".
 */
struct pet_scop *PetScan::kill(Stmt *stmt, struct pet_array *array)
{
        isl_map *access;
        struct pet_expr *expr;

        if (!array)
                return NULL;
        access = isl_map_from_range(isl_set_copy(array->extent));
        expr = pet_expr_kill_from_access(access);
        return extract(stmt, expr);
}

/* Construct a pet_scop for a (single) variable declaration.
 *
 * The scop contains the variable being declared (as an array)
 * and a statement killing the array.
 *
 * If the variable is initialized in the AST, then the scop
 * also contains an assignment to the variable.
 */
struct pet_scop *PetScan::extract(DeclStmt *stmt)
{
        Decl *decl;
        VarDecl *vd;
        struct pet_expr *lhs, *rhs, *pe;
        struct pet_scop *scop_decl, *scop;
        struct pet_array *array;

        if (!stmt->isSingleDecl()) {
                unsupported(stmt);
                return NULL;
        }

        decl = stmt->getSingleDecl();
        vd = cast<VarDecl>(decl);

        array = extract_array(ctx, vd);
        if (array)
                array->declared = 1;
        scop_decl = kill(stmt, array);
        scop_decl = pet_scop_add_array(scop_decl, array);

        if (!vd->getInit())
                return scop_decl;

        lhs = extract_access_expr(vd);
        rhs = extract_expr(vd->getInit());

        mark_write(lhs);
        assign(lhs, vd->getInit());

        pe = pet_expr_new_binary(ctx, pet_op_assign, lhs, rhs);
        scop = extract(stmt, pe);

        scop_decl = pet_scop_prefix(scop_decl, 0);
        scop = pet_scop_prefix(scop, 1);

        scop = pet_scop_add_seq(ctx, scop_decl, scop);

        return scop;
}

/* Construct a pet_expr representing a conditional operation.
 *
 * We first try to extract the condition as an affine expression.
 * If that fails, we construct a pet_expr tree representing the condition.
 */
struct pet_expr *PetScan::extract_expr(ConditionalOperator *expr)
{
        struct pet_expr *cond, *lhs, *rhs;
        isl_pw_aff *pa;

        pa = try_extract_affine(expr->getCond());
        if (pa) {
                isl_multi_pw_aff *test = isl_multi_pw_aff_from_pw_aff(pa);
                test = isl_multi_pw_aff_from_range(test);
                cond = pet_expr_from_index(test);
        } else
                cond = extract_expr(expr->getCond());
        lhs = extract_expr(expr->getTrueExpr());
        rhs = extract_expr(expr->getFalseExpr());

        return pet_expr_new_ternary(ctx, cond, lhs, rhs);
}

struct pet_expr *PetScan::extract_expr(ImplicitCastExpr *expr)
{
        return extract_expr(expr->getSubExpr());
}

/* Construct a pet_expr representing a floating point value.
 *
 * If the floating point literal does not appear in a macro,
 * then we use the original representation in the source code
 * as the string representation.  Otherwise, we use the pretty
 * printer to produce a string representation.
 */
struct pet_expr *PetScan::extract_expr(FloatingLiteral *expr)
{
        double d;
        string s;
        const LangOptions &LO = PP.getLangOpts();
        SourceLocation loc = expr->getLocation();

        if (!loc.isMacroID()) {
                SourceManager &SM = PP.getSourceManager();
                unsigned len = Lexer::MeasureTokenLength(loc, SM, LO);
                s = string(SM.getCharacterData(loc), len);
        } else {
                llvm::raw_string_ostream S(s);
                expr->printPretty(S, 0, PrintingPolicy(LO));
                S.str();
        }
        d = expr->getValueAsApproximateDouble();
        return pet_expr_new_double(ctx, d, s.c_str());
}

/* Extract an index expression from "expr" and then convert it into
 * an access pet_expr.
 */
struct pet_expr *PetScan::extract_access_expr(Expr *expr)
{
        isl_multi_pw_aff *index;
        struct pet_expr *pe;
        int depth;

        index = extract_index(expr);
        depth = extract_depth(index);

        pe = pet_expr_from_index_and_depth(index, depth);

        return pe;
}

/* Extract an index expression from "decl" and then convert it into
 * an access pet_expr.
 */
struct pet_expr *PetScan::extract_access_expr(ValueDecl *decl)
{
        isl_multi_pw_aff *index;
        struct pet_expr *pe;
        int depth;

        index = extract_index(decl);
        depth = extract_depth(index);

        pe = pet_expr_from_index_and_depth(index, depth);

        return pe;
}

struct pet_expr *PetScan::extract_expr(ParenExpr *expr)
{
        return extract_expr(expr->getSubExpr());
}

/* Construct a pet_expr representing a function call.
 *
 * If we are passing along a pointer to an array element
 * or an entire row or even higher dimensional slice of an array,
 * then the function being called may write into the array.
 *
 * We assume here that if the function is declared to take a pointer
 * to a const type, then the function will perform a read
 * and that otherwise, it will perform a write.
 */
struct pet_expr *PetScan::extract_expr(CallExpr *expr)
{
        struct pet_expr *res = NULL;
        FunctionDecl *fd;
        string name;

        fd = expr->getDirectCallee();
        if (!fd) {
                unsupported(expr);
                return NULL;
        }

        name = fd->getDeclName().getAsString();
        res = pet_expr_new_call(ctx, name.c_str(), expr->getNumArgs());
        if (!res)
                return NULL;

        for (int i = 0; i < expr->getNumArgs(); ++i) {
                Expr *arg = expr->getArg(i);
                int is_addr = 0;
                pet_expr *main_arg;

                if (arg->getStmtClass() == Stmt::ImplicitCastExprClass) {
                        ImplicitCastExpr *ice = cast<ImplicitCastExpr>(arg);
                        arg = ice->getSubExpr();
                }
                if (arg->getStmtClass() == Stmt::UnaryOperatorClass) {
                        UnaryOperator *op = cast<UnaryOperator>(arg);
                        if (op->getOpcode() == UO_AddrOf) {
                                is_addr = 1;
                                arg = op->getSubExpr();
                        }
                }
                res->args[i] = PetScan::extract_expr(arg);
                main_arg = res->args[i];
                if (is_addr)
                        res->args[i] = pet_expr_new_unary(ctx,
                                        pet_op_address_of, res->args[i]);
                if (!res->args[i])
                        goto error;
                if (arg->getStmtClass() == Stmt::ArraySubscriptExprClass &&
                    array_depth(arg->getType().getTypePtr()) > 0)
                        is_addr = 1;
                if (is_addr && main_arg->type == pet_expr_access) {
                        ParmVarDecl *parm;
                        if (!fd->hasPrototype()) {
                                unsupported(expr, "prototype required");
                                goto error;
                        }
                        parm = fd->getParamDecl(i);
                        if (!const_base(parm->getType()))
                                mark_write(main_arg);
                }
        }

        return res;
error:
        pet_expr_free(res);
        return NULL;
}

/* Construct a pet_expr representing a (C style) cast.
 */
struct pet_expr *PetScan::extract_expr(CStyleCastExpr *expr)
{
        struct pet_expr *arg;
        QualType type;

        arg = extract_expr(expr->getSubExpr());
        if (!arg)
                return NULL;

        type = expr->getTypeAsWritten();
        return pet_expr_new_cast(ctx, type.getAsString().c_str(), arg);
}

/* Try and onstruct a pet_expr representing "expr".
 */
struct pet_expr *PetScan::extract_expr(Expr *expr)
{
        switch (expr->getStmtClass()) {
        case Stmt::UnaryOperatorClass:
                return extract_expr(cast<UnaryOperator>(expr));
        case Stmt::CompoundAssignOperatorClass:
        case Stmt::BinaryOperatorClass:
                return extract_expr(cast<BinaryOperator>(expr));
        case Stmt::ImplicitCastExprClass:
                return extract_expr(cast<ImplicitCastExpr>(expr));
        case Stmt::ArraySubscriptExprClass:
        case Stmt::DeclRefExprClass:
        case Stmt::IntegerLiteralClass:
                return extract_access_expr(expr);
        case Stmt::FloatingLiteralClass:
                return extract_expr(cast<FloatingLiteral>(expr));
        case Stmt::ParenExprClass:
                return extract_expr(cast<ParenExpr>(expr));
        case Stmt::ConditionalOperatorClass:
                return extract_expr(cast<ConditionalOperator>(expr));
        case Stmt::CallExprClass:
                return extract_expr(cast<CallExpr>(expr));
        case Stmt::CStyleCastExprClass:
                return extract_expr(cast<CStyleCastExpr>(expr));
        default:
                unsupported(expr);
        }
        return NULL;
}

/* Check if the given initialization statement is an assignment.
 * If so, return that assignment.  Otherwise return NULL.
 */
BinaryOperator *PetScan::initialization_assignment(Stmt *init)
{
        BinaryOperator *ass;

        if (init->getStmtClass() != Stmt::BinaryOperatorClass)
                return NULL;

        ass = cast<BinaryOperator>(init);
        if (ass->getOpcode() != BO_Assign)
                return NULL;

        return ass;
}

/* Check if the given initialization statement is a declaration
 * of a single variable.
 * If so, return that declaration.  Otherwise return NULL.
 */
Decl *PetScan::initialization_declaration(Stmt *init)
{
        DeclStmt *decl;

        if (init->getStmtClass() != Stmt::DeclStmtClass)
                return NULL;

        decl = cast<DeclStmt>(init);

        if (!decl->isSingleDecl())
                return NULL;

        return decl->getSingleDecl();
}

/* Given the assignment operator in the initialization of a for loop,
 * extract the induction variable, i.e., the (integer)variable being
 * assigned.
 */
ValueDecl *PetScan::extract_induction_variable(BinaryOperator *init)
{
        Expr *lhs;
        DeclRefExpr *ref;
        ValueDecl *decl;
        const Type *type;

        lhs = init->getLHS();
        if (lhs->getStmtClass() != Stmt::DeclRefExprClass) {
                unsupported(init);
                return NULL;
        }

        ref = cast<DeclRefExpr>(lhs);
        decl = ref->getDecl();
        type = decl->getType().getTypePtr();

        if (!type->isIntegerType()) {
                unsupported(lhs);
                return NULL;
        }

        return decl;
}

/* Given the initialization statement of a for loop and the single
 * declaration in this initialization statement,
 * extract the induction variable, i.e., the (integer) variable being
 * declared.
 */
VarDecl *PetScan::extract_induction_variable(Stmt *init, Decl *decl)
{
        VarDecl *vd;

        vd = cast<VarDecl>(decl);

        const QualType type = vd->getType();
        if (!type->isIntegerType()) {
                unsupported(init);
                return NULL;
        }

        if (!vd->getInit()) {
                unsupported(init);
                return NULL;
        }

        return vd;
}

/* Check that op is of the form iv++ or iv--.
 * Return an affine expression "1" or "-1" accordingly.
 */
__isl_give isl_pw_aff *PetScan::extract_unary_increment(
        clang::UnaryOperator *op, clang::ValueDecl *iv)
{
        Expr *sub;
        DeclRefExpr *ref;
        isl_space *space;
        isl_aff *aff;

        if (!op->isIncrementDecrementOp()) {
                unsupported(op);
                return NULL;
        }

        sub = op->getSubExpr();
        if (sub->getStmtClass() != Stmt::DeclRefExprClass) {
                unsupported(op);
                return NULL;
        }

        ref = cast<DeclRefExpr>(sub);
        if (ref->getDecl() != iv) {
                unsupported(op);
                return NULL;
        }

        space = isl_space_params_alloc(ctx, 0);
        aff = isl_aff_zero_on_domain(isl_local_space_from_space(space));

        if (op->isIncrementOp())
                aff = isl_aff_add_constant_si(aff, 1);
        else
                aff = isl_aff_add_constant_si(aff, -1);

        return isl_pw_aff_from_aff(aff);
}

/* If the isl_pw_aff on which isl_pw_aff_foreach_piece is called
 * has a single constant expression, then put this constant in *user.
 * The caller is assumed to have checked that this function will
 * be called exactly once.
 */
static int extract_cst(__isl_take isl_set *set, __isl_take isl_aff *aff,
        void *user)
{
        isl_val **inc = (isl_val **)user;
        int res = 0;

        if (isl_aff_is_cst(aff))
                *inc = isl_aff_get_constant_val(aff);
        else
                res = -1;

        isl_set_free(set);
        isl_aff_free(aff);

        return res;
}

/* Check if op is of the form
 *
 *      iv = iv + inc
 *
 * and return inc as an affine expression.
 *
 * We extract an affine expression from the RHS, subtract iv and return
 * the result.
 */
__isl_give isl_pw_aff *PetScan::extract_binary_increment(BinaryOperator *op,
        clang::ValueDecl *iv)
{
        Expr *lhs;
        DeclRefExpr *ref;
        isl_id *id;
        isl_space *dim;
        isl_aff *aff;
        isl_pw_aff *val;

        if (op->getOpcode() != BO_Assign) {
                unsupported(op);
                return NULL;
        }

        lhs = op->getLHS();
        if (lhs->getStmtClass() != Stmt::DeclRefExprClass) {
                unsupported(op);
                return NULL;
        }

        ref = cast<DeclRefExpr>(lhs);
        if (ref->getDecl() != iv) {
                unsupported(op);
                return NULL;
        }

        val = extract_affine(op->getRHS());

        id = isl_id_alloc(ctx, iv->getName().str().c_str(), iv);

        dim = isl_space_params_alloc(ctx, 1);
        dim = isl_space_set_dim_id(dim, isl_dim_param, 0, id);
        aff = isl_aff_zero_on_domain(isl_local_space_from_space(dim));
        aff = isl_aff_add_coefficient_si(aff, isl_dim_param, 0, 1);

        val = isl_pw_aff_sub(val, isl_pw_aff_from_aff(aff));

        return val;
}

/* Check that op is of the form iv += cst or iv -= cst
 * and return an affine expression corresponding oto cst or -cst accordingly.
 */
__isl_give isl_pw_aff *PetScan::extract_compound_increment(
        CompoundAssignOperator *op, clang::ValueDecl *iv)
{
        Expr *lhs;
        DeclRefExpr *ref;
        bool neg = false;
        isl_pw_aff *val;
        BinaryOperatorKind opcode;

