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b69143c6a9
Fix ScalarEvolution bugs uncovered by this. git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@194928 91177308-0d34-0410-b5e6-96231b3b80d8
7721 lines
299 KiB
C++
7721 lines
299 KiB
C++
//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
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//
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// The LLVM Compiler Infrastructure
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//
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// This file is distributed under the University of Illinois Open Source
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// License. See LICENSE.TXT for details.
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//
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//===----------------------------------------------------------------------===//
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//
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// This file contains the implementation of the scalar evolution analysis
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// engine, which is used primarily to analyze expressions involving induction
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// variables in loops.
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//
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// There are several aspects to this library. First is the representation of
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// scalar expressions, which are represented as subclasses of the SCEV class.
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// These classes are used to represent certain types of subexpressions that we
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// can handle. We only create one SCEV of a particular shape, so
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// pointer-comparisons for equality are legal.
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//
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// One important aspect of the SCEV objects is that they are never cyclic, even
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// if there is a cycle in the dataflow for an expression (ie, a PHI node). If
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// the PHI node is one of the idioms that we can represent (e.g., a polynomial
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// recurrence) then we represent it directly as a recurrence node, otherwise we
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// represent it as a SCEVUnknown node.
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//
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// In addition to being able to represent expressions of various types, we also
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// have folders that are used to build the *canonical* representation for a
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// particular expression. These folders are capable of using a variety of
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// rewrite rules to simplify the expressions.
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//
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// Once the folders are defined, we can implement the more interesting
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// higher-level code, such as the code that recognizes PHI nodes of various
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// types, computes the execution count of a loop, etc.
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//
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// TODO: We should use these routines and value representations to implement
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// dependence analysis!
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//
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//===----------------------------------------------------------------------===//
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//
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// There are several good references for the techniques used in this analysis.
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//
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// Chains of recurrences -- a method to expedite the evaluation
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// of closed-form functions
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// Olaf Bachmann, Paul S. Wang, Eugene V. Zima
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//
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// On computational properties of chains of recurrences
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// Eugene V. Zima
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//
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// Symbolic Evaluation of Chains of Recurrences for Loop Optimization
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// Robert A. van Engelen
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//
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// Efficient Symbolic Analysis for Optimizing Compilers
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// Robert A. van Engelen
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//
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// Using the chains of recurrences algebra for data dependence testing and
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// induction variable substitution
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// MS Thesis, Johnie Birch
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//
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//===----------------------------------------------------------------------===//
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#define DEBUG_TYPE "scalar-evolution"
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#include "llvm/Analysis/ScalarEvolution.h"
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#include "llvm/ADT/STLExtras.h"
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#include "llvm/ADT/SmallPtrSet.h"
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#include "llvm/ADT/Statistic.h"
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#include "llvm/Analysis/ConstantFolding.h"
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#include "llvm/Analysis/Dominators.h"
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#include "llvm/Analysis/InstructionSimplify.h"
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#include "llvm/Analysis/LoopInfo.h"
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#include "llvm/Analysis/ScalarEvolutionExpressions.h"
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#include "llvm/Analysis/ValueTracking.h"
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#include "llvm/Assembly/Writer.h"
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#include "llvm/IR/Constants.h"
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#include "llvm/IR/DataLayout.h"
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#include "llvm/IR/DerivedTypes.h"
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#include "llvm/IR/GlobalAlias.h"
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#include "llvm/IR/GlobalVariable.h"
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#include "llvm/IR/Instructions.h"
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#include "llvm/IR/LLVMContext.h"
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#include "llvm/IR/Operator.h"
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#include "llvm/Support/CommandLine.h"
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#include "llvm/Support/ConstantRange.h"
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#include "llvm/Support/Debug.h"
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#include "llvm/Support/ErrorHandling.h"
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#include "llvm/Support/GetElementPtrTypeIterator.h"
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#include "llvm/Support/InstIterator.h"
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#include "llvm/Support/MathExtras.h"
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#include "llvm/Support/raw_ostream.h"
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#include "llvm/Target/TargetLibraryInfo.h"
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#include <algorithm>
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using namespace llvm;
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STATISTIC(NumArrayLenItCounts,
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"Number of trip counts computed with array length");
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STATISTIC(NumTripCountsComputed,
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"Number of loops with predictable loop counts");
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STATISTIC(NumTripCountsNotComputed,
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"Number of loops without predictable loop counts");
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STATISTIC(NumBruteForceTripCountsComputed,
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"Number of loops with trip counts computed by force");
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static cl::opt<unsigned>
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MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
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cl::desc("Maximum number of iterations SCEV will "
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"symbolically execute a constant "
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"derived loop"),
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cl::init(100));
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// FIXME: Enable this with XDEBUG when the test suite is clean.
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static cl::opt<bool>
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VerifySCEV("verify-scev",
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cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
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INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution",
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"Scalar Evolution Analysis", false, true)
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INITIALIZE_PASS_DEPENDENCY(LoopInfo)
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INITIALIZE_PASS_DEPENDENCY(DominatorTree)
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INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfo)
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INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution",
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"Scalar Evolution Analysis", false, true)
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char ScalarEvolution::ID = 0;
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//===----------------------------------------------------------------------===//
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// SCEV class definitions
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//===----------------------------------------------------------------------===//
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//===----------------------------------------------------------------------===//
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// Implementation of the SCEV class.
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//
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#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
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void SCEV::dump() const {
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print(dbgs());
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dbgs() << '\n';
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}
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#endif
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void SCEV::print(raw_ostream &OS) const {
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switch (getSCEVType()) {
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case scConstant:
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WriteAsOperand(OS, cast<SCEVConstant>(this)->getValue(), false);
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return;
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case scTruncate: {
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const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
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const SCEV *Op = Trunc->getOperand();
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OS << "(trunc " << *Op->getType() << " " << *Op << " to "
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<< *Trunc->getType() << ")";
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return;
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}
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case scZeroExtend: {
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const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
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const SCEV *Op = ZExt->getOperand();
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OS << "(zext " << *Op->getType() << " " << *Op << " to "
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<< *ZExt->getType() << ")";
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return;
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}
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case scSignExtend: {
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const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
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const SCEV *Op = SExt->getOperand();
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OS << "(sext " << *Op->getType() << " " << *Op << " to "
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<< *SExt->getType() << ")";
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return;
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}
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case scAddRecExpr: {
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const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
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OS << "{" << *AR->getOperand(0);
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for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
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OS << ",+," << *AR->getOperand(i);
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OS << "}<";
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if (AR->getNoWrapFlags(FlagNUW))
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OS << "nuw><";
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if (AR->getNoWrapFlags(FlagNSW))
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OS << "nsw><";
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if (AR->getNoWrapFlags(FlagNW) &&
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!AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
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OS << "nw><";
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WriteAsOperand(OS, AR->getLoop()->getHeader(), /*PrintType=*/false);
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OS << ">";
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return;
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}
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case scAddExpr:
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case scMulExpr:
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case scUMaxExpr:
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case scSMaxExpr: {
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const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
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const char *OpStr = 0;
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switch (NAry->getSCEVType()) {
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case scAddExpr: OpStr = " + "; break;
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case scMulExpr: OpStr = " * "; break;
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case scUMaxExpr: OpStr = " umax "; break;
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case scSMaxExpr: OpStr = " smax "; break;
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}
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OS << "(";
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for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
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I != E; ++I) {
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OS << **I;
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if (llvm::next(I) != E)
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OS << OpStr;
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}
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OS << ")";
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switch (NAry->getSCEVType()) {
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case scAddExpr:
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case scMulExpr:
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if (NAry->getNoWrapFlags(FlagNUW))
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OS << "<nuw>";
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if (NAry->getNoWrapFlags(FlagNSW))
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OS << "<nsw>";
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}
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return;
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}
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case scUDivExpr: {
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const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
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OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
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return;
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}
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case scUnknown: {
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const SCEVUnknown *U = cast<SCEVUnknown>(this);
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Type *AllocTy;
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if (U->isSizeOf(AllocTy)) {
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OS << "sizeof(" << *AllocTy << ")";
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return;
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}
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if (U->isAlignOf(AllocTy)) {
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OS << "alignof(" << *AllocTy << ")";
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return;
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}
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Type *CTy;
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Constant *FieldNo;
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if (U->isOffsetOf(CTy, FieldNo)) {
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OS << "offsetof(" << *CTy << ", ";
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WriteAsOperand(OS, FieldNo, false);
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OS << ")";
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return;
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}
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// Otherwise just print it normally.
