[analyzer][solver] Iterate to a fixpoint during symbol simplification with constants
D103314 introduced symbol simplification when a new constant constraint is
added. Currently, we simplify existing equivalence classes by iterating over
all existing members of them and trying to simplify each member symbol with
simplifySVal.
At the end of such a simplification round we may end up introducing a
new constant constraint. Example:
```
if (a + b + c != d)
return;
if (c + b != 0)
return;
// Simplification starts here.
if (b != 0)
return;
```
The `c == 0` constraint is the result of the first simplification iteration.
However, we could do another round of simplification to reach the conclusion
that `a == d`. Generally, we could do as many new iterations until we reach a
fixpoint.
We can reach to a fixpoint by recursively calling `State->assume` on the
newly simplified symbol. By calling `State->assume` we re-ignite the
whole assume machinery (along e.g with adjustment handling).
Why should we do this? By reaching a fixpoint in simplification we are capable
of discovering infeasible states at the moment of the introduction of the
**first** constant constraint.
Let's modify the previous example just a bit, and consider what happens without
the fixpoint iteration.
```
if (a + b + c != d)
return;
if (c + b != 0)
return;
// Adding a new constraint.
if (a == d)
return;
// This brings in a contradiction.
if (b != 0)
return;
clang_analyzer_warnIfReached(); // This produces a warning.
// The path is already infeasible...
if (c == 0) // ...but we realize that only when we evaluate `c == 0`.
return;
```
What happens currently, without the fixpoint iteration? As the inline comments
suggest, without the fixpoint iteration we are doomed to realize that we are on
an infeasible path only after we are already walking on that. With fixpoint
iteration we can detect that before stepping on that. With fixpoint iteration,
the `clang_analyzer_warnIfReached` does not warn in the above example b/c
during the evaluation of `b == 0` we realize the contradiction. The engine and
the checkers do rely on that either `assume(Cond)` or `assume(!Cond)` should be
feasible. This is in fact assured by the so called expensive checks
(LLVM_ENABLE_EXPENSIVE_CHECKS). The StdLibraryFuncionsChecker is notably one of
the checkers that has a very similar assertion.
Before this patch, we simply added the simplified symbol to the equivalence
class. In this patch, after we have added the simplified symbol, we remove the
old (more complex) symbol from the members of the equivalence class
(`ClassMembers`). Removing the old symbol is beneficial because during the next
iteration of the simplification we don't have to consider again the old symbol.
Contrary to how we handle `ClassMembers`, we don't remove the old Sym->Class
relation from the `ClassMap`. This is important for two reasons: The
constraints of the old symbol can still be found via it's equivalence class
that it used to be the member of (1). We can spare one removal and thus one
additional tree in the forest of `ClassMap` (2).
Performance and complexity: Let us assume that in a State we have N non-trivial
equivalence classes and that all constraints and disequality info is related to
non-trivial classes. In the worst case, we can simplify only one symbol of one
class in each iteration. The number of symbols in one class cannot grow b/c we
replace the old symbol with the simplified one. Also, the number of the
equivalence classes can decrease only, b/c the algorithm does a merge operation
optionally. We need N iterations in this case to reach the fixpoint. Thus, the
steps needed to be done in the worst case is proportional to `N*N`. Empirical
results (attached) show that there is some hardly noticeable run-time and peak
memory discrepancy compared to the baseline. In my opinion, these differences
could be the result of measurement error.
This worst case scenario can be extended to that cases when we have trivial
classes in the constraints and in the disequality map are transforming to such
a State where there are only non-trivial classes, b/c the algorithm does merge
operations. A merge operation on two trivial classes results in one non-trivial
class.
Differential Revision: https://reviews.llvm.org/D106823
2021-07-27 04:55:44 +08:00
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// RUN: %clang_analyze_cc1 %s \
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// RUN: -analyzer-checker=core \
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// RUN: -analyzer-checker=debug.ExprInspection \
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// RUN: 2>&1 | FileCheck %s
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// In this test we check whether the solver's symbol simplification mechanism
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// is capable of reaching a fixpoint. This should be done after TWO iterations.