        opcode = op->getOpcode();
        if (opcode != BO_AddAssign && opcode != BO_SubAssign) {
                unsupported(op);
                return NULL;
        }
        if (opcode == BO_SubAssign)
                neg = true;

        lhs = op->getLHS();
        if (lhs->getStmtClass() != Stmt::DeclRefExprClass) {
                unsupported(op);
                return NULL;
        }

        ref = cast<DeclRefExpr>(lhs);
        if (ref->getDecl() != iv) {
                unsupported(op);
                return NULL;
        }

        val = extract_affine(op->getRHS());
        if (neg)
                val = isl_pw_aff_neg(val);

        return val;
}

/* Check that the increment of the given for loop increments
 * (or decrements) the induction variable "iv" and return
 * the increment as an affine expression if successful.
 */
__isl_give isl_pw_aff *PetScan::extract_increment(clang::ForStmt *stmt,
        ValueDecl *iv)
{
        Stmt *inc = stmt->getInc();

        if (!inc) {
                unsupported(stmt);
                return NULL;
        }

        if (inc->getStmtClass() == Stmt::UnaryOperatorClass)
                return extract_unary_increment(cast<UnaryOperator>(inc), iv);
        if (inc->getStmtClass() == Stmt::CompoundAssignOperatorClass)
                return extract_compound_increment(
                                cast<CompoundAssignOperator>(inc), iv);
        if (inc->getStmtClass() == Stmt::BinaryOperatorClass)
                return extract_binary_increment(cast<BinaryOperator>(inc), iv);

        unsupported(inc);
        return NULL;
}

/* Embed the given iteration domain in an extra outer loop
 * with induction variable "var".
 * If this variable appeared as a parameter in the constraints,
 * it is replaced by the new outermost dimension.
 */
static __isl_give isl_set *embed(__isl_take isl_set *set,
        __isl_take isl_id *var)
{
        int pos;

        set = isl_set_insert_dims(set, isl_dim_set, 0, 1);
        pos = isl_set_find_dim_by_id(set, isl_dim_param, var);
        if (pos >= 0) {
                set = isl_set_equate(set, isl_dim_param, pos, isl_dim_set, 0);
                set = isl_set_project_out(set, isl_dim_param, pos, 1);
        }

        isl_id_free(var);
        return set;
}

/* Return those elements in the space of "cond" that come after
 * (based on "sign") an element in "cond".
 */
static __isl_give isl_set *after(__isl_take isl_set *cond, int sign)
{
        isl_map *previous_to_this;

        if (sign > 0)
                previous_to_this = isl_map_lex_lt(isl_set_get_space(cond));
        else
                previous_to_this = isl_map_lex_gt(isl_set_get_space(cond));

        cond = isl_set_apply(cond, previous_to_this);

        return cond;
}

/* Create the infinite iteration domain
 *
 *      { [id] : id >= 0 }
 *
 * If "scop" has an affine skip of type pet_skip_later,
 * then remove those iterations i that have an earlier iteration
 * where the skip condition is satisfied, meaning that iteration i
 * is not executed.
 * Since we are dealing with a loop without loop iterator,
 * the skip condition cannot refer to the current loop iterator and
 * so effectively, the returned set is of the form
 *
 *      { [0]; [id] : id >= 1 and not skip }
 */
static __isl_give isl_set *infinite_domain(__isl_take isl_id *id,
        struct pet_scop *scop)
{
        isl_ctx *ctx = isl_id_get_ctx(id);
        isl_set *domain;
        isl_set *skip;

        domain = isl_set_nat_universe(isl_space_set_alloc(ctx, 0, 1));
        domain = isl_set_set_dim_id(domain, isl_dim_set, 0, id);

        if (!pet_scop_has_affine_skip(scop, pet_skip_later))
                return domain;

        skip = pet_scop_get_affine_skip_domain(scop, pet_skip_later);
        skip = embed(skip, isl_id_copy(id));
        skip = isl_set_intersect(skip , isl_set_copy(domain));
        domain = isl_set_subtract(domain, after(skip, 1));

        return domain;
}

/* Create an identity affine expression on the space containing "domain",
 * which is assumed to be one-dimensional.
 */
static __isl_give isl_aff *identity_aff(__isl_keep isl_set *domain)
{
        isl_local_space *ls;

        ls = isl_local_space_from_space(isl_set_get_space(domain));
        return isl_aff_var_on_domain(ls, isl_dim_set, 0);
}

/* Create a map that maps elements of a single-dimensional array "id_test"
 * to the previous element (according to "inc"), provided this element
 * belongs to "domain".  That is, create the map
 *
 *      { id[x] -> id[x - inc] : x - inc in domain }
 */
static __isl_give isl_map *map_to_previous(__isl_take isl_id *id_test,
        __isl_take isl_set *domain, __isl_take isl_val *inc)
{
        isl_space *space;
        isl_local_space *ls;
        isl_aff *aff;
        isl_map *prev;

        space = isl_set_get_space(domain);
        ls = isl_local_space_from_space(space);
        aff = isl_aff_var_on_domain(ls, isl_dim_set, 0);
        aff = isl_aff_add_constant_val(aff, isl_val_neg(inc));
        prev = isl_map_from_aff(aff);
        prev = isl_map_intersect_range(prev, domain);
        prev = isl_map_set_tuple_id(prev, isl_dim_out, id_test);

        return prev;
}

/* Add an implication to "scop" expressing that if an element of
 * virtual array "id_test" has value "satisfied" then all previous elements
 * of this array also have that value.  The set of previous elements
 * is bounded by "domain".  If "sign" is negative then iterator
 * is decreasing and we express that all subsequent array elements
 * (but still defined previously) have the same value.
 */
static struct pet_scop *add_implication(struct pet_scop *scop,
        __isl_take isl_id *id_test, __isl_take isl_set *domain, int sign,
        int satisfied)
{
        isl_space *space;
        isl_map *map;

        domain = isl_set_set_tuple_id(domain, id_test);
        space = isl_set_get_space(domain);
        if (sign > 0)
                map = isl_map_lex_ge(space);
        else
                map = isl_map_lex_le(space);
        map = isl_map_intersect_range(map, domain);
        scop = pet_scop_add_implication(scop, map, satisfied);

        return scop;
}

/* Add a filter to "scop" that imposes that it is only executed
 * when the variable identified by "id_test" has a zero value
 * for all previous iterations of "domain".
 *
 * In particular, add a filter that imposes that the array
 * has a zero value at the previous iteration of domain and
 * add an implication that implies that it then has that
 * value for all previous iterations.
 */
static struct pet_scop *scop_add_break(struct pet_scop *scop,
        __isl_take isl_id *id_test, __isl_take isl_set *domain,
        __isl_take isl_val *inc)
{
        isl_map *prev;
        int sign = isl_val_sgn(inc);

        prev = map_to_previous(isl_id_copy(id_test), isl_set_copy(domain), inc);
        scop = add_implication(scop, id_test, domain, sign, 0);
        scop = pet_scop_filter(scop, prev, 0);

        return scop;
}

/* Construct a pet_scop for an infinite loop around the given body.
 *
 * We extract a pet_scop for the body and then embed it in a loop with
 * iteration domain
 *
 *      { [t] : t >= 0 }
 *
 * and schedule
 *
 *      { [t] -> [t] }
 *
 * If the body contains any break, then it is taken into
 * account in infinite_domain (if the skip condition is affine)
 * or in scop_add_break (if the skip condition is not affine).
 */
struct pet_scop *PetScan::extract_infinite_loop(Stmt *body)
{
        isl_id *id, *id_test;
        isl_set *domain;
        isl_aff *ident;
        struct pet_scop *scop;
        bool has_var_break;

        scop = extract(body);
        if (!scop)
                return NULL;

        id = isl_id_alloc(ctx, "t", NULL);
        domain = infinite_domain(isl_id_copy(id), scop);
        ident = identity_aff(domain);

        has_var_break = pet_scop_has_var_skip(scop, pet_skip_later);
        if (has_var_break)
                id_test = pet_scop_get_skip_id(scop, pet_skip_later);

        scop = pet_scop_embed(scop, isl_set_copy(domain),
                            isl_map_from_aff(isl_aff_copy(ident)), ident, id);
        if (has_var_break)
                scop = scop_add_break(scop, id_test, domain, isl_val_one(ctx));
        else
                isl_set_free(domain);

        return scop;
}

/* Construct a pet_scop for an infinite loop, i.e., a loop of the form
 *
 *      for (;;)
 *              body
 *
 */
struct pet_scop *PetScan::extract_infinite_for(ForStmt *stmt)
{
        return extract_infinite_loop(stmt->getBody());
}

/* Create an index expression for an access to a virtual array
 * representing the result of a condition.
 * Unlike other accessed data, the id of the array is NULL as
 * there is no ValueDecl in the program corresponding to the virtual
 * array.
 * The array starts out as a scalar, but grows along with the
 * statement writing to the array in pet_scop_embed.
 */
static __isl_give isl_multi_pw_aff *create_test_index(isl_ctx *ctx, int test_nr)
{
        isl_space *dim = isl_space_alloc(ctx, 0, 0, 0);
        isl_id *id;
        char name[50];

        snprintf(name, sizeof(name), "__pet_test_%d", test_nr);
        id = isl_id_alloc(ctx, name, NULL);
        dim = isl_space_set_tuple_id(dim, isl_dim_out, id);
        return isl_multi_pw_aff_zero(dim);
}

/* Create an access to a virtual array representing the result
 * of a condition.
 */
static __isl_give isl_map *create_test_access(isl_ctx *ctx, int test_nr)
{
        return isl_map_from_multi_pw_aff(create_test_index(ctx, test_nr));
}

/* Add an array with the given extent ("access") to the list
 * of arrays in "scop" and return the extended pet_scop.
 * The array is marked as attaining values 0 and 1 only and
 * as each element being assigned at most once.
 */
static struct pet_scop *scop_add_array(struct pet_scop *scop,
        __isl_keep isl_map *access, clang::ASTContext &ast_ctx)
{
        isl_ctx *ctx = isl_map_get_ctx(access);
        isl_space *dim;
        struct pet_array *array;

        if (!scop)
                return NULL;
        if (!ctx)
                goto error;

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

        array->extent = isl_map_range(isl_map_copy(access));
        dim = isl_space_params_alloc(ctx, 0);
        array->context = isl_set_universe(dim);
        dim = isl_space_set_alloc(ctx, 0, 1);
        array->value_bounds = isl_set_universe(dim);
        array->value_bounds = isl_set_lower_bound_si(array->value_bounds,
                                                isl_dim_set, 0, 0);
        array->value_bounds = isl_set_upper_bound_si(array->value_bounds,
                                                isl_dim_set, 0, 1);
        array->element_type = strdup("int");
        array->element_size = ast_ctx.getTypeInfo(ast_ctx.IntTy).first / 8;
        array->uniquely_defined = 1;

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

        scop = pet_scop_add_array(scop, array);

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

/* Construct a pet_scop for a while loop of the form
 *
 *      while (pa)
 *              body
 *
 * In particular, construct a scop for an infinite loop around body and
 * intersect the domain with the affine expression.
 * Note that this intersection may result in an empty loop.
 */
struct pet_scop *PetScan::extract_affine_while(__isl_take isl_pw_aff *pa,
        Stmt *body)
{
        struct pet_scop *scop;
        isl_set *dom;
        isl_set *valid;

        valid = isl_pw_aff_domain(isl_pw_aff_copy(pa));
        dom = isl_pw_aff_non_zero_set(pa);
        scop = extract_infinite_loop(body);
        scop = pet_scop_restrict(scop, dom);
        scop = pet_scop_restrict_context(scop, valid);

        return scop;
}

/* Construct a scop for a while, given the scops for the condition
 * and the body, the filter identifier and the iteration domain of
 * the while loop.
 *
 * In particular, the scop for the condition is filtered to depend
 * on "id_test" evaluating to true for all previous iterations
 * of the loop, while the scop for the body is filtered to depend
 * on "id_test" evaluating to true for all iterations up to the
 * current iteration.
 * The actual filter only imposes that this virtual array has
 * value one on the previous or the current iteration.
 * The fact that this condition also applies to the previous
 * iterations is enforced by an implication.
 *
 * These filtered scops are then combined into a single scop.
 *
 * "sign" is positive if the iterator increases and negative
 * if it decreases.
 */
static struct pet_scop *scop_add_while(struct pet_scop *scop_cond,
        struct pet_scop *scop_body, __isl_take isl_id *id_test,
        __isl_take isl_set *domain, __isl_take isl_val *inc)
{
        isl_ctx *ctx = isl_set_get_ctx(domain);
        isl_space *space;
        isl_map *test_access;
        isl_map *prev;
        int sign = isl_val_sgn(inc);
        struct pet_scop *scop;

        prev = map_to_previous(isl_id_copy(id_test), isl_set_copy(domain), inc);
        scop_cond = pet_scop_filter(scop_cond, prev, 1);

        space = isl_space_map_from_set(isl_set_get_space(domain));
        test_access = isl_map_identity(space);
        test_access = isl_map_set_tuple_id(test_access, isl_dim_out,
                                                isl_id_copy(id_test));
        scop_body = pet_scop_filter(scop_body, test_access, 1);

        scop = pet_scop_add_seq(ctx, scop_cond, scop_body);
        scop = add_implication(scop, id_test, domain, sign, 1);

        return scop;
}

/* Check if the while loop is of the form
 *
 *      while (affine expression)
 *              body
 *
 * If so, call extract_affine_while to construct a scop.
 *
 * Otherwise, construct a generic while scop, with iteration domain
 * { [t] : t >= 0 }.  The scop consists of two parts, one for
 * evaluating the condition and one for the body.
 * The schedule is adjusted to reflect that the condition is evaluated
 * before the body is executed and the body is filtered to depend
 * on the result of the condition evaluating to true on all iterations
 * up to the current iteration, while the evaluation the condition itself
 * is filtered to depend on the result of the condition evaluating to true
 * on all previous iterations.
 * The context of the scop representing the body is dropped
 * because we don't know how many times the body will be executed,
 * if at all.
 *
 * If the body contains any break, then it is taken into
 * account in infinite_domain (if the skip condition is affine)
 * or in scop_add_break (if the skip condition is not affine).
 */
struct pet_scop *PetScan::extract(WhileStmt *stmt)
{
        Expr *cond;
        isl_id *id, *id_test, *id_break_test;
        isl_multi_pw_aff *test_index;
        isl_map *test_access;
        isl_set *domain;
        isl_aff *ident;
        isl_pw_aff *pa;
        struct pet_scop *scop, *scop_body;
        bool has_var_break;

