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llvm-mirror/lib/Transforms/Scalar/ABCD.cpp
Nick Lewycky 0376e34268 Add ABCD, a generalized implementation of the Elimination of Array Bounds 
Checks on Demand algorithm which looks at arbitrary branches instead of loop
iterations. This is GSoC work by Andre Tavares with only editorial changes
applied!

llvm-svn: 85382
2009-10-28 07:03:15 +00:00

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//===------- ABCD.cpp - Removes redundant conditional branches ------------===//
//
// The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This pass removes redundant branch instructions. This algorithm was
// described by Rastislav Bodik, Rajiv Gupta and Vivek Sarkar in their paper
// "ABCD: Eliminating Array Bounds Checks on Demand (2000)". The original
// Algorithm was created to remove array bound checks for strongly typed
// languages. This implementation expands the idea and removes any conditional
// branches that can be proved redundant, not only those used in array bound
// checks. With the SSI representation, each variable has a
// constraint. By analyzing these constraints we can proof that a branch is
// redundant. When a branch is proved redundant it means that
// one direction will always be taken; thus, we can change this branch into an
// unconditional jump.
// It is advisable to run SimplifyCFG and Aggressive Dead Code Elimination
// after ABCD to clean up the code.
// This implementation was created based on the implementation of the ABCD
// algorithm implemented for the compiler Jitrino.
//
//===----------------------------------------------------------------------===//
#define DEBUG_TYPE "abcd"
#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/ADT/Statistic.h"
#include "llvm/Constants.h"
#include "llvm/Function.h"
#include "llvm/Instructions.h"
#include "llvm/Pass.h"
#include "llvm/Support/raw_ostream.h"
#include "llvm/Support/Debug.h"
#include "llvm/Transforms/Scalar.h"
#include "llvm/Transforms/Utils/SSI.h"
using namespace llvm;
STATISTIC(NumBranchTested, "Number of conditional branches analyzed");
STATISTIC(NumBranchRemoved, "Number of conditional branches removed");
//namespace {
class ABCD : public FunctionPass {
public:
static char ID; // Pass identification, replacement for typeid.
ABCD() : FunctionPass(&ID) {}
void getAnalysisUsage(AnalysisUsage &AU) const {
AU.addRequired<SSI>();
}
bool runOnFunction(Function &F);
private:
bool modified;
enum ProveResult {
False = 0,
Reduced = 1,
True = 2
};
typedef ProveResult (*meet_function)(ProveResult, ProveResult);
static ProveResult max(ProveResult res1, ProveResult res2) {
return (ProveResult) std::max(res1, res2);
}
static ProveResult min(ProveResult res1, ProveResult res2) {
return (ProveResult) std::min(res1, res2);
}
class Bound {
public:
Bound(APInt v, bool upper) : value(v), upper_bound(upper) {}
Bound(const Bound *b, int cnst)
: value(b->value - cnst), upper_bound(b->upper_bound) {}
Bound(const Bound *b, const APInt &cnst)
: value(b->value - cnst), upper_bound(b->upper_bound) {}
/// Test if Bound is an upper bound
bool isUpperBound() const { return upper_bound; }
/// Get the bitwidth of this bound
int32_t getBitWidth() const { return value.getBitWidth(); }
/// Creates a Bound incrementing the one received
static Bound *createIncrement(const Bound *b) {
return new Bound(b->isUpperBound() ? b->value+1 : b->value-1,
b->upper_bound);
}
/// Creates a Bound decrementing the one received
static Bound *createDecrement(const Bound *b) {
return new Bound(b->isUpperBound() ? b->value-1 : b->value+1,
b->upper_bound);
}
/// Test if two bounds are equal
static bool eq(const Bound *a, const Bound *b) {
if (!a || !b) return false;
assert(a->isUpperBound() == b->isUpperBound());
return a->value == b->value;
}
/// Test if val is less than or equal to Bound b
static bool leq(APInt val, const Bound *b) {
if (!b) return false;
return b->isUpperBound() ? val.sle(b->value) : val.sge(b->value);
}
/// Test if Bound a is less then or equal to Bound
static bool leq(const Bound *a, const Bound *b) {
if (!a || !b) return false;
assert(a->isUpperBound() == b->isUpperBound());
return a->isUpperBound() ? a->value.sle(b->value) :
a->value.sge(b->value);
}
/// Test if Bound a is less then Bound b
static bool lt(const Bound *a, const Bound *b) {
if (!a || !b) return false;
assert(a->isUpperBound() == b->isUpperBound());
return a->isUpperBound() ? a->value.slt(b->value) :
a->value.sgt(b->value);
}
/// Test if Bound b is greater then or equal val
static bool geq(const Bound *b, APInt val) {
return leq(val, b);
}
/// Test if Bound a is greater then or equal Bound b
static bool geq(const Bound *a, const Bound *b) {
return leq(b, a);
}
private:
APInt value;
bool upper_bound;
};
/// This class is used to store results some parts of the graph,
/// so information does not need to be recalculated. The maximum false,
/// minimum true and minimum reduced results are stored
class MemoizedResultChart {
public:
MemoizedResultChart() : max_false(NULL), min_true(NULL),
min_reduced(NULL) {}
/// Returns the max false
Bound *getFalse() const { return max_false; }
/// Returns the min true
Bound *getTrue() const { return min_true; }
/// Returns the min reduced
Bound *getReduced() const { return min_reduced; }
/// Return the stored result for this bound
ProveResult getResult(const Bound *bound) const;
/// Stores a false found
void addFalse(Bound *bound);
/// Stores a true found
void addTrue(Bound *bound);
/// Stores a Reduced found
void addReduced(Bound *bound);
/// Clears redundant reduced
/// If a min_true is smaller than a min_reduced then the min_reduced
/// is unnecessary and then removed. It also works for min_reduced
/// begin smaller than max_false.
