Hi Richard, I think I misunderstood yesterday's answer and deviated a
little bit. But now I want to focus on this:
> > * the process in GCC that generates the constraints for NULL works
> > fine (i.e., feeding the constraints generated by GCC to an external
> > solver should yield a conservatively correct answer) but the process
> > that solves the constraints relaxes the solutions for the NULL
> > constraint variable (i.e., GCC has deviated from the constraint
> > solving algorithm somehow)
>
> No, that part should work OK.
>
So, let's ignore the other solver for now and instead focus on the
concrete example I presented on the previous email. If GCC is solving
these constraints:
```
ANYTHING = &ANYTHING
ESCAPED = *ESCAPED
ESCAPED = ESCAPED + UNKNOWN
*ESCAPED = NONLOCAL
NONLOCAL = &NONLOCAL
NONLOCAL = &ESCAPED
INTEGER = &ANYTHING
ISRA.4 = &NONLOCAL
derefaddrtmp(9) = &NULL
*ISRA.4 = derefaddrtmp(9)
i = NONLOCAL
i = &NONLOCAL
ESCAPED = &NONLOCAL
_2 = *ISRA.4
```
What would a hand calculated solution gives us vs what was the
solution given by GCC?
I am following the algorithm stated on Section 3.3 of Structure
Aliasing in GCC, and I will be ignoring the ESCAPED = ESCAPED +
UNKNOWN constraint since there isn't any other field offset that needs
to be calculated.
First, I want to make some adjustments. I am going to be using "=" to
signify the \supseteq symbol and I will be adding curly braces to
specify the element in a set as opposed to the whole set. Therefore
the constraints will now become (ordered slightly differently):
```
====direct contraints========
ANYTHING = { ANYTHING }
ESCAPED = { NONLOCAL }
NONLOCAL = { NONLOCAL }
NONLOCAL = { ESCAPED }
INTEGER = { ANYTHING }
ISRA.4 = { NONLOCAL }
derefaddrtmp(9) = { NULL }
i = { NONLOCAL }
====complex constraints======
ESCAPED = *ESCAPED
*ESCAPED = NONLOCAL
*ISRA.4 = derefaddrtmp(9)
_2 = *ISRA.4
===== copy-constraints======
ESCAPED = ESCAPED // again ignoring the + UNKNOWN since I don't think
it will matter...
i = NONLOCAL
```
Solution sets are basically the direct constraints at the moment.
Let's now create the graph
1. node ESCAPED has an edge going to itself (due to the copy constraint)
2. node ISRA.4 has no outgoing copy edges
3. node derefaddrtmp(9) has no outgoing edges
4. node _2 has no outgoing edges
5. node i has an outgoing edge to NONLOCAL (due to the copy constraint)
6. node NONLOCAL has no outgoing edge
Now, we can iterate over this set of nodes
1. Walking over node ESCAPED. Sol(ESCAPED) = {NONLOCAL}. There are no
edges, but it has complex-constraints. Let's modify the graph.
1. Looking at ESCAPED = *ESCAPED we note that we need to add a copy
edge from ESCAPED to NONLOCAL.
2. Looking at *ESCAPED = NONLOCAL we note that we need to add a copy
edge from NONLOCAL to NONLOCAL
The graph is now transformed to
1. node ESCAPED has an edge going to ESCAPED and NONLOCAL
2. node ISRA.4 has no outgoing copy edges
3. node derefaddrtmp(9) has no outgoing edges
4. node _2 has no outgoing edges
5. node i has an outgoing edge to NONLOCAL (due to the copy constraint)
6. node NONLOCAL has an edge going to NONLOCAL
The solution set of escaped is now Sol(ESCAPED) = Sol(ESCAPED) U
Sol(NONLOCAL) = {NONLOCAL, ESCAPED}
Now we continue walking
2. Walking over node ISRA.4. It has the solution set { NONLOCAL }.
There are no edges, but it has complex-constraints. Let's modify the
graph.
1. Looking at *ISRA.4 = derefaddrtmp(9), we note that we need to add
a copy edge from NONLOCAL to derefaddrtmp(9).
The graph is now transformed to
1. node ESCAPED has an edge going to ESCAPED and NONLOCAL
2. node ISRA.4 has no outgoing copy edges
3. node derefaddrtmp(9) has no outgoing edges
4. node _2 has no outgoing edges
5. node i has an outgoing edge to NONLOCAL (due to the copy constraint)
6. node NONLOCAL has an edge going to NONLOCAL, derefaddrtmp(9)
The Sol(NONLOCAL) = Sol(NONLOCAL) U Sol(derefaddrtmp(9)) = {NONLOCAL,
ESCAPED, NULL}.
Now I could continue, but here is already something that is not shown
in the points-to sets in the dump. It shows that
NONLOCAL = {NONLOCAL, ESCAPED, NULL}
Looking at the data that I showed yesterday:
```
NONLOCAL = { ESCAPED NONLOCAL } same as i
```
we see that NULL is not in the solution set of NONLOCAL.
Now, yesterday you said that NULL is not conservatively correctly
represented in the constraints. You also said today the points-to
analysis should be solving the constraints fine. What I now understand
from this is that while NULL may be pointed to by some constraints, it
doesn't mean that not being on the set means that a pointer will not
point to NULL. However, it should still be shown in the dumps where
the points-to sets are shown for the constraint variables since it is
solved using the same analysis? Is this correct? Am I doing the points
to analysis by hand wrong somehow? Why would NULL not be in
Sol(NONLOCAL) if it is solving the same constraints that I am solving
by hand?
