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llvm-6502/lib/Analysis/ScalarEvolution.cpp
Dan Gohman f7b37b2d0e In the special case, call the comparison function instead of 
manually performing the comparison. This allows the special
case to work correctly even in the case where someone is
experimenting with a different comparison function :-).


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2008-04-14 18:23:56 +00:00

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//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
//
// The LLVM Compiler Infrastructure
//
// This file 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
//
//===----------------------------------------------------------------------===//
#define DEBUG_TYPE "scalar-evolution"
#include "llvm/Analysis/ScalarEvolutionExpressions.h"
#include "llvm/Constants.h"
#include "llvm/DerivedTypes.h"
#include "llvm/GlobalVariable.h"
#include "llvm/Instructions.h"
#include "llvm/Analysis/ConstantFolding.h"
#include "llvm/Analysis/LoopInfo.h"
#include "llvm/Assembly/Writer.h"
#include "llvm/Transforms/Scalar.h"
#include "llvm/Support/CFG.h"
#include "llvm/Support/CommandLine.h"
#include "llvm/Support/Compiler.h"
#include "llvm/Support/ConstantRange.h"
#include "llvm/Support/InstIterator.h"
#include "llvm/Support/ManagedStatic.h"
#include "llvm/Support/MathExtras.h"
#include "llvm/Support/Streams.h"
#include "llvm/ADT/Statistic.h"
#include <ostream>
#include <algorithm>
#include <cmath>
using namespace llvm;
STATISTIC(NumBruteForceEvaluations,
"Number of brute force evaluations needed to "
"calculate high-order polynomial exit values");
STATISTIC(NumArrayLenItCounts,
"Number of trip counts computed with array length");
STATISTIC(NumTripCountsComputed,
"Number of loops with predictable loop counts");
STATISTIC(NumTripCountsNotComputed,
"Number of loops without predictable loop counts");
STATISTIC(NumBruteForceTripCountsComputed,
"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));
namespace {
RegisterPass<ScalarEvolution>
R("scalar-evolution", "Scalar Evolution Analysis", false, true);
}
char ScalarEvolution::ID = 0;
//===----------------------------------------------------------------------===//
// SCEV class definitions
//===----------------------------------------------------------------------===//
//===----------------------------------------------------------------------===//
// Implementation of the SCEV class.
//
SCEV::~SCEV() {}
void SCEV::dump() const {
print(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!");
// Default to a full range if no better information is available.
return ConstantRange(getBitWidth());
}
uint32_t SCEV::getBitWidth() const {
if (const IntegerType* ITy = dyn_cast<IntegerType>(getType()))
return ITy->getBitWidth();
return 0;
}
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;
}
SCEVHandle SCEVCouldNotCompute::
replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
const SCEVHandle &Conc,
ScalarEvolution &SE) const {
return this;
}
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 ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
SCEVConstant::~SCEVConstant() {
SCEVConstants->erase(V);
}
SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) {
SCEVConstant *&R = (*SCEVConstants)[V];
if (R == 0) R = new SCEVConstant(V);
return R;
}
SCEVHandle ScalarEvolution::getConstant(const APInt& Val) {
return getConstant(ConstantInt::get(Val));
}
ConstantRange SCEVConstant::getValueRange() const {
return ConstantRange(V->getValue());
}
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 ManagedStatic<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() &&
"Cannot truncate non-integer value!");
assert(Op->getType()->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()
&& "This is not a truncating conversion!");
}
SCEVTruncateExpr::~SCEVTruncateExpr() {
SCEVTruncates->erase(std::make_pair(Op, Ty));
}
ConstantRange SCEVTruncateExpr::getValueRange() const {
return getOperand()->getValueRange().truncate(getBitWidth());
}
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 ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
SCEVZeroExtendExpr*> > SCEVZeroExtends;
SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
: SCEV(scZeroExtend), Op(op), Ty(ty) {
assert(Op->getType()->isInteger() && Ty->isInteger() &&
"Cannot zero extend non-integer value!");
assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits()
&& "This is not an extending conversion!");
}
SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
SCEVZeroExtends->erase(std::make_pair(Op, Ty));
}
ConstantRange SCEVZeroExtendExpr::getValueRange() const {
return getOperand()->getValueRange().zeroExtend(getBitWidth());
}
void SCEVZeroExtendExpr::print(std::ostream &OS) const {
OS << "(zeroextend " << *Op << " to " << *Ty << ")";
}
// SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
// particular input. Don't use a SCEVHandle here, or else the object will never
// be deleted!
static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
SCEVSignExtendExpr*> > SCEVSignExtends;
SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
: SCEV(scSignExtend), Op(op), Ty(ty) {
assert(Op->getType()->isInteger() && Ty->isInteger() &&
"Cannot sign extend non-integer value!");
assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits()
&& "This is not an extending conversion!");
}
SCEVSignExtendExpr::~SCEVSignExtendExpr() {
SCEVSignExtends->erase(std::make_pair(Op, Ty));
}
ConstantRange SCEVSignExtendExpr::getValueRange() const {
return getOperand()->getValueRange().signExtend(getBitWidth());
}
void SCEVSignExtendExpr::print(std::ostream &OS) const {
OS << "(signextend " << *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 ManagedStatic<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 << ")";
}
SCEVHandle SCEVCommutativeExpr::
replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
const SCEVHandle &Conc,
ScalarEvolution &SE) const {
for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
SCEVHandle H =
getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
if (H != getOperand(i)) {
std::vector<SCEVHandle> NewOps;
NewOps.reserve(getNumOperands());
for (unsigned j = 0; j != i; ++j)
NewOps.push_back(getOperand(j));
NewOps.push_back(H);
for (++i; i != e; ++i)
NewOps.push_back(getOperand(i)->
replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
if (isa<SCEVAddExpr>(this))
return SE.getAddExpr(NewOps);
else if (isa<SCEVMulExpr>(this))
return SE.getMulExpr(NewOps);
else if (isa<SCEVSMaxExpr>(this))
return SE.getSMaxExpr(NewOps);
else if (isa<SCEVUMaxExpr>(this))
return SE.getUMaxExpr(NewOps);
else
assert(0 && "Unknown commutative expr!");
}
}
return this;
}
// 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 ManagedStatic<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 {
return LHS->getType();
}
// 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 ManagedStatic<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())));
}
SCEVHandle SCEVAddRecExpr::
replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
const SCEVHandle &Conc,
ScalarEvolution &SE) const {
for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
SCEVHandle H =
getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
if (H != getOperand(i)) {
std::vector<SCEVHandle> NewOps;
NewOps.reserve(getNumOperands());
for (unsigned j = 0; j != i; ++j)
NewOps.push_back(getOperand(j));
NewOps.push_back(H);
for (++i; i != e; ++i)
NewOps.push_back(getOperand(i)->
replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
return SE.getAddRecExpr(NewOps, L);
}
}
return this;
}
bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
// This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
// contain L and if the start is invariant.
