//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
//
// The LLVM Compiler Infrastructure
//
// This file was developed by the LLVM research group and is distributed under
// the University of Illinois Open Source License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This file contains the implementation of the scalar evolution analysis
// engine, which is used primarily to analyze expressions involving induction
// variables in loops.
//
// There are several aspects to this library. First is the representation of
// scalar expressions, which are represented as subclasses of the SCEV class.
// These classes are used to represent certain types of subexpressions that we
// can handle. These classes are reference counted, managed by the SCEVHandle
// class. We only create one SCEV of a particular shape, so pointer-comparisons
// for equality are legal.
//
// One important aspect of the SCEV objects is that they are never cyclic, even
// if there is a cycle in the dataflow for an expression (ie, a PHI node). If
// the PHI node is one of the idioms that we can represent (e.g., a polynomial
// recurrence) then we represent it directly as a recurrence node, otherwise we
// represent it as a SCEVUnknown node.
//
// In addition to being able to represent expressions of various types, we also
// have folders that are used to build the *canonical* representation for a
// particular expression. These folders are capable of using a variety of
// rewrite rules to simplify the expressions.
//
// Once the folders are defined, we can implement the more interesting
// higher-level code, such as the code that recognizes PHI nodes of various
// types, computes the execution count of a loop, etc.
//
// TODO: We should use these routines and value representations to implement
// dependence analysis!
//
//===----------------------------------------------------------------------===//
//
// There are several good references for the techniques used in this analysis.
//
// Chains of recurrences -- a method to expedite the evaluation
// of closed-form functions
// Olaf Bachmann, Paul S. Wang, Eugene V. Zima
//
// On computational properties of chains of recurrences
// Eugene V. Zima
//
// Symbolic Evaluation of Chains of Recurrences for Loop Optimization
// Robert A. van Engelen
//
// Efficient Symbolic Analysis for Optimizing Compilers
// Robert A. van Engelen
//
// Using the chains of recurrences algebra for data dependence testing and
// induction variable substitution
// MS Thesis, Johnie Birch
//
//===----------------------------------------------------------------------===//
#include "llvm/Analysis/ScalarEvolutionExpressions.h"
#include "llvm/Constants.h"
#include "llvm/DerivedTypes.h"
#include "llvm/Instructions.h"
#include "llvm/Type.h"
#include "llvm/Value.h"
#include "llvm/Analysis/LoopInfo.h"
#include "llvm/Assembly/Writer.h"
#include "llvm/Transforms/Scalar.h"
#include "llvm/Transforms/Utils/Local.h"
#include "llvm/Support/CFG.h"
#include "llvm/Support/ConstantRange.h"
#include "llvm/Support/InstIterator.h"
#include "Support/CommandLine.h"
#include "Support/Statistic.h"
#include <cmath>
using namespace llvm;
namespace {
RegisterAnalysis<ScalarEvolution>
R("scalar-evolution", "Scalar Evolution Analysis");
Statistic<>
NumBruteForceEvaluations("scalar-evolution",
"Number of brute force evaluations needed to calculate high-order polynomial exit values");
Statistic<>
NumTripCountsComputed("scalar-evolution",
"Number of loops with predictable loop counts");
Statistic<>
NumTripCountsNotComputed("scalar-evolution",
"Number of loops without predictable loop counts");
Statistic<>
NumBruteForceTripCountsComputed("scalar-evolution",
"Number of loops with trip counts computed by force");
cl::opt<unsigned>
MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
cl::desc("Maximum number of iterations SCEV will symbolically execute a constant derived loop"),
cl::init(100));
}
//===----------------------------------------------------------------------===//
// SCEV class definitions
//===----------------------------------------------------------------------===//
//===----------------------------------------------------------------------===//
// Implementation of the SCEV class.
//
namespace {
/// SCEVComplexityCompare - Return true if the complexity of the LHS is less
/// than the complexity of the RHS. If the SCEVs have identical complexity,
/// order them by their addresses. This comparator is used to canonicalize
/// expressions.
struct SCEVComplexityCompare {
bool operator()(SCEV *LHS, SCEV *RHS) {
if (LHS->getSCEVType() < RHS->getSCEVType())
return true;
if (LHS->getSCEVType() == RHS->getSCEVType())
return LHS < RHS;
return false;
}
};
}
SCEV::~SCEV() {}
void SCEV::dump() const {
print(std::cerr);
}
/// getValueRange - Return the tightest constant bounds that this value is
/// known to have. This method is only valid on integer SCEV objects.
ConstantRange SCEV::getValueRange() const {
const Type *Ty = getType();
assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!");
Ty = Ty->getUnsignedVersion();
// Default to a full range if no better information is available.
return ConstantRange(getType());
}
SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
return false;
}
const Type *SCEVCouldNotCompute::getType() const {
assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
return 0;
}
bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
return false;
}
void SCEVCouldNotCompute::print(std::ostream &OS) const {
OS << "***COULDNOTCOMPUTE***";
}
bool SCEVCouldNotCompute::classof(const SCEV *S) {
return S->getSCEVType() == scCouldNotCompute;
}
// SCEVConstants - Only allow the creation of one SCEVConstant for any
// particular value. Don't use a SCEVHandle here, or else the object will
// never be deleted!
static std::map<ConstantInt*, SCEVConstant*> SCEVConstants;
SCEVConstant::~SCEVConstant() {
SCEVConstants.erase(V);
}
SCEVHandle SCEVConstant::get(ConstantInt *V) {
// Make sure that SCEVConstant instances are all unsigned.
if (V->getType()->isSigned()) {
const Type *NewTy = V->getType()->getUnsignedVersion();
V = cast<ConstantUInt>(ConstantExpr::getCast(V, NewTy));
}
SCEVConstant *&R = SCEVConstants[V];
if (R == 0) R = new SCEVConstant(V);
return R;
}
ConstantRange SCEVConstant::getValueRange() const {
return ConstantRange(V);
}
const Type *SCEVConstant::getType() const { return V->getType(); }
void SCEVConstant::print(std::ostream &OS) const {
WriteAsOperand(OS, V, false);
}
// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
// particular input. Don't use a SCEVHandle here, or else the object will
// never be deleted!
static std::map<std::pair<SCEV*, const Type*>, SCEVTruncateExpr*> SCEVTruncates;
SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
: SCEV(scTruncate), Op(op), Ty(ty) {
assert(Op->getType()->isInteger() && Ty->isInteger() &&
Ty->isUnsigned() &&
"Cannot truncate non-integer value!");
assert(Op->getType()->getPrimitiveSize() > Ty->getPrimitiveSize() &&
"This is not a truncating conversion!");
}
SCEVTruncateExpr::~SCEVTruncateExpr() {
SCEVTruncates.erase(std::make_pair(Op, Ty));
}
ConstantRange SCEVTruncateExpr::getValueRange() const {
return getOperand()->getValueRange().truncate(getType());
}
void SCEVTruncateExpr::print(std::ostream &OS) const {
OS << "(truncate " << *Op << " to " << *Ty << ")";
}
// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
// particular input. Don't use a SCEVHandle here, or else the object will never
// be deleted!
static std::map<std::pair<SCEV*, const Type*>,
SCEVZeroExtendExpr*> SCEVZeroExtends;
SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
: SCEV(scTruncate), Op(Op), Ty(ty) {
assert(Op->getType()->isInteger() && Ty->isInteger() &&
Ty->isUnsigned() &&
"Cannot zero extend non-integer value!");
assert(Op->getType()->getPrimitiveSize() < Ty->getPrimitiveSize() &&
"This is not an extending conversion!");
}
SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
SCEVZeroExtends.erase(std::make_pair(Op, Ty));
}
ConstantRange SCEVZeroExtendExpr::getValueRange() const {
return getOperand()->getValueRange().zeroExtend(getType());
}
void SCEVZeroExtendExpr::print(std::ostream &OS) const {
OS << "(zeroextend " << *Op << " to " << *Ty << ")";
}
// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
// particular input. Don't use a SCEVHandle here, or else the object will never
// be deleted!
static std::map<std::pair<unsigned, std::vector<SCEV*> >,
SCEVCommutativeExpr*> SCEVCommExprs;
SCEVCommutativeExpr::~SCEVCommutativeExpr() {
SCEVCommExprs.erase(std::make_pair(getSCEVType(),
std::vector<SCEV*>(Operands.begin(),
Operands.end())));
}
void SCEVCommutativeExpr::print(std::ostream &OS) const {
assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
const char *OpStr = getOperationStr();
OS << "(" << *Operands[0];
for (unsigned i = 1, e = Operands.size(); i != e; ++i)
OS << OpStr << *Operands[i];
OS << ")";
}
// SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
// input. Don't use a SCEVHandle here, or else the object will never be
// deleted!