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WriteAsOperand(OS, U->getValue(), false);
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return;
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}
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case scCouldNotCompute:
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OS << "***COULDNOTCOMPUTE***";
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return;
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default: break;
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}
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llvm_unreachable("Unknown SCEV kind!");
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}
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Type *SCEV::getType() const {
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switch (getSCEVType()) {
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case scConstant:
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return cast<SCEVConstant>(this)->getType();
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case scTruncate:
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case scZeroExtend:
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case scSignExtend:
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return cast<SCEVCastExpr>(this)->getType();
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case scAddRecExpr:
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case scMulExpr:
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case scUMaxExpr:
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case scSMaxExpr:
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return cast<SCEVNAryExpr>(this)->getType();
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case scAddExpr:
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return cast<SCEVAddExpr>(this)->getType();
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case scUDivExpr:
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return cast<SCEVUDivExpr>(this)->getType();
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case scUnknown:
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return cast<SCEVUnknown>(this)->getType();
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case scCouldNotCompute:
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llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
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default:
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llvm_unreachable("Unknown SCEV kind!");
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}
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}
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bool SCEV::isZero() const {
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if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
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return SC->getValue()->isZero();
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return false;
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}
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bool SCEV::isOne() const {
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if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
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return SC->getValue()->isOne();
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return false;
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}
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bool SCEV::isAllOnesValue() const {
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if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
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return SC->getValue()->isAllOnesValue();
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return false;
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}
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/// isNonConstantNegative - Return true if the specified scev is negated, but
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/// not a constant.
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bool SCEV::isNonConstantNegative() const {
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const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
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if (!Mul) return false;
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// If there is a constant factor, it will be first.
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const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
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if (!SC) return false;
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// Return true if the value is negative, this matches things like (-42 * V).
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return SC->getValue()->getValue().isNegative();
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}
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SCEVCouldNotCompute::SCEVCouldNotCompute() :
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SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
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bool SCEVCouldNotCompute::classof(const SCEV *S) {
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return S->getSCEVType() == scCouldNotCompute;
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}
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const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
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FoldingSetNodeID ID;
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ID.AddInteger(scConstant);
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ID.AddPointer(V);
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void *IP = 0;
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if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
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SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
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UniqueSCEVs.InsertNode(S, IP);
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return S;
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}
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const SCEV *ScalarEvolution::getConstant(const APInt& Val) {
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return getConstant(ConstantInt::get(getContext(), Val));
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}
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const SCEV *
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ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
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IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
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return getConstant(ConstantInt::get(ITy, V, isSigned));
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}
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SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
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unsigned SCEVTy, const SCEV *op, Type *ty)
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: SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
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SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
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const SCEV *op, Type *ty)
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: SCEVCastExpr(ID, scTruncate, op, ty) {
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assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
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(Ty->isIntegerTy() || Ty->isPointerTy()) &&
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"Cannot truncate non-integer value!");
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}
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SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
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const SCEV *op, Type *ty)
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: SCEVCastExpr(ID, scZeroExtend, op, ty) {
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assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
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(Ty->isIntegerTy() || Ty->isPointerTy()) &&
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"Cannot zero extend non-integer value!");
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}
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SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
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const SCEV *op, Type *ty)
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: SCEVCastExpr(ID, scSignExtend, op, ty) {
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assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
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(Ty->isIntegerTy() || Ty->isPointerTy()) &&
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"Cannot sign extend non-integer value!");
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}
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void SCEVUnknown::deleted() {
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// Clear this SCEVUnknown from various maps.
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SE->forgetMemoizedResults(this);
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// Remove this SCEVUnknown from the uniquing map.
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SE->UniqueSCEVs.RemoveNode(this);
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// Release the value.
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setValPtr(0);
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}
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void SCEVUnknown::allUsesReplacedWith(Value *New) {
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// Clear this SCEVUnknown from various maps.
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SE->forgetMemoizedResults(this);
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// Remove this SCEVUnknown from the uniquing map.
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SE->UniqueSCEVs.RemoveNode(this);
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// Update this SCEVUnknown to point to the new value. This is needed
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// because there may still be outstanding SCEVs which still point to
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// this SCEVUnknown.
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setValPtr(New);
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}
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bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
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if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
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if (VCE->getOpcode() == Instruction::PtrToInt)
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if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
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if (CE->getOpcode() == Instruction::GetElementPtr &&
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CE->getOperand(0)->isNullValue() &&
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CE->getNumOperands() == 2)
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if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
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if (CI->isOne()) {
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AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
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->getElementType();
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return true;
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}
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return false;
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}
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bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
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if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
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if (VCE->getOpcode() == Instruction::PtrToInt)
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if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
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if (CE->getOpcode() == Instruction::GetElementPtr &&
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CE->getOperand(0)->isNullValue()) {
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Type *Ty =
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cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
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if (StructType *STy = dyn_cast<StructType>(Ty))
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if (!STy->isPacked() &&
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CE->getNumOperands() == 3 &&
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CE->getOperand(1)->isNullValue()) {
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if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
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if (CI->isOne() &&
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STy->getNumElements() == 2 &&
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STy->getElementType(0)->isIntegerTy(1)) {
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AllocTy = STy->getElementType(1);
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return true;
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}
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}
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}
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return false;
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}
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bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
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if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
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if (VCE->getOpcode() == Instruction::PtrToInt)
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if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
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if (CE->getOpcode() == Instruction::GetElementPtr &&
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CE->getNumOperands() == 3 &&
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CE->getOperand(0)->isNullValue() &&
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CE->getOperand(1)->isNullValue()) {
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Type *Ty =
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cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
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// Ignore vector types here so that ScalarEvolutionExpander doesn't
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// emit getelementptrs that index into vectors.
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if (Ty->isStructTy() || Ty->isArrayTy()) {
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CTy = Ty;
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FieldNo = CE->getOperand(2);
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return true;
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}
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}
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return false;
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}
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//===----------------------------------------------------------------------===//
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// SCEV Utilities
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//===----------------------------------------------------------------------===//
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namespace {
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/// SCEVComplexityCompare - Return true if the complexity of the LHS is less
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/// than the complexity of the RHS. This comparator is used to canonicalize
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/// expressions.
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class SCEVComplexityCompare {
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const LoopInfo *const LI;
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public:
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explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
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// Return true or false if LHS is less than, or at least RHS, respectively.
