/// <summary>
/// The abstract transition relation.
/// 'cmd' is allowed to be a StateCmd.
/// </summary>
static NativeLattice.Element Step(NativeLattice lattice, Cmd cmd, NativeLattice.Element elmt)
{
Contract.Requires(lattice != null);
Contract.Requires(cmd != null);
Contract.Requires(elmt != null);
Contract.Ensures(Contract.Result <NativeLattice.Element>() != null);
if (cmd is AssignCmd)
{
// parallel assignment
var c = (AssignCmd)cmd;
elmt = lattice.Update(elmt, c.AsSimpleAssignCmd);
}
else if (cmd is HavocCmd)
{
var c = (HavocCmd)cmd;
foreach (IdentifierExpr id in c.Vars)
{
Contract.Assert(id != null);
elmt = lattice.Eliminate(elmt, id.Decl);
}
}
else if (cmd is PredicateCmd)
{
var c = (PredicateCmd)cmd;
var conjuncts = new List <Expr>();
foreach (var ee in Conjuncts(c.Expr))
{
Contract.Assert(ee != null);
elmt = lattice.Constrain(elmt, ee);
}
}
else if (cmd is StateCmd)
{
var c = (StateCmd)cmd;
// Iterate the abstract transition on all the commands in the desugaring of the call
foreach (Cmd callDesug in c.Cmds)
{
Contract.Assert(callDesug != null);
elmt = Step(lattice, callDesug, elmt);
}
// Project out the local variables of the StateCmd
foreach (Variable local in c.Locals)
{
Contract.Assert(local != null);
elmt = lattice.Eliminate(elmt, local);
}
}
else if (cmd is SugaredCmd)
{
var c = (SugaredCmd)cmd;
elmt = Step(lattice, c.Desugaring, elmt);
}
else if (cmd is CommentCmd)
{
// skip
}
else
{
Contract.Assert(false); // unknown command
}
return(elmt);
}
public static void Analyze(Implementation impl, NativeLattice lattice, NativeLattice.Element start)
{
// We need to keep track of some information for each(some) block(s). To do that efficiently,
// we number the implementation's blocks sequentially, and then we can use arrays to store
// the additional information.
var pre = new NativeLattice.Element[impl.Blocks.Count]; // set to null if we never compute a join/widen at this block
var post = CommandLineOptions.Clo.InstrumentInfer == CommandLineOptions.InstrumentationPlaces.Everywhere ? new NativeLattice.Element[impl.Blocks.Count] : null;
var iterations = new int[impl.Blocks.Count];
var bottom = lattice.Bottom;
int n = 0;
foreach (var block in impl.Blocks) {
block.aiId = n;
// Note: The forward analysis below will store lattice elements in pre[n] if pre[n] is non-null.
// Thus, the assignment "pre[n] = bottom;" below must be done under the following condition:
// n == 0 || block.widenBlock
// One possible strategy would be to do it only under that condition. Alternatively,
// one could do the assignment under the following condition:
// n == 0 || block.widenBlock || block.Predecessors.Length != 1
// (which would require first setting the Predecessors field). In any case, if
// CommandLineOptions.Clo.InstrumentInfer == CommandLineOptions.InstrumentationPlaces.Everywhere
// then all pre[n] should be set.