void clearRedundantReduced();
void clear() {
delete max_false;
delete min_true;
delete min_reduced;
}
private:
Bound *max_false, *min_true, *min_reduced;
};
/// This class stores the result found for a node of the graph,
/// so these results do not need to be recalculate and only searched for.
class MemoizedResult {
public:
/// Test if there is true result stored from b to a
/// that is less then the bound
bool hasTrue(Value *b, const Bound *bound) const {
Bound *trueBound = map.lookup(b).getTrue();
return trueBound && Bound::leq(trueBound, bound);
}
/// Test if there is false result stored from b to a
/// that is less then the bound
bool hasFalse(Value *b, const Bound *bound) const {
Bound *falseBound = map.lookup(b).getFalse();
return falseBound && Bound::leq(falseBound, bound);
}
/// Test if there is reduced result stored from b to a
/// that is less then the bound
bool hasReduced(Value *b, const Bound *bound) const {
Bound *reducedBound = map.lookup(b).getReduced();
return reducedBound && Bound::leq(reducedBound, bound);
}
/// Returns the stored bound for b
ProveResult getBoundResult(Value *b, Bound *bound) {
return map[b].getResult(bound);
}
/// Clears the map
void clear() {
DenseMapIterator<Value*, MemoizedResultChart> begin = map.begin();
DenseMapIterator<Value*, MemoizedResultChart> end = map.end();
for (; begin != end; ++begin) {
begin->second.clear();
}
map.clear();
}
/// Stores the bound found
void updateBound(Value *b, Bound *bound, const ProveResult res);
private:
// Maps a nod in the graph with its results found.
DenseMap<Value*, MemoizedResultChart> map;
};
/// This class represents an edge in the inequality graph used by the
/// ABCD algorithm. An edge connects node v to node u with a value c if
/// we could infer a constraint v <= u + c in the source program.
class Edge {
public:
Edge(Value *V, APInt val, bool upper) : vertex(V), value(val),
upper_bound(upper)
{}
Value *getVertex() const { return vertex; }
const APInt &getValue() const { return value; }
bool isUpperBound() const { return upper_bound; }
private:
Value *vertex;
APInt value;
bool upper_bound;
};
/// Weighted and Directed graph to represent constraints.
/// There is one type of constraint, a <= b + X, which will generate an
/// edge from b to a with weight X.
class InequalityGraph {
public:
/// Adds an edge from V_from to V_to with weight value
void addEdge(Value *V_from, Value *V_to, APInt value, bool upper);
/// Test if there is a node V
bool hasNode(Value *V) const { return graph.count(V); }
/// Test if there is any edge from V in the upper direction
bool hasEdge(Value *V, bool upper) const;
/// Returns all edges pointed by vertex V
SmallPtrSet<Edge *, 16> getEdges(Value *V) const {
return graph.lookup(V);
}
/// Prints the graph in dot format.
/// Blue edges represent upper bound and Red lower bound.
void printGraph(raw_ostream &OS, Function &F) const {
printHeader(OS, F);
printBody(OS);
printFooter(OS);
}
/// Clear the graph
void clear() {
graph.clear();
}
private:
DenseMap<Value *, SmallPtrSet<Edge *, 16> > graph;
/// Adds a Node to the graph.
DenseMap<Value *, SmallPtrSet<Edge *, 16> >::iterator addNode(Value *V) {
SmallPtrSet<Edge *, 16> p;
return graph.insert(std::make_pair(V, p)).first;
}
/// Prints the header of the dot file
void printHeader(raw_ostream &OS, Function &F) const;
/// Prints the footer of the dot file
void printFooter(raw_ostream &OS) const {
OS << "}\n";
}
/// Prints the body of the dot file
void printBody(raw_ostream &OS) const;
/// Prints vertex source to the dot file
void printVertex(raw_ostream &OS, Value *source) const;
/// Prints the edge to the dot file
void printEdge(raw_ostream &OS, Value *source, Edge *edge) const;
void printName(raw_ostream &OS, Value *info) const;
};
/// Iterates through all BasicBlocks, if the Terminator Instruction
/// uses an Comparator Instruction, all operands of this comparator
/// are sent to be transformed to SSI. Only Instruction operands are
/// transformed.
void createSSI(Function &F);
/// Creates the graphs for this function.