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bool operator()(const SCEV *LHS, const SCEV *RHS) const {
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return compare(LHS, RHS) < 0;
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}
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// Return negative, zero, or positive, if LHS is less than, equal to, or
|
|
// greater than RHS, respectively. A three-way result allows recursive
|
|
// comparisons to be more efficient.
|
|
int compare(const SCEV *LHS, const SCEV *RHS) const {
|
|
// Fast-path: SCEVs are uniqued so we can do a quick equality check.
|
|
if (LHS == RHS)
|
|
return 0;
|
|
|
|
// Primarily, sort the SCEVs by their getSCEVType().
|
|
unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
|
|
if (LType != RType)
|
|
return (int)LType - (int)RType;
|
|
|
|
// Aside from the getSCEVType() ordering, the particular ordering
|
|
// isn't very important except that it's beneficial to be consistent,
|
|
// so that (a + b) and (b + a) don't end up as different expressions.
|
|
switch (LType) {
|
|
case scUnknown: {
|
|
const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
|
|
const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
|
|
|
|
// Sort SCEVUnknown values with some loose heuristics. TODO: This is
|
|
// not as complete as it could be.
|
|
const Value *LV = LU->getValue(), *RV = RU->getValue();
|
|
|
|
// Order pointer values after integer values. This helps SCEVExpander
|
|
// form GEPs.
|
|
bool LIsPointer = LV->getType()->isPointerTy(),
|
|
RIsPointer = RV->getType()->isPointerTy();
|
|
if (LIsPointer != RIsPointer)
|
|
return (int)LIsPointer - (int)RIsPointer;
|
|
|
|
// Compare getValueID values.
|
|
unsigned LID = LV->getValueID(),
|
|
RID = RV->getValueID();
|
|
if (LID != RID)
|
|
return (int)LID - (int)RID;
|
|
|
|
// Sort arguments by their position.
|
|
if (const Argument *LA = dyn_cast<Argument>(LV)) {
|
|
const Argument *RA = cast<Argument>(RV);
|
|
unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
|
|
return (int)LArgNo - (int)RArgNo;
|
|
}
|
|
|
|
// For instructions, compare their loop depth, and their operand
|
|
// count. This is pretty loose.
|
|
if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
|
|
const Instruction *RInst = cast<Instruction>(RV);
|
|
|
|
// Compare loop depths.
|
|
const BasicBlock *LParent = LInst->getParent(),
|
|
*RParent = RInst->getParent();
|
|
if (LParent != RParent) {
|
|
unsigned LDepth = LI->getLoopDepth(LParent),
|
|
RDepth = LI->getLoopDepth(RParent);
|
|
if (LDepth != RDepth)
|
|
return (int)LDepth - (int)RDepth;
|
|
}
|
|
|
|
// Compare the number of operands.
|
|
unsigned LNumOps = LInst->getNumOperands(),
|
|
RNumOps = RInst->getNumOperands();
|
|
return (int)LNumOps - (int)RNumOps;
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
case scConstant: {
|
|
const SCEVConstant *LC = cast<SCEVConstant>(LHS);
|
|
const SCEVConstant *RC = cast<SCEVConstant>(RHS);
|
|
|
|
// Compare constant values.
|
|
const APInt &LA = LC->getValue()->getValue();
|
|
const APInt &RA = RC->getValue()->getValue();
|
|
unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
|
|
if (LBitWidth != RBitWidth)
|
|
return (int)LBitWidth - (int)RBitWidth;
|
|
return LA.ult(RA) ? -1 : 1;
|
|
}
|
|
|
|
case scAddRecExpr: {
|
|
const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
|
|
const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
|
|
|
|
// Compare addrec loop depths.
|
|
const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
|
|
if (LLoop != RLoop) {
|
|
unsigned LDepth = LLoop->getLoopDepth(),
|
|
RDepth = RLoop->getLoopDepth();
|
|
if (LDepth != RDepth)
|
|
return (int)LDepth - (int)RDepth;
|
|
}
|
|
|
|
// Addrec complexity grows with operand count.
|
|
unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
|
|
if (LNumOps != RNumOps)
|
|
return (int)LNumOps - (int)RNumOps;
|
|
|
|
// Lexicographically compare.
|
|
for (unsigned i = 0; i != LNumOps; ++i) {
|
|
long X = compare(LA->getOperand(i), RA->getOperand(i));
|
|
if (X != 0)
|
|
return X;
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
case scAddExpr:
|
|
case scMulExpr:
|
|
case scSMaxExpr:
|
|
case scUMaxExpr: {
|
|
const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
|
|
const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
|
|
|
|
// Lexicographically compare n-ary expressions.
|
|
unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
|
|
if (LNumOps != RNumOps)
|
|
return (int)LNumOps - (int)RNumOps;
|
|
|
|
for (unsigned i = 0; i != LNumOps; ++i) {
|
|
if (i >= RNumOps)
|
|
return 1;
|
|
long X = compare(LC->getOperand(i), RC->getOperand(i));
|
|
if (X != 0)
|
|
return X;
|
|
}
|
|
return (int)LNumOps - (int)RNumOps;
|
|
}
|
|
|
|
case scUDivExpr: {
|
|
const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
|
|
const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
|
|
|
|
// Lexicographically compare udiv expressions.
|
|
long X = compare(LC->getLHS(), RC->getLHS());
|
|
if (X != 0)
|
|
return X;
|
|
return compare(LC->getRHS(), RC->getRHS());
|
|
}
|
|
|
|
case scTruncate:
|
|
case scZeroExtend:
|
|
case scSignExtend: {
|
|
const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
|
|
const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
|
|
|
|
// Compare cast expressions by operand.
|
|
return compare(LC->getOperand(), RC->getOperand());
|
|
}
|
|
|
|
default:
|
|
llvm_unreachable("Unknown SCEV kind!");
|
|
}
|
|
}
|
|
};
|
|
}
|
|
|
|
/// 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 deterministic
|
|
/// 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(SmallVectorImpl<const SCEV *> &Ops,
|
|
LoopInfo *LI) {
|
|
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.
|
|
const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
|
|
if (SCEVComplexityCompare(LI)(RHS, LHS))
|
|
std::swap(LHS, RHS);
|
|
return;
|
|
}
|
|
|
|
// Do the rough sort by complexity.
|
|
std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
|
|
|
|
// 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) {
|
|
const 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
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
/// BinomialCoefficient - Compute BC(It, K). The result has width W.
|
|
/// Assume, K > 0.
|
|
static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
|
|
ScalarEvolution &SE,
|
|
Type *ResultTy) {
|
|
// Handle the simplest case efficiently.
|
|
if (K == 1)
|
|
return SE.getTruncateOrZeroExtend(It, ResultTy);
|
|
|
|
// 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 the return value. 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.
|
|
//
|
|
// However, this code doesn't use exactly that formula; the formula it uses
|
|
// is something like the following, where T is the number of factors of 2 in
|
|
// K! (i.e. trailing zeros in the binary representation of K!), and ^ is
|
|
// exponentiation:
|
|
//
|
|
// BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
|
|
//
|
|
// This formula is trivially equivalent to the previous formula. However,
|
|
// this formula can be implemented much more efficiently. The trick is that
|
|
// K! / 2^T is odd, and exact division by an odd number *is* safe in modular
|
|
// arithmetic. To do exact division in modular arithmetic, all we have
|
|
// to do is multiply by the inverse. Therefore, this step can be done at
|
|
// width W.