        cond = stmt->getCond();
        if (!cond) {
                unsupported(stmt);
                return NULL;
        }

        clear_assignments clear(assigned_value);
        clear.TraverseStmt(stmt->getBody());

        pa = try_extract_affine_condition(cond);
        if (pa)
                return extract_affine_while(pa, stmt->getBody());

        if (!allow_nested) {
                unsupported(stmt);
                return NULL;
        }

        test_index = create_test_index(ctx, n_test++);
        scop = extract_non_affine_condition(cond,
                                            isl_multi_pw_aff_copy(test_index));
        test_access = isl_map_from_multi_pw_aff(test_index);
        scop = scop_add_array(scop, test_access, ast_context);
        id_test = isl_map_get_tuple_id(test_access, isl_dim_out);
        isl_map_free(test_access);
        scop_body = extract(stmt->getBody());

        id = isl_id_alloc(ctx, "t", NULL);
        domain = infinite_domain(isl_id_copy(id), scop_body);
        ident = identity_aff(domain);

        has_var_break = pet_scop_has_var_skip(scop_body, pet_skip_later);
        if (has_var_break)
                id_break_test = pet_scop_get_skip_id(scop_body, pet_skip_later);

        scop = pet_scop_prefix(scop, 0);
        scop = pet_scop_embed(scop, isl_set_copy(domain),
                                isl_map_from_aff(isl_aff_copy(ident)),
                                isl_aff_copy(ident), isl_id_copy(id));
        scop_body = pet_scop_reset_context(scop_body);
        scop_body = pet_scop_prefix(scop_body, 1);
        scop_body = pet_scop_embed(scop_body, isl_set_copy(domain),
                            isl_map_from_aff(isl_aff_copy(ident)), ident, id);

        if (has_var_break) {
                scop = scop_add_break(scop, isl_id_copy(id_break_test),
                                        isl_set_copy(domain), isl_val_one(ctx));
                scop_body = scop_add_break(scop_body, id_break_test,
                                        isl_set_copy(domain), isl_val_one(ctx));
        }
        scop = scop_add_while(scop, scop_body, id_test, domain,
                                isl_val_one(ctx));

        return scop;
}

/* Check whether "cond" expresses a simple loop bound
 * on the only set dimension.
 * In particular, if "up" is set then "cond" should contain only
 * upper bounds on the set dimension.
 * Otherwise, it should contain only lower bounds.
 */
static bool is_simple_bound(__isl_keep isl_set *cond, __isl_keep isl_val *inc)
{
        if (isl_val_is_pos(inc))
                return !isl_set_dim_has_any_lower_bound(cond, isl_dim_set, 0);
        else
                return !isl_set_dim_has_any_upper_bound(cond, isl_dim_set, 0);
}

/* Extend a condition on a given iteration of a loop to one that
 * imposes the same condition on all previous iterations.
 * "domain" expresses the lower [upper] bound on the iterations
 * when inc is positive [negative].
 *
 * In particular, we construct the condition (when inc is positive)
 *
 *      forall i' : (domain(i') and i' <= i) => cond(i')
 *
 * which is equivalent to
 *
 *      not exists i' : domain(i') and i' <= i and not cond(i')
 *
 * We construct this set by negating cond, applying a map
 *
 *      { [i'] -> [i] : domain(i') and i' <= i }
 *
 * and then negating the result again.
 */
static __isl_give isl_set *valid_for_each_iteration(__isl_take isl_set *cond,
        __isl_take isl_set *domain, __isl_take isl_val *inc)
{
        isl_map *previous_to_this;

        if (isl_val_is_pos(inc))
                previous_to_this = isl_map_lex_le(isl_set_get_space(domain));
        else
                previous_to_this = isl_map_lex_ge(isl_set_get_space(domain));

        previous_to_this = isl_map_intersect_domain(previous_to_this, domain);

        cond = isl_set_complement(cond);
        cond = isl_set_apply(cond, previous_to_this);
        cond = isl_set_complement(cond);

        isl_val_free(inc);

        return cond;
}

/* Construct a domain of the form
 *
 * [id] -> { : exists a: id = init + a * inc and a >= 0 }
 */
static __isl_give isl_set *strided_domain(__isl_take isl_id *id,
        __isl_take isl_pw_aff *init, __isl_take isl_val *inc)
{
        isl_aff *aff;
        isl_space *dim;
        isl_set *set;

        init = isl_pw_aff_insert_dims(init, isl_dim_in, 0, 1);
        dim = isl_pw_aff_get_domain_space(init);
        aff = isl_aff_zero_on_domain(isl_local_space_from_space(dim));
        aff = isl_aff_add_coefficient_val(aff, isl_dim_in, 0, inc);
        init = isl_pw_aff_add(init, isl_pw_aff_from_aff(aff));

        dim = isl_space_set_alloc(isl_pw_aff_get_ctx(init), 1, 1);
        dim = isl_space_set_dim_id(dim, isl_dim_param, 0, id);
        aff = isl_aff_zero_on_domain(isl_local_space_from_space(dim));
        aff = isl_aff_add_coefficient_si(aff, isl_dim_param, 0, 1);

        set = isl_pw_aff_eq_set(isl_pw_aff_from_aff(aff), init);

        set = isl_set_lower_bound_si(set, isl_dim_set, 0, 0);

        return isl_set_params(set);
}

/* Assuming "cond" represents a bound on a loop where the loop
 * iterator "iv" is incremented (or decremented) by one, check if wrapping
 * is possible.
 *
 * Under the given assumptions, wrapping is only possible if "cond" allows
 * for the last value before wrapping, i.e., 2^width - 1 in case of an
 * increasing iterator and 0 in case of a decreasing iterator.
 */
static bool can_wrap(__isl_keep isl_set *cond, ValueDecl *iv,
        __isl_keep isl_val *inc)
{
        bool cw;
        isl_ctx *ctx;
        isl_val *limit;
        isl_set *test;

        test = isl_set_copy(cond);

        ctx = isl_set_get_ctx(test);
        if (isl_val_is_neg(inc))
                limit = isl_val_zero(ctx);
        else {
                limit = isl_val_int_from_ui(ctx, get_type_size(iv));
                limit = isl_val_2exp(limit);
                limit = isl_val_sub_ui(limit, 1);
        }

        test = isl_set_fix_val(cond, isl_dim_set, 0, limit);
        cw = !isl_set_is_empty(test);
        isl_set_free(test);

        return cw;
}

/* Given a one-dimensional space, construct the following affine expression
 * on this space
 *
 *      { [v] -> [v mod 2^width] }
 *
 * where width is the number of bits used to represent the values
 * of the unsigned variable "iv".
 */
static __isl_give isl_aff *compute_wrapping(__isl_take isl_space *dim,
        ValueDecl *iv)
{
        isl_ctx *ctx;
        isl_val *mod;
        isl_aff *aff;
        isl_map *map;

        ctx = isl_space_get_ctx(dim);
        mod = isl_val_int_from_ui(ctx, get_type_size(iv));
        mod = isl_val_2exp(mod);

        aff = isl_aff_zero_on_domain(isl_local_space_from_space(dim));
        aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
        aff = isl_aff_mod_val(aff, mod);

        return aff;
}

/* Project out the parameter "id" from "set".
 */
static __isl_give isl_set *set_project_out_by_id(__isl_take isl_set *set,
        __isl_keep isl_id *id)
{
        int pos;

        pos = isl_set_find_dim_by_id(set, isl_dim_param, id);
        if (pos >= 0)
                set = isl_set_project_out(set, isl_dim_param, pos, 1);

        return set;
}

/* Compute the set of parameters for which "set1" is a subset of "set2".
 *
 * set1 is a subset of set2 if
 *
 *      forall i in set1 : i in set2
 *
 * or
 *
 *      not exists i in set1 and i not in set2
 *
 * i.e.,
 *
 *      not exists i in set1 \ set2
 */
static __isl_give isl_set *enforce_subset(__isl_take isl_set *set1,
        __isl_take isl_set *set2)
{
        return isl_set_complement(isl_set_params(isl_set_subtract(set1, set2)));
}

/* Compute the set of parameter values for which "cond" holds
 * on the next iteration for each element of "dom".
 *
 * We first construct mapping { [i] -> [i + inc] }, apply that to "dom"
 * and then compute the set of parameters for which the result is a subset
 * of "cond".
 */
static __isl_give isl_set *valid_on_next(__isl_take isl_set *cond,
        __isl_take isl_set *dom, __isl_take isl_val *inc)
{
        isl_space *space;
        isl_aff *aff;
        isl_map *next;

        space = isl_set_get_space(dom);
        aff = isl_aff_zero_on_domain(isl_local_space_from_space(space));
        aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
        aff = isl_aff_add_constant_val(aff, inc);
        next = isl_map_from_basic_map(isl_basic_map_from_aff(aff));

        dom = isl_set_apply(dom, next);

        return enforce_subset(dom, cond);
}

/* Does "id" refer to a nested access?
 */
static bool is_nested_parameter(__isl_keep isl_id *id)
{
        return id && isl_id_get_user(id) && !isl_id_get_name(id);
}

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

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

        return nested;
}

/* Does "space" involve any parameters that refer to nested
 * accesses, i.e., parameters with no name?
 */
static bool has_nested(__isl_keep isl_space *space)
{
        int nparam;

        nparam = isl_space_dim(space, isl_dim_param);
        for (int i = 0; i < nparam; ++i)
                if (is_nested_parameter(space, i))
                        return true;

        return false;
}

/* Does "pa" involve any parameters that refer to nested
 * accesses, i.e., parameters with no name?
 */
static bool has_nested(__isl_keep isl_pw_aff *pa)
{
        isl_space *space;
        bool nested;

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

        return nested;
}

/* Construct a pet_scop for a for statement.
 * The for loop is required to be of the form
 *
 *      for (i = init; condition; ++i)
 *
 * or
 *
 *      for (i = init; condition; --i)
 *
 * The initialization of the for loop should either be an assignment
 * to an integer variable, or a declaration of such a variable with
 * initialization.
 *
 * The condition is allowed to contain nested accesses, provided
 * they are not being written to inside the body of the loop.
 * Otherwise, or if the condition is otherwise non-affine, the for loop is
 * essentially treated as a while loop, with iteration domain
 * { [i] : i >= init }.
 *
 * We extract a pet_scop for the body and then embed it in a loop with
 * iteration domain and schedule
 *
 *      { [i] : i >= init and condition' }
 *      { [i] -> [i] }
 *
 * or
 *
 *      { [i] : i <= init and condition' }
 *      { [i] -> [-i] }
 *
 * Where condition' is equal to condition if the latter is
 * a simple upper [lower] bound and a condition that is extended
 * to apply to all previous iterations otherwise.
 *
 * If the condition is non-affine, then we drop the condition from the
 * iteration domain and instead create a separate statement
 * for evaluating the condition.  The body is then filtered to depend
 * on the result of the condition evaluating to true on all iterations
 * up to the current iteration, while the evaluation the condition itself
 * is filtered to depend on the result of the condition evaluating to true
 * on all previous iterations.
 * The context of the scop representing the body is dropped
 * because we don't know how many times the body will be executed,
 * if at all.
 *
 * If the stride of the loop is not 1, then "i >= init" is replaced by
 *
 *      (exists a: i = init + stride * a and a >= 0)
 *
 * If the loop iterator i is unsigned, then wrapping may occur.
 * During the computation, we work with a virtual iterator that
 * does not wrap.  However, the condition in the code applies
 * to the wrapped value, so we need to change condition(i)
 * into condition([i % 2^width]).
 * After computing the virtual domain and schedule, we apply
 * the function { [v] -> [v % 2^width] } to the domain and the domain
 * of the schedule.  In order not to lose any information, we also
 * need to intersect the domain of the schedule with the virtual domain
 * first, since some iterations in the wrapped domain may be scheduled
 * several times, typically an infinite number of times.
 * Note that there may be no need to perform this final wrapping
 * if the loop condition (after wrapping) satisfies certain conditions.
 * However, the is_simple_bound condition is not enough since it doesn't
 * check if there even is an upper bound.
 *
 * If the loop condition is non-affine, then we keep the virtual
 * iterator in the iteration domain and instead replace all accesses
 * to the original iterator by the wrapping of the virtual iterator.
 *
 * Wrapping on unsigned iterators can be avoided entirely if
 * loop condition is simple, the loop iterator is incremented
 * [decremented] by one and the last value before wrapping cannot
 * possibly satisfy the loop condition.
 *
 * Before extracting a pet_scop from the body we remove all
 * assignments in assigned_value to variables that are assigned
 * somewhere in the body of the loop.
 *
 * Valid parameters for a for loop are those for which the initial
 * value itself, the increment on each domain iteration and
 * the condition on both the initial value and
 * the result of incrementing the iterator for each iteration of the domain
 * can be evaluated.
 * If the loop condition is non-affine, then we only consider validity
 * of the initial value.
 *
 * If the body contains any break, then we keep track of it in "skip"
 * (if the skip condition is affine) or it is handled in scop_add_break
 * (if the skip condition is not affine).
 * Note that the affine break condition needs to be considered with
 * respect to previous iterations in the virtual domain (if any)
 * and that the domain needs to be kept virtual if there is a non-affine
 * break condition.
 */
struct pet_scop *PetScan::extract_for(ForStmt *stmt)
{
        BinaryOperator *ass;
        Decl *decl;
        Stmt *init;
        Expr *lhs, *rhs;
        ValueDecl *iv;
        isl_space *space;
        isl_set *domain;
        isl_map *sched;
        isl_set *cond = NULL;
        isl_set *skip = NULL;
        isl_id *id, *id_test = NULL, *id_break_test;
        struct pet_scop *scop, *scop_cond = NULL;
        assigned_value_cache cache(assigned_value);
        isl_val *inc;
        bool is_one;
        bool is_unsigned;
        bool is_simple;
        bool is_virtual;
        bool keep_virtual = false;
        bool has_affine_break;
        bool has_var_break;
        isl_aff *wrap = NULL;
        isl_pw_aff *pa, *pa_inc, *init_val;
        isl_set *valid_init;
        isl_set *valid_cond;
        isl_set *valid_cond_init;
        isl_set *valid_cond_next;
        isl_set *valid_inc;
        int stmt_id;