return !QueryLoop->contains(L->getHeader()) &&
getOperand(0)->isLoopInvariant(QueryLoop);
}
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 ManagedStatic<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);
}
//===----------------------------------------------------------------------===//
// SCEV Utilities
//===----------------------------------------------------------------------===//
namespace {
/// SCEVComplexityCompare - Return true if the complexity of the LHS is less
/// than the complexity of the RHS. This comparator is used to canonicalize
/// expressions.
struct VISIBILITY_HIDDEN SCEVComplexityCompare {
bool operator()(const SCEV *LHS, const SCEV *RHS) const {
return LHS->getSCEVType() < RHS->getSCEVType();
}
};
}
/// GroupByComplexity - Given a list of SCEV objects, order them by their
/// complexity, and group objects of the same complexity together by value.
/// When this routine is finished, we know that any duplicates in the vector are
/// consecutive and that complexity is monotonically increasing.
///
/// Note that we go take special precautions to ensure that we get determinstic
/// results from this routine. In other words, we don't want the results of
/// this to depend on where the addresses of various SCEV objects happened to
/// land in memory.
///
static void GroupByComplexity(std::vector<SCEVHandle> &Ops) {
if (Ops.size() < 2) return; // Noop
if (Ops.size() == 2) {
// This is the common case, which also happens to be trivially simple.
// Special case it.
if (SCEVComplexityCompare()(Ops[1], Ops[0]))
std::swap(Ops[0], Ops[1]);
return;
}
// Do the rough sort by complexity.
std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
// Now that we are sorted by complexity, group elements of the same
// complexity. Note that this is, at worst, N^2, but the vector is likely to
// be extremely short in practice. Note that we take this approach because we
// do not want to depend on the addresses of the objects we are grouping.
for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
SCEV *S = Ops[i];
unsigned Complexity = S->getSCEVType();
// If there are any objects of the same complexity and same value as this
// one, group them.
for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
if (Ops[j] == S) { // Found a duplicate.
// Move it to immediately after i'th element.
std::swap(Ops[i+1], Ops[j]);
++i; // no need to rescan it.
if (i == e-2) return; // Done!
}
}
}
}
//===----------------------------------------------------------------------===//
// 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 ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
Constant *C;
if (Val == 0)
C = Constant::getNullValue(Ty);
else if (Ty->isFloatingPoint())
C = ConstantFP::get(Ty, APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
APFloat::IEEEdouble, Val));
else
C = ConstantInt::get(Ty, Val);
return getUnknown(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,
ScalarEvolution &SE) {
const Type *SrcTy = V->getType();
assert(SrcTy->isInteger() && Ty->isInteger() &&
"Cannot truncate or zero extend with non-integer arguments!");
if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits())
return V; // No conversion
if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits())
return SE.getTruncateExpr(V, Ty);
return SE.getZeroExtendExpr(V, Ty);
}
/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
///
SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) {
if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
return getUnknown(ConstantExpr::getNeg(VC->getValue()));
return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(V->getType())));
}
/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) {
if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
return getUnknown(ConstantExpr::getNot(VC->getValue()));
SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(V->getType()));
return getMinusSCEV(AllOnes, V);
}
/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
///
SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS,
const SCEVHandle &RHS) {
// X - Y --> X + -Y
return getAddExpr(LHS, getNegativeSCEV(RHS));
}
/// BinomialCoefficient - Compute BC(It, K). The result is of the same type as
/// It. Assume, K > 0.
static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K,
ScalarEvolution &SE) {
// We are using the following formula for BC(It, K):
//
// BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
//
// Suppose, W is the bitwidth of It (and of the return value as well). We
// must be prepared for overflow. Hence, we must assure that the result of
// our computation is equal to the accurate one modulo 2^W. Unfortunately,
// division isn't safe in modular arithmetic. This means we must perform the
// whole computation accurately and then truncate the result to W bits.
//
// The dividend of the formula is a multiplication of K integers of bitwidth
// W. K*W bits suffice to compute it accurately.
//
// FIXME: We assume the divisor can be accurately computed using 16-bit
// unsigned integer type. It is true up to K = 8 (AddRecs of length 9). In
// future we may use APInt to use the minimum number of bits necessary to
// compute it accurately.
//
// It is safe to use unsigned division here: the dividend is nonnegative and
// the divisor is positive.
// Handle the simplest case efficiently.
if (K == 1)
return It;
assert(K < 9 && "We cannot handle such long AddRecs yet.");
// FIXME: A temporary hack to remove in future. Arbitrary precision integers
// aren't supported by the code generator yet. For the dividend, the bitwidth
// we use is the smallest power of 2 greater or equal to K*W and less or equal
// to 64. Note that setting the upper bound for bitwidth may still lead to
// miscompilation in some cases.
unsigned DividendBits = 1U << Log2_32_Ceil(K * It->getBitWidth());
if (DividendBits > 64)
DividendBits = 64;
#if 0 // Waiting for the APInt support in the code generator...
unsigned DividendBits = K * It->getBitWidth();
#endif
const IntegerType *DividendTy = IntegerType::get(DividendBits);
const SCEVHandle ExIt = SE.getZeroExtendExpr(It, DividendTy);
// The final number of bits we need to perform the division is the maximum of
// dividend and divisor bitwidths.
const IntegerType *DivisionTy =
IntegerType::get(std::max(DividendBits, 16U));
// Compute K! We know K >= 2 here.
unsigned F = 2;
for (unsigned i = 3; i <= K; ++i)
F *= i;
APInt Divisor(DivisionTy->getBitWidth(), F);
// Handle this case efficiently, it is common to have constant iteration
// counts while computing loop exit values.