static std::map<std::pair<SCEV*, SCEV*>, SCEVUDivExpr*> SCEVUDivs;
SCEVUDivExpr::~SCEVUDivExpr() {
SCEVUDivs.erase(std::make_pair(LHS, RHS));
}
void SCEVUDivExpr::print(std::ostream &OS) const {
OS << "(" << *LHS << " /u " << *RHS << ")";
}
const Type *SCEVUDivExpr::getType() const {
const Type *Ty = LHS->getType();
if (Ty->isSigned()) Ty = Ty->getUnsignedVersion();
return Ty;
}
// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
// particular input. Don't use a SCEVHandle here, or else the object will never
// be deleted!
static std::map<std::pair<const Loop *, std::vector<SCEV*> >,
SCEVAddRecExpr*> SCEVAddRecExprs;
SCEVAddRecExpr::~SCEVAddRecExpr() {
SCEVAddRecExprs.erase(std::make_pair(L,
std::vector<SCEV*>(Operands.begin(),
Operands.end())));
}
bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
// This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
// contain L.
return !QueryLoop->contains(L->getHeader());
}
void SCEVAddRecExpr::print(std::ostream &OS) const {
OS << "{" << *Operands[0];
for (unsigned i = 1, e = Operands.size(); i != e; ++i)
OS << ",+," << *Operands[i];
OS << "}<" << L->getHeader()->getName() + ">";
}
// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
// value. Don't use a SCEVHandle here, or else the object will never be
// deleted!
static std::map<Value*, SCEVUnknown*> SCEVUnknowns;
SCEVUnknown::~SCEVUnknown() { SCEVUnknowns.erase(V); }
bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
// All non-instruction values are loop invariant. All instructions are loop
// invariant if they are not contained in the specified loop.
if (Instruction *I = dyn_cast<Instruction>(V))
return !L->contains(I->getParent());
return true;
}
const Type *SCEVUnknown::getType() const {
return V->getType();
}
void SCEVUnknown::print(std::ostream &OS) const {
WriteAsOperand(OS, V, false);
}
//===----------------------------------------------------------------------===//
// Simple SCEV method implementations
//===----------------------------------------------------------------------===//
/// getIntegerSCEV - Given an integer or FP type, create a constant for the
/// specified signed integer value and return a SCEV for the constant.
SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) {
Constant *C;
if (Val == 0)
C = Constant::getNullValue(Ty);
else if (Ty->isFloatingPoint())
C = ConstantFP::get(Ty, Val);
else if (Ty->isSigned())
C = ConstantSInt::get(Ty, Val);
else {
C = ConstantSInt::get(Ty->getSignedVersion(), Val);
C = ConstantExpr::getCast(C, Ty);
}
return SCEVUnknown::get(C);
}
/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
/// input value to the specified type. If the type must be extended, it is zero
/// extended.
static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
const Type *SrcTy = V->getType();
assert(SrcTy->isInteger() && Ty->isInteger() &&
"Cannot truncate or zero extend with non-integer arguments!");
if (SrcTy->getPrimitiveSize() == Ty->getPrimitiveSize())
return V; // No conversion
if (SrcTy->getPrimitiveSize() > Ty->getPrimitiveSize())
return SCEVTruncateExpr::get(V, Ty);
return SCEVZeroExtendExpr::get(V, Ty);
}
/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
///
static SCEVHandle getNegativeSCEV(const SCEVHandle &V) {
if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue()));
return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType()));
}
/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
///
static SCEVHandle getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) {
// X - Y --> X + -Y
return SCEVAddExpr::get(LHS, getNegativeSCEV(RHS));
}
/// Binomial - Evaluate N!/((N-M)!*M!) . Note that N is often large and M is
/// often very small, so we try to reduce the number of N! terms we need to
/// evaluate by evaluating this as (N!/(N-M)!)/M!
static ConstantInt *Binomial(ConstantInt *N, unsigned M) {
uint64_t NVal = N->getRawValue();
uint64_t FirstTerm = 1;
for (unsigned i = 0; i != M; ++i)
FirstTerm *= NVal-i;
unsigned MFactorial = 1;
for (; M; --M)
MFactorial *= M;
Constant *Result = ConstantUInt::get(Type::ULongTy, FirstTerm/MFactorial);
Result = ConstantExpr::getCast(Result, N->getType());
assert(isa<ConstantInt>(Result) && "Cast of integer not folded??");
return cast<ConstantInt>(Result);
}
/// PartialFact - Compute V!/(V-NumSteps)!
static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) {
// Handle this case efficiently, it is common to have constant iteration
// counts while computing loop exit values.
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) {
uint64_t Val = SC->getValue()->getRawValue();
uint64_t Result = 1;
for (; NumSteps; --NumSteps)
Result *= Val-(NumSteps-1);
Constant *Res = ConstantUInt::get(Type::ULongTy, Result);
return SCEVUnknown::get(ConstantExpr::getCast(Res, V->getType()));
}
const Type *Ty = V->getType();
if (NumSteps == 0)
return SCEVUnknown::getIntegerSCEV(1, Ty);
SCEVHandle Result = V;
for (unsigned i = 1; i != NumSteps; ++i)
Result = SCEVMulExpr::get(Result, getMinusSCEV(V,
SCEVUnknown::getIntegerSCEV(i, Ty)));
return Result;
}
/// evaluateAtIteration - Return the value of this chain of recurrences at
/// the specified iteration number. We can evaluate this recurrence by
/// multiplying each element in the chain by the binomial coefficient
/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
///
/// A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3)
///
/// FIXME/VERIFY: I don't trust that this is correct in the face of overflow.
/// Is the binomial equation safe using modular arithmetic??
///
SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const {
SCEVHandle Result = getStart();
int Divisor = 1;
const Type *Ty = It->getType();
for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
SCEVHandle BC = PartialFact(It, i);
Divisor *= i;
SCEVHandle Val = SCEVUDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)),
SCEVUnknown::getIntegerSCEV(Divisor,Ty));
Result = SCEVAddExpr::get(Result, Val);
}
return Result;
}
//===----------------------------------------------------------------------===//
// SCEV Expression folder implementations
//===----------------------------------------------------------------------===//
SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) {
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty));
// If the input value is a chrec scev made out of constants, truncate
// all of the constants.
if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
std::vector<SCEVHandle> Operands;
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
// FIXME: This should allow truncation of other expression types!
if (isa<SCEVConstant>(AddRec->getOperand(i)))
Operands.push_back(get(AddRec->getOperand(i), Ty));
else
break;
if (Operands.size() == AddRec->getNumOperands())
return SCEVAddRecExpr::get(Operands, AddRec->getLoop());
}
SCEVTruncateExpr *&Result = SCEVTruncates[std::make_pair(Op, Ty)];
if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
return Result;
}
SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) {
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty));
// FIXME: If the input value is a chrec scev, and we can prove that the value
// did not overflow the old, smaller, value, we can zero extend all of the
// operands (often constants). This would allow analysis of something like
// this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
SCEVZeroExtendExpr *&Result = SCEVZeroExtends[std::make_pair(Op, Ty)];
if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
return Result;
}
// get - Get a canonical add expression, or something simpler if possible.
SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) {
assert(!Ops.empty() && "Cannot get empty add!");
if (Ops.size() == 1) return Ops[0];
// Sort by complexity, this groups all similar expression types together.
std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
// If there are any constants, fold them together.
unsigned Idx = 0;
if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
++Idx;
assert(Idx < Ops.size());
while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
// We found two constants, fold them together!
Constant *Fold = ConstantExpr::getAdd(LHSC->getValue(), RHSC->getValue());
if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
Ops[0] = SCEVConstant::get(CI);
Ops.erase(Ops.begin()+1); // Erase the folded element
if (Ops.size() == 1) return Ops[0];
} else {
// If we couldn't fold the expression, move to the next constant. Note
// that this is impossible to happen in practice because we always
// constant fold constant ints to constant ints.
++Idx;
}
}
// If we are left with a constant zero being added, strip it off.
if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) {
Ops.erase(Ops.begin());
--Idx;
}
}
if (Ops.size() == 1) return Ops[0];
// Okay, check to see if the same value occurs in the operand list twice. If
// so, merge them together into an multiply expression. Since we sorted the
// list, these values are required to be adjacent.
const Type *Ty = Ops[0]->getType();
for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
// Found a match, merge the two values into a multiply, and add any
// remaining values to the result.
SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty);
SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two);
if (Ops.size() == 2)
return Mul;
Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
Ops.push_back(Mul);
return SCEVAddExpr::get(Ops);
}
// Okay, now we know the first non-constant operand. If there are add
// operands they would be next.
if (Idx < Ops.size()) {
bool DeletedAdd = false;
while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
// If we have an add, expand the add operands onto the end of the operands
// list.
Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
Ops.erase(Ops.begin()+Idx);
DeletedAdd = true;
}
// If we deleted at least one add, we added operands to the end of the list,
// and they are not necessarily sorted. Recurse to resort and resimplify
// any operands we just aquired.
if (DeletedAdd)
return get(Ops);
}
// Skip over the add expression until we get to a multiply.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
++Idx;
// If we are adding something to a multiply expression, make sure the
// something is not already an operand of the multiply. If so, merge it into
// the multiply.
for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
SCEV *MulOpSCEV = Mul->getOperand(MulOp);
for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
if (MulOpSCEV == Ops[AddOp] &&
(Mul->getNumOperands() != 2 || !isa<SCEVConstant>(MulOpSCEV))) {
// Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
if (Mul->getNumOperands() != 2) {
// If the multiply has more than two operands, we must get the
// Y*Z term.
std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
MulOps.erase(MulOps.begin()+MulOp);
InnerMul = SCEVMulExpr::get(MulOps);
}
SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty);
SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One);
SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]);
if (Ops.size() == 2) return OuterMul;
if (AddOp < Idx) {
Ops.erase(Ops.begin()+AddOp);
Ops.erase(Ops.begin()+Idx-1);
} else {
Ops.erase(Ops.begin()+Idx);
Ops.erase(Ops.begin()+AddOp-1);
}
Ops.push_back(OuterMul);
return SCEVAddExpr::get(Ops);
}
// Check this multiply against other multiplies being added together.
for (unsigned OtherMulIdx = Idx+1;
OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
++OtherMulIdx) {
SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
// If MulOp occurs in OtherMul, we can fold the two multiplies
// together.
for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
OMulOp != e; ++OMulOp)
if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
// Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
if (Mul->getNumOperands() != 2) {
std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
MulOps.erase(MulOps.begin()+MulOp);
InnerMul1 = SCEVMulExpr::get(MulOps);
}
SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
if (OtherMul->getNumOperands() != 2) {
std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
OtherMul->op_end());
MulOps.erase(MulOps.begin()+OMulOp);
InnerMul2 = SCEVMulExpr::get(MulOps);
}
SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2);
SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum);
if (Ops.size() == 2) return OuterMul;
Ops.erase(Ops.begin()+Idx);
Ops.erase(Ops.begin()+OtherMulIdx-1);
Ops.push_back(OuterMul);
return SCEVAddExpr::get(Ops);
}
}
}
}
// If there are any add recurrences in the operands list, see if any other
// added values are loop invariant. If so, we can fold them into the
// recurrence.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
++Idx;
// Scan over all recurrences, trying to fold loop invariants into them.
for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
// Scan all of the other operands to this add and add them to the vector if
// they are loop invariant w.r.t. the recurrence.
std::vector<SCEVHandle> LIOps;
SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
LIOps.push_back(Ops[i]);
Ops.erase(Ops.begin()+i);
--i; --e;
}
// If we found some loop invariants, fold them into the recurrence.
if (!LIOps.empty()) {
// NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step }
LIOps.push_back(AddRec->getStart());
std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
AddRecOps[0] = SCEVAddExpr::get(LIOps);
SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop());
// If all of the other operands were loop invariant, we are done.
if (Ops.size() == 1) return NewRec;
// Otherwise, add the folded AddRec by the non-liv parts.
for (unsigned i = 0;; ++i)
if (Ops[i] == AddRec) {
Ops[i] = NewRec;
break;
}
return SCEVAddExpr::get(Ops);
}
// Okay, if there weren't any loop invariants to be folded, check to see if
// there are multiple AddRec's with the same loop induction variable being
// added together. If so, we can fold them.
for (unsigned OtherIdx = Idx+1;
OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
if (OtherIdx != Idx) {
SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
if (AddRec->getLoop() == OtherAddRec->getLoop()) {
// Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
if (i >= NewOps.size()) {
NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
OtherAddRec->op_end());
break;
}
NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i));
}
SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
if (Ops.size() == 2) return NewAddRec;
Ops.erase(Ops.begin()+Idx);
Ops.erase(Ops.begin()+OtherIdx-1);
Ops.push_back(NewAddRec);
return SCEVAddExpr::get(Ops);
}
}
// Otherwise couldn't fold anything into this recurrence. Move onto the
// next one.
}
// Okay, it looks like we really DO need an add expr. Check to see if we
// already have one, otherwise create a new one.
std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scAddExpr,
SCEVOps)];
if (Result == 0) Result = new SCEVAddExpr(Ops);
return Result;
}
SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) {
assert(!Ops.empty() && "Cannot get empty mul!");
// Sort by complexity, this groups all similar expression types together.
std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
// If there are any constants, fold them together.
unsigned Idx = 0;
if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
// C1*(C2+V) -> C1*C2 + C1*V
if (Ops.size() == 2)
if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
if (Add->getNumOperands() == 2 &&
isa<SCEVConstant>(Add->getOperand(0)))
return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)),
SCEVMulExpr::get(LHSC, Add->getOperand(1)));
++Idx;
while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
// We found two constants, fold them together!
Constant *Fold = ConstantExpr::getMul(LHSC->getValue(), RHSC->getValue());
if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
Ops[0] = SCEVConstant::get(CI);
Ops.erase(Ops.begin()+1); // Erase the folded element
if (Ops.size() == 1) return Ops[0];
} else {
// If we couldn't fold the expression, move to the next constant. Note
// that this is impossible to happen in practice because we always
// constant fold constant ints to constant ints.
++Idx;
}
}
// If we are left with a constant one being multiplied, strip it off.
if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
Ops.erase(Ops.begin());
--Idx;
} else if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) {
// If we have a multiply of zero, it will always be zero.
return Ops[0];
}
}
// Skip over the add expression until we get to a multiply.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
++Idx;
if (Ops.size() == 1)
return Ops[0];
// If there are mul operands inline them all into this expression.
if (Idx < Ops.size()) {
bool DeletedMul = false;
while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
// If we have an mul, expand the mul operands onto the end of the operands
// list.
Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
Ops.erase(Ops.begin()+Idx);
DeletedMul = true;
}
// If we deleted at least one mul, we added operands to the end of the list,
// and they are not necessarily sorted. Recurse to resort and resimplify
// any operands we just aquired.
if (DeletedMul)
return get(Ops);
}
// If there are any add recurrences in the operands list, see if any other
// added values are loop invariant. If so, we can fold them into the
// recurrence.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
++Idx;
// Scan over all recurrences, trying to fold loop invariants into them.
for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
// Scan all of the other operands to this mul and add them to the vector if
// they are loop invariant w.r.t. the recurrence.
std::vector<SCEVHandle> LIOps;
SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
LIOps.push_back(Ops[i]);
Ops.erase(Ops.begin()+i);
--i; --e;
}
// If we found some loop invariants, fold them into the recurrence.
if (!LIOps.empty()) {
// NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step }
std::vector<SCEVHandle> NewOps;
NewOps.reserve(AddRec->getNumOperands());
if (LIOps.size() == 1) {
SCEV *Scale = LIOps[0];
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i)));
} else {
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
std::vector<SCEVHandle> MulOps(LIOps);
MulOps.push_back(AddRec->getOperand(i));
NewOps.push_back(SCEVMulExpr::get(MulOps));
}
}
SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
// If all of the other operands were loop invariant, we are done.
if (Ops.size() == 1) return NewRec;
// Otherwise, multiply the folded AddRec by the non-liv parts.
for (unsigned i = 0;; ++i)
if (Ops[i] == AddRec) {
Ops[i] = NewRec;
break;
}
return SCEVMulExpr::get(Ops);
}
// Okay, if there weren't any loop invariants to be folded, check to see if
// there are multiple AddRec's with the same loop induction variable being
// multiplied together. If so, we can fold them.
for (unsigned OtherIdx = Idx+1;
OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
if (OtherIdx != Idx) {
SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
if (AddRec->getLoop() == OtherAddRec->getLoop()) {
// F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(),
G->getStart());
SCEVHandle B = F->getStepRecurrence();
SCEVHandle D = G->getStepRecurrence();
SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D),
SCEVMulExpr::get(G, B),
SCEVMulExpr::get(B, D));
SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep,
F->getLoop());
if (Ops.size() == 2) return NewAddRec;
Ops.erase(Ops.begin()+Idx);
Ops.erase(Ops.begin()+OtherIdx-1);
Ops.push_back(NewAddRec);
return SCEVMulExpr::get(Ops);
}
}
// Otherwise couldn't fold anything into this recurrence. Move onto the
// next one.