|
|
//
|
|
// The next issue is how to safely do the division by 2^T. The way this
|
|
// is done is by doing the multiplication step at a width of at least W + T
|
|
// bits. This way, the bottom W+T bits of the product are accurate. Then,
|
|
// when we perform the division by 2^T (which is equivalent to a right shift
|
|
// by T), the bottom W bits are accurate. Extra bits are okay; they'll get
|
|
// truncated out after the division by 2^T.
|
|
//
|
|
// In comparison to just directly using the first formula, this technique
|
|
// is much more efficient; using the first formula requires W * K bits,
|
|
// but this formula less than W + K bits. Also, the first formula requires
|
|
// a division step, whereas this formula only requires multiplies and shifts.
|
|
//
|
|
// It doesn't matter whether the subtraction step is done in the calculation
|
|
// width or the input iteration count's width; if the subtraction overflows,
|
|
// the result must be zero anyway. We prefer here to do it in the width of
|
|
// the induction variable because it helps a lot for certain cases; CodeGen
|
|
// isn't smart enough to ignore the overflow, which leads to much less
|
|
// efficient code if the width of the subtraction is wider than the native
|
|
// register width.
|
|
//
|
|
// (It's possible to not widen at all by pulling out factors of 2 before
|
|
// the multiplication; for example, K=2 can be calculated as
|
|
// It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
|
|
// extra arithmetic, so it's not an obvious win, and it gets
|
|
// much more complicated for K > 3.)
|
|
|
|
// Protection from insane SCEVs; this bound is conservative,
|
|
// but it probably doesn't matter.
|
|
if (K > 1000)
|
|
return SE.getCouldNotCompute();
|
|
|
|
unsigned W = SE.getTypeSizeInBits(ResultTy);
|
|
|
|
// Calculate K! / 2^T and T; we divide out the factors of two before
|
|
// multiplying for calculating K! / 2^T to avoid overflow.
|
|
// Other overflow doesn't matter because we only care about the bottom
|
|
// W bits of the result.
|
|
APInt OddFactorial(W, 1);
|
|
unsigned T = 1;
|
|
for (unsigned i = 3; i <= K; ++i) {
|
|
APInt Mult(W, i);
|
|
unsigned TwoFactors = Mult.countTrailingZeros();
|
|
T += TwoFactors;
|
|
Mult = Mult.lshr(TwoFactors);
|
|
OddFactorial *= Mult;
|
|
}
|
|
|
|
// We need at least W + T bits for the multiplication step
|
|
unsigned CalculationBits = W + T;
|
|
|
|
// Calculate 2^T, at width T+W.
|
|
APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
|
|
|
|
// Calculate the multiplicative inverse of K! / 2^T;
|
|
// this multiplication factor will perform the exact division by
|
|
// K! / 2^T.
|
|
APInt Mod = APInt::getSignedMinValue(W+1);
|
|
APInt MultiplyFactor = OddFactorial.zext(W+1);
|
|
MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
|
|
MultiplyFactor = MultiplyFactor.trunc(W);
|
|
|
|
// Calculate the product, at width T+W
|
|
IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
|
|
CalculationBits);
|
|
const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
|
|
for (unsigned i = 1; i != K; ++i) {
|
|
const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
|
|
Dividend = SE.getMulExpr(Dividend,
|
|
SE.getTruncateOrZeroExtend(S, CalculationTy));
|
|
}
|
|
|
|
// Divide by 2^T
|
|
const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
|
|
|
|
// Truncate the result, and divide by K! / 2^T.
|
|
|
|
return SE.getMulExpr(SE.getConstant(MultiplyFactor),
|
|
SE.getTruncateOrZeroExtend(DivResult, ResultTy));
|
|
}
|
|
|
|
/// 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.
|
|
///
|
|
const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
|
|
ScalarEvolution &SE) const {
|
|
const SCEV *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.
|
|
const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
|
|
if (isa<SCEVCouldNotCompute>(Coeff))
|
|
return Coeff;
|
|
|
|
Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
|
|
}
|
|
return Result;
|
|
}
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// SCEV Expression folder implementations
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
|
|
Type *Ty) {
|
|
assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
|
|
"This is not a truncating conversion!");
|
|
assert(isSCEVable(Ty) &&
|
|
"This is not a conversion to a SCEVable type!");
|
|
Ty = getEffectiveSCEVType(Ty);
|
|
|
|
FoldingSetNodeID ID;
|
|
ID.AddInteger(scTruncate);
|
|
ID.AddPointer(Op);
|
|
ID.AddPointer(Ty);
|
|
void *IP = 0;
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
|
|
// Fold if the operand is constant.
|
|
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
|
|
return getConstant(
|
|
cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
|
|
|
|
// trunc(trunc(x)) --> trunc(x)
|
|
if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
|
|
return getTruncateExpr(ST->getOperand(), Ty);
|
|
|
|
// trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
|
|
if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
|
|
return getTruncateOrSignExtend(SS->getOperand(), Ty);
|
|
|
|
// trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
|
|
if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
|
|
return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
|
|
|
|
// trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
|
|
// eliminate all the truncates.
|
|
if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
|
|
SmallVector<const SCEV *, 4> Operands;
|
|
bool hasTrunc = false;
|
|
for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
|
|
const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
|
|
hasTrunc = isa<SCEVTruncateExpr>(S);
|
|
Operands.push_back(S);
|
|
}
|
|
if (!hasTrunc)
|
|
return getAddExpr(Operands);
|
|
UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
|
|
}
|
|
|
|
// trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
|
|
// eliminate all the truncates.
|
|
if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
|
|
SmallVector<const SCEV *, 4> Operands;
|
|
bool hasTrunc = false;
|
|
for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
|
|
const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
|
|
hasTrunc = isa<SCEVTruncateExpr>(S);
|
|
Operands.push_back(S);
|
|
}
|
|
if (!hasTrunc)
|
|
return getMulExpr(Operands);
|
|
UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
|
|
}
|
|
|
|
// If the input value is a chrec scev, truncate the chrec's operands.
|
|
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
|
|
SmallVector<const SCEV *, 4> Operands;
|
|
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
|
|
Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
|
|
return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
|
|
}
|
|
|
|
// The cast wasn't folded; create an explicit cast node. We can reuse
|
|
// the existing insert position since if we get here, we won't have
|
|
// made any changes which would invalidate it.
|
|
SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
|
|
Op, Ty);
|
|
UniqueSCEVs.InsertNode(S, IP);
|
|
return S;
|
|
}
|
|
|
|
const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
|
|
Type *Ty) {
|
|
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
|
|
"This is not an extending conversion!");
|
|
assert(isSCEVable(Ty) &&
|
|
"This is not a conversion to a SCEVable type!");
|
|
Ty = getEffectiveSCEVType(Ty);
|
|
|
|
// Fold if the operand is constant.
|
|
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
|
|
return getConstant(
|
|
cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
|
|
|
|
// zext(zext(x)) --> zext(x)
|
|
if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
|
|
return getZeroExtendExpr(SZ->getOperand(), Ty);
|
|
|
|
// Before doing any expensive analysis, check to see if we've already
|
|
// computed a SCEV for this Op and Ty.
|
|
FoldingSetNodeID ID;
|
|
ID.AddInteger(scZeroExtend);
|
|
ID.AddPointer(Op);
|
|
ID.AddPointer(Ty);
|
|
void *IP = 0;
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
|
|
// zext(trunc(x)) --> zext(x) or x or trunc(x)
|
|
if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
|
|
// It's possible the bits taken off by the truncate were all zero bits. If
|
|
// so, we should be able to simplify this further.