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(ExIt)) {
const APInt& N = SC->getValue()->getValue();
APInt Dividend(N.getBitWidth(), 1);
for (; K; --K)
Dividend *= N-(K-1);
if (DividendTy != DivisionTy)
Dividend = Dividend.zext(DivisionTy->getBitWidth());
return SE.getConstant(Dividend.udiv(Divisor).trunc(It->getBitWidth()));
}
SCEVHandle Dividend = ExIt;
for (unsigned i = 1; i != K; ++i)
Dividend =
SE.getMulExpr(Dividend,
SE.getMinusSCEV(ExIt, SE.getIntegerSCEV(i, DividendTy)));
if (DividendTy != DivisionTy)
Dividend = SE.getZeroExtendExpr(Dividend, DivisionTy);
return
SE.getTruncateExpr(SE.getUDivExpr(Dividend, SE.getConstant(Divisor)),
It->getType());
}
/// 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*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
///
/// where BC(It, k) stands for binomial coefficient.
///
SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It,
ScalarEvolution &SE) const {
SCEVHandle Result = getStart();
for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
// The computation is correct in the face of overflow provided that the
// multiplication is performed _after_ the evaluation of the binomial
// coefficient.
SCEVHandle Val = SE.getMulExpr(getOperand(i),
BinomialCoefficient(It, i, SE));
Result = SE.getAddExpr(Result, Val);
}
return Result;
}
//===----------------------------------------------------------------------===//
// SCEV Expression folder implementations
//===----------------------------------------------------------------------===//
SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op, const Type *Ty) {
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
return getUnknown(
ConstantExpr::getTrunc(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(getTruncateExpr(AddRec->getOperand(i), Ty));
else
break;
if (Operands.size() == AddRec->getNumOperands())
return getAddRecExpr(Operands, AddRec->getLoop());
}
SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
return Result;
}
SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op, const Type *Ty) {
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
return getUnknown(
ConstantExpr::getZExt(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;
}
SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op, const Type *Ty) {
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
return getUnknown(
ConstantExpr::getSExt(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 sign extend all of the
// operands (often constants). This would allow analysis of something like
// this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
return Result;
}
// get - Get a canonical add expression, or something simpler if possible.
SCEVHandle ScalarEvolution::getAddExpr(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.
GroupByComplexity(Ops);
// 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!
ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() +
RHSC->getValue()->getValue());
Ops[0] = getConstant(Fold);
Ops.erase(Ops.begin()+1); // Erase the folded element
if (Ops.size() == 1) return Ops[0];
LHSC = cast<SCEVConstant>(Ops[0]);
}
// If we are left with a constant zero being added, strip it off.
if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
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 = getIntegerSCEV(2, Ty);
SCEVHandle Mul = getMulExpr(Ops[i], Two);
if (Ops.size() == 2)
return Mul;
Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
Ops.push_back(Mul);
return getAddExpr(Ops);
}
// Now we know the first non-constant operand. Skip past any cast SCEVs.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
++Idx;
// 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 getAddExpr(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] && !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 = getMulExpr(MulOps);
}
SCEVHandle One = getIntegerSCEV(1, Ty);
SCEVHandle AddOne = getAddExpr(InnerMul, One);
SCEVHandle OuterMul = getMulExpr(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 getAddExpr(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 = getMulExpr(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 = getMulExpr(MulOps);
}
SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
if (Ops.size() == 2) return OuterMul;
Ops.erase(Ops.begin()+Idx);
Ops.erase(Ops.begin()+OtherMulIdx-1);
Ops.push_back(OuterMul);
return getAddExpr(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] = getAddExpr(LIOps);
SCEVHandle NewRec = getAddRecExpr(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 getAddExpr(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] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
}
SCEVHandle NewAddRec = getAddRecExpr(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 getAddExpr(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 ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) {
assert(!Ops.empty() && "Cannot get empty mul!");
// Sort by complexity, this groups all similar expression types together.
GroupByComplexity(Ops);
// 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 getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
getMulExpr(LHSC, Add->getOperand(1)));
++Idx;
while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
// We found two constants, fold them together!
ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
RHSC->getValue()->getValue());
Ops[0] = getConstant(Fold);
Ops.erase(Ops.begin()+1); // Erase the folded element
if (Ops.size() == 1) return Ops[0];
LHSC = cast<SCEVConstant>(Ops[0]);
}
// 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()->isZero()) {
// 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 getMulExpr(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(getMulExpr(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(getMulExpr(MulOps));
}
}
SCEVHandle NewRec = getAddRecExpr(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 getMulExpr(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 = getMulExpr(F->getStart(),
G->getStart());
SCEVHandle B = F->getStepRecurrence(*this);
SCEVHandle D = G->getStepRecurrence(*this);
SCEVHandle NewStep = getAddExpr(getMulExpr(F, D),
getMulExpr(G, B),
getMulExpr(B, D));
SCEVHandle NewAddRec = getAddRecExpr(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 getMulExpr(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 ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) {
if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
if (RHSC->getValue()->equalsInt(1))
return LHS; // X udiv 1 --> x
if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
Constant *LHSCV = LHSC->getValue();
Constant *RHSCV = RHSC->getValue();
return getUnknown(ConstantExpr::getUDiv(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 ScalarEvolution::getAddRecExpr(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 getAddRecExpr(Operands, L);
}
Operands.push_back(Step);
return getAddRecExpr(Operands, L);
}
/// SCEVAddRecExpr::get - Get a add recurrence expression for the
/// specified loop. Simplify the expression as much as possible.
SCEVHandle ScalarEvolution::getAddRecExpr(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()->isZero()) {
Operands.pop_back();
return getAddRecExpr(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 ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS,
const SCEVHandle &RHS) {
std::vector<SCEVHandle> Ops;
Ops.push_back(LHS);
Ops.push_back(RHS);
return getSMaxExpr(Ops);
}
SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) {
assert(!Ops.empty() && "Cannot get empty smax!");
if (Ops.size() == 1) return Ops[0];
// Sort by complexity, this groups all similar expression types together.
GroupByComplexity(Ops);
// 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!