}
// Okay, it looks like we really DO need an mul expr. Check to see if we
// already have one, otherwise create a new one.
std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scMulExpr,
SCEVOps)];
if (Result == 0) Result = new SCEVMulExpr(Ops);
return Result;
}
SCEVHandle SCEVUDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) {
if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
if (RHSC->getValue()->equalsInt(1))
return LHS; // X /u 1 --> x
if (RHSC->getValue()->isAllOnesValue())
return getNegativeSCEV(LHS); // X /u -1 --> -x
if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
Constant *LHSCV = LHSC->getValue();
Constant *RHSCV = RHSC->getValue();
if (LHSCV->getType()->isSigned())
LHSCV = ConstantExpr::getCast(LHSCV,
LHSCV->getType()->getUnsignedVersion());
if (RHSCV->getType()->isSigned())
RHSCV = ConstantExpr::getCast(RHSCV, LHSCV->getType());
return SCEVUnknown::get(ConstantExpr::getDiv(LHSCV, RHSCV));
}
}
// FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
SCEVUDivExpr *&Result = SCEVUDivs[std::make_pair(LHS, RHS)];
if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
return Result;
}
/// SCEVAddRecExpr::get - Get a add recurrence expression for the
/// specified loop. Simplify the expression as much as possible.
SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start,
const SCEVHandle &Step, const Loop *L) {
std::vector<SCEVHandle> Operands;
Operands.push_back(Start);
if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
if (StepChrec->getLoop() == L) {
Operands.insert(Operands.end(), StepChrec->op_begin(),
StepChrec->op_end());
return get(Operands, L);
}
Operands.push_back(Step);
return get(Operands, L);
}
/// SCEVAddRecExpr::get - Get a add recurrence expression for the
/// specified loop. Simplify the expression as much as possible.
SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands,
const Loop *L) {
if (Operands.size() == 1) return Operands[0];
if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back()))
if (StepC->getValue()->isNullValue()) {
Operands.pop_back();
return get(Operands, L); // { X,+,0 } --> X
}
SCEVAddRecExpr *&Result =
SCEVAddRecExprs[std::make_pair(L, std::vector<SCEV*>(Operands.begin(),
Operands.end()))];
if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
return Result;
}
SCEVHandle SCEVUnknown::get(Value *V) {
if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
return SCEVConstant::get(CI);
SCEVUnknown *&Result = SCEVUnknowns[V];
if (Result == 0) Result = new SCEVUnknown(V);
return Result;
}
//===----------------------------------------------------------------------===//
// ScalarEvolutionsImpl Definition and Implementation
//===----------------------------------------------------------------------===//
//
/// ScalarEvolutionsImpl - This class implements the main driver for the scalar
/// evolution code.
///
namespace {
struct ScalarEvolutionsImpl {
/// F - The function we are analyzing.
///
Function &F;
/// LI - The loop information for the function we are currently analyzing.
///
LoopInfo &LI;
/// UnknownValue - This SCEV is used to represent unknown trip counts and
/// things.
SCEVHandle UnknownValue;
/// Scalars - This is a cache of the scalars we have analyzed so far.
///
std::map<Value*, SCEVHandle> Scalars;
/// IterationCounts - Cache the iteration count of the loops for this
/// function as they are computed.
std::map<const Loop*, SCEVHandle> IterationCounts;
/// ConstantEvolutionLoopExitValue - This map contains entries for all of
/// the PHI instructions that we attempt to compute constant evolutions for.
/// This allows us to avoid potentially expensive recomputation of these
/// properties. An instruction maps to null if we are unable to compute its
/// exit value.
std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
public:
ScalarEvolutionsImpl(Function &f, LoopInfo &li)
: F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {}
/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
/// expression and create a new one.
SCEVHandle getSCEV(Value *V);
/// getSCEVAtScope - Compute the value of the specified expression within
/// the indicated loop (which may be null to indicate in no loop). If the
/// expression cannot be evaluated, return UnknownValue itself.
SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L);
/// hasLoopInvariantIterationCount - Return true if the specified loop has
/// an analyzable loop-invariant iteration count.
bool hasLoopInvariantIterationCount(const Loop *L);
/// getIterationCount - If the specified loop has a predictable iteration
/// count, return it. Note that it is not valid to call this method on a
/// loop without a loop-invariant iteration count.
SCEVHandle getIterationCount(const Loop *L);
/// deleteInstructionFromRecords - This method should be called by the
/// client before it removes an instruction from the program, to make sure
/// that no dangling references are left around.
void deleteInstructionFromRecords(Instruction *I);
private:
/// createSCEV - We know that there is no SCEV for the specified value.
/// Analyze the expression.
SCEVHandle createSCEV(Value *V);
SCEVHandle createNodeForCast(CastInst *CI);
/// createNodeForPHI - Provide the special handling we need to analyze PHI
/// SCEVs.
SCEVHandle createNodeForPHI(PHINode *PN);
void UpdatePHIUserScalarEntries(Instruction *I, PHINode *PN,
std::set<Instruction*> &UpdatedInsts);
/// ComputeIterationCount - Compute the number of times the specified loop
/// will iterate.
SCEVHandle ComputeIterationCount(const Loop *L);
/// ComputeIterationCountExhaustively - If the trip is known to execute a
/// constant number of times (the condition evolves only from constants),
/// try to evaluate a few iterations of the loop until we get the exit
/// condition gets a value of ExitWhen (true or false). If we cannot
/// evaluate the trip count of the loop, return UnknownValue.
SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond,
bool ExitWhen);
/// HowFarToZero - Return the number of times a backedge comparing the
/// specified value to zero will execute. If not computable, return
/// UnknownValue
SCEVHandle HowFarToZero(SCEV *V, const Loop *L);
/// HowFarToNonZero - Return the number of times a backedge checking the
/// specified value for nonzero will execute. If not computable, return
/// UnknownValue
SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L);
/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
/// in the header of its containing loop, we know the loop executes a
/// constant number of times, and the PHI node is just a recurrence
/// involving constants, fold it.
Constant *getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its,
const Loop *L);
};
}
//===----------------------------------------------------------------------===//
// Basic SCEV Analysis and PHI Idiom Recognition Code
//
/// deleteInstructionFromRecords - This method should be called by the
/// client before it removes an instruction from the program, to make sure
/// that no dangling references are left around.
void ScalarEvolutionsImpl::deleteInstructionFromRecords(Instruction *I) {
Scalars.erase(I);
if (PHINode *PN = dyn_cast<PHINode>(I))
ConstantEvolutionLoopExitValue.erase(PN);
}
/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
/// expression and create a new one.
SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) {
assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!");
std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
if (I != Scalars.end()) return I->second;
SCEVHandle S = createSCEV(V);
Scalars.insert(std::make_pair(V, S));
return S;
}
/// UpdatePHIUserScalarEntries - After PHI node analysis, we have a bunch of
/// entries in the scalar map that refer to the "symbolic" PHI value instead of
/// the recurrence value. After we resolve the PHI we must loop over all of the
/// using instructions that have scalar map entries and update them.
void ScalarEvolutionsImpl::UpdatePHIUserScalarEntries(Instruction *I,
PHINode *PN,
std::set<Instruction*> &UpdatedInsts) {
std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
if (SI == Scalars.end()) return; // This scalar wasn't previous processed.
if (UpdatedInsts.insert(I).second) {
Scalars.erase(SI); // Remove the old entry
getSCEV(I); // Calculate the new entry
for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
UI != E; ++UI)
UpdatePHIUserScalarEntries(cast<Instruction>(*UI), PN, UpdatedInsts);
}
}
/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
/// a loop header, making it a potential recurrence, or it doesn't.
///
SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) {
if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
if (const Loop *L = LI.getLoopFor(PN->getParent()))
if (L->getHeader() == PN->getParent()) {
// If it lives in the loop header, it has two incoming values, one
// from outside the loop, and one from inside.
unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
unsigned BackEdge = IncomingEdge^1;
// While we are analyzing this PHI node, handle its value symbolically.
SCEVHandle SymbolicName = SCEVUnknown::get(PN);
assert(Scalars.find(PN) == Scalars.end() &&
"PHI node already processed?");
Scalars.insert(std::make_pair(PN, SymbolicName));
// Using this symbolic name for the PHI, analyze the value coming around
// the back-edge.
SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
// NOTE: If BEValue is loop invariant, we know that the PHI node just
// has a special value for the first iteration of the loop.