|
|
const SCEV *X = ST->getOperand();
|
|
ConstantRange CR = getUnsignedRange(X);
|
|
unsigned TruncBits = getTypeSizeInBits(ST->getType());
|
|
unsigned NewBits = getTypeSizeInBits(Ty);
|
|
if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
|
|
CR.zextOrTrunc(NewBits)))
|
|
return getTruncateOrZeroExtend(X, Ty);
|
|
}
|
|
|
|
// 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 allows analysis of something like
|
|
// this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
|
|
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
|
|
if (AR->isAffine()) {
|
|
const SCEV *Start = AR->getStart();
|
|
const SCEV *Step = AR->getStepRecurrence(*this);
|
|
unsigned BitWidth = getTypeSizeInBits(AR->getType());
|
|
const Loop *L = AR->getLoop();
|
|
|
|
// If we have special knowledge that this addrec won't overflow,
|
|
// we don't need to do any further analysis.
|
|
if (AR->getNoWrapFlags(SCEV::FlagNUW))
|
|
return getAddRecExpr(getZeroExtendExpr(Start, Ty),
|
|
getZeroExtendExpr(Step, Ty),
|
|
L, AR->getNoWrapFlags());
|
|
|
|
// Check whether the backedge-taken count is SCEVCouldNotCompute.
|
|
// Note that this serves two purposes: It filters out loops that are
|
|
// simply not analyzable, and it covers the case where this code is
|
|
// being called from within backedge-taken count analysis, such that
|
|
// attempting to ask for the backedge-taken count would likely result
|
|
// in infinite recursion. In the later case, the analysis code will
|
|
// cope with a conservative value, and it will take care to purge
|
|
// that value once it has finished.
|
|
const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
|
|
if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
|
|
// Manually compute the final value for AR, checking for
|
|
// overflow.
|
|
|
|
// Check whether the backedge-taken count can be losslessly casted to
|
|
// the addrec's type. The count is always unsigned.
|
|
const SCEV *CastedMaxBECount =
|
|
getTruncateOrZeroExtend(MaxBECount, Start->getType());
|
|
const SCEV *RecastedMaxBECount =
|
|
getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
|
|
if (MaxBECount == RecastedMaxBECount) {
|
|
Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
|
|
// Check whether Start+Step*MaxBECount has no unsigned overflow.
|
|
const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
|
|
const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
|
|
const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
|
|
const SCEV *WideMaxBECount =
|
|
getZeroExtendExpr(CastedMaxBECount, WideTy);
|
|
const SCEV *OperandExtendedAdd =
|
|
getAddExpr(WideStart,
|
|
getMulExpr(WideMaxBECount,
|
|
getZeroExtendExpr(Step, WideTy)));
|
|
if (ZAdd == OperandExtendedAdd) {
|
|
// Cache knowledge of AR NUW, which is propagated to this AddRec.
|
|
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
|
|
// Return the expression with the addrec on the outside.
|
|
return getAddRecExpr(getZeroExtendExpr(Start, Ty),
|
|
getZeroExtendExpr(Step, Ty),
|
|
L, AR->getNoWrapFlags());
|
|
}
|
|
// Similar to above, only this time treat the step value as signed.
|
|
// This covers loops that count down.
|
|
OperandExtendedAdd =
|
|
getAddExpr(WideStart,
|
|
getMulExpr(WideMaxBECount,
|
|
getSignExtendExpr(Step, WideTy)));
|
|
if (ZAdd == OperandExtendedAdd) {
|
|
// Cache knowledge of AR NW, which is propagated to this AddRec.
|
|
// Negative step causes unsigned wrap, but it still can't self-wrap.
|
|
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
|
|
// Return the expression with the addrec on the outside.
|
|
return getAddRecExpr(getZeroExtendExpr(Start, Ty),
|
|
getSignExtendExpr(Step, Ty),
|
|
L, AR->getNoWrapFlags());
|
|
}
|
|
}
|
|
|
|
// If the backedge is guarded by a comparison with the pre-inc value
|
|
// the addrec is safe. Also, if the entry is guarded by a comparison
|
|
// with the start value and the backedge is guarded by a comparison
|
|
// with the post-inc value, the addrec is safe.
|
|
if (isKnownPositive(Step)) {
|
|
const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
|
|
getUnsignedRange(Step).getUnsignedMax());
|
|
if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
|
|
(isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
|
|
isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
|
|
AR->getPostIncExpr(*this), N))) {
|
|
// Cache knowledge of AR NUW, which is propagated to this AddRec.
|
|
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
|
|
// Return the expression with the addrec on the outside.
|
|
return getAddRecExpr(getZeroExtendExpr(Start, Ty),
|
|
getZeroExtendExpr(Step, Ty),
|
|
L, AR->getNoWrapFlags());
|
|
}
|
|
} else if (isKnownNegative(Step)) {
|
|
const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
|
|
getSignedRange(Step).getSignedMin());
|
|
if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
|
|
(isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
|
|
isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
|
|
AR->getPostIncExpr(*this), N))) {
|
|
// Cache knowledge of AR NW, which is propagated to this AddRec.
|
|
// Negative step causes unsigned wrap, but it still can't self-wrap.
|
|
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
|
|
// Return the expression with the addrec on the outside.
|
|
return getAddRecExpr(getZeroExtendExpr(Start, Ty),
|
|
getSignExtendExpr(Step, Ty),
|
|
L, AR->getNoWrapFlags());
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// The cast wasn't folded; create an explicit cast node.
|
|
// Recompute the insert position, as it may have been invalidated.
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
|
|
Op, Ty);
|
|
UniqueSCEVs.InsertNode(S, IP);
|
|
return S;
|
|
}
|
|
|
|
// Get the limit of a recurrence such that incrementing by Step cannot cause
|
|
// signed overflow as long as the value of the recurrence within the loop does
|
|
// not exceed this limit before incrementing.
|
|
static const SCEV *getOverflowLimitForStep(const SCEV *Step,
|
|
ICmpInst::Predicate *Pred,
|
|
ScalarEvolution *SE) {
|
|
unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
|
|
if (SE->isKnownPositive(Step)) {
|
|
*Pred = ICmpInst::ICMP_SLT;
|
|
return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
|
|
SE->getSignedRange(Step).getSignedMax());
|
|
}
|
|
if (SE->isKnownNegative(Step)) {
|
|
*Pred = ICmpInst::ICMP_SGT;
|
|
return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
|
|
SE->getSignedRange(Step).getSignedMin());
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
// The recurrence AR has been shown to have no signed wrap. Typically, if we can
|
|
// prove NSW for AR, then we can just as easily prove NSW for its preincrement
|
|
// or postincrement sibling. This allows normalizing a sign extended AddRec as
|
|
// such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a
|
|
// result, the expression "Step + sext(PreIncAR)" is congruent with
|
|
// "sext(PostIncAR)"
|
|
static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR,
|
|
Type *Ty,
|
|
ScalarEvolution *SE) {
|
|
const Loop *L = AR->getLoop();
|
|
const SCEV *Start = AR->getStart();
|
|
const SCEV *Step = AR->getStepRecurrence(*SE);
|
|
|
|
// Check for a simple looking step prior to loop entry.
|
|
const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
|
|
if (!SA)
|
|
return 0;
|
|
|
|
// Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
|
|
// subtraction is expensive. For this purpose, perform a quick and dirty
|
|
// difference, by checking for Step in the operand list.