        if (!stmt->getInit() && !stmt->getCond() && !stmt->getInc())
                return extract_infinite_for(stmt);

        init = stmt->getInit();
        if (!init) {
                unsupported(stmt);
                return NULL;
        }
        if ((ass = initialization_assignment(init)) != NULL) {
                iv = extract_induction_variable(ass);
                if (!iv)
                        return NULL;
                lhs = ass->getLHS();
                rhs = ass->getRHS();
        } else if ((decl = initialization_declaration(init)) != NULL) {
                VarDecl *var = extract_induction_variable(init, decl);
                if (!var)
                        return NULL;
                iv = var;
                rhs = var->getInit();
                lhs = create_DeclRefExpr(var);
        } else {
                unsupported(stmt->getInit());
                return NULL;
        }

        pa_inc = extract_increment(stmt, iv);
        if (!pa_inc)
                return NULL;

        inc = NULL;
        if (isl_pw_aff_n_piece(pa_inc) != 1 ||
            isl_pw_aff_foreach_piece(pa_inc, &extract_cst, &inc) < 0) {
                isl_pw_aff_free(pa_inc);
                unsupported(stmt->getInc());
                isl_val_free(inc);
                return NULL;
        }
        valid_inc = isl_pw_aff_domain(pa_inc);

        is_unsigned = iv->getType()->isUnsignedIntegerType();

        assigned_value.erase(iv);
        clear_assignments clear(assigned_value);
        clear.TraverseStmt(stmt->getBody());

        id = isl_id_alloc(ctx, iv->getName().str().c_str(), iv);

        pa = try_extract_nested_condition(stmt->getCond());
        if (allow_nested && (!pa || has_nested(pa)))
                stmt_id = n_stmt++;

        scop = extract(stmt->getBody());

        has_affine_break = scop &&
                                pet_scop_has_affine_skip(scop, pet_skip_later);
        if (has_affine_break)
                skip = pet_scop_get_affine_skip_domain(scop, pet_skip_later);
        has_var_break = scop && pet_scop_has_var_skip(scop, pet_skip_later);
        if (has_var_break) {
                id_break_test = pet_scop_get_skip_id(scop, pet_skip_later);
                keep_virtual = true;
        }

        if (pa && !is_nested_allowed(pa, scop)) {
                isl_pw_aff_free(pa);
                pa = NULL;
        }

        if (!allow_nested && !pa)
                pa = try_extract_affine_condition(stmt->getCond());
        valid_cond = isl_pw_aff_domain(isl_pw_aff_copy(pa));
        cond = isl_pw_aff_non_zero_set(pa);
        if (allow_nested && !cond) {
                isl_multi_pw_aff *test_index;
                isl_map *test_access;
                int save_n_stmt = n_stmt;
                test_index = create_test_index(ctx, n_test++);
                n_stmt = stmt_id;
                scop_cond = extract_non_affine_condition(stmt->getCond(),
                                            isl_multi_pw_aff_copy(test_index));
                n_stmt = save_n_stmt;
                test_access = isl_map_from_multi_pw_aff(test_index);
                scop_cond = scop_add_array(scop_cond, test_access, ast_context);
                id_test = isl_map_get_tuple_id(test_access, isl_dim_out);
                isl_map_free(test_access);
                scop_cond = pet_scop_prefix(scop_cond, 0);
                scop = pet_scop_reset_context(scop);
                scop = pet_scop_prefix(scop, 1);
                keep_virtual = true;
                cond = isl_set_universe(isl_space_set_alloc(ctx, 0, 0));
        }

        cond = embed(cond, isl_id_copy(id));
        skip = embed(skip, isl_id_copy(id));
        valid_cond = isl_set_coalesce(valid_cond);
        valid_cond = embed(valid_cond, isl_id_copy(id));
        valid_inc = embed(valid_inc, isl_id_copy(id));
        is_one = isl_val_is_one(inc) || isl_val_is_negone(inc);
        is_virtual = is_unsigned && (!is_one || can_wrap(cond, iv, inc));

        init_val = extract_affine(rhs);
        valid_cond_init = enforce_subset(
                isl_set_from_pw_aff(isl_pw_aff_copy(init_val)),
                isl_set_copy(valid_cond));
        if (is_one && !is_virtual) {
                isl_pw_aff_free(init_val);
                pa = extract_comparison(isl_val_is_pos(inc) ? BO_GE : BO_LE,
                                lhs, rhs, init);
                valid_init = isl_pw_aff_domain(isl_pw_aff_copy(pa));
                valid_init = set_project_out_by_id(valid_init, id);
                domain = isl_pw_aff_non_zero_set(pa);
        } else {
                valid_init = isl_pw_aff_domain(isl_pw_aff_copy(init_val));
                domain = strided_domain(isl_id_copy(id), init_val,
                                        isl_val_copy(inc));
        }

        domain = embed(domain, isl_id_copy(id));
        if (is_virtual) {
                isl_map *rev_wrap;
                wrap = compute_wrapping(isl_set_get_space(cond), iv);
                rev_wrap = isl_map_from_aff(isl_aff_copy(wrap));
                rev_wrap = isl_map_reverse(rev_wrap);
                cond = isl_set_apply(cond, isl_map_copy(rev_wrap));
                skip = isl_set_apply(skip, isl_map_copy(rev_wrap));
                valid_cond = isl_set_apply(valid_cond, isl_map_copy(rev_wrap));
                valid_inc = isl_set_apply(valid_inc, rev_wrap);
        }
        is_simple = is_simple_bound(cond, inc);
        if (!is_simple) {
                cond = isl_set_gist(cond, isl_set_copy(domain));
                is_simple = is_simple_bound(cond, inc);
        }
        if (!is_simple)
                cond = valid_for_each_iteration(cond,
                                    isl_set_copy(domain), isl_val_copy(inc));
        domain = isl_set_intersect(domain, cond);
        if (has_affine_break) {
                skip = isl_set_intersect(skip , isl_set_copy(domain));
                skip = after(skip, isl_val_sgn(inc));
                domain = isl_set_subtract(domain, skip);
        }
        domain = isl_set_set_dim_id(domain, isl_dim_set, 0, isl_id_copy(id));
        space = isl_space_from_domain(isl_set_get_space(domain));
        space = isl_space_add_dims(space, isl_dim_out, 1);
        sched = isl_map_universe(space);
        if (isl_val_is_pos(inc))
                sched = isl_map_equate(sched, isl_dim_in, 0, isl_dim_out, 0);
        else
                sched = isl_map_oppose(sched, isl_dim_in, 0, isl_dim_out, 0);

        valid_cond_next = valid_on_next(valid_cond, isl_set_copy(domain),
                                        isl_val_copy(inc));
        valid_inc = enforce_subset(isl_set_copy(domain), valid_inc);

        if (is_virtual && !keep_virtual) {
                isl_map *wrap_map = isl_map_from_aff(wrap);
                wrap_map = isl_map_set_dim_id(wrap_map,
                                            isl_dim_out, 0, isl_id_copy(id));
                sched = isl_map_intersect_domain(sched, isl_set_copy(domain));
                domain = isl_set_apply(domain, isl_map_copy(wrap_map));
                sched = isl_map_apply_domain(sched, wrap_map);
        }
        if (!(is_virtual && keep_virtual))
                wrap = identity_aff(domain);

        scop_cond = pet_scop_embed(scop_cond, isl_set_copy(domain),
                    isl_map_copy(sched), isl_aff_copy(wrap), isl_id_copy(id));
        scop = pet_scop_embed(scop, isl_set_copy(domain), sched, wrap, id);
        scop = resolve_nested(scop);
        if (has_var_break)
                scop = scop_add_break(scop, id_break_test, isl_set_copy(domain),
                                        isl_val_copy(inc));
        if (id_test) {
                scop = scop_add_while(scop_cond, scop, id_test, domain,
                                        isl_val_copy(inc));
                isl_set_free(valid_inc);
        } else {
                scop = pet_scop_restrict_context(scop, valid_inc);
                scop = pet_scop_restrict_context(scop, valid_cond_next);
                scop = pet_scop_restrict_context(scop, valid_cond_init);
                isl_set_free(domain);
        }
        clear_assignment(assigned_value, iv);

        isl_val_free(inc);

        scop = pet_scop_restrict_context(scop, valid_init);

        return scop;
}

struct pet_scop *PetScan::extract(CompoundStmt *stmt, bool skip_declarations)
{
        return extract(stmt->children(), true, skip_declarations);
}

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

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

        return nested;
}

/* How many parameters of "space" refer to nested accesses, i.e., have no name?
 */
static int n_nested_parameter(__isl_keep isl_space *space)
{
        int n = 0;
        int nparam;

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

        return n;
}

/* How many parameters of "map" refer to nested accesses, i.e., have no name?
 */
static int n_nested_parameter(__isl_keep isl_map *map)
{
        isl_space *space;
        int n;

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

        return n;
}

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

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

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

                nested = (Expr *) isl_id_get_user(id);
                args[n_arg] = extract_expr(nested);
                if (!args[n_arg])
                        return -1;

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

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

                isl_id_free(id);
        }

        return n_arg;
}

/* For each nested access parameter in the access relations in "expr",
 * construct a corresponding pet_expr, place it in expr->args and
 * record its position in "param2pos".
 * n is the number of nested access parameters.
 */
struct pet_expr *PetScan::extract_nested(struct pet_expr *expr, int n,
        std::map<int,int> &param2pos)
{
        isl_space *space;

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

        space = isl_map_get_space(expr->acc.access);
        n = extract_nested(space, 0, expr->args, param2pos);
        isl_space_free(space);

        if (n < 0)
                goto error;

        expr->n_arg = n;
        return expr;
error:
        pet_expr_free(expr);
        return NULL;
}

/* Look for parameters in any access relation in "expr" that
 * refer to nested accesses.  In particular, these are
 * parameters with no name.
 *
 * If there are any such parameters, then the domain of the access
 * relation, which is still [] at this point, is replaced by
 * [[] -> [t_1,...,t_n]], with n the number of these parameters
 * (after identifying identical nested accesses).
 * The parameters are then equated to the corresponding t dimensions
 * and subsequently projected out.
 * param2pos maps the position of the parameter to the position
 * of the corresponding t dimension.
 */
struct pet_expr *PetScan::resolve_nested(struct pet_expr *expr)
{
        int n;
        int nparam;
        int n_in;
        isl_space *dim;
        isl_map *map;
        std::map<int,int> param2pos;

        if (!expr)
                return expr;

        for (int i = 0; i < expr->n_arg; ++i) {
                expr->args[i] = resolve_nested(expr->args[i]);
                if (!expr->args[i]) {
                        pet_expr_free(expr);
                        return NULL;
                }
        }

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

        n = n_nested_parameter(expr->acc.access);
        if (n == 0)
                return expr;

        expr = extract_nested(expr, n, param2pos);
        if (!expr)
                return NULL;

        n = expr->n_arg;
        nparam = isl_map_dim(expr->acc.access, isl_dim_param);
        n_in = isl_map_dim(expr->acc.access, isl_dim_in);
        dim = isl_map_get_space(expr->acc.access);
        dim = isl_space_domain(dim);
        dim = isl_space_from_domain(dim);
        dim = isl_space_add_dims(dim, isl_dim_out, n);
        map = isl_map_universe(dim);
        map = isl_map_domain_map(map);
        map = isl_map_reverse(map);
        expr->acc.access = isl_map_apply_domain(expr->acc.access, map);

        for (int i = nparam - 1; i >= 0; --i) {
                isl_id *id = isl_map_get_dim_id(expr->acc.access,
                                                isl_dim_param, i);
                if (!is_nested_parameter(id)) {
                        isl_id_free(id);
                        continue;
                }

                expr->acc.access = isl_map_equate(expr->acc.access,
                                        isl_dim_param, i, isl_dim_in,
                                        n_in + param2pos[i]);
                expr->acc.access = isl_map_project_out(expr->acc.access,
                                        isl_dim_param, i, 1);

                isl_id_free(id);
        }

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

/* Return the file offset of the expansion location of "Loc".
 */
static unsigned getExpansionOffset(SourceManager &SM, SourceLocation Loc)
{
        return SM.getFileOffset(SM.getExpansionLoc(Loc));
}

#ifdef HAVE_FINDLOCATIONAFTERTOKEN

/* Return a SourceLocation for the location after the first semicolon
 * after "loc".  If Lexer::findLocationAfterToken is available, we simply
 * call it and also skip trailing spaces and newline.
 */
static SourceLocation location_after_semi(SourceLocation loc, SourceManager &SM,
        const LangOptions &LO)
{
        return Lexer::findLocationAfterToken(loc, tok::semi, SM, LO, true);
}

#else

/* Return a SourceLocation for the location after the first semicolon
 * after "loc".  If Lexer::findLocationAfterToken is not available,
 * we look in the underlying character data for the first semicolon.
 */
static SourceLocation location_after_semi(SourceLocation loc, SourceManager &SM,
        const LangOptions &LO)
{
        const char *semi;
        const char *s = SM.getCharacterData(loc);

        semi = strchr(s, ';');
        if (!semi)
                return SourceLocation();
        return loc.getFileLocWithOffset(semi + 1 - s);
}

#endif

/* If the token at "loc" is the first token on the line, then return
 * a location referring to the start of the line.
 * Otherwise, return "loc".
 *
 * This function is used to extend a scop to the start of the line
 * if the first token of the scop is also the first token on the line.
 *
 * We look for the first token on the line.  If its location is equal to "loc",
 * then the latter is the location of the first token on the line.
 */
static SourceLocation move_to_start_of_line_if_first_token(SourceLocation loc,
        SourceManager &SM, const LangOptions &LO)
{
        std::pair<FileID, unsigned> file_offset_pair;
        llvm::StringRef file;
        const char *pos;
        Token tok;
        SourceLocation token_loc, line_loc;
        int col;

        loc = SM.getExpansionLoc(loc);
        col = SM.getExpansionColumnNumber(loc);
        line_loc = loc.getLocWithOffset(1 - col);
        file_offset_pair = SM.getDecomposedLoc(line_loc);
        file = SM.getBufferData(file_offset_pair.first, NULL);
        pos = file.data() + file_offset_pair.second;