/// It will look for all comparators used in branches, and create them.
/// These comparators will create constraints for any instruction as an
/// operand.
void executeABCD(Function &F);
/// Seeks redundancies in the comparator instruction CI.
/// If the ABCD algorithm can prove that the comparator CI always
/// takes one way, then the Terminator Instruction TI is substituted from
/// a conditional branch to a unconditional one.
/// This code basically receives a comparator, and verifies which kind of
/// instruction it is. Depending on the kind of instruction, we use different
/// strategies to prove its redundancy.
void seekRedundancy(ICmpInst *ICI, TerminatorInst *TI);
/// Substitutes Terminator Instruction TI, that is a conditional branch,
/// with one unconditional branch. Succ_edge determines if the new
/// unconditional edge will be the first or second edge of the former TI
/// instruction.
void removeRedundancy(TerminatorInst *TI, bool Succ_edge);
/// When an conditional branch is removed, the BasicBlock that is no longer
/// reachable will have problems in phi functions. This method fixes these
/// phis removing the former BasicBlock from the list of incoming BasicBlocks
/// of all phis. In case the phi remains with no predecessor it will be
/// marked to be removed later.
void fixPhi(BasicBlock *BB, BasicBlock *Succ);
/// Removes phis that have no predecessor
void removePhis();
/// Creates constraints for Instructions.
/// If the constraint for this instruction has already been created
/// nothing is done.
void createConstraintInstruction(Instruction *I);
/// Creates constraints for Binary Operators.
/// It will create constraints only for addition and subtraction,
/// the other binary operations are not treated by ABCD.
/// For additions in the form a = b + X and a = X + b, where X is a constant,
/// the constraint a <= b + X can be obtained. For this constraint, an edge
/// a->b with weight X is added to the lower bound graph, and an edge
/// b->a with weight -X is added to the upper bound graph.
/// Only subtractions in the format a = b - X is used by ABCD.
/// Edges are created using the same semantic as addition.
void createConstraintBinaryOperator(BinaryOperator *BO);
/// Creates constraints for Comparator Instructions.
/// Only comparators that have any of the following operators
/// are used to create constraints: >=, >, <=, <. And only if
/// at least one operand is an Instruction. In a Comparator Instruction
/// a op b, there will be 4 sigma functions a_t, a_f, b_t and b_f. Where
/// t and f represent sigma for operands in true and false branches. The
/// following constraints can be obtained. a_t <= a, a_f <= a, b_t <= b and
/// b_f <= b. There are two more constraints that depend on the operator.
/// For the operator <= : a_t <= b_t and b_f <= a_f-1
/// For the operator < : a_t <= b_t-1 and b_f <= a_f
/// For the operator >= : b_t <= a_t and a_f <= b_f-1
/// For the operator > : b_t <= a_t-1 and a_f <= b_f
void createConstraintCmpInst(ICmpInst *ICI, TerminatorInst *TI);
/// Creates constraints for PHI nodes.
/// In a PHI node a = phi(b,c) we can create the constraint
/// a<= max(b,c). With this constraint there will be the edges,
/// b->a and c->a with weight 0 in the lower bound graph, and the edges
/// a->b and a->c with weight 0 in the upper bound graph.
void createConstraintPHINode(PHINode *PN);
/// Given a binary operator, we are only interest in the case
/// that one operand is an Instruction and the other is a ConstantInt. In
/// this case the method returns true, otherwise false. It also obtains the
/// Instruction and ConstantInt from the BinaryOperator and returns it.
bool createBinaryOperatorInfo(BinaryOperator *BO, Instruction **I1,
Instruction **I2, ConstantInt **C1,
ConstantInt **C2);
/// This method creates a constraint between a Sigma and an Instruction.
/// These constraints are created as soon as we find a comparator that uses a
/// SSI variable.
void createConstraintSigInst(Instruction *I_op, BasicBlock *BB_succ_t,
BasicBlock *BB_succ_f, PHINode **SIG_op_t,
PHINode **SIG_op_f);
/// If PN_op1 and PN_o2 are different from NULL, create a constraint
/// PN_op2 -> PN_op1 with value. In case any of them is NULL, replace
/// with the respective V_op#, if V_op# is a ConstantInt.
void createConstraintSigSig(PHINode *SIG_op1, PHINode *SIG_op2, APInt value);
/// Returns the sigma representing the Instruction I in BasicBlock BB.
/// Returns NULL in case there is no sigma for this Instruction in this
/// Basic Block. This methods assume that sigmas are the first instructions
/// in a block, and that there can be only two sigmas in a block. So it will
/// only look on the first two instructions of BasicBlock BB.