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void clang_analyzer_printState();
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void test(int a, int b, int c, int d) {
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if (a + b + c != d)
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return;
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if (c + b != 0)
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return;
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clang_analyzer_printState();
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// CHECK: "constraints": [
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// CHECK-NEXT: { "symbol": "(((reg_$0<int a>) + (reg_$1<int b>)) + (reg_$2<int c>)) != (reg_$3<int d>)", "range": "{ [0, 0] }" },
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// CHECK-NEXT: { "symbol": "(reg_$2<int c>) + (reg_$1<int b>)", "range": "{ [0, 0] }" }
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// CHECK-NEXT: ],
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// CHECK-NEXT: "equivalence_classes": [
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// CHECK-NEXT: [ "((reg_$0<int a>) + (reg_$1<int b>)) + (reg_$2<int c>)", "reg_$3<int d>" ]
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// CHECK-NEXT: ],
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// CHECK-NEXT: "disequality_info": null,
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// Simplification starts here.
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if (b != 0)
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return;
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clang_analyzer_printState();
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[Analyzer][solver] Simplification: Do a fixpoint iteration before the eq class merge
This reverts commit f02c5f3478318075d1a469203900e452ba651421 and
addresses the issue mentioned in D114619 differently.
Repeating the issue here:
Currently, during symbol simplification we remove the original member
symbol from the equivalence class (`ClassMembers` trait). However, we
keep the reverse link (`ClassMap` trait), in order to be able the query
the related constraints even for the old member. This asymmetry can lead
to a problem when we merge equivalence classes:
```
ClassA: [a, b] // ClassMembers trait,
a->a, b->a // ClassMap trait, a is the representative symbol
```
Now let,s delete `a`:
```
ClassA: [b]
a->a, b->a
```
Let's merge ClassA into the trivial class `c`:
```
ClassA: [c, b]
c->c, b->c, a->a
```
Now, after the merge operation, `c` and `a` are actually in different
equivalence classes, which is inconsistent.
This issue manifests in a test case (added in D103317):
```
void recurring_symbol(int b) {
if (b * b != b)
if ((b * b) * b * b != (b * b) * b)
if (b * b == 1)
}
```
Before the simplification we have these equivalence classes:
```
trivial EQ1: [b * b != b]
trivial EQ2: [(b * b) * b * b != (b * b) * b]
```
During the simplification with `b * b == 1`, EQ1 is merged with `1 != b`
`EQ1: [b * b != b, 1 != b]` and we remove the complex symbol, so
`EQ1: [1 != b]`
Then we start to simplify the only symbol in EQ2:
`(b * b) * b * b != (b * b) * b --> 1 * b * b != 1 * b --> b * b != b`
But `b * b != b` is such a symbol that had been removed previously from
EQ1, thus we reach the above mentioned inconsistency.
This patch addresses the issue by making it impossible to synthesise a
symbol that had been simplified before. We achieve this by simplifying
the given symbol to the absolute simplest form.
Differential Revision: https://reviews.llvm.org/D114887
2021-12-01 23:47:22 +08:00
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// CHECK: "constraints": [
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// CHECK-NEXT: { "symbol": "(reg_$0<int a>) != (reg_$3<int d>)", "range": "{ [0, 0] }" },
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// CHECK-NEXT: { "symbol": "reg_$1<int b>", "range": "{ [0, 0] }" },
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// CHECK-NEXT: { "symbol": "reg_$2<int c>", "range": "{ [0, 0] }" }
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// CHECK-NEXT: ],
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// CHECK-NEXT: "equivalence_classes": [
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// CHECK-NEXT: [ "(reg_$0<int a>) != (reg_$3<int d>)" ],
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// CHECK-NEXT: [ "reg_$0<int a>", "reg_$3<int d>" ],
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// CHECK-NEXT: [ "reg_$2<int c>" ]
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// CHECK-NEXT: ],
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// CHECK-NEXT: "disequality_info": null,
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[analyzer][solver] Iterate to a fixpoint during symbol simplification with constants
D103314 introduced symbol simplification when a new constant constraint is
added. Currently, we simplify existing equivalence classes by iterating over
all existing members of them and trying to simplify each member symbol with
simplifySVal.