ConstantInt *Fold = ConstantInt::get(
APIntOps::smax(LHSC->getValue()->getValue(),
RHSC->getValue()->getValue()));
Ops[0] = getConstant(Fold);
Ops.erase(Ops.begin()+1); // Erase the folded element
if (Ops.size() == 1) return Ops[0];
LHSC = cast<SCEVConstant>(Ops[0]);
}
// If we are left with a constant -inf, strip it off.
if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
Ops.erase(Ops.begin());
--Idx;
}
}
if (Ops.size() == 1) return Ops[0];
// Find the first SMax
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
++Idx;
// Check to see if one of the operands is an SMax. If so, expand its operands
// onto our operand list, and recurse to simplify.
if (Idx < Ops.size()) {
bool DeletedSMax = false;
while (SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
Ops.erase(Ops.begin()+Idx);
DeletedSMax = true;
}
if (DeletedSMax)
return getSMaxExpr(Ops);
}
// Okay, check to see if the same value occurs in the operand list twice. If
// so, delete one. Since we sorted the list, these values are required to
// be adjacent.
for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
--i; --e;
}
if (Ops.size() == 1) return Ops[0];
assert(!Ops.empty() && "Reduced smax down to nothing!");
// Okay, it looks like we really DO need an smax 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(scSMaxExpr,
SCEVOps)];
if (Result == 0) Result = new SCEVSMaxExpr(Ops);
return Result;
}
SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS,
const SCEVHandle &RHS) {
std::vector<SCEVHandle> Ops;
Ops.push_back(LHS);
Ops.push_back(RHS);
return getUMaxExpr(Ops);
}
SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) {
assert(!Ops.empty() && "Cannot get empty umax!");
if (Ops.size() == 1) return Ops[0];
// Sort by complexity, this groups all similar expression types together.
GroupByComplexity(Ops);
// 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!
ConstantInt *Fold = ConstantInt::get(
APIntOps::umax(LHSC->getValue()->getValue(),
RHSC->getValue()->getValue()));
Ops[0] = getConstant(Fold);
Ops.erase(Ops.begin()+1); // Erase the folded element
if (Ops.size() == 1) return Ops[0];
LHSC = cast<SCEVConstant>(Ops[0]);
}
// If we are left with a constant zero, strip it off.
if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
Ops.erase(Ops.begin());
--Idx;
}
}
if (Ops.size() == 1) return Ops[0];
// Find the first UMax
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
++Idx;
// Check to see if one of the operands is a UMax. If so, expand its operands
// onto our operand list, and recurse to simplify.
if (Idx < Ops.size()) {
bool DeletedUMax = false;
while (SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
Ops.erase(Ops.begin()+Idx);
DeletedUMax = true;
}
if (DeletedUMax)
return getUMaxExpr(Ops);
}
// Okay, check to see if the same value occurs in the operand list twice. If
// so, delete one. Since we sorted the list, these values are required to
// be adjacent.
for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
--i; --e;
}
if (Ops.size() == 1) return Ops[0];
assert(!Ops.empty() && "Reduced umax down to nothing!");
// Okay, it looks like we really DO need a umax 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(scUMaxExpr,
SCEVOps)];
if (Result == 0) Result = new SCEVUMaxExpr(Ops);
return Result;
}
SCEVHandle ScalarEvolution::getUnknown(Value *V) {
if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
return getConstant(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 VISIBILITY_HIDDEN ScalarEvolutionsImpl {
/// SE - A reference to the public ScalarEvolution object.
ScalarEvolution &SE;
/// 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(ScalarEvolution &se, Function &f, LoopInfo &li)
: SE(se), 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);
/// hasSCEV - Return true if the SCEV for this value has already been
/// computed.
bool hasSCEV(Value *V) const {
return Scalars.count(V);
}
/// setSCEV - Insert the specified SCEV into the map of current SCEVs for
/// the specified value.
void setSCEV(Value *V, const SCEVHandle &H) {
bool isNew = Scalars.insert(std::make_pair(V, H)).second;
assert(isNew && "This entry already existed!");
}
/// 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);
/// deleteValueFromRecords - This method should be called by the
/// client before it removes a value from the program, to make sure
/// that no dangling references are left around.
void deleteValueFromRecords(Value *V);
private:
/// createSCEV - We know that there is no SCEV for the specified value.
/// Analyze the expression.
SCEVHandle createSCEV(Value *V);
/// createNodeForPHI - Provide the special handling we need to analyze PHI
/// SCEVs.
SCEVHandle createNodeForPHI(PHINode *PN);
/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value
/// for the specified instruction and replaces any references to the
/// symbolic value SymName with the specified value. This is used during
/// PHI resolution.
void ReplaceSymbolicValueWithConcrete(Instruction *I,
const SCEVHandle &SymName,
const SCEVHandle &NewVal);
/// ComputeIterationCount - Compute the number of times the specified loop
/// will iterate.
SCEVHandle ComputeIterationCount(const Loop *L);
/// ComputeLoadConstantCompareIterationCount - Given an exit condition of
/// 'icmp op load X, cst', try to see if we can compute the trip count.
SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI,
Constant *RHS,
const Loop *L,
ICmpInst::Predicate p);
/// 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);
/// HowManyLessThans - Return the number of times a backedge containing the
/// specified less-than comparison will execute. If not computable, return
/// UnknownValue. isSigned specifies whether the less-than is signed.
SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L,
bool isSigned);
/// 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, const APInt& Its,
const Loop *L);
};
}
//===----------------------------------------------------------------------===//
// Basic SCEV Analysis and PHI Idiom Recognition Code
//
/// deleteValueFromRecords - 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::deleteValueFromRecords(Value *V) {
SmallVector<Value *, 16> Worklist;
if (Scalars.erase(V)) {
if (PHINode *PN = dyn_cast<PHINode>(V))
ConstantEvolutionLoopExitValue.erase(PN);
Worklist.push_back(V);
}
while (!Worklist.empty()) {
Value *VV = Worklist.back();
Worklist.pop_back();
for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end();
UI != UE; ++UI) {
Instruction *Inst = cast<Instruction>(*UI);
if (Scalars.erase(Inst)) {
if (PHINode *PN = dyn_cast<PHINode>(VV))
ConstantEvolutionLoopExitValue.erase(PN);
Worklist.push_back(Inst);
}
}
}
}
/// 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;
}
/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
/// the specified instruction and replaces any references to the symbolic value
/// SymName with the specified value. This is used during PHI resolution.
void ScalarEvolutionsImpl::
ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
const SCEVHandle &NewVal) {
std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
if (SI == Scalars.end()) return;
SCEVHandle NV =
SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, SE);
if (NV == SI->second) return; // No change.