PHINode *findSigma(BasicBlock *BB, Instruction *I);
/// Original ABCD algorithm to prove redundant checks.
/// This implementation works on any kind of inequality branch.
bool demandProve(Value *a, Value *b, int c, bool upper_bound);
/// Prove that distance between b and a is <= bound
ProveResult prove(Value *a, Value *b, Bound *bound, unsigned level);
/// Updates the distance value for a and b
void updateMemDistance(Value *a, Value *b, Bound *bound, unsigned level,
meet_function meet);
InequalityGraph inequality_graph;
MemoizedResult mem_result;
DenseMap<Value*, Bound*> active;
SmallPtrSet<Value*, 16> created;
SmallVector<PHINode *, 16> phis_to_remove;
};
//} // end anonymous namespace.
char ABCD::ID = 0;
static RegisterPass<ABCD> X("abcd", "ABCD: Eliminating Array Bounds Checks on Demand");
bool ABCD::runOnFunction(Function &F) {
modified = false;
createSSI(F);
executeABCD(F);
DEBUG(inequality_graph.printGraph(errs(), F));
removePhis();
inequality_graph.clear();
mem_result.clear();
active.clear();
created.clear();
phis_to_remove.clear();
return modified;
}
/// Iterates through all BasicBlocks, if the Terminator Instruction
/// uses an Comparator Instruction, all operands of this comparator
/// are sent to be transformed to SSI. Only Instruction operands are
/// transformed.
void ABCD::createSSI(Function &F) {
SSI *ssi = &getAnalysis<SSI>();
SmallVector<Instruction *, 16> Insts;
for (Function::iterator begin = F.begin(), end = F.end();
begin != end; ++begin) {
BasicBlock *BB = begin;
TerminatorInst *TI = BB->getTerminator();
if (TI->getNumOperands() == 0)
continue;
if (ICmpInst *ICI = dyn_cast<ICmpInst>(TI->getOperand(0))) {
if (Instruction *I = dyn_cast<Instruction>(ICI->getOperand(0))) {
modified = true; // XXX: but yet createSSI might do nothing
Insts.push_back(I);
}
if (Instruction *I = dyn_cast<Instruction>(ICI->getOperand(1))) {
modified = true;
Insts.push_back(I);
}
}
}
ssi->createSSI(Insts);
}
/// Creates the graphs for this function.
/// It will look for all comparators used in branches, and create them.
/// These comparators will create constraints for any instruction as an
/// operand.
void ABCD::executeABCD(Function &F) {
for (Function::iterator begin = F.begin(), end = F.end();
begin != end; ++begin) {
BasicBlock *BB = begin;
TerminatorInst *TI = BB->getTerminator();
if (TI->getNumOperands() == 0)
continue;
ICmpInst *ICI = dyn_cast<ICmpInst>(TI->getOperand(0));
if (!ICI || !isa<IntegerType>(ICI->getOperand(0)->getType()))
continue;
createConstraintCmpInst(ICI, TI);
seekRedundancy(ICI, TI);
}
}
/// Seeks redundancies in the comparator instruction CI.
/// If the ABCD algorithm can prove that the comparator CI always
/// takes one way, then the Terminator Instruction TI is substituted from
/// a conditional branch to a unconditional one.
/// This code basically receives a comparator, and verifies which kind of
/// instruction it is. Depending on the kind of instruction, we use different
/// strategies to prove its redundancy.
void ABCD::seekRedundancy(ICmpInst *ICI, TerminatorInst *TI) {
CmpInst::Predicate Pred = ICI->getPredicate();
Value *source, *dest;
int distance1, distance2;
bool upper;
switch(Pred) {
case CmpInst::ICMP_SGT: // signed greater than
upper = false;
distance1 = 1;
distance2 = 0;
break;
case CmpInst::ICMP_SGE: // signed greater or equal
upper = false;
distance1 = 0;
distance2 = -1;
break;
case CmpInst::ICMP_SLT: // signed less than
upper = true;
distance1 = -1;
distance2 = 0;
break;
case CmpInst::ICMP_SLE: // signed less or equal
upper = true;
distance1 = 0;
distance2 = 1;
break;
default:
return;
}
++NumBranchTested;
source = ICI->getOperand(0);
dest = ICI->getOperand(1);
if (demandProve(dest, source, distance1, upper)) {
removeRedundancy(TI, true);
} else if (demandProve(dest, source, distance2, !upper)) {
removeRedundancy(TI, false);
}
}
/// Substitutes Terminator Instruction TI, that is a conditional branch,
/// with one unconditional branch. Succ_edge determines if the new
/// unconditional edge will be the first or second edge of the former TI
/// instruction.