// If the value coming around the backedge is an add with the symbolic
// value we just inserted, then we found a simple induction variable!
if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
// If there is a single occurrence of the symbolic value, replace it
// with a recurrence.
unsigned FoundIndex = Add->getNumOperands();
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
if (Add->getOperand(i) == SymbolicName)
if (FoundIndex == e) {
FoundIndex = i;
break;
}
if (FoundIndex != Add->getNumOperands()) {
// Create an add with everything but the specified operand.
std::vector<SCEVHandle> Ops;
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
if (i != FoundIndex)
Ops.push_back(Add->getOperand(i));
SCEVHandle Accum = SCEVAddExpr::get(Ops);
// This is not a valid addrec if the step amount is varying each
// loop iteration, but is not itself an addrec in this loop.
if (Accum->isLoopInvariant(L) ||
(isa<SCEVAddRecExpr>(Accum) &&
cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L);
// Okay, for the entire analysis of this edge we assumed the PHI
// to be symbolic. We now need to go back and update all of the
// entries for the scalars that use the PHI (except for the PHI
// itself) to use the new analyzed value instead of the "symbolic"
// value.
Scalars.find(PN)->second = PHISCEV; // Update the PHI value
std::set<Instruction*> UpdatedInsts;
UpdatedInsts.insert(PN);
for (Value::use_iterator UI = PN->use_begin(), E = PN->use_end();
UI != E; ++UI)
UpdatePHIUserScalarEntries(cast<Instruction>(*UI), PN,
UpdatedInsts);
return PHISCEV;
}
}
}
return SymbolicName;
}
// If it's not a loop phi, we can't handle it yet.
return SCEVUnknown::get(PN);
}
/// createNodeForCast - Handle the various forms of casts that we support.
///
SCEVHandle ScalarEvolutionsImpl::createNodeForCast(CastInst *CI) {
const Type *SrcTy = CI->getOperand(0)->getType();
const Type *DestTy = CI->getType();
// If this is a noop cast (ie, conversion from int to uint), ignore it.
if (SrcTy->isLosslesslyConvertibleTo(DestTy))
return getSCEV(CI->getOperand(0));
if (SrcTy->isInteger() && DestTy->isInteger()) {
// Otherwise, if this is a truncating integer cast, we can represent this
// cast.
if (SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize())
return SCEVTruncateExpr::get(getSCEV(CI->getOperand(0)),
CI->getType()->getUnsignedVersion());
if (SrcTy->isUnsigned() &&
SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize())
return SCEVZeroExtendExpr::get(getSCEV(CI->getOperand(0)),
CI->getType()->getUnsignedVersion());
}
// If this is an sign or zero extending cast and we can prove that the value
// will never overflow, we could do similar transformations.
// Otherwise, we can't handle this cast!
return SCEVUnknown::get(CI);
}
/// createSCEV - We know that there is no SCEV for the specified value.
/// Analyze the expression.
///
SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) {
if (Instruction *I = dyn_cast<Instruction>(V)) {
switch (I->getOpcode()) {
case Instruction::Add:
return SCEVAddExpr::get(getSCEV(I->getOperand(0)),
getSCEV(I->getOperand(1)));
case Instruction::Mul:
return SCEVMulExpr::get(getSCEV(I->getOperand(0)),
getSCEV(I->getOperand(1)));
case Instruction::Div:
if (V->getType()->isInteger() && V->getType()->isUnsigned())
return SCEVUDivExpr::get(getSCEV(I->getOperand(0)),
getSCEV(I->getOperand(1)));
break;
case Instruction::Sub:
return getMinusSCEV(getSCEV(I->getOperand(0)), getSCEV(I->getOperand(1)));
case Instruction::Shl:
// Turn shift left of a constant amount into a multiply.
if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) {
Constant *X = ConstantInt::get(V->getType(), 1);
X = ConstantExpr::getShl(X, SA);
return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X));
}
break;
case Instruction::Shr:
if (ConstantUInt *SA = dyn_cast<ConstantUInt>(I->getOperand(1)))
if (V->getType()->isUnsigned()) {
Constant *X = ConstantInt::get(V->getType(), 1);
X = ConstantExpr::getShl(X, SA);
return SCEVUDivExpr::get(getSCEV(I->getOperand(0)), getSCEV(X));
}
break;
case Instruction::Cast:
return createNodeForCast(cast<CastInst>(I));
case Instruction::PHI:
return createNodeForPHI(cast<PHINode>(I));
default: // We cannot analyze this expression.
break;
}
}
return SCEVUnknown::get(V);
}
//===----------------------------------------------------------------------===//
// Iteration Count Computation Code
//
/// getIterationCount - If the specified loop has a predictable iteration
/// count, return it. Note that it is not valid to call this method on a
/// loop without a loop-invariant iteration count.
SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) {
std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L);
if (I == IterationCounts.end()) {
SCEVHandle ItCount = ComputeIterationCount(L);
I = IterationCounts.insert(std::make_pair(L, ItCount)).first;
if (ItCount != UnknownValue) {
assert(ItCount->isLoopInvariant(L) &&
"Computed trip count isn't loop invariant for loop!");
++NumTripCountsComputed;
} else if (isa<PHINode>(L->getHeader()->begin())) {
// Only count loops that have phi nodes as not being computable.
++NumTripCountsNotComputed;
}
}
return I->second;
}
/// ComputeIterationCount - Compute the number of times the specified loop
/// will iterate.
SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) {
// If the loop has a non-one exit block count, we can't analyze it.
std::vector<BasicBlock*> ExitBlocks;
L->getExitBlocks(ExitBlocks);
if (ExitBlocks.size() != 1) return UnknownValue;
// Okay, there is one exit block. Try to find the condition that causes the
// loop to be exited.
BasicBlock *ExitBlock = ExitBlocks[0];
BasicBlock *ExitingBlock = 0;
for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
PI != E; ++PI)
if (L->contains(*PI)) {
if (ExitingBlock == 0)
ExitingBlock = *PI;
else
return UnknownValue; // More than one block exiting!
}
assert(ExitingBlock && "No exits from loop, something is broken!");
// Okay, we've computed the exiting block. See what condition causes us to
// exit.
//
// FIXME: we should be able to handle switch instructions (with a single exit)
// FIXME: We should handle cast of int to bool as well
BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
if (ExitBr == 0) return UnknownValue;
assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
SetCondInst *ExitCond = dyn_cast<SetCondInst>(ExitBr->getCondition());
if (ExitCond == 0) // Not a setcc
return ComputeIterationCountExhaustively(L, ExitBr->getCondition(),
ExitBr->getSuccessor(0) == ExitBlock);
SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
// Try to evaluate any dependencies out of the loop.
SCEVHandle Tmp = getSCEVAtScope(LHS, L);
if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
Tmp = getSCEVAtScope(RHS, L);
if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
// If the condition was exit on true, convert the condition to exit on false.
Instruction::BinaryOps Cond;
if (ExitBr->getSuccessor(1) == ExitBlock)
Cond = ExitCond->getOpcode();
else
Cond = ExitCond->getInverseCondition();
// At this point, we would like to compute how many iterations of the loop the
// predicate will return true for these inputs.
if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) {
// If there is a constant, force it into the RHS.
std::swap(LHS, RHS);
Cond = SetCondInst::getSwappedCondition(Cond);
}
// FIXME: think about handling pointer comparisons! i.e.:
// while (P != P+100) ++P;
// If we have a comparison of a chrec against a constant, try to use value
// ranges to answer this query.
if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
if (AddRec->getLoop() == L) {
// Form the comparison range using the constant of the correct type so
// that the ConstantRange class knows to do a signed or unsigned
// comparison.
ConstantInt *CompVal = RHSC->getValue();
const Type *RealTy = ExitCond->getOperand(0)->getType();
CompVal = dyn_cast<ConstantInt>(ConstantExpr::getCast(CompVal, RealTy));
if (CompVal) {
// Form the constant range.