|
|
SmallVector<const SCEV *, 4> DiffOps;
|
|
for (SCEVAddExpr::op_iterator I = SA->op_begin(), E = SA->op_end();
|
|
I != E; ++I) {
|
|
if (*I != Step)
|
|
DiffOps.push_back(*I);
|
|
}
|
|
if (DiffOps.size() == SA->getNumOperands())
|
|
return 0;
|
|
|
|
// This is a postinc AR. Check for overflow on the preinc recurrence using the
|
|
// same three conditions that getSignExtendedExpr checks.
|
|
|
|
// 1. NSW flags on the step increment.
|
|
const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
|
|
const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
|
|
SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
|
|
|
|
if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW))
|
|
return PreStart;
|
|
|
|
// 2. Direct overflow check on the step operation's expression.
|
|
unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
|
|
Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
|
|
const SCEV *OperandExtendedStart =
|
|
SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy),
|
|
SE->getSignExtendExpr(Step, WideTy));
|
|
if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) {
|
|
// Cache knowledge of PreAR NSW.
|
|
if (PreAR)
|
|
const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW);
|
|
// FIXME: this optimization needs a unit test
|
|
DEBUG(dbgs() << "SCEV: untested prestart overflow check\n");
|
|
return PreStart;
|
|
}
|
|
|
|
// 3. Loop precondition.
|
|
ICmpInst::Predicate Pred;
|
|
const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE);
|
|
|
|
if (OverflowLimit &&
|
|
SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
|
|
return PreStart;
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
// Get the normalized sign-extended expression for this AddRec's Start.
|
|
static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR,
|
|
Type *Ty,
|
|
ScalarEvolution *SE) {
|
|
const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE);
|
|
if (!PreStart)
|
|
return SE->getSignExtendExpr(AR->getStart(), Ty);
|
|
|
|
return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty),
|
|
SE->getSignExtendExpr(PreStart, Ty));
|
|
}
|
|
|
|
const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
|
|
Type *Ty) {
|
|
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
|
|
"This is not an extending conversion!");
|
|
assert(isSCEVable(Ty) &&
|
|
"This is not a conversion to a SCEVable type!");
|
|
Ty = getEffectiveSCEVType(Ty);
|
|
|
|
// Fold if the operand is constant.
|
|
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
|
|
return getConstant(
|
|
cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
|
|
|
|
// sext(sext(x)) --> sext(x)
|
|
if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
|
|
return getSignExtendExpr(SS->getOperand(), Ty);
|
|
|
|
// sext(zext(x)) --> zext(x)
|
|
if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
|
|
return getZeroExtendExpr(SZ->getOperand(), Ty);
|
|
|
|
// Before doing any expensive analysis, check to see if we've already
|
|
// computed a SCEV for this Op and Ty.
|
|
FoldingSetNodeID ID;
|
|
ID.AddInteger(scSignExtend);
|
|
ID.AddPointer(Op);
|
|
ID.AddPointer(Ty);
|
|
void *IP = 0;
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
|
|
// If the input value is provably positive, build a zext instead.
|
|
if (isKnownNonNegative(Op))
|
|
return getZeroExtendExpr(Op, Ty);
|
|
|
|
// sext(trunc(x)) --> sext(x) or x or trunc(x)
|
|
if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
|
|
// It's possible the bits taken off by the truncate were all sign bits. If
|
|
// so, we should be able to simplify this further.
|
|
const SCEV *X = ST->getOperand();
|
|
ConstantRange CR = getSignedRange(X);
|
|
unsigned TruncBits = getTypeSizeInBits(ST->getType());
|
|
unsigned NewBits = getTypeSizeInBits(Ty);
|
|
if (CR.truncate(TruncBits).signExtend(NewBits).contains(
|
|
CR.sextOrTrunc(NewBits)))
|
|
return getTruncateOrSignExtend(X, Ty);
|
|
}
|
|
|
|
// 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 allows analysis of something like
|
|
// this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
|
|
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
|
|
if (AR->isAffine()) {
|
|
const SCEV *Start = AR->getStart();
|
|
const SCEV *Step = AR->getStepRecurrence(*this);
|
|
unsigned BitWidth = getTypeSizeInBits(AR->getType());
|
|
const Loop *L = AR->getLoop();
|
|
|
|
// If we have special knowledge that this addrec won't overflow,
|
|
// we don't need to do any further analysis.
|
|
if (AR->getNoWrapFlags(SCEV::FlagNSW))
|
|
return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
|
|
getSignExtendExpr(Step, Ty),
|
|
L, SCEV::FlagNSW);
|
|
|
|
// Check whether the backedge-taken count is SCEVCouldNotCompute.
|
|
// Note that this serves two purposes: It filters out loops that are
|
|
// simply not analyzable, and it covers the case where this code is
|
|
// being called from within backedge-taken count analysis, such that
|
|
// attempting to ask for the backedge-taken count would likely result
|
|
// in infinite recursion. In the later case, the analysis code will
|
|
// cope with a conservative value, and it will take care to purge
|
|
// that value once it has finished.
|
|
const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
|
|
if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
|
|
// Manually compute the final value for AR, checking for
|
|
// overflow.
|
|
|
|
// Check whether the backedge-taken count can be losslessly casted to
|
|
// the addrec's type. The count is always unsigned.
|
|
const SCEV *CastedMaxBECount =
|
|
getTruncateOrZeroExtend(MaxBECount, Start->getType());
|
|
const SCEV *RecastedMaxBECount =
|
|
getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
|
|
if (MaxBECount == RecastedMaxBECount) {
|
|
Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
|
|
// Check whether Start+Step*MaxBECount has no signed overflow.
|
|
const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
|
|
const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
|
|
const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
|
|
const SCEV *WideMaxBECount =
|
|
getZeroExtendExpr(CastedMaxBECount, WideTy);
|
|
const SCEV *OperandExtendedAdd =
|
|
getAddExpr(WideStart,
|
|
getMulExpr(WideMaxBECount,
|
|
getSignExtendExpr(Step, WideTy)));
|
|
if (SAdd == OperandExtendedAdd) {
|
|
// Cache knowledge of AR NSW, which is propagated to this AddRec.
|
|
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
|
|
// Return the expression with the addrec on the outside.
|
|
return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
|
|
getSignExtendExpr(Step, Ty),
|
|
L, AR->getNoWrapFlags());
|
|
}
|
|
// Similar to above, only this time treat the step value as unsigned.
|
|
// This covers loops that count up with an unsigned step.
|
|
OperandExtendedAdd =
|
|
getAddExpr(WideStart,
|
|
getMulExpr(WideMaxBECount,
|
|
getZeroExtendExpr(Step, WideTy)));
|
|
if (SAdd == OperandExtendedAdd) {
|
|
// Cache knowledge of AR NSW, which is propagated to this AddRec.
|
|
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
|
|
// Return the expression with the addrec on the outside.
|
|
return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
|
|
getZeroExtendExpr(Step, Ty),
|
|
L, AR->getNoWrapFlags());
|
|
}
|
|
}
|
|
|
|
// If the backedge is guarded by a comparison with the pre-inc value
|
|
// the addrec is safe. Also, if the entry is guarded by a comparison
|
|
// with the start value and the backedge is guarded by a comparison
|
|
// with the post-inc value, the addrec is safe.
|
|
ICmpInst::Predicate Pred;
|
|
const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
|
|
if (OverflowLimit &&
|
|
(isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
|
|
(isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
|
|
isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
|
|
OverflowLimit)))) {
|
|
// Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
|
|
const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
|
|
return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
|
|
getSignExtendExpr(Step, Ty),
|
|
L, AR->getNoWrapFlags());
|
|
}
|
|
}
|
|
}
|
|
|
|
// The cast wasn't folded; create an explicit cast node.
|
|
// Recompute the insert position, as it may have been invalidated.