        Lexer lexer(SM.getLocForStartOfFile(file_offset_pair.first), LO,
                                        file.begin(), pos, file.end());
        lexer.LexFromRawLexer(tok);
        token_loc = tok.getLocation();

        if (token_loc == loc)
                return line_loc;
        else
                return loc;
}

/* Convert a top-level pet_expr to a pet_scop with one statement.
 * This mainly involves resolving nested expression parameters
 * and setting the name of the iteration space.
 * The name is given by "label" if it is non-NULL.  Otherwise,
 * it is of the form S_<n_stmt>.
 * start and end of the pet_scop are derived from those of "stmt".
 */
struct pet_scop *PetScan::extract(Stmt *stmt, struct pet_expr *expr,
        __isl_take isl_id *label)
{
        struct pet_stmt *ps;
        struct pet_scop *scop;
        SourceLocation loc = stmt->getLocStart();
        SourceManager &SM = PP.getSourceManager();
        const LangOptions &LO = PP.getLangOpts();
        int line = PP.getSourceManager().getExpansionLineNumber(loc);
        unsigned start, end;

        expr = resolve_nested(expr);
        ps = pet_stmt_from_pet_expr(ctx, line, label, n_stmt++, expr);
        scop = pet_scop_from_pet_stmt(ctx, ps);

        loc = move_to_start_of_line_if_first_token(loc, SM, LO);
        start = getExpansionOffset(SM, loc);
        loc = stmt->getLocEnd();
        loc = location_after_semi(loc, SM, LO);
        end = getExpansionOffset(SM, loc);

        scop = pet_scop_update_start_end(scop, start, end);
        return scop;
}

/* Check if we can extract an affine expression from "expr".
 * Return the expressions as an isl_pw_aff if we can and NULL otherwise.
 * We turn on autodetection so that we won't generate any warnings
 * and turn off nesting, so that we won't accept any non-affine constructs.
 */
__isl_give isl_pw_aff *PetScan::try_extract_affine(Expr *expr)
{
        isl_pw_aff *pwaff;
        int save_autodetect = options->autodetect;
        bool save_nesting = nesting_enabled;

        options->autodetect = 1;
        nesting_enabled = false;

        pwaff = extract_affine(expr);

        options->autodetect = save_autodetect;
        nesting_enabled = save_nesting;

        return pwaff;
}

/* Check whether "expr" is an affine expression.
 */
bool PetScan::is_affine(Expr *expr)
{
        isl_pw_aff *pwaff;

        pwaff = try_extract_affine(expr);
        isl_pw_aff_free(pwaff);

        return pwaff != NULL;
}

/* Check if we can extract an affine constraint from "expr".
 * Return the constraint as an isl_set if we can and NULL otherwise.
 * We turn on autodetection so that we won't generate any warnings
 * and turn off nesting, so that we won't accept any non-affine constructs.
 */
__isl_give isl_pw_aff *PetScan::try_extract_affine_condition(Expr *expr)
{
        isl_pw_aff *cond;
        int save_autodetect = options->autodetect;
        bool save_nesting = nesting_enabled;

        options->autodetect = 1;
        nesting_enabled = false;

        cond = extract_condition(expr);

        options->autodetect = save_autodetect;
        nesting_enabled = save_nesting;

        return cond;
}

/* Check whether "expr" is an affine constraint.
 */
bool PetScan::is_affine_condition(Expr *expr)
{
        isl_pw_aff *cond;

        cond = try_extract_affine_condition(expr);
        isl_pw_aff_free(cond);

        return cond != NULL;
}

/* Check if we can extract a condition from "expr".
 * Return the condition as an isl_pw_aff if we can and NULL otherwise.
 * If allow_nested is set, then the condition may involve parameters
 * corresponding to nested accesses.
 * We turn on autodetection so that we won't generate any warnings.
 */
__isl_give isl_pw_aff *PetScan::try_extract_nested_condition(Expr *expr)
{
        isl_pw_aff *cond;
        int save_autodetect = options->autodetect;
        bool save_nesting = nesting_enabled;

        options->autodetect = 1;
        nesting_enabled = allow_nested;
        cond = extract_condition(expr);

        options->autodetect = save_autodetect;
        nesting_enabled = save_nesting;

        return cond;
}

/* If the top-level expression of "stmt" is an assignment, then
 * return that assignment as a BinaryOperator.
 * Otherwise return NULL.
 */
static BinaryOperator *top_assignment_or_null(Stmt *stmt)
{
        BinaryOperator *ass;

        if (!stmt)
                return NULL;
        if (stmt->getStmtClass() != Stmt::BinaryOperatorClass)
                return NULL;

        ass = cast<BinaryOperator>(stmt);
        if(ass->getOpcode() != BO_Assign)
                return NULL;

        return ass;
}

/* Check if the given if statement is a conditional assignement
 * with a non-affine condition.  If so, construct a pet_scop
 * corresponding to this conditional assignment.  Otherwise return NULL.
 *
 * In particular we check if "stmt" is of the form
 *
 *      if (condition)
 *              a = f(...);
 *      else
 *              a = g(...);
 *
 * where a is some array or scalar access.
 * The constructed pet_scop then corresponds to the expression
 *
 *      a = condition ? f(...) : g(...)
 *
 * All access relations in f(...) are intersected with condition
 * while all access relation in g(...) are intersected with the complement.
 */
struct pet_scop *PetScan::extract_conditional_assignment(IfStmt *stmt)
{
        BinaryOperator *ass_then, *ass_else;
        isl_multi_pw_aff *write_then, *write_else;
        isl_set *cond, *comp;
        isl_multi_pw_aff *index;
        isl_pw_aff *pa;
        int equal;
        struct pet_expr *pe_cond, *pe_then, *pe_else, *pe, *pe_write;
        bool save_nesting = nesting_enabled;

        if (!options->detect_conditional_assignment)
                return NULL;

        ass_then = top_assignment_or_null(stmt->getThen());
        ass_else = top_assignment_or_null(stmt->getElse());

        if (!ass_then || !ass_else)
                return NULL;

        if (is_affine_condition(stmt->getCond()))
                return NULL;

        write_then = extract_index(ass_then->getLHS());
        write_else = extract_index(ass_else->getLHS());

        equal = isl_multi_pw_aff_plain_is_equal(write_then, write_else);
        isl_multi_pw_aff_free(write_else);
        if (equal < 0 || !equal) {
                isl_multi_pw_aff_free(write_then);
                return NULL;
        }

        nesting_enabled = allow_nested;
        pa = extract_condition(stmt->getCond());
        nesting_enabled = save_nesting;
        cond = isl_pw_aff_non_zero_set(isl_pw_aff_copy(pa));
        comp = isl_pw_aff_zero_set(isl_pw_aff_copy(pa));
        index = isl_multi_pw_aff_from_range(isl_multi_pw_aff_from_pw_aff(pa));

        pe_cond = pet_expr_from_index(index);

        pe_then = extract_expr(ass_then->getRHS());
        pe_then = pet_expr_restrict(pe_then, cond);
        pe_else = extract_expr(ass_else->getRHS());
        pe_else = pet_expr_restrict(pe_else, comp);

        pe = pet_expr_new_ternary(ctx, pe_cond, pe_then, pe_else);
        pe_write = pet_expr_from_index_and_depth(write_then,
                                                extract_depth(write_then));
        if (pe_write) {
                pe_write->acc.write = 1;
                pe_write->acc.read = 0;
        }
        pe = pet_expr_new_binary(ctx, pet_op_assign, pe_write, pe);
        return extract(stmt, pe);
}

/* Create a pet_scop with a single statement evaluating "cond"
 * and writing the result to a virtual scalar, as expressed by
 * "index".
 */
struct pet_scop *PetScan::extract_non_affine_condition(Expr *cond,
        __isl_take isl_multi_pw_aff *index)
{
        struct pet_expr *expr, *write;
        struct pet_stmt *ps;
        struct pet_scop *scop;
        SourceLocation loc = cond->getLocStart();
        int line = PP.getSourceManager().getExpansionLineNumber(loc);

        write = pet_expr_from_index(index);
        if (write) {
                write->acc.write = 1;
                write->acc.read = 0;
        }
        expr = extract_expr(cond);
        expr = resolve_nested(expr);
        expr = pet_expr_new_binary(ctx, pet_op_assign, write, expr);
        ps = pet_stmt_from_pet_expr(ctx, line, NULL, n_stmt++, expr);
        scop = pet_scop_from_pet_stmt(ctx, ps);
        scop = resolve_nested(scop);

        return scop;
}

extern "C" {
        static struct pet_expr *embed_access(struct pet_expr *expr, void *user);
}

/* Apply the map pointed to by "user" to the domain of the access 
 * relation associated to "expr", thereby embedding it in the range of the map.
 * The domain of both relations is the zero-dimensional domain.
 */
static struct pet_expr *embed_access(struct pet_expr *expr, void *user)
{
        isl_map *map = (isl_map *) user;

        expr->acc.access = isl_map_apply_domain(expr->acc.access,
                                                isl_map_copy(map));
        if (!expr->acc.access)
                goto error;

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

/* Apply "map" to all access relations in "expr".
 */
static struct pet_expr *embed(struct pet_expr *expr, __isl_keep isl_map *map)
{
        return pet_expr_map_access(expr, &embed_access, map);
}

/* How many parameters of "set" refer to nested accesses, i.e., have no name?
 */
static int n_nested_parameter(__isl_keep isl_set *set)
{
        isl_space *space;
        int n;

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

        return n;
}

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

        space = isl_map_get_space(map);
        nparam = isl_space_dim(space, isl_dim_param);
        for (int i = nparam - 1; i >= 0; --i)
                if (is_nested_parameter(space, i))
                        map = isl_map_project_out(map, isl_dim_param, i, 1);
        isl_space_free(space);

        return map;
}

/* Remove all parameters from the access relation of "expr"
 * that refer to nested accesses.
 */
static struct pet_expr *remove_nested_parameters(struct pet_expr *expr)
{
        expr->acc.access = remove_nested_parameters(expr->acc.access);
        if (!expr->acc.access)
                goto error;

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

extern "C" {
        static struct pet_expr *expr_remove_nested_parameters(
                struct pet_expr *expr, void *user);
}

static struct pet_expr *expr_remove_nested_parameters(
        struct pet_expr *expr, void *user)
{
        return remove_nested_parameters(expr);
}

/* Remove all nested access parameters from the schedule and all
 * accesses of "stmt".
 * There is no need to remove them from the domain as these parameters
 * have already been removed from the domain when this function is called.
 */
static struct pet_stmt *remove_nested_parameters(struct pet_stmt *stmt)
{
        if (!stmt)
                return NULL;
        stmt->schedule = remove_nested_parameters(stmt->schedule);
        stmt->body = pet_expr_map_access(stmt->body,
                            &expr_remove_nested_parameters, NULL);
        if (!stmt->schedule || !stmt->body)
                goto error;
        for (int i = 0; i < stmt->n_arg; ++i) {
                stmt->args[i] = pet_expr_map_access(stmt->args[i],
                            &expr_remove_nested_parameters, NULL);
                if (!stmt->args[i])
                        goto error;
        }

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

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

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

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

        if (n_arg < 0)
                goto error;

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

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

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

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

        map = isl_set_unwrap(stmt->domain);

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

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

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

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

/* Look for parameters in the iteration domain of "stmt" that
 * refer to nested accesses.  In particular, these are
 * parameters with no name.
 *
 * If there are any such parameters, then as many extra variables
 * (after identifying identical nested accesses) are inserted in the
 * range of the map wrapped inside the domain, before the original variables.
 * If the original domain is not a wrapped map, then a new wrapped
 * map is created with zero output dimensions.
 * The parameters are then equated to the corresponding output dimensions
 * and subsequently projected out, from the iteration domain,
 * the schedule and the access relations.
 * For each of the output dimensions, a corresponding argument
 * expression is inserted.  Initially they are created with
 * a zero-dimensional domain, so they have to be embedded
 * in the current iteration domain.
 * param2pos maps the position of the parameter to the position
 * of the corresponding output dimension in the wrapped map.
 */
struct pet_stmt *PetScan::resolve_nested(struct pet_stmt *stmt)
{
        int n;
        int nparam;
        unsigned n_arg;
        isl_map *map;
        std::map<int,int> param2pos;

        if (!stmt)
                return NULL;

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

        n_arg = stmt->n_arg;
        stmt = extract_nested(stmt, n, param2pos);
        if (!stmt)
                return NULL;

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

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

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

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

        stmt->domain = isl_map_wrap(map);

        map = isl_set_unwrap(isl_set_copy(stmt->domain));
        map = isl_map_from_range(isl_map_domain(map));
        for (int pos = 0; pos < n; ++pos)
                stmt->args[pos] = embed(stmt->args[pos], map);
        isl_map_free(map);

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

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

/* For each statement in "scop", move the parameters that correspond
 * to nested access into the ranges of the domains and create
 * corresponding argument expressions.
 */
struct pet_scop *PetScan::resolve_nested(struct pet_scop *scop)
{
        if (!scop)
                return NULL;

        for (int i = 0; i < scop->n_stmt; ++i) {
                scop->stmts[i] = resolve_nested(scop->stmts[i]);
                if (!scop->stmts[i])
                        goto error;
        }

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

/* Given an access expression "expr", is the variable accessed by
 * "expr" assigned anywhere inside "scop"?
 */
static bool is_assigned(pet_expr *expr, pet_scop *scop)
{
        bool assigned = false;
        isl_id *id;

        id = pet_expr_access_get_id(expr);
        assigned = pet_scop_writes(scop, id);
        isl_id_free(id);

        return assigned;
}

/* Are all nested access parameters in "pa" allowed given "scop".
 * In particular, is none of them written by anywhere inside "scop".
 *
 * If "scop" has any skip conditions, then no nested access parameters
 * are allowed.  In particular, if there is any nested access in a guard
 * for a piece of code containing a "continue", then we want to introduce
 * a separate statement for evaluating this guard so that we can express
 * that the result is false for all previous iterations.
 */
bool PetScan::is_nested_allowed(__isl_keep isl_pw_aff *pa, pet_scop *scop)
{
        int nparam;

        if (!scop)
                return true;

        nparam = isl_pw_aff_dim(pa, isl_dim_param);
        for (int i = 0; i < nparam; ++i) {
                Expr *nested;
                isl_id *id = isl_pw_aff_get_dim_id(pa, isl_dim_param, i);
                pet_expr *expr;
                bool allowed;