void ABCD::removeRedundancy(TerminatorInst *TI, bool Succ_edge) {
BasicBlock *Succ;
if (Succ_edge) {
Succ = TI->getSuccessor(0);
fixPhi(TI->getParent(), TI->getSuccessor(1));
} else {
Succ = TI->getSuccessor(1);
fixPhi(TI->getParent(), TI->getSuccessor(0));
}
BranchInst::Create(Succ, TI);
TI->eraseFromParent(); // XXX: invoke
++NumBranchRemoved;
modified = true;
}
/// When an conditional branch is removed, the BasicBlock that is no longer
/// reachable will have problems in phi functions. This method fixes these
/// phis removing the former BasicBlock from the list of incoming BasicBlocks
/// of all phis. In case the phi remains with no predecessor it will be
/// marked to be removed later.
void ABCD::fixPhi(BasicBlock *BB, BasicBlock *Succ) {
BasicBlock::iterator begin = Succ->begin();
while (PHINode *PN = dyn_cast<PHINode>(begin++)) {
PN->removeIncomingValue(BB, false);
if (PN->getNumIncomingValues() == 0)
phis_to_remove.push_back(PN);
}
}
/// Removes phis that have no predecessor
void ABCD::removePhis() {
for (unsigned i = 0, end = phis_to_remove.size(); i < end; ++i) {
PHINode *PN = phis_to_remove[i];
PN->replaceAllUsesWith(UndefValue::get(PN->getType()));
PN->eraseFromParent();
}
}
/// Creates constraints for Instructions.
/// If the constraint for this instruction has already been created
/// nothing is done.
void ABCD::createConstraintInstruction(Instruction *I) {
// Test if this instruction has not been created before
if (created.insert(I)) {
if (BinaryOperator *BO = dyn_cast<BinaryOperator>(I)) {
createConstraintBinaryOperator(BO);
} else if (PHINode *PN = dyn_cast<PHINode>(I)) {
createConstraintPHINode(PN);
}
}
}
/// Creates constraints for Binary Operators.
/// It will create constraints only for addition and subtraction,
/// the other binary operations are not treated by ABCD.
/// For additions in the form a = b + X and a = X + b, where X is a constant,
/// the constraint a <= b + X can be obtained. For this constraint, an edge
/// a->b with weight X is added to the lower bound graph, and an edge
/// b->a with weight -X is added to the upper bound graph.
/// Only subtractions in the format a = b - X is used by ABCD.
/// Edges are created using the same semantic as addition.
void ABCD::createConstraintBinaryOperator(BinaryOperator *BO) {
Instruction *I1 = NULL, *I2 = NULL;
ConstantInt *CI1 = NULL, *CI2 = NULL;
// Test if an operand is an Instruction and the other is a Constant
if (!createBinaryOperatorInfo(BO, &I1, &I2, &CI1, &CI2))
return;
Instruction *I = 0;
APInt value;
switch (BO->getOpcode()) {
case Instruction::Add:
if (I1) {
I = I1;
value = CI2->getValue();
} else if (I2) {
I = I2;
value = CI1->getValue();
}
break;
case Instruction::Sub:
// Instructions like a = X-b, where X is a constant are not represented
// in the graph.
if (!I1)
return;
I = I1;
value = -CI2->getValue();
break;
default:
return;
}
APInt MinusOne = APInt::getAllOnesValue(value.getBitWidth());
inequality_graph.addEdge(I, BO, value, true);
inequality_graph.addEdge(BO, I, value * MinusOne, false);
createConstraintInstruction(I);
}
/// Given a binary operator, we are only interest in the case
/// that one operand is an Instruction and the other is a ConstantInt. In
/// this case the method returns true, otherwise false. It also obtains the
/// Instruction and ConstantInt from the BinaryOperator and returns it.
bool ABCD::createBinaryOperatorInfo(BinaryOperator *BO, Instruction **I1,
Instruction **I2, ConstantInt **C1,
ConstantInt **C2) {
Value *op1 = BO->getOperand(0);
Value *op2 = BO->getOperand(1);
if ((*I1 = dyn_cast<Instruction>(op1))) {
if ((*C2 = dyn_cast<ConstantInt>(op2)))
return true; // First is Instruction and second ConstantInt
return false; // Both are Instruction
} else {
if ((*C1 = dyn_cast<ConstantInt>(op1)) &&
(*I2 = dyn_cast<Instruction>(op2)))
return true; // First is ConstantInt and second Instruction
return false; // Both are not Instruction
}
}
/// Creates constraints for Comparator Instructions.
/// Only comparators that have any of the following operators
/// are used to create constraints: >=, >, <=, <. And only if
/// at least one operand is an Instruction. In a Comparator Instruction
/// a op b, there will be 4 sigma functions a_t, a_f, b_t and b_f. Where
/// t and f represent sigma for operands in true and false branches. The
/// following constraints can be obtained. a_t <= a, a_f <= a, b_t <= b and
/// b_f <= b. There are two more constraints that depend on the operator.