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
|
|
Op, Ty);
|
|
UniqueSCEVs.InsertNode(S, IP);
|
|
return S;
|
|
}
|
|
|
|
/// getAnyExtendExpr - Return a SCEV for the given operand extended with
|
|
/// unspecified bits out to the given type.
|
|
///
|
|
const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
|
|
Type *Ty) {
|
|
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
|
|
"This is not an extending conversion!");
|
|
assert(isSCEVable(Ty) &&
|
|
"This is not a conversion to a SCEVable type!");
|
|
Ty = getEffectiveSCEVType(Ty);
|
|
|
|
// Sign-extend negative constants.
|
|
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
|
|
if (SC->getValue()->getValue().isNegative())
|
|
return getSignExtendExpr(Op, Ty);
|
|
|
|
// Peel off a truncate cast.
|
|
if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
|
|
const SCEV *NewOp = T->getOperand();
|
|
if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
|
|
return getAnyExtendExpr(NewOp, Ty);
|
|
return getTruncateOrNoop(NewOp, Ty);
|
|
}
|
|
|
|
// Next try a zext cast. If the cast is folded, use it.
|
|
const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
|
|
if (!isa<SCEVZeroExtendExpr>(ZExt))
|
|
return ZExt;
|
|
|
|
// Next try a sext cast. If the cast is folded, use it.
|
|
const SCEV *SExt = getSignExtendExpr(Op, Ty);
|
|
if (!isa<SCEVSignExtendExpr>(SExt))
|
|
return SExt;
|
|
|
|
// Force the cast to be folded into the operands of an addrec.
|
|
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
|
|
SmallVector<const SCEV *, 4> Ops;
|
|
for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
|
|
I != E; ++I)
|
|
Ops.push_back(getAnyExtendExpr(*I, Ty));
|
|
return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
|
|
}
|
|
|
|
// If the expression is obviously signed, use the sext cast value.
|
|
if (isa<SCEVSMaxExpr>(Op))
|
|
return SExt;
|
|
|
|
// Absent any other information, use the zext cast value.
|
|
return ZExt;
|
|
}
|
|
|
|
/// CollectAddOperandsWithScales - Process the given Ops list, which is
|
|
/// a list of operands to be added under the given scale, update the given
|
|
/// map. This is a helper function for getAddRecExpr. As an example of
|
|
/// what it does, given a sequence of operands that would form an add
|
|
/// expression like this:
|
|
///
|
|
/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
|
|
///
|
|
/// where A and B are constants, update the map with these values:
|
|
///
|
|
/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
|
|
///
|
|
/// and add 13 + A*B*29 to AccumulatedConstant.
|
|
/// This will allow getAddRecExpr to produce this:
|
|
///
|
|
/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
|
|
///
|
|
/// This form often exposes folding opportunities that are hidden in
|
|
/// the original operand list.
|
|
///
|
|
/// Return true iff it appears that any interesting folding opportunities
|
|
/// may be exposed. This helps getAddRecExpr short-circuit extra work in
|
|
/// the common case where no interesting opportunities are present, and
|
|
/// is also used as a check to avoid infinite recursion.
|
|
///
|
|
static bool
|
|
CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
|
|
SmallVectorImpl<const SCEV *> &NewOps,
|
|
APInt &AccumulatedConstant,
|
|
const SCEV *const *Ops, size_t NumOperands,
|
|
const APInt &Scale,
|
|
ScalarEvolution &SE) {
|
|
bool Interesting = false;
|
|
|
|
// Iterate over the add operands. They are sorted, with constants first.
|
|
unsigned i = 0;
|
|
while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
|
|
++i;
|
|
// Pull a buried constant out to the outside.
|
|
if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
|
|
Interesting = true;
|
|
AccumulatedConstant += Scale * C->getValue()->getValue();
|
|
}
|
|
|
|
// Next comes everything else. We're especially interested in multiplies
|
|
// here, but they're in the middle, so just visit the rest with one loop.
|
|
for (; i != NumOperands; ++i) {
|
|
const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
|
|
if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
|
|
APInt NewScale =
|
|
Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
|
|
if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
|
|
// A multiplication of a constant with another add; recurse.
|
|
const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
|
|
Interesting |=
|
|
CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
|
|
Add->op_begin(), Add->getNumOperands(),
|
|
NewScale, SE);
|
|
} else {
|
|
// A multiplication of a constant with some other value. Update
|
|
// the map.
|
|
SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
|
|
const SCEV *Key = SE.getMulExpr(MulOps);
|
|
std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
|
|
M.insert(std::make_pair(Key, NewScale));
|
|
if (Pair.second) {
|
|
NewOps.push_back(Pair.first->first);
|
|
} else {
|
|
Pair.first->second += NewScale;
|
|
// The map already had an entry for this value, which may indicate
|
|
// a folding opportunity.
|
|
Interesting = true;
|
|
}
|
|
}
|
|
} else {
|
|
// An ordinary operand. Update the map.
|
|
std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
|
|
M.insert(std::make_pair(Ops[i], Scale));
|
|
if (Pair.second) {
|
|
NewOps.push_back(Pair.first->first);
|
|
} else {
|
|
Pair.first->second += Scale;
|
|
// The map already had an entry for this value, which may indicate
|
|
// a folding opportunity.
|
|
Interesting = true;
|
|
}
|
|
}
|
|
}
|
|
|
|
return Interesting;
|
|
}
|
|
|
|
namespace {
|
|
struct APIntCompare {
|
|
bool operator()(const APInt &LHS, const APInt &RHS) const {
|
|
return LHS.ult(RHS);
|
|
}
|
|
};
|
|
}
|
|
|
|
/// getAddExpr - Get a canonical add expression, or something simpler if
|
|
/// possible.
|
|
const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
|
|
SCEV::NoWrapFlags Flags) {
|
|
assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
|
|
"only nuw or nsw allowed");
|
|
assert(!Ops.empty() && "Cannot get empty add!");
|
|
if (Ops.size() == 1) return Ops[0];
|
|
#ifndef NDEBUG
|
|
Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
|
|
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
|
|
assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
|
|
"SCEVAddExpr operand types don't match!");
|
|
#endif
|
|
|
|
// If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
|
|
// And vice-versa.
|
|
int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
|
|
SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
|
|
if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
|
|
bool All = true;
|
|
for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
|
|
E = Ops.end(); I != E; ++I)
|
|
if (!isKnownNonNegative(*I)) {
|
|
All = false;
|
|
break;
|
|
}
|
|
if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
|
|
}
|
|
|
|
// Sort by complexity, this groups all similar expression types together.
|
|
GroupByComplexity(Ops, LI);
|
|
|
|
// If there are any constants, fold them together.
|
|
unsigned Idx = 0;
|
|
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
|
|
++Idx;
|
|
assert(Idx < Ops.size());
|
|
while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
|
|
// We found two constants, fold them together!