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

                if (pet_scop_has_skip(scop, pet_skip_now)) {
                        isl_id_free(id);
                        return false;
                }

                nested = (Expr *) isl_id_get_user(id);
                expr = extract_expr(nested);
                allowed = expr && expr->type == pet_expr_access &&
                            !is_assigned(expr, scop);

                pet_expr_free(expr);
                isl_id_free(id);

                if (!allowed)
                        return false;
        }

        return true;
}

/* Do we need to construct a skip condition of the given type
 * on an if statement, given that the if condition is non-affine?
 *
 * pet_scop_filter_skip can only handle the case where the if condition
 * holds (the then branch) and the skip condition is universal.
 * In any other case, we need to construct a new skip condition.
 */
static bool need_skip(struct pet_scop *scop_then, struct pet_scop *scop_else,
        bool have_else, enum pet_skip type)
{
        if (have_else && scop_else && pet_scop_has_skip(scop_else, type))
                return true;
        if (scop_then && pet_scop_has_skip(scop_then, type) &&
            !pet_scop_has_universal_skip(scop_then, type))
                return true;
        return false;
}

/* Do we need to construct a skip condition of the given type
 * on an if statement, given that the if condition is affine?
 *
 * There is no need to construct a new skip condition if all
 * the skip conditions are affine.
 */
static bool need_skip_aff(struct pet_scop *scop_then,
        struct pet_scop *scop_else, bool have_else, enum pet_skip type)
{
        if (scop_then && pet_scop_has_var_skip(scop_then, type))
                return true;
        if (have_else && scop_else && pet_scop_has_var_skip(scop_else, type))
                return true;
        return false;
}

/* Do we need to construct a skip condition of the given type
 * on an if statement?
 */
static bool need_skip(struct pet_scop *scop_then, struct pet_scop *scop_else,
        bool have_else, enum pet_skip type, bool affine)
{
        if (affine)
                return need_skip_aff(scop_then, scop_else, have_else, type);
        else
                return need_skip(scop_then, scop_else, have_else, type);
}

/* Construct an affine expression pet_expr that evaluates
 * to the constant "val".
 */
static struct pet_expr *universally(isl_ctx *ctx, int val)
{
        isl_local_space *ls;
        isl_val *v;
        isl_aff *aff;
        isl_multi_pw_aff *mpa;

        ls = isl_local_space_from_space(isl_space_set_alloc(ctx, 0, 0));
        aff = isl_aff_val_on_domain(ls, isl_val_int_from_si(ctx, val));
        mpa = isl_multi_pw_aff_from_pw_aff(isl_pw_aff_from_aff(aff));

        return pet_expr_from_index(mpa);
}

/* Construct an affine expression pet_expr that evaluates
 * to the constant 1.
 */
static struct pet_expr *universally_true(isl_ctx *ctx)
{
        return universally(ctx, 1);
}

/* Construct an affine expression pet_expr that evaluates
 * to the constant 0.
 */
static struct pet_expr *universally_false(isl_ctx *ctx)
{
        return universally(ctx, 0);
}

/* Given an index expression "test_index" for the if condition,
 * an access relation "skip_access" for the skip condition and
 * scops for the then and else branches, construct a scop for
 * computing "skip_access".
 *
 * The computed scop contains a single statement that essentially does
 *
 *      skip_cond = test_cond ? skip_cond_then : skip_cond_else
 *
 * If the skip conditions of the then and/or else branch are not affine,
 * then they need to be filtered by test_index.
 * If they are missing, then this means the skip condition is false.
 *
 * Since we are constructing a skip condition for the if statement,
 * the skip conditions on the then and else branches are removed.
 */
static struct pet_scop *extract_skip(PetScan *scan,
        __isl_take isl_multi_pw_aff *test_index,
        __isl_take isl_map *skip_access,
        struct pet_scop *scop_then, struct pet_scop *scop_else, bool have_else,
        enum pet_skip type)
{
        struct pet_expr *expr_then, *expr_else, *expr, *expr_skip;
        struct pet_stmt *stmt;
        struct pet_scop *scop;
        isl_ctx *ctx = scan->ctx;
        isl_map *test_access;

        if (!scop_then)
                goto error;
        if (have_else && !scop_else)
                goto error;

        test_access = isl_map_from_multi_pw_aff(
                                isl_multi_pw_aff_copy(test_index));
        if (pet_scop_has_skip(scop_then, type)) {
                expr_then = pet_scop_get_skip_expr(scop_then, type);
                pet_scop_reset_skip(scop_then, type);
                if (!pet_expr_is_affine(expr_then))
                        expr_then = pet_expr_filter(expr_then,
                                            isl_map_copy(test_access), 1);
        } else
                expr_then = universally_false(ctx);

        if (have_else && pet_scop_has_skip(scop_else, type)) {
                expr_else = pet_scop_get_skip_expr(scop_else, type);
                pet_scop_reset_skip(scop_else, type);
                if (!pet_expr_is_affine(expr_else))
                        expr_else = pet_expr_filter(expr_else,
                                            isl_map_copy(test_access), 0);
        } else
                expr_else = universally_false(ctx);
        isl_map_free(test_access);

        expr = pet_expr_from_index(test_index);
        expr = pet_expr_new_ternary(ctx, expr, expr_then, expr_else);
        expr_skip = pet_expr_from_access(isl_map_copy(skip_access));
        if (expr_skip) {
                expr_skip->acc.write = 1;
                expr_skip->acc.read = 0;
        }
        expr = pet_expr_new_binary(ctx, pet_op_assign, expr_skip, expr);
        stmt = pet_stmt_from_pet_expr(ctx, -1, NULL, scan->n_stmt++, expr);

        scop = pet_scop_from_pet_stmt(ctx, stmt);
        scop = scop_add_array(scop, skip_access, scan->ast_context);
        isl_map_free(skip_access);

        return scop;
error:
        isl_multi_pw_aff_free(test_index);
        isl_map_free(skip_access);
        return NULL;
}

/* Is scop's skip_now condition equal to its skip_later condition?
 * In particular, this means that it either has no skip_now condition
 * or both a skip_now and a skip_later condition (that are equal to each other).
 */
static bool skip_equals_skip_later(struct pet_scop *scop)
{
        int has_skip_now, has_skip_later;
        int equal;
        isl_set *skip_now, *skip_later;

        if (!scop)
                return false;
        has_skip_now = pet_scop_has_skip(scop, pet_skip_now);
        has_skip_later = pet_scop_has_skip(scop, pet_skip_later);
        if (has_skip_now != has_skip_later)
                return false;
        if (!has_skip_now)
                return true;

        skip_now = pet_scop_get_skip(scop, pet_skip_now);
        skip_later = pet_scop_get_skip(scop, pet_skip_later);
        equal = isl_set_is_equal(skip_now, skip_later);
        isl_set_free(skip_now);
        isl_set_free(skip_later);

        return equal;
}

/* Drop the skip conditions of type pet_skip_later from scop1 and scop2.
 */
static void drop_skip_later(struct pet_scop *scop1, struct pet_scop *scop2)
{
        pet_scop_reset_skip(scop1, pet_skip_later);
        pet_scop_reset_skip(scop2, pet_skip_later);
}

/* Structure that handles the construction of skip conditions.
 *
 * scop_then and scop_else represent the then and else branches
 *      of the if statement
 *
 * skip[type] is true if we need to construct a skip condition of that type
 * equal is set if the skip conditions of types pet_skip_now and pet_skip_later
 *      are equal to each other
 * access[type] is the virtual array representing the skip condition
 * scop[type] is a scop for computing the skip condition
 */
struct pet_skip_info {
        isl_ctx *ctx;

        bool skip[2];
        bool equal;
        isl_map *access[2];
        struct pet_scop *scop[2];

        pet_skip_info(isl_ctx *ctx) : ctx(ctx) {}

        operator bool() { return skip[pet_skip_now] || skip[pet_skip_later]; }
};

/* Structure that handles the construction of skip conditions on if statements.
 *
 * scop_then and scop_else represent the then and else branches
 *      of the if statement
 */
struct pet_skip_info_if : public pet_skip_info {
        struct pet_scop *scop_then, *scop_else;
        bool have_else;

        pet_skip_info_if(isl_ctx *ctx, struct pet_scop *scop_then,
                      struct pet_scop *scop_else, bool have_else, bool affine);
        void extract(PetScan *scan, __isl_keep isl_multi_pw_aff *index,
                     enum pet_skip type);
        void extract(PetScan *scan, __isl_keep isl_multi_pw_aff *index);
        void extract(PetScan *scan, __isl_keep isl_pw_aff *cond);
        struct pet_scop *add(struct pet_scop *scop, enum pet_skip type,
                                int offset);
        struct pet_scop *add(struct pet_scop *scop, int offset);
};

/* Initialize a pet_skip_info_if structure based on the then and else branches
 * and based on whether the if condition is affine or not.
 */
pet_skip_info_if::pet_skip_info_if(isl_ctx *ctx, struct pet_scop *scop_then,
        struct pet_scop *scop_else, bool have_else, bool affine) :
        pet_skip_info(ctx), scop_then(scop_then), scop_else(scop_else),
        have_else(have_else)
{
        skip[pet_skip_now] =
            need_skip(scop_then, scop_else, have_else, pet_skip_now, affine);
        equal = skip[pet_skip_now] && skip_equals_skip_later(scop_then) &&
                            (!have_else || skip_equals_skip_later(scop_else));
        skip[pet_skip_later] = skip[pet_skip_now] && !equal &&
            need_skip(scop_then, scop_else, have_else, pet_skip_later, affine);
}

/* If we need to construct a skip condition of the given type,
 * then do so now.
 *
 * "index" represents the if condition.
 */
void pet_skip_info_if::extract(PetScan *scan,
        __isl_keep isl_multi_pw_aff *index, enum pet_skip type)
{
        isl_ctx *ctx;

        if (!skip[type])
                return;

        ctx = isl_multi_pw_aff_get_ctx(index);
        access[type] = create_test_access(ctx, scan->n_test++);
        scop[type] = extract_skip(scan, isl_multi_pw_aff_copy(index),
                                isl_map_copy(access[type]),
                                scop_then, scop_else, have_else, type);
}

/* Construct the required skip conditions, given the if condition "index".
 */
void pet_skip_info_if::extract(PetScan *scan,
        __isl_keep isl_multi_pw_aff *index)
{
        extract(scan, index, pet_skip_now);
        extract(scan, index, pet_skip_later);
        if (equal)
                drop_skip_later(scop_then, scop_else);
}

/* Construct the required skip conditions, given the if condition "cond".
 */
void pet_skip_info_if::extract(PetScan *scan, __isl_keep isl_pw_aff *cond)
{
        isl_multi_pw_aff *test;

        if (!skip[pet_skip_now] && !skip[pet_skip_later])
                return;

        test = isl_multi_pw_aff_from_pw_aff(isl_pw_aff_copy(cond));
        test = isl_multi_pw_aff_from_range(test);
        extract(scan, test);
        isl_multi_pw_aff_free(test);
}

/* Add the computed skip condition of the give type to "main" and 
 * add the scop for computing the condition at the given offset.
 *
 * If equal is set, then we only computed a skip condition for pet_skip_now,
 * but we also need to set it as main's pet_skip_later.
 */
struct pet_scop *pet_skip_info_if::add(struct pet_scop *main,
        enum pet_skip type, int offset)
{
        isl_set *skip_set;

        if (!skip[type])
                return main;

        skip_set = isl_map_range(access[type]);
        access[type] = NULL;
        scop[type] = pet_scop_prefix(scop[type], offset);
        main = pet_scop_add_par(ctx, main, scop[type]);
        scop[type] = NULL;

        if (equal)
                main = pet_scop_set_skip(main, pet_skip_later,
                                            isl_set_copy(skip_set));

        main = pet_scop_set_skip(main, type, skip_set);

        return main;
}

/* Add the computed skip conditions to "main" and 
 * add the scops for computing the conditions at the given offset.
 */
struct pet_scop *pet_skip_info_if::add(struct pet_scop *scop, int offset)
{
        scop = add(scop, pet_skip_now, offset);
        scop = add(scop, pet_skip_later, offset);

        return scop;
}

/* Construct a pet_scop for a non-affine if statement.
 *
 * We create a separate statement that writes the result
 * of the non-affine condition to a virtual scalar.
 * A constraint requiring the value of this virtual scalar to be one
 * is added to the iteration domains of the then branch.
 * Similarly, a constraint requiring the value of this virtual scalar
 * to be zero is added to the iteration domains of the else branch, if any.
 * We adjust the schedules to ensure that the virtual scalar is written
 * before it is read.
 *
 * If there are any breaks or continues in the then and/or else
 * branches, then we may have to compute a new skip condition.
 * This is handled using a pet_skip_info_if object.
 * On initialization, the object checks if skip conditions need
 * to be computed.  If so, it does so in "extract" and adds them in "add".
 */
struct pet_scop *PetScan::extract_non_affine_if(Expr *cond,
        struct pet_scop *scop_then, struct pet_scop *scop_else,
        bool have_else, int stmt_id)
{
        struct pet_scop *scop;
        isl_multi_pw_aff *test_index;
        isl_map *test_access;
        int save_n_stmt = n_stmt;

        test_index = create_test_index(ctx, n_test++);
        test_access = isl_map_from_multi_pw_aff(
                                        isl_multi_pw_aff_copy(test_index));
        n_stmt = stmt_id;
        scop = extract_non_affine_condition(cond,
                                        isl_multi_pw_aff_copy(test_index));
        n_stmt = save_n_stmt;
        scop = scop_add_array(scop, test_access, ast_context);