SI->second = NV; // Update the scalars map!
// Any instruction values that use this instruction might also need to be
// updated!
for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
UI != E; ++UI)
ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
}
/// 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 = SE.getUnknown(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 = SE.getAddExpr(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 = SE.getAddRecExpr(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.
ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
return PHISCEV;
}
}
} else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) {
// Otherwise, this could be a loop like this:
// i = 0; for (j = 1; ..; ++j) { .... i = j; }
// In this case, j = {1,+,1} and BEValue is j.
// Because the other in-value of i (0) fits the evolution of BEValue
// i really is an addrec evolution.
if (AddRec->getLoop() == L && AddRec->isAffine()) {
SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
// If StartVal = j.start - j.stride, we can use StartVal as the
// initial step of the addrec evolution.
if (StartVal == SE.getMinusSCEV(AddRec->getOperand(0),
AddRec->getOperand(1))) {
SCEVHandle PHISCEV =
SE.getAddRecExpr(StartVal, AddRec->getOperand(1), 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.
ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
return PHISCEV;
}
}
}
return SymbolicName;
}
// If it's not a loop phi, we can't handle it yet.
return SE.getUnknown(PN);
}
/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
/// guaranteed to end in (at every loop iteration). It is, at the same time,
/// the minimum number of times S is divisible by 2. For example, given {4,+,8}
/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
static uint32_t GetMinTrailingZeros(SCEVHandle S) {
if (SCEVConstant *C = dyn_cast<SCEVConstant>(S))
return C->getValue()->getValue().countTrailingZeros();
if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
return std::min(GetMinTrailingZeros(T->getOperand()), T->getBitWidth());
if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes;
}
if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes;
}
if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
// The result is the min of all operands results.
uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
return MinOpRes;
}
if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
// The result is the sum of all operands results.
uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
uint32_t BitWidth = M->getBitWidth();
for (unsigned i = 1, e = M->getNumOperands();
SumOpRes != BitWidth && i != e; ++i)
SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
BitWidth);
return SumOpRes;
}
if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
// The result is the min of all operands results.
uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
return MinOpRes;
}
if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
// The result is the min of all operands results.
uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
return MinOpRes;
}
if (SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
// The result is the min of all operands results.
uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
return MinOpRes;
}
// SCEVUDivExpr, SCEVUnknown
return 0;
}
/// createSCEV - We know that there is no SCEV for the specified value.
/// Analyze the expression.
///
SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) {
if (!isa<IntegerType>(V->getType()))
return SE.getUnknown(V);
if (Instruction *I = dyn_cast<Instruction>(V)) {
switch (I->getOpcode()) {
case Instruction::Add:
return SE.getAddExpr(getSCEV(I->getOperand(0)),
getSCEV(I->getOperand(1)));
case Instruction::Mul:
return SE.getMulExpr(getSCEV(I->getOperand(0)),
getSCEV(I->getOperand(1)));
case Instruction::UDiv:
return SE.getUDivExpr(getSCEV(I->getOperand(0)),
getSCEV(I->getOperand(1)));
case Instruction::Sub:
return SE.getMinusSCEV(getSCEV(I->getOperand(0)),
getSCEV(I->getOperand(1)));
case Instruction::Or:
// If the RHS of the Or is a constant, we may have something like:
// X*4+1 which got turned into X*4|1. Handle this as an Add so loop
// optimizations will transparently handle this case.
//
// In order for this transformation to be safe, the LHS must be of the
// form X*(2^n) and the Or constant must be less than 2^n.
if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) {
SCEVHandle LHS = getSCEV(I->getOperand(0));
const APInt &CIVal = CI->getValue();
if (GetMinTrailingZeros(LHS) >=
(CIVal.getBitWidth() - CIVal.countLeadingZeros()))
return SE.getAddExpr(LHS, getSCEV(I->getOperand(1)));
}
break;
case Instruction::Xor:
// If the RHS of the xor is a signbit, then this is just an add.
// Instcombine turns add of signbit into xor as a strength reduction step.
if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) {
if (CI->getValue().isSignBit())
return SE.getAddExpr(getSCEV(I->getOperand(0)),
getSCEV(I->getOperand(1)));
else if (CI->isAllOnesValue())
return SE.getNotSCEV(getSCEV(I->getOperand(0)));
}
break;
case Instruction::Shl:
// Turn shift left of a constant amount into a multiply.
if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) {
uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
Constant *X = ConstantInt::get(
APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
return SE.getMulExpr(getSCEV(I->getOperand(0)), getSCEV(X));
}
break;
case Instruction::Trunc:
return SE.getTruncateExpr(getSCEV(I->getOperand(0)), I->getType());
case Instruction::ZExt:
return SE.getZeroExtendExpr(getSCEV(I->getOperand(0)), I->getType());
case Instruction::SExt:
return SE.getSignExtendExpr(getSCEV(I->getOperand(0)), I->getType());
case Instruction::BitCast:
// BitCasts are no-op casts so we just eliminate the cast.
if (I->getType()->isInteger() &&
I->getOperand(0)->getType()->isInteger())
return getSCEV(I->getOperand(0));
break;
case Instruction::PHI:
return createNodeForPHI(cast<PHINode>(I));
case Instruction::Select:
// This could be a smax or umax that was lowered earlier.