/// For the operator <= : a_t <= b_t and b_f <= a_f-1
/// For the operator < : a_t <= b_t-1 and b_f <= a_f
/// For the operator >= : b_t <= a_t and a_f <= b_f-1
/// For the operator > : b_t <= a_t-1 and a_f <= b_f
void ABCD::createConstraintCmpInst(ICmpInst *ICI, TerminatorInst *TI) {
Value *V_op1 = ICI->getOperand(0);
Value *V_op2 = ICI->getOperand(1);
if (!isa<IntegerType>(V_op1->getType()))
return;
Instruction *I_op1 = dyn_cast<Instruction>(V_op1);
Instruction *I_op2 = dyn_cast<Instruction>(V_op2);
// Test if at least one operand is an Instruction
if (!I_op1 && !I_op2)
return;
BasicBlock *BB_succ_t = TI->getSuccessor(0);
BasicBlock *BB_succ_f = TI->getSuccessor(1);
PHINode *SIG_op1_t = NULL, *SIG_op1_f = NULL,
*SIG_op2_t = NULL, *SIG_op2_f = NULL;
createConstraintSigInst(I_op1, BB_succ_t, BB_succ_f,
&SIG_op1_t, &SIG_op1_f);
createConstraintSigInst(I_op2, BB_succ_t, BB_succ_f,
&SIG_op2_t, &SIG_op2_f);
int32_t width = cast<IntegerType>(V_op1->getType())->getBitWidth();
APInt MinusOne = APInt::getAllOnesValue(width);
APInt Zero = APInt::getNullValue(width);
CmpInst::Predicate Pred = ICI->getPredicate();
switch (Pred) {
case CmpInst::ICMP_SGT: // signed greater than
createConstraintSigSig(SIG_op2_t, SIG_op1_t, MinusOne);
createConstraintSigSig(SIG_op1_f, SIG_op2_f, Zero);
break;
case CmpInst::ICMP_SGE: // signed greater or equal
createConstraintSigSig(SIG_op2_t, SIG_op1_t, Zero);
createConstraintSigSig(SIG_op1_f, SIG_op2_f, MinusOne);
break;
case CmpInst::ICMP_SLT: // signed less than
createConstraintSigSig(SIG_op1_t, SIG_op2_t, MinusOne);
createConstraintSigSig(SIG_op2_f, SIG_op1_f, Zero);
break;
case CmpInst::ICMP_SLE: // signed less or equal
createConstraintSigSig(SIG_op1_t, SIG_op2_t, Zero);
createConstraintSigSig(SIG_op2_f, SIG_op1_f, MinusOne);
break;
default:
break;
}
if (I_op1)
createConstraintInstruction(I_op1);
if (I_op2)
createConstraintInstruction(I_op2);
}
/// Creates constraints for PHI nodes.
/// In a PHI node a = phi(b,c) we can create the constraint
/// a<= max(b,c). With this constraint there will be the edges,
/// b->a and c->a with weight 0 in the lower bound graph, and the edges
/// a->b and a->c with weight 0 in the upper bound graph.
void ABCD::createConstraintPHINode(PHINode *PN) {
int32_t width = cast<IntegerType>(PN->getType())->getBitWidth();
for (unsigned i = 0, end = PN->getNumIncomingValues(); i < end; ++i) {
Value *V = PN->getIncomingValue(i);
if (Instruction *I = dyn_cast<Instruction>(V)) {
createConstraintInstruction(I);
}
inequality_graph.addEdge(V, PN, APInt(width, 0), true);
inequality_graph.addEdge(V, PN, APInt(width, 0), false);
}
}
/// This method creates a constraint between a Sigma and an Instruction.
/// These constraints are created as soon as we find a comparator that uses a
/// SSI variable.
void ABCD::createConstraintSigInst(Instruction *I_op, BasicBlock *BB_succ_t,
BasicBlock *BB_succ_f, PHINode **SIG_op_t,
PHINode **SIG_op_f) {
*SIG_op_t = findSigma(BB_succ_t, I_op);
*SIG_op_f = findSigma(BB_succ_f, I_op);
if (*SIG_op_t) {
int32_t width = cast<IntegerType>((*SIG_op_t)->getType())->getBitWidth();
inequality_graph.addEdge(I_op, *SIG_op_t, APInt(width, 0), true);
inequality_graph.addEdge(*SIG_op_t, I_op, APInt(width, 0), false);
created.insert(*SIG_op_t);
}
if (*SIG_op_f) {
int32_t width = cast<IntegerType>((*SIG_op_f)->getType())->getBitWidth();
inequality_graph.addEdge(I_op, *SIG_op_f, APInt(width, 0), true);
inequality_graph.addEdge(*SIG_op_f, I_op, APInt(width, 0), false);
created.insert(*SIG_op_f);
}
}
/// If PN_op1 and PN_o2 are different from NULL, create a constraint
/// PN_op2 -> PN_op1 with value. In case any of them is NULL, replace
/// with the respective V_op#, if V_op# is a ConstantInt.
void ABCD::createConstraintSigSig(PHINode *SIG_op1, PHINode *SIG_op2,
APInt value) {
if (SIG_op1 && SIG_op2) {
APInt MinusOne = APInt::getAllOnesValue(value.getBitWidth());
inequality_graph.addEdge(SIG_op2, SIG_op1, value, true);
inequality_graph.addEdge(SIG_op1, SIG_op2, value * MinusOne, false);
}
}
/// Returns the sigma representing the Instruction I in BasicBlock BB.