        pet_skip_info_if skip(ctx, scop_then, scop_else, have_else, false);
        skip.extract(this, test_index);
        isl_multi_pw_aff_free(test_index);

        scop = pet_scop_prefix(scop, 0);
        scop_then = pet_scop_prefix(scop_then, 1);
        scop_then = pet_scop_filter(scop_then, isl_map_copy(test_access), 1);
        if (have_else) {
                scop_else = pet_scop_prefix(scop_else, 1);
                scop_else = pet_scop_filter(scop_else, test_access, 0);
                scop_then = pet_scop_add_par(ctx, scop_then, scop_else);
        } else
                isl_map_free(test_access);

        scop = pet_scop_add_seq(ctx, scop, scop_then);

        scop = skip.add(scop, 2);

        return scop;
}

/* Construct a pet_scop for an if statement.
 *
 * If the condition fits the pattern of a conditional assignment,
 * then it is handled by extract_conditional_assignment.
 * Otherwise, we do the following.
 *
 * If the condition is affine, then the condition is added
 * to the iteration domains of the then branch, while the
 * opposite of the condition in added to the iteration domains
 * of the else branch, if any.
 * We allow the condition to be dynamic, i.e., to refer to
 * scalars or array elements that may be written to outside
 * of the given if statement.  These nested accesses are then represented
 * as output dimensions in the wrapping iteration domain.
 * If it also written _inside_ the then or else branch, then
 * we treat the condition as non-affine.
 * As explained in extract_non_affine_if, this will introduce
 * an extra statement.
 * For aesthetic reasons, we want this statement to have a statement
 * number that is lower than those of the then and else branches.
 * In order to evaluate if will need such a statement, however, we
 * first construct scops for the then and else branches.
 * We therefore reserve a statement number if we might have to
 * introduce such an extra statement.
 *
 * If the condition is not affine, then the scop is created in
 * extract_non_affine_if.
 *
 * If there are any breaks or continues in the then and/or else
 * branches, then we may have to compute a new skip condition.
 * This is handled using a pet_skip_info_if object.
 * On initialization, the object checks if skip conditions need
 * to be computed.  If so, it does so in "extract" and adds them in "add".
 */
struct pet_scop *PetScan::extract(IfStmt *stmt)
{
        struct pet_scop *scop_then, *scop_else = NULL, *scop;
        isl_pw_aff *cond;
        int stmt_id;
        isl_set *set;
        isl_set *valid;

        scop = extract_conditional_assignment(stmt);
        if (scop)
                return scop;

        cond = try_extract_nested_condition(stmt->getCond());
        if (allow_nested && (!cond || has_nested(cond)))
                stmt_id = n_stmt++;

        {
                assigned_value_cache cache(assigned_value);
                scop_then = extract(stmt->getThen());
        }

        if (stmt->getElse()) {
                assigned_value_cache cache(assigned_value);
                scop_else = extract(stmt->getElse());
                if (options->autodetect) {
                        if (scop_then && !scop_else) {
                                partial = true;
                                isl_pw_aff_free(cond);
                                return scop_then;
                        }
                        if (!scop_then && scop_else) {
                                partial = true;
                                isl_pw_aff_free(cond);
                                return scop_else;
                        }
                }
        }

        if (cond &&
            (!is_nested_allowed(cond, scop_then) ||
             (stmt->getElse() && !is_nested_allowed(cond, scop_else)))) {
                isl_pw_aff_free(cond);
                cond = NULL;
        }
        if (allow_nested && !cond)
                return extract_non_affine_if(stmt->getCond(), scop_then,
                                        scop_else, stmt->getElse(), stmt_id);

        if (!cond)
                cond = extract_condition(stmt->getCond());

        pet_skip_info_if skip(ctx, scop_then, scop_else, stmt->getElse(), true);
        skip.extract(this, cond);

        valid = isl_pw_aff_domain(isl_pw_aff_copy(cond));
        set = isl_pw_aff_non_zero_set(cond);
        scop = pet_scop_restrict(scop_then, isl_set_copy(set));

        if (stmt->getElse()) {
                set = isl_set_subtract(isl_set_copy(valid), set);
                scop_else = pet_scop_restrict(scop_else, set);
                scop = pet_scop_add_par(ctx, scop, scop_else);
        } else
                isl_set_free(set);
        scop = resolve_nested(scop);
        scop = pet_scop_restrict_context(scop, valid);

        if (skip)
                scop = pet_scop_prefix(scop, 0);
        scop = skip.add(scop, 1);

        return scop;
}

/* Try and construct a pet_scop for a label statement.
 * We currently only allow labels on expression statements.
 */
struct pet_scop *PetScan::extract(LabelStmt *stmt)
{
        isl_id *label;
        Stmt *sub;

        sub = stmt->getSubStmt();
        if (!isa<Expr>(sub)) {
                unsupported(stmt);
                return NULL;
        }

        label = isl_id_alloc(ctx, stmt->getName(), NULL);

        return extract(sub, extract_expr(cast<Expr>(sub)), label);
}

/* Construct a pet_scop for a continue statement.
 *
 * We simply create an empty scop with a universal pet_skip_now
 * skip condition.  This skip condition will then be taken into
 * account by the enclosing loop construct, possibly after
 * being incorporated into outer skip conditions.
 */
struct pet_scop *PetScan::extract(ContinueStmt *stmt)
{
        pet_scop *scop;
        isl_space *space;
        isl_set *set;

        scop = pet_scop_empty(ctx);
        if (!scop)
                return NULL;

        space = isl_space_set_alloc(ctx, 0, 1);
        set = isl_set_universe(space);
        set = isl_set_fix_si(set, isl_dim_set, 0, 1);
        scop = pet_scop_set_skip(scop, pet_skip_now, set);

        return scop;
}

/* Construct a pet_scop for a break statement.
 *
 * We simply create an empty scop with both a universal pet_skip_now
 * skip condition and a universal pet_skip_later skip condition.
 * These skip conditions will then be taken into
 * account by the enclosing loop construct, possibly after
 * being incorporated into outer skip conditions.
 */
struct pet_scop *PetScan::extract(BreakStmt *stmt)
{
        pet_scop *scop;
        isl_space *space;
        isl_set *set;

        scop = pet_scop_empty(ctx);
        if (!scop)
                return NULL;

        space = isl_space_set_alloc(ctx, 0, 1);
        set = isl_set_universe(space);
        set = isl_set_fix_si(set, isl_dim_set, 0, 1);
        scop = pet_scop_set_skip(scop, pet_skip_now, isl_set_copy(set));
        scop = pet_scop_set_skip(scop, pet_skip_later, set);

        return scop;
}

/* Try and construct a pet_scop corresponding to "stmt".
 *
 * If "stmt" is a compound statement, then "skip_declarations"
 * indicates whether we should skip initial declarations in the
 * compound statement.
 *
 * If the constructed pet_scop is not a (possibly) partial representation
 * of "stmt", we update start and end of the pet_scop to those of "stmt".
 * In particular, if skip_declarations, then we may have skipped declarations
 * inside "stmt" and so the pet_scop may not represent the entire "stmt".
 * Note that this function may be called with "stmt" referring to the entire
 * body of the function, including the outer braces.  In such cases,
 * skip_declarations will be set and the braces will not be taken into
 * account in scop->start and scop->end.
 */
struct pet_scop *PetScan::extract(Stmt *stmt, bool skip_declarations)
{
        struct pet_scop *scop;
        unsigned start, end;
        SourceLocation loc;
        SourceManager &SM = PP.getSourceManager();
        const LangOptions &LO = PP.getLangOpts();

        if (isa<Expr>(stmt))
                return extract(stmt, extract_expr(cast<Expr>(stmt)));

        switch (stmt->getStmtClass()) {
        case Stmt::WhileStmtClass:
                scop = extract(cast<WhileStmt>(stmt));
                break;
        case Stmt::ForStmtClass:
                scop = extract_for(cast<ForStmt>(stmt));
                break;
        case Stmt::IfStmtClass:
                scop = extract(cast<IfStmt>(stmt));
                break;
        case Stmt::CompoundStmtClass:
                scop = extract(cast<CompoundStmt>(stmt), skip_declarations);
                break;
        case Stmt::LabelStmtClass:
                scop = extract(cast<LabelStmt>(stmt));
                break;
        case Stmt::ContinueStmtClass:
                scop = extract(cast<ContinueStmt>(stmt));
                break;
        case Stmt::BreakStmtClass:
                scop = extract(cast<BreakStmt>(stmt));
                break;
        case Stmt::DeclStmtClass:
                scop = extract(cast<DeclStmt>(stmt));
                break;
        default:
                unsupported(stmt);
                return NULL;
        }

        if (partial || skip_declarations)
                return scop;

        loc = stmt->getLocStart();
        loc = move_to_start_of_line_if_first_token(loc, SM, LO);
        start = getExpansionOffset(SM, loc);
        loc = PP.getLocForEndOfToken(stmt->getLocEnd());
        end = getExpansionOffset(SM, loc);
        scop = pet_scop_update_start_end(scop, start, end);

        return scop;
}

/* Do we need to construct a skip condition of the given type
 * on a sequence of statements?
 *
 * There is no need to construct a new skip condition if only
 * only of the two statements has a skip condition or if both
 * of their skip conditions are affine.
 *
 * In principle we also don't need a new continuation variable if
 * the continuation of scop2 is affine, but then we would need
 * to allow more complicated forms of continuations.
 */
static bool need_skip_seq(struct pet_scop *scop1, struct pet_scop *scop2,
        enum pet_skip type)
{
        if (!scop1 || !pet_scop_has_skip(scop1, type))
                return false;
        if (!scop2 || !pet_scop_has_skip(scop2, type))
                return false;
        if (pet_scop_has_affine_skip(scop1, type) &&
            pet_scop_has_affine_skip(scop2, type))
                return false;
        return true;
}

/* Construct a scop for computing the skip condition of the given type and
 * with access relation "skip_access" for a sequence of two scops "scop1"
 * and "scop2".
 *
 * The computed scop contains a single statement that essentially does
 *
 *      skip_cond = skip_cond_1 ? 1 : skip_cond_2
 *
 * or, in other words, skip_cond1 || skip_cond2.
 * In this expression, skip_cond_2 is filtered to reflect that it is
 * only evaluated when skip_cond_1 is false.
 *
 * The skip condition on scop1 is not removed because it still needs
 * to be applied to scop2 when these two scops are combined.
 */
static struct pet_scop *extract_skip_seq(PetScan *ps,
        __isl_take isl_map *skip_access,
        struct pet_scop *scop1, struct pet_scop *scop2, enum pet_skip type)
{
        isl_map *access;
        struct pet_expr *expr1, *expr2, *expr, *expr_skip;
        struct pet_stmt *stmt;
        struct pet_scop *scop;
        isl_ctx *ctx = ps->ctx;

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

        expr1 = pet_scop_get_skip_expr(scop1, type);
        expr2 = pet_scop_get_skip_expr(scop2, type);
        pet_scop_reset_skip(scop2, type);

        expr2 = pet_expr_filter(expr2, isl_map_copy(expr1->acc.access), 0);

        expr = universally_true(ctx);
        expr = pet_expr_new_ternary(ctx, expr1, expr, expr2);
        expr_skip = pet_expr_from_access(isl_map_copy(skip_access));
        if (expr_skip) {
                expr_skip->acc.write = 1;
                expr_skip->acc.read = 0;
        }
        expr = pet_expr_new_binary(ctx, pet_op_assign, expr_skip, expr);
        stmt = pet_stmt_from_pet_expr(ctx, -1, NULL, ps->n_stmt++, expr);

        scop = pet_scop_from_pet_stmt(ctx, stmt);
        scop = scop_add_array(scop, skip_access, ps->ast_context);
        isl_map_free(skip_access);

        return scop;
error:
        isl_map_free(skip_access);
        return NULL;
}

/* Structure that handles the construction of skip conditions
 * on sequences of statements.
 *
 * scop1 and scop2 represent the two statements that are combined
 */
struct pet_skip_info_seq : public pet_skip_info {
        struct pet_scop *scop1, *scop2;

        pet_skip_info_seq(isl_ctx *ctx, struct pet_scop *scop1,
                            struct pet_scop *scop2);
        void extract(PetScan *scan, enum pet_skip type);
        void extract(PetScan *scan);
        struct pet_scop *add(struct pet_scop *scop, enum pet_skip type,
                                int offset);
        struct pet_scop *add(struct pet_scop *scop, int offset);
};

/* Initialize a pet_skip_info_seq structure based on
 * on the two statements that are going to be combined.
 */
pet_skip_info_seq::pet_skip_info_seq(isl_ctx *ctx, struct pet_scop *scop1,
        struct pet_scop *scop2) : pet_skip_info(ctx), scop1(scop1), scop2(scop2)
{
        skip[pet_skip_now] = need_skip_seq(scop1, scop2, pet_skip_now);
        equal = skip[pet_skip_now] && skip_equals_skip_later(scop1) &&
                                skip_equals_skip_later(scop2);
        skip[pet_skip_later] = skip[pet_skip_now] && !equal &&
                        need_skip_seq(scop1, scop2, pet_skip_later);
}

/* If we need to construct a skip condition of the given type,
 * then do so now.
 */
void pet_skip_info_seq::extract(PetScan *scan, enum pet_skip type)
{
        if (!skip[type])
                return;

        access[type] = create_test_access(ctx, scan->n_test++);
        scop[type] = extract_skip_seq(scan, isl_map_copy(access[type]),
                                    scop1, scop2, type);
}

/* Construct the required skip conditions.
 */
void pet_skip_info_seq::extract(PetScan *scan)
{
        extract(scan, pet_skip_now);
        extract(scan, pet_skip_later);
        if (equal)
                drop_skip_later(scop1, scop2);
}