// Try to recover it.
if (ICmpInst *ICI = dyn_cast<ICmpInst>(I->getOperand(0))) {
Value *LHS = ICI->getOperand(0);
Value *RHS = ICI->getOperand(1);
switch (ICI->getPredicate()) {
case ICmpInst::ICMP_SLT:
case ICmpInst::ICMP_SLE:
std::swap(LHS, RHS);
// fall through
case ICmpInst::ICMP_SGT:
case ICmpInst::ICMP_SGE:
if (LHS == I->getOperand(1) && RHS == I->getOperand(2))
return SE.getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
else if (LHS == I->getOperand(2) && RHS == I->getOperand(1))
// -smax(-x, -y) == smin(x, y).
return SE.getNegativeSCEV(SE.getSMaxExpr(
SE.getNegativeSCEV(getSCEV(LHS)),
SE.getNegativeSCEV(getSCEV(RHS))));
break;
case ICmpInst::ICMP_ULT:
case ICmpInst::ICMP_ULE:
std::swap(LHS, RHS);
// fall through
case ICmpInst::ICMP_UGT:
case ICmpInst::ICMP_UGE:
if (LHS == I->getOperand(1) && RHS == I->getOperand(2))
return SE.getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
else if (LHS == I->getOperand(2) && RHS == I->getOperand(1))
// ~umax(~x, ~y) == umin(x, y)
return SE.getNotSCEV(SE.getUMaxExpr(SE.getNotSCEV(getSCEV(LHS)),
SE.getNotSCEV(getSCEV(RHS))));
break;
default:
break;
}
}
default: // We cannot analyze this expression.
break;
}
}
return SE.getUnknown(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.
SmallVector<BasicBlock*, 8> 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)
BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
if (ExitBr == 0) return UnknownValue;
assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
// At this point, we know we have a conditional branch that determines whether
// the loop is exited. However, we don't know if the branch is executed each
// time through the loop. If not, then the execution count of the branch will
// not be equal to the trip count of the loop.
//
// Currently we check for this by checking to see if the Exit branch goes to
// the loop header. If so, we know it will always execute the same number of
// times as the loop. We also handle the case where the exit block *is* the
// loop header. This is common for un-rotated loops. More extensive analysis
// could be done to handle more cases here.
if (ExitBr->getSuccessor(0) != L->getHeader() &&
ExitBr->getSuccessor(1) != L->getHeader() &&
ExitBr->getParent() != L->getHeader())
return UnknownValue;
ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
// If it's not an integer comparison then compute it the hard way.
// Note that ICmpInst deals with pointer comparisons too so we must check
// the type of the operand.
if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType()))
return ComputeIterationCountExhaustively(L, ExitBr->getCondition(),
ExitBr->getSuccessor(0) == ExitBlock);
// If the condition was exit on true, convert the condition to exit on false
ICmpInst::Predicate Cond;
if (ExitBr->getSuccessor(1) == ExitBlock)
Cond = ExitCond->getPredicate();
else
Cond = ExitCond->getInversePredicate();
// Handle common loops like: for (X = "string"; *X; ++X)
if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
SCEVHandle ItCnt =
ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond);
if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
}
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;
// 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 = ICmpInst::getSwappedPredicate(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::getBitCast(CompVal, RealTy));
if (CompVal) {
// Form the constant range.
ConstantRange CompRange(
ICmpInst::makeConstantRange(Cond, CompVal->getValue()));
SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, SE);
if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
}
}
switch (Cond) {
case ICmpInst::ICMP_NE: { // while (X != Y)
// Convert to: while (X-Y != 0)
SCEVHandle TC = HowFarToZero(SE.getMinusSCEV(LHS, RHS), L);
if (!isa<SCEVCouldNotCompute>(TC)) return TC;
break;
}
case ICmpInst::ICMP_EQ: {
// Convert to: while (X-Y == 0) // while (X == Y)
SCEVHandle TC = HowFarToNonZero(SE.getMinusSCEV(LHS, RHS), L);
if (!isa<SCEVCouldNotCompute>(TC)) return TC;
break;
}
case ICmpInst::ICMP_SLT: {
SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true);
if (!isa<SCEVCouldNotCompute>(TC)) return TC;
break;
}
case ICmpInst::ICMP_SGT: {
SCEVHandle TC = HowManyLessThans(SE.getNegativeSCEV(LHS),
SE.getNegativeSCEV(RHS), L, true);
if (!isa<SCEVCouldNotCompute>(TC)) return TC;
break;
}
case ICmpInst::ICMP_ULT: {
SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false);
if (!isa<SCEVCouldNotCompute>(TC)) return TC;
break;
}
case ICmpInst::ICMP_UGT: {
SCEVHandle TC = HowManyLessThans(SE.getNegativeSCEV(LHS),
SE.getNegativeSCEV(RHS), L, false);
if (!isa<SCEVCouldNotCompute>(TC)) return TC;
break;
}
default:
#if 0
cerr << "ComputeIterationCount ";
if (ExitCond->getOperand(0)->getType()->isUnsigned())
cerr << "[unsigned] ";
cerr << *LHS << " "
<< Instruction::getOpcodeName(Instruction::ICmp)
<< " " << *RHS << "\n";
#endif
break;
}
return ComputeIterationCountExhaustively(L, ExitCond,
ExitBr->getSuccessor(0) == ExitBlock);
}
static ConstantInt *
EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
ScalarEvolution &SE) {
SCEVHandle InVal = SE.getConstant(C);
SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE);
assert(isa<SCEVConstant>(Val) &&
"Evaluation of SCEV at constant didn't fold correctly?");
return cast<SCEVConstant>(Val)->getValue();
}
/// GetAddressedElementFromGlobal - Given a global variable with an initializer
/// and a GEP expression (missing the pointer index) indexing into it, return
/// the addressed element of the initializer or null if the index expression is
/// invalid.
static Constant *
GetAddressedElementFromGlobal(GlobalVariable *GV,
const std::vector<ConstantInt*> &Indices) {
Constant *Init = GV->getInitializer();
for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
uint64_t Idx = Indices[i]->getZExtValue();
if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
assert(Idx < CS->getNumOperands() && "Bad struct index!");
Init = cast<Constant>(CS->getOperand(Idx));
} else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
if (Idx >= CA->getNumOperands()) return 0; // Bogus program
Init = cast<Constant>(CA->getOperand(Idx));
} else if (isa<ConstantAggregateZero>(Init)) {
if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
assert(Idx < STy->getNumElements() && "Bad struct index!");
Init = Constant::getNullValue(STy->getElementType(Idx));
} else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
if (Idx >= ATy->getNumElements()) return 0; // Bogus program
Init = Constant::getNullValue(ATy->getElementType());
} else {
assert(0 && "Unknown constant aggregate type!");
}
return 0;
} else {
return 0; // Unknown initializer type
}
}
return Init;
}
/// ComputeLoadConstantCompareIterationCount - Given an exit condition of
/// 'icmp op load X, cst', try to se if we can compute the trip count.