ConstantRange CompRange(Cond, CompVal);
// Now that we have it, if it's signed, convert it to an unsigned
// range.
if (CompRange.getLower()->getType()->isSigned()) {
const Type *NewTy = RHSC->getValue()->getType();
Constant *NewL = ConstantExpr::getCast(CompRange.getLower(), NewTy);
Constant *NewU = ConstantExpr::getCast(CompRange.getUpper(), NewTy);
CompRange = ConstantRange(NewL, NewU);
}
SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange);
if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
}
}
switch (Cond) {
case Instruction::SetNE: // while (X != Y)
// Convert to: while (X-Y != 0)
if (LHS->getType()->isInteger()) {
SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
if (!isa<SCEVCouldNotCompute>(TC)) return TC;
}
break;
case Instruction::SetEQ:
// Convert to: while (X-Y == 0) // while (X == Y)
if (LHS->getType()->isInteger()) {
SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
if (!isa<SCEVCouldNotCompute>(TC)) return TC;
}
break;
default:
#if 0
std::cerr << "ComputeIterationCount ";
if (ExitCond->getOperand(0)->getType()->isUnsigned())
std::cerr << "[unsigned] ";
std::cerr << *LHS << " "
<< Instruction::getOpcodeName(Cond) << " " << *RHS << "\n";
#endif
break;
}
return ComputeIterationCountExhaustively(L, ExitCond,
ExitBr->getSuccessor(0) == ExitBlock);
}
/// CanConstantFold - Return true if we can constant fold an instruction of the
/// specified type, assuming that all operands were constants.
static bool CanConstantFold(const Instruction *I) {
if (isa<BinaryOperator>(I) || isa<ShiftInst>(I) ||
isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
return true;
if (const CallInst *CI = dyn_cast<CallInst>(I))
if (const Function *F = CI->getCalledFunction())
return canConstantFoldCallTo((Function*)F); // FIXME: elim cast
return false;
}
/// ConstantFold - Constant fold an instruction of the specified type with the
/// specified constant operands. This function may modify the operands vector.
static Constant *ConstantFold(const Instruction *I,
std::vector<Constant*> &Operands) {
if (isa<BinaryOperator>(I) || isa<ShiftInst>(I))
return ConstantExpr::get(I->getOpcode(), Operands[0], Operands[1]);
switch (I->getOpcode()) {
case Instruction::Cast:
return ConstantExpr::getCast(Operands[0], I->getType());
case Instruction::Select:
return ConstantExpr::getSelect(Operands[0], Operands[1], Operands[2]);
case Instruction::Call:
if (ConstantPointerRef *CPR = dyn_cast<ConstantPointerRef>(Operands[0])) {
Operands.erase(Operands.begin());
return ConstantFoldCall(cast<Function>(CPR->getValue()), Operands);
}
return 0;
case Instruction::GetElementPtr:
Constant *Base = Operands[0];
Operands.erase(Operands.begin());
return ConstantExpr::getGetElementPtr(Base, Operands);
}
return 0;
}
/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
/// in the loop that V is derived from. We allow arbitrary operations along the
/// way, but the operands of an operation must either be constants or a value
/// derived from a constant PHI. If this expression does not fit with these
/// constraints, return null.
static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
// If this is not an instruction, or if this is an instruction outside of the
// loop, it can't be derived from a loop PHI.
Instruction *I = dyn_cast<Instruction>(V);
if (I == 0 || !L->contains(I->getParent())) return 0;
if (PHINode *PN = dyn_cast<PHINode>(I))
if (L->getHeader() == I->getParent())
return PN;
else
// We don't currently keep track of the control flow needed to evaluate
// PHIs, so we cannot handle PHIs inside of loops.
return 0;
// If we won't be able to constant fold this expression even if the operands
// are constants, return early.
if (!CanConstantFold(I)) return 0;
// Otherwise, we can evaluate this instruction if all of its operands are
// constant or derived from a PHI node themselves.
PHINode *PHI = 0;
for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
if (!(isa<Constant>(I->getOperand(Op)) ||
isa<GlobalValue>(I->getOperand(Op)))) {
PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
if (P == 0) return 0; // Not evolving from PHI
if (PHI == 0)
PHI = P;
else if (PHI != P)
return 0; // Evolving from multiple different PHIs.
}
// This is a expression evolving from a constant PHI!
return PHI;
}
/// EvaluateExpression - Given an expression that passes the
/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
/// in the loop has the value PHIVal. If we can't fold this expression for some
/// reason, return null.
static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
if (isa<PHINode>(V)) return PHIVal;
if (Constant *C = dyn_cast<Constant>(V)) return C;
if (GlobalValue *GV = dyn_cast<GlobalValue>(V))
return ConstantPointerRef::get(GV);
Instruction *I = cast<Instruction>(V);
std::vector<Constant*> Operands;
Operands.resize(I->getNumOperands());
for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
if (Operands[i] == 0) return 0;
}
return ConstantFold(I, Operands);
}
/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
/// in the header of its containing loop, we know the loop executes a
/// constant number of times, and the PHI node is just a recurrence
/// involving constants, fold it.
Constant *ScalarEvolutionsImpl::
getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, const Loop *L) {
std::map<PHINode*, Constant*>::iterator I =
ConstantEvolutionLoopExitValue.find(PN);
if (I != ConstantEvolutionLoopExitValue.end())
return I->second;
if (Its > MaxBruteForceIterations)
return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
// Since the loop is canonicalized, the PHI node must have two entries. One
// entry must be a constant (coming in from outside of the loop), and the
// second must be derived from the same PHI.
bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
Constant *StartCST =
dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
if (StartCST == 0)
return RetVal = 0; // Must be a constant.
Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
if (PN2 != PN)
return RetVal = 0; // Not derived from same PHI.
// Execute the loop symbolically to determine the exit value.
unsigned IterationNum = 0;
unsigned NumIterations = Its;
if (NumIterations != Its)
return RetVal = 0; // More than 2^32 iterations??
for (Constant *PHIVal = StartCST; ; ++IterationNum) {
if (IterationNum == NumIterations)
return RetVal = PHIVal; // Got exit value!
// Compute the value of the PHI node for the next iteration.
Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
if (NextPHI == PHIVal)
return RetVal = NextPHI; // Stopped evolving!
if (NextPHI == 0)
return 0; // Couldn't evaluate!
PHIVal = NextPHI;
}
}
/// ComputeIterationCountExhaustively - If the trip is known to execute a
/// constant number of times (the condition evolves only from constants),
/// try to evaluate a few iterations of the loop until we get the exit
/// condition gets a value of ExitWhen (true or false). If we cannot
/// evaluate the trip count of the loop, return UnknownValue.
SCEVHandle ScalarEvolutionsImpl::
ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
PHINode *PN = getConstantEvolvingPHI(Cond, L);
if (PN == 0) return UnknownValue;
// Since the loop is canonicalized, the PHI node must have two entries. One
// entry must be a constant (coming in from outside of the loop), and the
// second must be derived from the same PHI.
bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
Constant *StartCST =
dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
if (StartCST == 0) return UnknownValue; // Must be a constant.
Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
// Okay, we find a PHI node that defines the trip count of this loop. Execute
// the loop symbolically to determine when the condition gets a value of
// "ExitWhen".
unsigned IterationNum = 0;
unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
for (Constant *PHIVal = StartCST;
IterationNum != MaxIterations; ++IterationNum) {
ConstantBool *CondVal =
dyn_cast_or_null<ConstantBool>(EvaluateExpression(Cond, PHIVal));
if (!CondVal) return UnknownValue; // Couldn't symbolically evaluate.
if (CondVal->getValue() == ExitWhen) {
ConstantEvolutionLoopExitValue[PN] = PHIVal;
++NumBruteForceTripCountsComputed;
return SCEVConstant::get(ConstantUInt::get(Type::UIntTy, IterationNum));
}
// Compute the value of the PHI node for the next iteration.
Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
if (NextPHI == 0 || NextPHI == PHIVal)
return UnknownValue; // Couldn't evaluate or not making progress...
PHIVal = NextPHI;
}
// Too many iterations were needed to evaluate.
return UnknownValue;
}
/// getSCEVAtScope - Compute the value of the specified expression within the
/// indicated loop (which may be null to indicate in no loop). If the
/// expression cannot be evaluated, return UnknownValue.
SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) {
// FIXME: this should be turned into a virtual method on SCEV!
if (isa<SCEVConstant>(V)) return V;
// If this instruction is evolves from a constant-evolving PHI, compute the
// exit value from the loop without using SCEVs.
if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
const Loop *LI = this->LI[I->getParent()];
if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
if (PHINode *PN = dyn_cast<PHINode>(I))
if (PN->getParent() == LI->getHeader()) {
// Okay, there is no closed form solution for the PHI node. Check
// to see if the loop that contains it has a known iteration count.
// If so, we may be able to force computation of the exit value.
SCEVHandle IterationCount = getIterationCount(LI);
if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) {
// Okay, we know how many times the containing loop executes. If
// this is a constant evolving PHI node, get the final value at
// the specified iteration number.