/* Add the computed skip condition of the given type to "main" and
 * add the scop for computing the condition at the given offset (the statement
 * number).  Within this offset, the condition is computed at position 1
 * to ensure that it is computed after the corresponding statement.
 *
 * If equal is set, then we only computed a skip condition for pet_skip_now,
 * but we also need to set it as main's pet_skip_later.
 */
struct pet_scop *pet_skip_info_seq::add(struct pet_scop *main,
        enum pet_skip type, int offset)
{
        isl_set *skip_set;

        if (!skip[type])
                return main;

        skip_set = isl_map_range(access[type]);
        access[type] = NULL;
        scop[type] = pet_scop_prefix(scop[type], 1);
        scop[type] = pet_scop_prefix(scop[type], offset);
        main = pet_scop_add_par(ctx, main, scop[type]);
        scop[type] = NULL;

        if (equal)
                main = pet_scop_set_skip(main, pet_skip_later,
                                            isl_set_copy(skip_set));

        main = pet_scop_set_skip(main, type, skip_set);

        return main;
}

/* Add the computed skip conditions to "main" and 
 * add the scops for computing the conditions at the given offset.
 */
struct pet_scop *pet_skip_info_seq::add(struct pet_scop *scop, int offset)
{
        scop = add(scop, pet_skip_now, offset);
        scop = add(scop, pet_skip_later, offset);

        return scop;
}

/* Extract a clone of the kill statement in "scop".
 * "scop" is expected to have been created from a DeclStmt
 * and should have the kill as its first statement.
 */
struct pet_stmt *PetScan::extract_kill(struct pet_scop *scop)
{
        struct pet_expr *kill;
        struct pet_stmt *stmt;
        isl_map *access;

        if (!scop)
                return NULL;
        if (scop->n_stmt < 1)
                isl_die(ctx, isl_error_internal,
                        "expecting at least one statement", return NULL);
        stmt = scop->stmts[0];
        if (stmt->body->type != pet_expr_unary ||
            stmt->body->op != pet_op_kill)
                isl_die(ctx, isl_error_internal,
                        "expecting kill statement", return NULL);

        access = isl_map_copy(stmt->body->args[0]->acc.access);
        access = isl_map_reset_tuple_id(access, isl_dim_in);
        kill = pet_expr_kill_from_access(access);
        return pet_stmt_from_pet_expr(ctx, stmt->line, NULL, n_stmt++, kill);
}

/* Mark all arrays in "scop" as being exposed.
 */
static struct pet_scop *mark_exposed(struct pet_scop *scop)
{
        if (!scop)
                return NULL;
        for (int i = 0; i < scop->n_array; ++i)
                scop->arrays[i]->exposed = 1;
        return scop;
}

/* Try and construct a pet_scop corresponding to (part of)
 * a sequence of statements.
 *
 * "block" is set if the sequence respresents the children of
 * a compound statement.
 * "skip_declarations" is set if we should skip initial declarations
 * in the sequence of statements.
 *
 * If there are any breaks or continues in the individual statements,
 * then we may have to compute a new skip condition.
 * This is handled using a pet_skip_info_seq object.
 * On initialization, the object checks if skip conditions need
 * to be computed.  If so, it does so in "extract" and adds them in "add".
 *
 * If "block" is set, then we need to insert kill statements at
 * the end of the block for any array that has been declared by
 * one of the statements in the sequence.  Each of these declarations
 * results in the construction of a kill statement at the place
 * of the declaration, so we simply collect duplicates of
 * those kill statements and append these duplicates to the constructed scop.
 *
 * If "block" is not set, then any array declared by one of the statements
 * in the sequence is marked as being exposed.
 */
struct pet_scop *PetScan::extract(StmtRange stmt_range, bool block,
        bool skip_declarations)
{
        pet_scop *scop;
        StmtIterator i;
        int j;
        bool partial_range = false;
        set<struct pet_stmt *> kills;
        set<struct pet_stmt *>::iterator it;

        scop = pet_scop_empty(ctx);
        for (i = stmt_range.first, j = 0; i != stmt_range.second; ++i, ++j) {
                Stmt *child = *i;
                struct pet_scop *scop_i;

                if (skip_declarations &&
                    child->getStmtClass() == Stmt::DeclStmtClass)
                        continue;

                scop_i = extract(child);
                if (scop && partial) {
                        pet_scop_free(scop_i);
                        break;
                }
                pet_skip_info_seq skip(ctx, scop, scop_i);
                skip.extract(this);
                if (skip)
                        scop_i = pet_scop_prefix(scop_i, 0);
                if (scop_i && child->getStmtClass() == Stmt::DeclStmtClass) {
                        if (block)
                                kills.insert(extract_kill(scop_i));
                        else
                                scop_i = mark_exposed(scop_i);
                }
                scop_i = pet_scop_prefix(scop_i, j);
                if (options->autodetect) {
                        if (scop_i)
                                scop = pet_scop_add_seq(ctx, scop, scop_i);
                        else
                                partial_range = true;
                        if (scop->n_stmt != 0 && !scop_i)
                                partial = true;
                } else {
                        scop = pet_scop_add_seq(ctx, scop, scop_i);
                }

                scop = skip.add(scop, j);

                if (partial)
                        break;
        }

        for (it = kills.begin(); it != kills.end(); ++it) {
                pet_scop *scop_j;
                scop_j = pet_scop_from_pet_stmt(ctx, *it);
                scop_j = pet_scop_prefix(scop_j, j);
                scop = pet_scop_add_seq(ctx, scop, scop_j);
        }

        if (scop && partial_range) {
                if (scop->n_stmt == 0) {
                        pet_scop_free(scop);
                        return NULL;
                }
                partial = true;
        }

        return scop;
}

/* Check if the scop marked by the user is exactly this Stmt
 * or part of this Stmt.
 * If so, return a pet_scop corresponding to the marked region.
 * Otherwise, return NULL.
 */
struct pet_scop *PetScan::scan(Stmt *stmt)
{
        SourceManager &SM = PP.getSourceManager();
        unsigned start_off, end_off;

        start_off = getExpansionOffset(SM, stmt->getLocStart());
        end_off = getExpansionOffset(SM, stmt->getLocEnd());

        if (start_off > loc.end)
                return NULL;
        if (end_off < loc.start)
                return NULL;
        if (start_off >= loc.start && end_off <= loc.end) {
                return extract(stmt);
        }

        StmtIterator start;
        for (start = stmt->child_begin(); start != stmt->child_end(); ++start) {
                Stmt *child = *start;
                if (!child)
                        continue;
                start_off = getExpansionOffset(SM, child->getLocStart());
                end_off = getExpansionOffset(SM, child->getLocEnd());
                if (start_off < loc.start && end_off >= loc.end)
                        return scan(child);
                if (start_off >= loc.start)
                        break;
        }

        StmtIterator end;
        for (end = start; end != stmt->child_end(); ++end) {
                Stmt *child = *end;
                start_off = SM.getFileOffset(child->getLocStart());
                if (start_off >= loc.end)
                        break;
        }

        return extract(StmtRange(start, end), false, false);
}

/* Set the size of index "pos" of "array" to "size".
 * In particular, add a constraint of the form
 *
 *      i_pos < size
 *
 * to array->extent and a constraint of the form
 *
 *      size >= 0
 *
 * to array->context.
 */
static struct pet_array *update_size(struct pet_array *array, int pos,
        __isl_take isl_pw_aff *size)
{
        isl_set *valid;
        isl_set *univ;
        isl_set *bound;
        isl_space *dim;
        isl_aff *aff;
        isl_pw_aff *index;
        isl_id *id;

        valid = isl_pw_aff_nonneg_set(isl_pw_aff_copy(size));
        array->context = isl_set_intersect(array->context, valid);

        dim = isl_set_get_space(array->extent);
        aff = isl_aff_zero_on_domain(isl_local_space_from_space(dim));
        aff = isl_aff_add_coefficient_si(aff, isl_dim_in, pos, 1);
        univ = isl_set_universe(isl_aff_get_domain_space(aff));
        index = isl_pw_aff_alloc(univ, aff);

        size = isl_pw_aff_add_dims(size, isl_dim_in,
                                isl_set_dim(array->extent, isl_dim_set));
        id = isl_set_get_tuple_id(array->extent);
        size = isl_pw_aff_set_tuple_id(size, isl_dim_in, id);
        bound = isl_pw_aff_lt_set(index, size);

        array->extent = isl_set_intersect(array->extent, bound);

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

        return array;
error:
        pet_array_free(array);
        return NULL;
}

/* Figure out the size of the array at position "pos" and all
 * subsequent positions from "type" and update "array" accordingly.
 */
struct pet_array *PetScan::set_upper_bounds(struct pet_array *array,
        const Type *type, int pos)
{
        const ArrayType *atype;
        isl_pw_aff *size;

        if (!array)
                return NULL;

        if (type->isPointerType()) {
                type = type->getPointeeType().getTypePtr();
                return set_upper_bounds(array, type, pos + 1);
        }
        if (!type->isArrayType())
                return array;

        type = type->getCanonicalTypeInternal().getTypePtr();
        atype = cast<ArrayType>(type);

        if (type->isConstantArrayType()) {
                const ConstantArrayType *ca = cast<ConstantArrayType>(atype);
                size = extract_affine(ca->getSize());
                array = update_size(array, pos, size);
        } else if (type->isVariableArrayType()) {
                const VariableArrayType *vla = cast<VariableArrayType>(atype);
                size = extract_affine(vla->getSizeExpr());
                array = update_size(array, pos, size);
        }

        type = atype->getElementType().getTypePtr();

        return set_upper_bounds(array, type, pos + 1);
}

/* Is "T" the type of a variable length array with static size?
 */
static bool is_vla_with_static_size(QualType T)
{
        const VariableArrayType *vlatype;

        if (!T->isVariableArrayType())
                return false;
        vlatype = cast<VariableArrayType>(T);
        return vlatype->getSizeModifier() == VariableArrayType::Static;
}

/* Return the type of "decl" as an array.
 *
 * In particular, if "decl" is a parameter declaration that
 * is a variable length array with a static size, then
 * return the original type (i.e., the variable length array).
 * Otherwise, return the type of decl.
 */
static QualType get_array_type(ValueDecl *decl)
{
        ParmVarDecl *parm;
        QualType T;

        parm = dyn_cast<ParmVarDecl>(decl);
        if (!parm)
                return decl->getType();

        T = parm->getOriginalType();
        if (!is_vla_with_static_size(T))
                return decl->getType();
        return T;
}

/* Construct and return a pet_array corresponding to the variable "decl".
 * In particular, initialize array->extent to
 *
 *      { name[i_1,...,i_d] : i_1,...,i_d >= 0 }
 *
 * and then call set_upper_bounds to set the upper bounds on the indices
 * based on the type of the variable.
 */
struct pet_array *PetScan::extract_array(isl_ctx *ctx, ValueDecl *decl)
{
        struct pet_array *array;
        QualType qt = get_array_type(decl);
        const Type *type = qt.getTypePtr();
        int depth = array_depth(type);
        QualType base = base_type(qt);
        string name;
        isl_id *id;
        isl_space *dim;

        array = isl_calloc_type(ctx, struct pet_array);
        if (!array)
                return NULL;

        id = isl_id_alloc(ctx, decl->getName().str().c_str(), decl);
        dim = isl_space_set_alloc(ctx, 0, depth);
        dim = isl_space_set_tuple_id(dim, isl_dim_set, id);

        array->extent = isl_set_nat_universe(dim);

        dim = isl_space_params_alloc(ctx, 0);
        array->context = isl_set_universe(dim);

        array = set_upper_bounds(array, type, 0);
        if (!array)
                return NULL;

        name = base.getAsString();
        array->element_type = strdup(name.c_str());
        array->element_size = decl->getASTContext().getTypeInfo(base).first / 8;

        return array;
}

/* Construct a list of pet_arrays, one for each array (or scalar)
 * accessed inside "scop", add this list to "scop" and return the result.
 *
 * The context of "scop" is updated with the intersection of
 * the contexts of all arrays, i.e., constraints on the parameters
 * that ensure that the arrays have a valid (non-negative) size.
 */
struct pet_scop *PetScan::scan_arrays(struct pet_scop *scop)
{
        int i;
        set<ValueDecl *> arrays;
        set<ValueDecl *>::iterator it;
        int n_array;
        struct pet_array **scop_arrays;

        if (!scop)
                return NULL;

        pet_scop_collect_arrays(scop, arrays);
        if (arrays.size() == 0)
                return scop;

        n_array = scop->n_array;

        scop_arrays = isl_realloc_array(ctx, scop->arrays, struct pet_array *,
                                        n_array + arrays.size());
        if (!scop_arrays)
                goto error;
        scop->arrays = scop_arrays;

        for (it = arrays.begin(), i = 0; it != arrays.end(); ++it, ++i) {
                struct pet_array *array;
                scop->arrays[n_array + i] = array = extract_array(ctx, *it);
                if (!scop->arrays[n_array + i])
                        goto error;
                scop->n_array++;
                scop->context = isl_set_intersect(scop->context,
                                                isl_set_copy(array->context));
                if (!scop->context)
                        goto error;
        }

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

/* Bound all parameters in scop->context to the possible values
 * of the corresponding C variable.
 */
static struct pet_scop *add_parameter_bounds(struct pet_scop *scop)
{
        int n;

        if (!scop)
                return NULL;

        n = isl_set_dim(scop->context, isl_dim_param);
        for (int i = 0; i < n; ++i) {
                isl_id *id;
                ValueDecl *decl;

                id = isl_set_get_dim_id(scop->context, isl_dim_param, i);
                if (is_nested_parameter(id)) {
                        isl_id_free(id);
                        isl_die(isl_set_get_ctx(scop->context),
                                isl_error_internal,
                                "unresolved nested parameter", goto error);
                }
                decl = (ValueDecl *) isl_id_get_user(id);
                isl_id_free(id);

                scop->context = set_parameter_bounds(scop->context, i, decl);

                if (!scop->context)
                        goto error;
        }

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

/* Construct a pet_scop from the given function.
 *
 * If the scop was delimited by scop and endscop pragmas, then we override
 * the file offsets by those derived from the pragmas.
 */
struct pet_scop *PetScan::scan(FunctionDecl *fd)
{
        pet_scop *scop;
        Stmt *stmt;

        stmt = fd->getBody();

        if (options->autodetect)
                scop = extract(stmt, true);
        else {
                scop = scan(stmt);
                scop = pet_scop_update_start_end(scop, loc.start, loc.end);
        }
        scop = pet_scop_detect_parameter_accesses(scop);
        scop = scan_arrays(scop);
        scop = add_parameter_bounds(scop);
        scop = pet_scop_gist(scop, value_bounds);

        return scop;
}