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llvm-project/llvm/lib/Transforms/Scalar/ABCD.cpp

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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 prove 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/OwningPtr.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:
/// Keep track of whether we've modified the program yet.
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 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 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) {
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) {
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) {
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() {}
MemoizedResultChart(const MemoizedResultChart &other) {
if (other.max_false)
max_false.reset(new Bound(*other.max_false));
if (other.min_true)
min_true.reset(new Bound(*other.min_true));
if (other.min_reduced)
min_reduced.reset(new Bound(*other.min_reduced));
}
/// Returns the max false
const Bound *getFalse() const { return max_false.get(); }
/// Returns the min true
const Bound *getTrue() const { return min_true.get(); }
/// Returns the min reduced
const Bound *getReduced() const { return min_reduced.get(); }
/// Return the stored result for this bound
ProveResult getResult(const Bound &bound) const;
/// Stores a false found
void addFalse(const Bound &bound);
/// Stores a true found
void addTrue(const Bound &bound);
/// Stores a Reduced found
void addReduced(const 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() {
max_false.reset();
min_true.reset();
min_reduced.reset();
}
private:
OwningPtr<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 recalculated, 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 {
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 {
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 {
const Bound *reducedBound = map.lookup(b).getReduced();
return reducedBound && Bound::leq(*reducedBound, bound);
}
/// Returns the stored bound for b
ProveResult getBoundResult(Value *b, const 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, const 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
SmallVector<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 *, SmallVector<Edge, 16> > graph;
/// 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, const 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,
ConstantInt *V_op1, ConstantInt *V_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, const Bound &bound, unsigned level);
/// Updates the distance value for a and b
void updateMemDistance(Value *a, Value *b, const Bound &bound, unsigned level,
meet_function meet);
InequalityGraph inequality_graph;
MemoizedResult mem_result;
DenseMap<Value*, const 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(dbgs(), 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 || !ICI->getOperand(0)->getType()->isIntegerTy())
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, e = phis_to_remove.size(); i != e; ++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;
}
inequality_graph.addEdge(I, BO, value, true);
inequality_graph.addEdge(BO, I, -value, 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 (!V_op1->getType()->isIntegerTy())
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();
ConstantInt *CI1 = dyn_cast<ConstantInt>(V_op1);
ConstantInt *CI2 = dyn_cast<ConstantInt>(V_op2);
switch (Pred) {
case CmpInst::ICMP_SGT: // signed greater than
createConstraintSigSig(SIG_op2_t, SIG_op1_t, CI2, CI1, MinusOne);
createConstraintSigSig(SIG_op1_f, SIG_op2_f, CI1, CI2, Zero);
break;
case CmpInst::ICMP_SGE: // signed greater or equal
createConstraintSigSig(SIG_op2_t, SIG_op1_t, CI2, CI1, Zero);
createConstraintSigSig(SIG_op1_f, SIG_op2_f, CI1, CI2, MinusOne);
break;
case CmpInst::ICMP_SLT: // signed less than
createConstraintSigSig(SIG_op1_t, SIG_op2_t, CI1, CI2, MinusOne);
createConstraintSigSig(SIG_op2_f, SIG_op1_f, CI2, CI1, Zero);
break;
case CmpInst::ICMP_SLE: // signed less or equal
createConstraintSigSig(SIG_op1_t, SIG_op2_t, CI1, CI2, Zero);
createConstraintSigSig(SIG_op2_f, SIG_op1_f, CI2, CI1, 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) {
// FIXME: We really want to disallow sigma nodes, but I don't know the best
// way to detect the other than this.
if (PN->getNumOperands() == 2) return;
int32_t width = cast<IntegerType>(PN->getType())->getBitWidth();
for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++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);
}
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);
}
}
/// 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,
ConstantInt *V_op1, ConstantInt *V_op2,
APInt value) {
if (SIG_op1 && SIG_op2) {
inequality_graph.addEdge(SIG_op2, SIG_op1, value, true);
inequality_graph.addEdge(SIG_op1, SIG_op2, -value, false);
} else if (SIG_op1 && V_op2) {
inequality_graph.addEdge(V_op2, SIG_op1, value, true);
inequality_graph.addEdge(SIG_op1, V_op2, -value, false);
} else if (SIG_op2 && V_op1) {
inequality_graph.addEdge(SIG_op2, V_op1, value, true);
inequality_graph.addEdge(V_op1, SIG_op2, -value, 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(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, const 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, const Bound &bound,
unsigned level, meet_function meet) {
ABCD::ProveResult res = (meet == max) ? False : True;
SmallVector<Edge, 16> Edges = inequality_graph.getEdges(b);
SmallVector<Edge, 16>::iterator begin = Edges.begin(), end = Edges.end();
for (; begin != end ; ++begin) {
if (((res >= Reduced) && (meet == max)) ||
((res == False) && (meet == min))) {
break;
}
const Edge &in = *begin;
if (in.isUpperBound() == bound.isUpperBound()) {
Value *succ = in.getVertex();
res = meet(res, prove(a, succ, 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(const Bound &bound) {
if (!max_false || Bound::leq(*max_false, bound))
max_false.reset(new Bound(bound));
if (Bound::eq(max_false.get(), min_reduced.get()))
min_reduced.reset(new Bound(Bound::createIncrement(*min_reduced)));
if (Bound::eq(max_false.get(), min_true.get()))
min_true.reset(new Bound(Bound::createIncrement(*min_true)));
if (Bound::eq(min_reduced.get(), min_true.get()))
min_reduced.reset();
clearRedundantReduced();
}
/// Stores a true found
void ABCD::MemoizedResultChart::addTrue(const Bound &bound) {
if (!min_true || Bound::leq(bound, *min_true))
min_true.reset(new Bound(bound));
if (Bound::eq(min_true.get(), min_reduced.get()))
min_reduced.reset(new Bound(Bound::createDecrement(*min_reduced)));
if (Bound::eq(min_true.get(), max_false.get()))
max_false.reset(new Bound(Bound::createDecrement(*max_false)));
if (Bound::eq(max_false.get(), min_reduced.get()))
min_reduced.reset();
clearRedundantReduced();
}
/// Stores a Reduced found
void ABCD::MemoizedResultChart::addReduced(const Bound &bound) {
if (!min_reduced || Bound::leq(bound, *min_reduced))
min_reduced.reset(new Bound(bound));
if (Bound::eq(min_reduced.get(), min_true.get()))
min_true.reset(new Bound(Bound::createIncrement(*min_true)));
if (Bound::eq(min_reduced.get(), max_false.get()))
max_false.reset(new Bound(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.reset();
if (max_false && min_reduced && Bound::lt(*min_reduced, *max_false))
min_reduced.reset();
}
/// Stores the bound found
void ABCD::MemoizedResult::updateBound(Value *b, const 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());
graph[V_from].push_back(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 {
SmallVector<Edge, 16> it = graph.lookup(V);
SmallVector<Edge, 16>::iterator begin = it.begin();
SmallVector<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 *, SmallVector<Edge, 16> >::const_iterator begin =
graph.begin(), end = graph.end();
for (; begin != end ; ++begin) {
SmallVector<Edge, 16>::const_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) {
const 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,
const 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;
} else {
if (!info->hasName()) {
info->setName("V");
}
OS << info->getNameStr();
}
}
/// createABCDPass - The public interface to this file...
FunctionPass *llvm::createABCDPass() {
return new ABCD();
}
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