Constant *RV = getConstantEvolutionLoopExitValue(PN,
ICC->getValue()->getRawValue(),
LI);
if (RV) return SCEVUnknown::get(RV);
}
}
// Okay, this is a some expression that we cannot symbolically evaluate
// into a SCEV. Check to see if it's possible to symbolically evaluate
// the arguments into constants, and if see, try to constant propagate the
// result. This is particularly useful for computing loop exit values.
if (CanConstantFold(I)) {
std::vector<Constant*> Operands;
Operands.reserve(I->getNumOperands());
for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
Value *Op = I->getOperand(i);
if (Constant *C = dyn_cast<Constant>(Op)) {
Operands.push_back(C);
} else if (GlobalValue *GV = dyn_cast<GlobalValue>(Op)) {
Operands.push_back(ConstantPointerRef::get(GV));
} else {
SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
Operands.push_back(ConstantExpr::getCast(SC->getValue(),
Op->getType()));
else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
if (Constant *C = dyn_cast<Constant>(SU->getValue()))
Operands.push_back(ConstantExpr::getCast(C, Op->getType()));
else
return V;
} else {
return V;
}
}
}
return SCEVUnknown::get(ConstantFold(I, Operands));
}
}
// This is some other type of SCEVUnknown, just return it.
return V;
}
if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
// Avoid performing the look-up in the common case where the specified
// expression has no loop-variant portions.
for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
if (OpAtScope != Comm->getOperand(i)) {
if (OpAtScope == UnknownValue) return UnknownValue;
// Okay, at least one of these operands is loop variant but might be
// foldable. Build a new instance of the folded commutative expression.
std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
NewOps.push_back(OpAtScope);
for (++i; i != e; ++i) {
OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
if (OpAtScope == UnknownValue) return UnknownValue;
NewOps.push_back(OpAtScope);
}
if (isa<SCEVAddExpr>(Comm))
return SCEVAddExpr::get(NewOps);
assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!");
return SCEVMulExpr::get(NewOps);
}
}
// If we got here, all operands are loop invariant.
return Comm;
}
if (SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(V)) {
SCEVHandle LHS = getSCEVAtScope(UDiv->getLHS(), L);
if (LHS == UnknownValue) return LHS;
SCEVHandle RHS = getSCEVAtScope(UDiv->getRHS(), L);
if (RHS == UnknownValue) return RHS;
if (LHS == UDiv->getLHS() && RHS == UDiv->getRHS())
return UDiv; // must be loop invariant
return SCEVUDivExpr::get(LHS, RHS);
}
// If this is a loop recurrence for a loop that does not contain L, then we
// are dealing with the final value computed by the loop.
if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
// To evaluate this recurrence, we need to know how many times the AddRec
// loop iterates. Compute this now.
SCEVHandle IterationCount = getIterationCount(AddRec->getLoop());
if (IterationCount == UnknownValue) return UnknownValue;
IterationCount = getTruncateOrZeroExtend(IterationCount,
AddRec->getType());
// If the value is affine, simplify the expression evaluation to just
// Start + Step*IterationCount.
if (AddRec->isAffine())
return SCEVAddExpr::get(AddRec->getStart(),
SCEVMulExpr::get(IterationCount,
AddRec->getOperand(1)));
// Otherwise, evaluate it the hard way.
return AddRec->evaluateAtIteration(IterationCount);
}
return UnknownValue;
}
//assert(0 && "Unknown SCEV type!");
return UnknownValue;
}
/// SolveQuadraticEquation - Find the roots of the quadratic equation for the
/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
/// might be the same) or two SCEVCouldNotCompute objects.
///
static std::pair<SCEVHandle,SCEVHandle>
SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) {
assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
SCEVConstant *L = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
SCEVConstant *M = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
SCEVConstant *N = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
// We currently can only solve this if the coefficients are constants.
if (!L || !M || !N) {
SCEV *CNC = new SCEVCouldNotCompute();
return std::make_pair(CNC, CNC);
}
Constant *Two = ConstantInt::get(L->getValue()->getType(), 2);
// Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
Constant *C = L->getValue();
// The B coefficient is M-N/2
Constant *B = ConstantExpr::getSub(M->getValue(),
ConstantExpr::getDiv(N->getValue(),
Two));
// The A coefficient is N/2
Constant *A = ConstantExpr::getDiv(N->getValue(), Two);
// Compute the B^2-4ac term.
Constant *SqrtTerm =
ConstantExpr::getMul(ConstantInt::get(C->getType(), 4),
ConstantExpr::getMul(A, C));
SqrtTerm = ConstantExpr::getSub(ConstantExpr::getMul(B, B), SqrtTerm);
// Compute floor(sqrt(B^2-4ac))
ConstantUInt *SqrtVal =
cast<ConstantUInt>(ConstantExpr::getCast(SqrtTerm,
SqrtTerm->getType()->getUnsignedVersion()));
uint64_t SqrtValV = SqrtVal->getValue();
uint64_t SqrtValV2 = (uint64_t)sqrt(SqrtValV);
// The square root might not be precise for arbitrary 64-bit integer
// values. Do some sanity checks to ensure it's correct.
if (SqrtValV2*SqrtValV2 > SqrtValV ||
(SqrtValV2+1)*(SqrtValV2+1) <= SqrtValV) {
SCEV *CNC = new SCEVCouldNotCompute();
return std::make_pair(CNC, CNC);
}
SqrtVal = ConstantUInt::get(Type::ULongTy, SqrtValV2);
SqrtTerm = ConstantExpr::getCast(SqrtVal, SqrtTerm->getType());
Constant *NegB = ConstantExpr::getNeg(B);
Constant *TwoA = ConstantExpr::getMul(A, Two);
// The divisions must be performed as signed divisions.
const Type *SignedTy = NegB->getType()->getSignedVersion();
NegB = ConstantExpr::getCast(NegB, SignedTy);
TwoA = ConstantExpr::getCast(TwoA, SignedTy);
SqrtTerm = ConstantExpr::getCast(SqrtTerm, SignedTy);
Constant *Solution1 =
ConstantExpr::getDiv(ConstantExpr::getAdd(NegB, SqrtTerm), TwoA);
Constant *Solution2 =
ConstantExpr::getDiv(ConstantExpr::getSub(NegB, SqrtTerm), TwoA);
return std::make_pair(SCEVUnknown::get(Solution1),
SCEVUnknown::get(Solution2));
}
/// HowFarToZero - Return the number of times a backedge comparing the specified
/// value to zero will execute. If not computable, return UnknownValue
SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) {
// If the value is a constant
if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
// If the value is already zero, the branch will execute zero times.
if (C->getValue()->isNullValue()) return C;
return UnknownValue; // Otherwise it will loop infinitely.
}
SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
if (!AddRec || AddRec->getLoop() != L)
return UnknownValue;
if (AddRec->isAffine()) {
// If this is an affine expression the execution count of this branch is
// equal to:
//
// (0 - Start/Step) iff Start % Step == 0
//
// Get the initial value for the loop.
SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
SCEVHandle Step = AddRec->getOperand(1);
Step = getSCEVAtScope(Step, L->getParentLoop());
// Figure out if Start % Step == 0.
// FIXME: We should add DivExpr and RemExpr operations to our AST.
if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
if (StepC->getValue()->equalsInt(1)) // N % 1 == 0
return getNegativeSCEV(Start); // 0 - Start/1 == -Start
if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0
return Start; // 0 - Start/-1 == Start
// Check to see if Start is divisible by SC with no remainder.
if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
ConstantInt *StartCC = StartC->getValue();
Constant *StartNegC = ConstantExpr::getNeg(StartCC);
Constant *Rem = ConstantExpr::getRem(StartNegC, StepC->getValue());
if (Rem->isNullValue()) {
Constant *Result =ConstantExpr::getDiv(StartNegC,StepC->getValue());
return SCEVUnknown::get(Result);
}
}
}
} else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
// If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
// the quadratic equation to solve it.
std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec);
SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
if (R1) {
#if 0
std::cerr << "HFTZ: " << *V << " - sol#1: " << *R1
<< " sol#2: " << *R2 << "\n";
#endif
// Pick the smallest positive root value.
assert(R1->getType()->isUnsigned()&&"Didn't canonicalize to unsigned?");
if (ConstantBool *CB =
dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(),
R2->getValue()))) {
if (CB != ConstantBool::True)
std::swap(R1, R2); // R1 is the minimum root now.
// We can only use this value if the chrec ends up with an exact zero
// value at this index. When solving for "X*X != 5", for example, we
// should not accept a root of 2.
SCEVHandle Val = AddRec->evaluateAtIteration(R1);
if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val))
if (EvalVal->getValue()->isNullValue())
return R1; // We found a quadratic root!
}
}
}
return UnknownValue;
}
/// HowFarToNonZero - Return the number of times a backedge checking the
/// specified value for nonzero will execute. If not computable, return
/// UnknownValue
SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) {
// Loops that look like: while (X == 0) are very strange indeed. We don't
// handle them yet except for the trivial case. This could be expanded in the
// future as needed.
// If the value is a constant, check to see if it is known to be non-zero
// already. If so, the backedge will execute zero times.
if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
Constant *Zero = Constant::getNullValue(C->getValue()->getType());
Constant *NonZero = ConstantExpr::getSetNE(C->getValue(), Zero);
if (NonZero == ConstantBool::True)
return getSCEV(Zero);
return UnknownValue; // Otherwise it will loop infinitely.