SCEVHandle ScalarEvolutionsImpl::
ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS,
const Loop *L,
ICmpInst::Predicate predicate) {
if (LI->isVolatile()) return UnknownValue;
// Check to see if the loaded pointer is a getelementptr of a global.
GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
if (!GEP) return UnknownValue;
// Make sure that it is really a constant global we are gepping, with an
// initializer, and make sure the first IDX is really 0.
GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
!cast<Constant>(GEP->getOperand(1))->isNullValue())
return UnknownValue;
// Okay, we allow one non-constant index into the GEP instruction.
Value *VarIdx = 0;
std::vector<ConstantInt*> Indexes;
unsigned VarIdxNum = 0;
for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
Indexes.push_back(CI);
} else if (!isa<ConstantInt>(GEP->getOperand(i))) {
if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
VarIdx = GEP->getOperand(i);
VarIdxNum = i-2;
Indexes.push_back(0);
}
// Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
// Check to see if X is a loop variant variable value now.
SCEVHandle Idx = getSCEV(VarIdx);
SCEVHandle Tmp = getSCEVAtScope(Idx, L);
if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
// We can only recognize very limited forms of loop index expressions, in
// particular, only affine AddRec's like {C1,+,C2}.
SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
!isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
!isa<SCEVConstant>(IdxExpr->getOperand(1)))
return UnknownValue;
unsigned MaxSteps = MaxBruteForceIterations;
for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
ConstantInt *ItCst =
ConstantInt::get(IdxExpr->getType(), IterationNum);
ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, SE);
// Form the GEP offset.
Indexes[VarIdxNum] = Val;
Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
if (Result == 0) break; // Cannot compute!
// Evaluate the condition for this iteration.
Result = ConstantExpr::getICmp(predicate, Result, RHS);
if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
#if 0
cerr << "\n***\n*** Computed loop count " << *ItCst
<< "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
<< "***\n";
#endif
++NumArrayLenItCounts;
return SE.getConstant(ItCst); // Found terminating iteration!
}
}
return UnknownValue;
}
/// 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<CmpInst>(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(F);
return false;
}
/// 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;
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;
}
if (const CmpInst *CI = dyn_cast<CmpInst>(I))
return ConstantFoldCompareInstOperands(CI->getPredicate(),
&Operands[0], Operands.size());
else
return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
&Operands[0], Operands.size());
}
/// 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, const APInt& Its, const Loop *L){
std::map<PHINode*, Constant*>::iterator I =
ConstantEvolutionLoopExitValue.find(PN);
if (I != ConstantEvolutionLoopExitValue.end())
return I->second;
if (Its.ugt(APInt(Its.getBitWidth(),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.
if (Its.getActiveBits() >= 32)
return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
unsigned NumIterations = Its.getZExtValue(); // must be in range
unsigned IterationNum = 0;
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) {
ConstantInt *CondVal =
dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
// Couldn't symbolically evaluate.
if (!CondVal) return UnknownValue;
if (CondVal->getValue() == uint64_t(ExitWhen)) {
ConstantEvolutionLoopExitValue[PN] = PHIVal;
++NumBruteForceTripCountsComputed;
return SE.getConstant(ConstantInt::get(Type::Int32Ty, 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 evolved 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()->getValue(),
LI);
if (RV) return SE.getUnknown(RV);
}
}
// Okay, this is an 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 so, 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 any of the operands is non-constant and if they are
// non-integer, don't even try to analyze them with scev techniques.
if (!isa<IntegerType>(Op->getType()))
return V;
SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(),
Op->getType(),
false));
else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
if (Constant *C = dyn_cast<Constant>(SU->getValue()))
Operands.push_back(ConstantExpr::getIntegerCast(C,
Op->getType(),
false));
else
return V;
} else {
return V;
}
}
}
Constant *C;
if (const CmpInst *CI = dyn_cast<CmpInst>(I))
C = ConstantFoldCompareInstOperands(CI->getPredicate(),
&Operands[0], Operands.size());
else
C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
&Operands[0], Operands.size());
return SE.getUnknown(C);
}
}
// 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 SE.getAddExpr(NewOps);
if (isa<SCEVMulExpr>(Comm))
return SE.getMulExpr(NewOps);
if (isa<SCEVSMaxExpr>(Comm))
return SE.getSMaxExpr(NewOps);
if (isa<SCEVUMaxExpr>(Comm))
return SE.getUMaxExpr(NewOps);
assert(0 && "Unknown commutative SCEV type!");
}
}
// If we got here, all operands are loop invariant.
return Comm;
}
if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
if (LHS == UnknownValue) return LHS;
SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
if (RHS == UnknownValue) return RHS;
if (LHS == Div->getLHS() && RHS == Div->getRHS())
return Div; // must be loop invariant
return SE.getUDivExpr(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(), SE);
// If the value is affine, simplify the expression evaluation to just
// Start + Step*IterationCount.
if (AddRec->isAffine())
return SE.getAddExpr(AddRec->getStart(),
SE.getMulExpr(IterationCount,
AddRec->getOperand(1)));
// Otherwise, evaluate it the hard way.
return AddRec->evaluateAtIteration(IterationCount, SE);
}
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, ScalarEvolution &SE) {
assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
// We currently can only solve this if the coefficients are constants.
if (!LC || !MC || !NC) {
SCEV *CNC = new SCEVCouldNotCompute();
return std::make_pair(CNC, CNC);
}
uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
const APInt &L = LC->getValue()->getValue();
const APInt &M = MC->getValue()->getValue();
const APInt &N = NC->getValue()->getValue();
APInt Two(BitWidth, 2);
APInt Four(BitWidth, 4);
{
using namespace APIntOps;
const APInt& C = L;
// Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
// The B coefficient is M-N/2
APInt B(M);
B -= sdiv(N,Two);
// The A coefficient is N/2
APInt A(N.sdiv(Two));
// Compute the B^2-4ac term.
APInt SqrtTerm(B);
SqrtTerm *= B;
SqrtTerm -= Four * (A * C);
// Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
// integer value or else APInt::sqrt() will assert.
APInt SqrtVal(SqrtTerm.sqrt());
// Compute the two solutions for the quadratic formula.