pre[n] = bottom;
n++;
}
Contract.Assert(n == impl.Blocks.Count);
var workItems = new Queue<Tuple<Block, NativeLattice.Element>>();
workItems.Enqueue(new Tuple<Block, NativeLattice.Element>(impl.Blocks[0], start));
//ComputeBlockInvariantsNative(impl, );
// compute a fixpoint here
while (workItems.Count > 0) {
var workItem = workItems.Dequeue();
var b = workItem.Item1;
var id = b.aiId;
var e = workItem.Item2;
if (pre[id] == null) {
// no pre information stored here, so just go ahead through the block
} else if (lattice.Below(e, pre[id])) {
// no change
continue;
} else if (b.widenBlock && CommandLineOptions.Clo.StepsBeforeWidening <= iterations[id]) {
e = lattice.Widen(pre[id], e);
pre[id] = e;
iterations[id]++;
} else {
e = lattice.Join(pre[id], e);
pre[id] = e;
iterations[id]++;
}
// propagate'e' through b.Cmds
foreach (Cmd cmd in b.Cmds) {
e = Step(lattice, cmd, e);
}
if (post != null && pre[id] != null) {
post[id] = e;
}
var g = b.TransferCmd as GotoCmd;
if (g != null) { // if g==null, it's a pity we didn't pay attention to that earlier, because then we could have skipped analyzing the code in this block
foreach (Block succ in g.labelTargets) {
workItems.Enqueue(new Tuple<Block, NativeLattice.Element>(succ, e));
}
}
}
Instrument(impl, pre, post);
}
public static void Analyze(Implementation impl, NativeLattice lattice, NativeLattice.Element start)
{
// We need to keep track of some information for each(some) block(s). To do that efficiently,
// we number the implementation's blocks sequentially, and then we can use arrays to store
// the additional information.
var pre = new NativeLattice.Element[impl.Blocks
.Count]; // set to null if we never compute a join/widen at this block
var post = CommandLineOptions.Clo.InstrumentInfer == CommandLineOptions.InstrumentationPlaces.Everywhere
? new NativeLattice.Element[impl.Blocks.Count]
: null;
var iterations = new int[impl.Blocks.Count];
var bottom = lattice.Bottom;
int n = 0;
foreach (var block in impl.Blocks)
{
block.aiId = n;
// Note: The forward analysis below will store lattice elements in pre[n] if pre[n] is non-null.
// Thus, the assignment "pre[n] = bottom;" below must be done under the following condition:
// n == 0 || block.widenBlock
// One possible strategy would be to do it only under that condition. Alternatively,
// one could do the assignment under the following condition:
// n == 0 || block.widenBlock || block.Predecessors.Length != 1
// (which would require first setting the Predecessors field). In any case, if
// CommandLineOptions.Clo.InstrumentInfer == CommandLineOptions.InstrumentationPlaces.Everywhere
// then all pre[n] should be set.
pre[n] = bottom;
n++;
}
Contract.Assert(n == impl.Blocks.Count);
var workItems = new Queue <Tuple <Block, NativeLattice.Element> >();
workItems.Enqueue(new Tuple <Block, NativeLattice.Element>(impl.Blocks[0], start));
//ComputeBlockInvariantsNative(impl, );
// compute a fixpoint here
while (workItems.Count > 0)
{
var workItem = workItems.Dequeue();
var b = workItem.Item1;
var id = b.aiId;
var e = workItem.Item2;
if (pre[id] == null)
{
// no pre information stored here, so just go ahead through the block
}
else if (lattice.Below(e, pre[id]))
{
// no change
continue;
}
else if (b.widenBlock && CommandLineOptions.Clo.Ai.StepsBeforeWidening <= iterations[id])
{
e = lattice.Widen(pre[id], e);
pre[id] = e;
iterations[id]++;
}
else
{
e = lattice.Join(pre[id], e);
pre[id] = e;
iterations[id]++;
}
// propagate'e' through b.Cmds
foreach (Cmd cmd in b.Cmds)
{
e = Step(lattice, cmd, e);
}
if (post != null && pre[id] != null)
{
post[id] = e;
}
var g = b.TransferCmd as GotoCmd;
if (g != null)
{
// if g==null, it's a pity we didn't pay attention to that earlier, because then we could have skipped analyzing the code in this block
foreach (Block succ in g.labelTargets)
{
workItems.Enqueue(new Tuple <Block, NativeLattice.Element>(succ, e));
}
}
}
Instrument(impl, pre, post);
}