}
// We could implement others, but I really doubt anyone writes loops like
// this, and if they did, they would already be constant folded.
return UnknownValue;
}
static ConstantInt *
EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) {
SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C));
SCEVHandle Val = AddRec->evaluateAtIteration(InVal);
assert(isa<SCEVConstant>(Val) &&
"Evaluation of SCEV at constant didn't fold correctly?");
return cast<SCEVConstant>(Val)->getValue();
}
/// getNumIterationsInRange - Return the number of iterations of this loop that
/// produce values in the specified constant range. Another way of looking at
/// this is that it returns the first iteration number where the value is not in
/// the condition, thus computing the exit count. If the iteration count can't
/// be computed, an instance of SCEVCouldNotCompute is returned.
SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range) const {
if (Range.isFullSet()) // Infinite loop.
return new SCEVCouldNotCompute();
// If the start is a non-zero constant, shift the range to simplify things.
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
if (!SC->getValue()->isNullValue()) {
std::vector<SCEVHandle> Operands(op_begin(), op_end());
Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType());
SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop());
if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
return ShiftedAddRec->getNumIterationsInRange(
Range.subtract(SC->getValue()));
// This is strange and shouldn't happen.
return new SCEVCouldNotCompute();
}
// The only time we can solve this is when we have all constant indices.
// Otherwise, we cannot determine the overflow conditions.
for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
if (!isa<SCEVConstant>(getOperand(i)))
return new SCEVCouldNotCompute();
// Okay at this point we know that all elements of the chrec are constants and
// that the start element is zero.
// First check to see if the range contains zero. If not, the first
// iteration exits.
ConstantInt *Zero = ConstantInt::get(getType(), 0);
if (!Range.contains(Zero)) return SCEVConstant::get(Zero);
if (isAffine()) {
// If this is an affine expression then we have this situation:
// Solve {0,+,A} in Range === Ax in Range
// Since we know that zero is in the range, we know that the upper value of
// the range must be the first possible exit value. Also note that we
// already checked for a full range.
ConstantInt *Upper = cast<ConstantInt>(Range.getUpper());
ConstantInt *A = cast<SCEVConstant>(getOperand(1))->getValue();
ConstantInt *One = ConstantInt::get(getType(), 1);
// The exit value should be (Upper+A-1)/A.
Constant *ExitValue = Upper;
if (A != One) {
ExitValue = ConstantExpr::getSub(ConstantExpr::getAdd(Upper, A), One);
ExitValue = ConstantExpr::getDiv(ExitValue, A);
}
assert(isa<ConstantInt>(ExitValue) &&
"Constant folding of integers not implemented?");
// Evaluate at the exit value. If we really did fall out of the valid
// range, then we computed our trip count, otherwise wrap around or other
// things must have happened.
ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue);
if (Range.contains(Val))
return new SCEVCouldNotCompute(); // Something strange happened
// Ensure that the previous value is in the range. This is a sanity check.
assert(Range.contains(EvaluateConstantChrecAtConstant(this,
ConstantExpr::getSub(ExitValue, One))) &&
"Linear scev computation is off in a bad way!");
return SCEVConstant::get(cast<ConstantInt>(ExitValue));
} else if (isQuadratic()) {
// If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
// quadratic equation to solve it. To do this, we must frame our problem in
// terms of figuring out when zero is crossed, instead of when
// Range.getUpper() is crossed.
std::vector<SCEVHandle> NewOps(op_begin(), op_end());
NewOps[0] = getNegativeSCEV(SCEVUnknown::get(Range.getUpper()));
SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop());
// Next, solve the constructed addrec
std::pair<SCEVHandle,SCEVHandle> Roots =
SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec));
SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
if (R1) {
// Pick the smallest positive root value.
assert(R1->getType()->isUnsigned() && "Didn't canonicalize to unsigned?");
if (ConstantBool *CB =
dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(),
R2->getValue()))) {
if (CB != ConstantBool::True)
std::swap(R1, R2); // R1 is the minimum root now.
// Make sure the root is not off by one. The returned iteration should
// not be in the range, but the previous one should be. When solving
// for "X*X < 5", for example, we should not return a root of 2.
ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
R1->getValue());
if (Range.contains(R1Val)) {
// The next iteration must be out of the range...
Constant *NextVal =
ConstantExpr::getAdd(R1->getValue(),
ConstantInt::get(R1->getType(), 1));
R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
if (!Range.contains(R1Val))
return SCEVUnknown::get(NextVal);
return new SCEVCouldNotCompute(); // Something strange happened
}
// If R1 was not in the range, then it is a good return value. Make
// sure that R1-1 WAS in the range though, just in case.
Constant *NextVal =
ConstantExpr::getSub(R1->getValue(),
ConstantInt::get(R1->getType(), 1));
R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
if (Range.contains(R1Val))
return R1;
return new SCEVCouldNotCompute(); // Something strange happened
}
}
}
// Fallback, if this is a general polynomial, figure out the progression
// through brute force: evaluate until we find an iteration that fails the
// test. This is likely to be slow, but getting an accurate trip count is
// incredibly important, we will be able to simplify the exit test a lot, and
// we are almost guaranteed to get a trip count in this case.
ConstantInt *TestVal = ConstantInt::get(getType(), 0);
ConstantInt *One = ConstantInt::get(getType(), 1);
ConstantInt *EndVal = TestVal; // Stop when we wrap around.
do {
++NumBruteForceEvaluations;
SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal));
if (!isa<SCEVConstant>(Val)) // This shouldn't happen.
return new SCEVCouldNotCompute();
// Check to see if we found the value!
if (!Range.contains(cast<SCEVConstant>(Val)->getValue()))
return SCEVConstant::get(TestVal);
// Increment to test the next index.
TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One));
} while (TestVal != EndVal);
return new SCEVCouldNotCompute();
}
//===----------------------------------------------------------------------===//
// ScalarEvolution Class Implementation
//===----------------------------------------------------------------------===//
bool ScalarEvolution::runOnFunction(Function &F) {
Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>());
return false;
}
void ScalarEvolution::releaseMemory() {
delete (ScalarEvolutionsImpl*)Impl;
Impl = 0;
}
void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
AU.setPreservesAll();
AU.addRequiredID(LoopSimplifyID);
AU.addRequiredTransitive<LoopInfo>();
}
SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
}
SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const {
return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L);
}
bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const {
return !isa<SCEVCouldNotCompute>(getIterationCount(L));
}
SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const {
return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L);
}
void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const {
return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I);
}
/// shouldSubstituteIndVar - Return true if we should perform induction variable
/// substitution for this variable. This is a hack because we don't have a
/// strength reduction pass yet. When we do we will promote all vars, because
/// we can strength reduce them later as desired.
bool ScalarEvolution::shouldSubstituteIndVar(const SCEV *S) const {
// Don't substitute high degree polynomials.
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S))
if (AddRec->getNumOperands() > 3) return false;
return true;
}
static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE,
const Loop *L) {
// Print all inner loops first
for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
PrintLoopInfo(OS, SE, *I);
std::cerr << "Loop " << L->getHeader()->getName() << ": ";
std::vector<BasicBlock*> ExitBlocks;
L->getExitBlocks(ExitBlocks);
if (ExitBlocks.size() != 1)
std::cerr << "<multiple exits> ";
if (SE->hasLoopInvariantIterationCount(L)) {
std::cerr << *SE->getIterationCount(L) << " iterations! ";
} else {
std::cerr << "Unpredictable iteration count. ";
}
std::cerr << "\n";
}
void ScalarEvolution::print(std::ostream &OS) const {
Function &F = ((ScalarEvolutionsImpl*)Impl)->F;
LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI;
OS << "Classifying expressions for: " << F.getName() << "\n";
for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
if (I->getType()->isInteger()) {
OS << *I;
OS << " --> ";
SCEVHandle SV = getSCEV(&*I);
SV->print(OS);
OS << "\t\t";
if ((*I).getType()->isIntegral()) {
ConstantRange Bounds = SV->getValueRange();
if (!Bounds.isFullSet())
OS << "Bounds: " << Bounds << " ";
}
if (const Loop *L = LI.getLoopFor((*I).getParent())) {
OS << "Exits: ";
SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop());
if (isa<SCEVCouldNotCompute>(ExitValue)) {
OS << "<<Unknown>>";
} else {
OS << *ExitValue;
}
}
OS << "\n";
}
OS << "Determining loop execution counts for: " << F.getName() << "\n";
for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
PrintLoopInfo(OS, this, *I);
}