At the end of such a simplification round we may end up introducing a
new constant constraint. Example:
```
if (a + b + c != d)
return;
if (c + b != 0)
return;
// Simplification starts here.
if (b != 0)
return;
```
The `c == 0` constraint is the result of the first simplification iteration.
However, we could do another round of simplification to reach the conclusion
that `a == d`. Generally, we could do as many new iterations until we reach a
fixpoint.
We can reach to a fixpoint by recursively calling `State->assume` on the
newly simplified symbol. By calling `State->assume` we re-ignite the
whole assume machinery (along e.g with adjustment handling).
Why should we do this? By reaching a fixpoint in simplification we are capable
of discovering infeasible states at the moment of the introduction of the
**first** constant constraint.
Let's modify the previous example just a bit, and consider what happens without
the fixpoint iteration.
```
if (a + b + c != d)
return;
if (c + b != 0)
return;
// Adding a new constraint.
if (a == d)
return;
// This brings in a contradiction.
if (b != 0)
return;
clang_analyzer_warnIfReached(); // This produces a warning.
// The path is already infeasible...
if (c == 0) // ...but we realize that only when we evaluate `c == 0`.
return;
```
What happens currently, without the fixpoint iteration? As the inline comments
suggest, without the fixpoint iteration we are doomed to realize that we are on
an infeasible path only after we are already walking on that. With fixpoint
iteration we can detect that before stepping on that. With fixpoint iteration,
the `clang_analyzer_warnIfReached` does not warn in the above example b/c
during the evaluation of `b == 0` we realize the contradiction. The engine and
the checkers do rely on that either `assume(Cond)` or `assume(!Cond)` should be
feasible. This is in fact assured by the so called expensive checks
(LLVM_ENABLE_EXPENSIVE_CHECKS). The StdLibraryFuncionsChecker is notably one of
the checkers that has a very similar assertion.
Before this patch, we simply added the simplified symbol to the equivalence
class. In this patch, after we have added the simplified symbol, we remove the
old (more complex) symbol from the members of the equivalence class
(`ClassMembers`). Removing the old symbol is beneficial because during the next
iteration of the simplification we don't have to consider again the old symbol.
Contrary to how we handle `ClassMembers`, we don't remove the old Sym->Class
relation from the `ClassMap`. This is important for two reasons: The
constraints of the old symbol can still be found via it's equivalence class
that it used to be the member of (1). We can spare one removal and thus one
additional tree in the forest of `ClassMap` (2).
Performance and complexity: Let us assume that in a State we have N non-trivial
equivalence classes and that all constraints and disequality info is related to
non-trivial classes. In the worst case, we can simplify only one symbol of one
class in each iteration. The number of symbols in one class cannot grow b/c we
replace the old symbol with the simplified one. Also, the number of the
equivalence classes can decrease only, b/c the algorithm does a merge operation
optionally. We need N iterations in this case to reach the fixpoint. Thus, the
steps needed to be done in the worst case is proportional to `N*N`. Empirical
results (attached) show that there is some hardly noticeable run-time and peak
memory discrepancy compared to the baseline. In my opinion, these differences
could be the result of measurement error.
This worst case scenario can be extended to that cases when we have trivial
classes in the constraints and in the disequality map are transforming to such
a State where there are only non-trivial classes, b/c the algorithm does merge
operations. A merge operation on two trivial classes results in one non-trivial
class.
Differential Revision: https://reviews.llvm.org/D106823
2021-07-27 04:55:44 +08:00
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// Keep the symbols and the constraints! alive.
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(void)(a * b * c * d);
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return;
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}
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