/// Returns NULL in case there is no sigma for this Instruction in this
/// Basic Block. This methods assume that sigmas are the first instructions
/// in a block, and that there can be only two sigmas in a block. So it will
/// only look on the first two instructions of BasicBlock BB.
PHINode *ABCD::findSigma(BasicBlock *BB, Instruction *I) {
// BB has more than one predecessor, BB cannot have sigmas.
if (I == NULL || BB->getSinglePredecessor() == NULL)
return NULL;
BasicBlock::iterator begin = BB->begin();
BasicBlock::iterator end = BB->end();
for (unsigned i = 0; i < 2 && begin != end; ++i, ++begin) {
Instruction *I_succ = begin;
if (PHINode *PN = dyn_cast<PHINode>(I_succ))
if (PN->getIncomingValue(0) == I)
return PN;
}
return NULL;
}
/// Original ABCD algorithm to prove redundant checks.
/// This implementation works on any kind of inequality branch.
bool ABCD::demandProve(Value *a, Value *b, int c, bool upper_bound) {
int32_t width = cast<IntegerType>(a->getType())->getBitWidth();
Bound *bound = new Bound(APInt(width, c), upper_bound);
mem_result.clear();
active.clear();
ProveResult res = prove(a, b, bound, 0);
return res != False;
}
/// Prove that distance between b and a is <= bound
ABCD::ProveResult ABCD::prove(Value *a, Value *b, Bound *bound,
unsigned level) {
// if (C[b-a<=e] == True for some e <= bound
// Same or stronger difference was already proven
if (mem_result.hasTrue(b, bound))
return True;
// if (C[b-a<=e] == False for some e >= bound
// Same or weaker difference was already disproved
if (mem_result.hasFalse(b, bound))
return False;
// if (C[b-a<=e] == Reduced for some e <= bound
// b is on a cycle that was reduced for same or stronger difference
if (mem_result.hasReduced(b, bound))
return Reduced;
// traversal reached the source vertex
if (a == b && Bound::geq(bound, APInt(bound->getBitWidth(), 0, true)))
return True;
// if b has no predecessor then fail
if (!inequality_graph.hasEdge(b, bound->isUpperBound()))
return False;
// a cycle was encountered
if (active.count(b)) {
if (Bound::leq(active.lookup(b), bound))
return Reduced; // a "harmless" cycle
return False; // an amplifying cycle
}
active[b] = bound;
PHINode *PN = dyn_cast<PHINode>(b);
// Test if a Value is a Phi. If it is a PHINode with more than 1 incoming
// value, then it is a phi, if it has 1 incoming value it is a sigma.
if (PN && PN->getNumIncomingValues() > 1)
updateMemDistance(a, b, bound, level, min);
else
updateMemDistance(a, b, bound, level, max);
active.erase(b);
ABCD::ProveResult res = mem_result.getBoundResult(b, bound);
return res;
}
/// Updates the distance value for a and b
void ABCD::updateMemDistance(Value *a, Value *b, Bound *bound, unsigned level,
meet_function meet) {
ABCD::ProveResult res = (meet == max) ? False : True;
SmallPtrSet<Edge *, 16> Edges = inequality_graph.getEdges(b);
SmallPtrSet<Edge *, 16>::iterator begin = Edges.begin(), end = Edges.end();
for (; begin != end ; ++begin) {
if (((res >= Reduced) && (meet == max)) ||
((res == False) && (meet == min))) {
break;
}
Edge *in = *begin;
if (in->isUpperBound() == bound->isUpperBound()) {
Value *succ = in->getVertex();
res = meet(res, prove(a, succ, new Bound(bound, in->getValue()),
level+1));
}
}
mem_result.updateBound(b, bound, res);
}
/// Return the stored result for this bound
ABCD::ProveResult ABCD::MemoizedResultChart::getResult(const Bound *bound)const{
if (max_false && Bound::leq(bound, max_false))
return False;
if (min_true && Bound::leq(min_true, bound))
return True;
if (min_reduced && Bound::leq(min_reduced, bound))
return Reduced;
return False;
}
/// Stores a false found
void ABCD::MemoizedResultChart::addFalse(Bound *bound) {
if (!max_false || Bound::leq(max_false, bound))
max_false = bound;
if (Bound::eq(max_false, min_reduced))
min_reduced = Bound::createIncrement(min_reduced);
if (Bound::eq(max_false, min_true))
min_true = Bound::createIncrement(min_true);
if (Bound::eq(min_reduced, min_true))
min_reduced = NULL;
clearRedundantReduced();
}
/// Stores a true found
void ABCD::MemoizedResultChart::addTrue(Bound *bound) {
if (!min_true || Bound::leq(bound, min_true))
min_true = bound;
if (Bound::eq(min_true, min_reduced))
min_reduced = Bound::createDecrement(min_reduced);
if (Bound::eq(min_true, max_false))
max_false = Bound::createDecrement(max_false);
if (Bound::eq(max_false, min_reduced))
min_reduced = NULL;
clearRedundantReduced();
}
/// Stores a Reduced found
void ABCD::MemoizedResultChart::addReduced(Bound *bound) {
if (!min_reduced || Bound::leq(bound, min_reduced))
min_reduced = bound;
if (Bound::eq(min_reduced, min_true))
min_true = Bound::createIncrement(min_true);
if (Bound::eq(min_reduced, max_false))
max_false = Bound::createDecrement(max_false);
}
/// Clears redundant reduced
/// If a min_true is smaller than a min_reduced then the min_reduced
/// is unnecessary and then removed. It also works for min_reduced
/// begin smaller than max_false.