// The divisions must be performed as signed divisions.
APInt NegB(-B);
APInt TwoA( A << 1 );
ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
return std::make_pair(SE.getConstant(Solution1),
SE.getConstant(Solution2));
} // end APIntOps namespace
}
/// 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()->isZero()) 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());
if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
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 SE.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::getSRem(StartNegC, StepC->getValue());
if (Rem->isNullValue()) {
Constant *Result =ConstantExpr::getSDiv(StartNegC,StepC->getValue());
return SE.getUnknown(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, SE);
SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
if (R1) {
#if 0
cerr << "HFTZ: " << *V << " - sol#1: " << *R1
<< " sol#2: " << *R2 << "\n";
#endif
// Pick the smallest positive root value.
if (ConstantInt *CB =
dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
R1->getValue(), R2->getValue()))) {
if (CB->getZExtValue() == false)
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, SE);
if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val))
if (EvalVal->getValue()->isZero())
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)) {
if (!C->getValue()->isNullValue())
return SE.getIntegerSCEV(0, C->getType());
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;
}
/// HowManyLessThans - Return the number of times a backedge containing the
/// specified less-than comparison will execute. If not computable, return
/// UnknownValue.
SCEVHandle ScalarEvolutionsImpl::
HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) {
// Only handle: "ADDREC < LoopInvariant".
if (!RHS->isLoopInvariant(L)) return UnknownValue;
SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
if (!AddRec || AddRec->getLoop() != L)
return UnknownValue;
if (AddRec->isAffine()) {
// FORNOW: We only support unit strides.
SCEVHandle One = SE.getIntegerSCEV(1, RHS->getType());
if (AddRec->getOperand(1) != One)
return UnknownValue;
// We know the LHS is of the form {n,+,1} and the RHS is some loop-invariant
// m. So, we count the number of iterations in which {n,+,1} < m is true.
// Note that we cannot simply return max(m-n,0) because it's not safe to
// treat m-n as signed nor unsigned due to overflow possibility.
// First, we get the value of the LHS in the first iteration: n
SCEVHandle Start = AddRec->getOperand(0);
// Then, we get the value of the LHS in the first iteration in which the
// above condition doesn't hold. This equals to max(m,n).
SCEVHandle End = isSigned ? SE.getSMaxExpr(RHS, Start)
: SE.getUMaxExpr(RHS, Start);
// Finally, we subtract these two values to get the number of times the
// backedge is executed: max(m,n)-n.
return SE.getMinusSCEV(End, Start);
}
return UnknownValue;
}
/// 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,
ScalarEvolution &SE) 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()->isZero()) {
std::vector<SCEVHandle> Operands(op_begin(), op_end());
Operands[0] = SE.getIntegerSCEV(0, SC->getType());
SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop());
if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
return ShiftedAddRec->getNumIterationsInRange(
Range.subtract(SC->getValue()->getValue()), SE);
// 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.
if (!Range.contains(APInt(getBitWidth(),0)))
return SE.getConstant(ConstantInt::get(getType(),0));
if (isAffine()) {
// If this is an affine expression then we have this situation:
// Solve {0,+,A} in Range === Ax in Range
// We know that zero is in the range. If A is positive then we know that
// the upper value of the range must be the first possible exit value.
// If A is negative then the lower of the range is the last possible loop
// value. Also note that we already checked for a full range.
APInt One(getBitWidth(),1);
APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
// The exit value should be (End+A)/A.
APInt ExitVal = (End + A).udiv(A);
ConstantInt *ExitValue = ConstantInt::get(ExitVal);
// 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, SE);
if (Range.contains(Val->getValue()))
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,
ConstantInt::get(ExitVal - One), SE)->getValue()) &&
"Linear scev computation is off in a bad way!");
return SE.getConstant(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] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
// Next, solve the constructed addrec
std::pair<SCEVHandle,SCEVHandle> Roots =
SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
if (R1) {
// Pick the smallest positive root value.
if (ConstantInt *CB =
dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
R1->getValue(), R2->getValue()))) {
if (CB->getZExtValue() == false)
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(),
SE);
if (Range.contains(R1Val->getValue())) {
// The next iteration must be out of the range...
ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
if (!Range.contains(R1Val->getValue()))
return SE.getConstant(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.
ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
if (Range.contains(R1Val->getValue()))
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 *EndVal = TestVal; // Stop when we wrap around.
do {
++NumBruteForceEvaluations;
SCEVHandle Val = evaluateAtIteration(SE.getConstant(TestVal), SE);
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()->getValue()))
return SE.getConstant(TestVal);
// Increment to test the next index.
TestVal = ConstantInt::get(TestVal->getValue()+1);
} while (TestVal != EndVal);
return new SCEVCouldNotCompute();
}
//===----------------------------------------------------------------------===//
// ScalarEvolution Class Implementation
//===----------------------------------------------------------------------===//
bool ScalarEvolution::runOnFunction(Function &F) {
Impl = new ScalarEvolutionsImpl(*this, F, getAnalysis<LoopInfo>());
return false;
}
void ScalarEvolution::releaseMemory() {
delete (ScalarEvolutionsImpl*)Impl;
Impl = 0;
}
void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
AU.setPreservesAll();
AU.addRequiredTransitive<LoopInfo>();
}
SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
}
/// hasSCEV - Return true if the SCEV for this value has already been
/// computed.
bool ScalarEvolution::hasSCEV(Value *V) const {
return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V);
}
/// setSCEV - Insert the specified SCEV into the map of current SCEVs for
/// the specified value.
void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) {
((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H);
}
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::deleteValueFromRecords(Value *V) const {
return ((ScalarEvolutionsImpl*)Impl)->deleteValueFromRecords(V);
}
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);
OS << "Loop " << L->getHeader()->getName() << ": ";
SmallVector<BasicBlock*, 8> ExitBlocks;
L->getExitBlocks(ExitBlocks);
if (ExitBlocks.size() != 1)
OS << "<multiple exits> ";
if (SE->hasLoopInvariantIterationCount(L)) {
OS << *SE->getIterationCount(L) << " iterations! ";
} else {
OS << "Unpredictable iteration count. ";
}
OS << "\n";
}
void ScalarEvolution::print(std::ostream &OS, const Module* ) 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()->isInteger()) {
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);
}
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