void ABCD::MemoizedResultChart::clearRedundantReduced() {
if (min_true && min_reduced && Bound::lt(min_true, min_reduced))
min_reduced = NULL;
if (max_false && min_reduced && Bound::lt(min_reduced, max_false))
min_reduced = NULL;
}
/// Stores the bound found
void ABCD::MemoizedResult::updateBound(Value *b, Bound *bound,
const ProveResult res) {
if (res == False) {
map[b].addFalse(bound);
} else if (res == True) {
map[b].addTrue(bound);
} else {
map[b].addReduced(bound);
}
}
/// Adds an edge from V_from to V_to with weight value
void ABCD::InequalityGraph::addEdge(Value *V_to, Value *V_from,
APInt value, bool upper) {
assert(V_from->getType() == V_to->getType());
assert(cast<IntegerType>(V_from->getType())->getBitWidth() ==
value.getBitWidth());
DenseMap<Value *, SmallPtrSet<Edge *, 16> >::iterator from;
from = addNode(V_from);
from->second.insert(new Edge(V_to, value, upper));
}
/// Test if there is any edge from V in the upper direction
bool ABCD::InequalityGraph::hasEdge(Value *V, bool upper) const {
SmallPtrSet<Edge *, 16> it = graph.lookup(V);
SmallPtrSet<Edge *, 16>::iterator begin = it.begin();
SmallPtrSet<Edge *, 16>::iterator end = it.end();
for (; begin != end; ++begin) {
if ((*begin)->isUpperBound() == upper) {
return true;
}
}
return false;
}
/// Prints the header of the dot file
void ABCD::InequalityGraph::printHeader(raw_ostream &OS, Function &F) const {
OS << "digraph dotgraph {\n";
OS << "label=\"Inequality Graph for \'";
OS << F.getNameStr() << "\' function\";\n";
OS << "node [shape=record,fontname=\"Times-Roman\",fontsize=14];\n";
}
/// Prints the body of the dot file
void ABCD::InequalityGraph::printBody(raw_ostream &OS) const {
DenseMap<Value *, SmallPtrSet<Edge *, 16> >::iterator begin =
graph.begin(), end = graph.end();
for (; begin != end ; ++begin) {
SmallPtrSet<Edge *, 16>::iterator begin_par =
begin->second.begin(), end_par = begin->second.end();
Value *source = begin->first;
printVertex(OS, source);
for (; begin_par != end_par ; ++begin_par) {
Edge *edge = *begin_par;
printEdge(OS, source, edge);
}
}
}
/// Prints vertex source to the dot file
///
void ABCD::InequalityGraph::printVertex(raw_ostream &OS, Value *source) const {
OS << "\"";
printName(OS, source);
OS << "\"";
OS << " [label=\"{";
printName(OS, source);
OS << "}\"];\n";
}
/// Prints the edge to the dot file
void ABCD::InequalityGraph::printEdge(raw_ostream &OS, Value *source,
Edge *edge) const {
Value *dest = edge->getVertex();
APInt value = edge->getValue();
bool upper = edge->isUpperBound();
OS << "\"";
printName(OS, source);
OS << "\"";
OS << " -> ";
OS << "\"";
printName(OS, dest);
OS << "\"";
OS << " [label=\"" << value << "\"";
if (upper) {
OS << "color=\"blue\"";
} else {
OS << "color=\"red\"";
}
OS << "];\n";
}
void ABCD::InequalityGraph::printName(raw_ostream &OS, Value *info) const {
if (ConstantInt *CI = dyn_cast<ConstantInt>(info)) {
OS << *CI->getValue().getRawData();
} else {
if (info->getName() == "") {
info->setName("V");
}
OS << info->getNameStr();
}
}
/// createABCDPass - The public interface to this file...
FunctionPass *llvm::createABCDPass() {
return new ABCD();
}
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