|
|
Ops[0] = getConstant(LHSC->getValue()->getValue() +
|
|
RHSC->getValue()->getValue());
|
|
if (Ops.size() == 2) return Ops[0];
|
|
Ops.erase(Ops.begin()+1); // Erase the folded element
|
|
LHSC = cast<SCEVConstant>(Ops[0]);
|
|
}
|
|
|
|
// If we are left with a constant zero being added, strip it off.
|
|
if (LHSC->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 more than
|
|
// once. If so, merge them together into an multiply expression. Since we
|
|
// sorted the list, these values are required to be adjacent.
|
|
Type *Ty = Ops[0]->getType();
|
|
bool FoundMatch = false;
|
|
for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
|
|
if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
|
|
// Scan ahead to count how many equal operands there are.
|
|
unsigned Count = 2;
|
|
while (i+Count != e && Ops[i+Count] == Ops[i])
|
|
++Count;
|
|
// Merge the values into a multiply.
|
|
const SCEV *Scale = getConstant(Ty, Count);
|
|
const SCEV *Mul = getMulExpr(Scale, Ops[i]);
|
|
if (Ops.size() == Count)
|
|
return Mul;
|
|
Ops[i] = Mul;
|
|
Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
|
|
--i; e -= Count - 1;
|
|
FoundMatch = true;
|
|
}
|
|
if (FoundMatch)
|
|
return getAddExpr(Ops, Flags);
|
|
|
|
// Check for truncates. If all the operands are truncated from the same
|
|
// type, see if factoring out the truncate would permit the result to be
|
|
// folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
|
|
// if the contents of the resulting outer trunc fold to something simple.
|
|
for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
|
|
const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
|
|
Type *DstType = Trunc->getType();
|
|
Type *SrcType = Trunc->getOperand()->getType();
|
|
SmallVector<const SCEV *, 8> LargeOps;
|
|
bool Ok = true;
|
|
// Check all the operands to see if they can be represented in the
|
|
// source type of the truncate.
|
|
for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
|
|
if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
|
|
if (T->getOperand()->getType() != SrcType) {
|
|
Ok = false;
|
|
break;
|
|
}
|
|
LargeOps.push_back(T->getOperand());
|
|
} else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
|
|
LargeOps.push_back(getAnyExtendExpr(C, SrcType));
|
|
} else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
|
|
SmallVector<const SCEV *, 8> LargeMulOps;
|
|
for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
|
|
if (const SCEVTruncateExpr *T =
|
|
dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
|
|
if (T->getOperand()->getType() != SrcType) {
|
|
Ok = false;
|
|
break;
|
|
}
|
|
LargeMulOps.push_back(T->getOperand());
|
|
} else if (const SCEVConstant *C =
|
|
dyn_cast<SCEVConstant>(M->getOperand(j))) {
|
|
LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
|
|
} else {
|
|
Ok = false;
|
|
break;
|
|
}
|
|
}
|
|
if (Ok)
|
|
LargeOps.push_back(getMulExpr(LargeMulOps));
|
|
} else {
|
|
Ok = false;
|
|
break;
|
|
}
|
|
}
|
|
if (Ok) {
|
|
// Evaluate the expression in the larger type.
|
|
const SCEV *Fold = getAddExpr(LargeOps, Flags);
|
|
// If it folds to something simple, use it. Otherwise, don't.
|
|
if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
|
|
return getTruncateExpr(Fold, DstType);
|
|
}
|
|
}
|
|
|
|
// Skip past any other 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 (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
|
|
// If we have an add, expand the add operands onto the end of the operands
|
|
// list.
|
|
Ops.erase(Ops.begin()+Idx);
|
|
Ops.append(Add->op_begin(), Add->op_end());
|
|
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 acquired.
|
|
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;
|
|
|
|
// Check to see if there are any folding opportunities present with
|
|
// operands multiplied by constant values.
|
|
if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
|
|
uint64_t BitWidth = getTypeSizeInBits(Ty);
|
|
DenseMap<const SCEV *, APInt> M;
|
|
SmallVector<const SCEV *, 8> NewOps;
|
|
APInt AccumulatedConstant(BitWidth, 0);
|
|
if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
|
|
Ops.data(), Ops.size(),
|
|
APInt(BitWidth, 1), *this)) {
|
|
// Some interesting folding opportunity is present, so its worthwhile to
|
|
// re-generate the operands list. Group the operands by constant scale,
|
|
// to avoid multiplying by the same constant scale multiple times.
|
|
std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
|
|
for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
|
|
E = NewOps.end(); I != E; ++I)
|
|
MulOpLists[M.find(*I)->second].push_back(*I);
|
|
// Re-generate the operands list.
|
|
Ops.clear();
|
|
if (AccumulatedConstant != 0)
|
|
Ops.push_back(getConstant(AccumulatedConstant));
|
|
for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
|
|
I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
|
|
if (I->first != 0)
|
|
Ops.push_back(getMulExpr(getConstant(I->first),
|
|
getAddExpr(I->second)));
|
|
if (Ops.empty())
|
|
return getConstant(Ty, 0);
|
|
if (Ops.size() == 1)
|
|
return Ops[0];
|
|
return getAddExpr(Ops);
|
|
}
|
|
}
|
|
|
|
// 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) {
|
|
const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
|
|
for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
|
|
const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
|
|
if (isa<SCEVConstant>(MulOpSCEV))
|
|
continue;
|
|
for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
|
|
if (MulOpSCEV == Ops[AddOp]) {
|
|
// Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
|
|
const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
|
|
if (Mul->getNumOperands() != 2) {
|
|
// If the multiply has more than two operands, we must get the
|
|
// Y*Z term.
|
|
SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
|
|
Mul->op_begin()+MulOp);
|
|
MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
|
|
InnerMul = getMulExpr(MulOps);
|
|
}
|
|
const SCEV *One = getConstant(Ty, 1);
|
|
const SCEV *AddOne = getAddExpr(One, InnerMul);
|
|
const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
|
|
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) {
|
|
const 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))
|
|
const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
|
|
if (Mul->getNumOperands() != 2) {
|
|
SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
|
|
Mul->op_begin()+MulOp);
|
|
MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
|
|
InnerMul1 = getMulExpr(MulOps);
|
|
}
|
|
const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
|
|
if (OtherMul->getNumOperands() != 2) {
|
|
SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
|
|
OtherMul->op_begin()+OMulOp);
|
|
MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
|
|
InnerMul2 = getMulExpr(MulOps);
|
|
}
|
|
const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
|
|
const SCEV *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.
|
|
SmallVector<const SCEV *, 8> LIOps;
|
|
const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
|
|
const Loop *AddRecLoop = AddRec->getLoop();
|
|
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
|
|
if (isLoopInvariant(Ops[i], AddRecLoop)) {
|
|
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());
|
|
|
|
SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
|
|
AddRec->op_end());
|
|
AddRecOps[0] = getAddExpr(LIOps);
|
|
|
|
// Build the new addrec. Propagate the NUW and NSW flags if both the
|
|
// outer add and the inner addrec are guaranteed to have no overflow.
|
|
// Always propagate NW.
|
|
Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
|
|
const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
|
|
|
|
// 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-invariant 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 (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
|
|
// Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
|
|
SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
|
|
AddRec->op_end());
|
|
for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
|
|
++OtherIdx)
|
|
if (const SCEVAddRecExpr *OtherAddRec =
|
|
dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
|
|
if (OtherAddRec->getLoop() == AddRecLoop) {
|
|
for (unsigned i = 0, e = OtherAddRec->getNumOperands();
|
|
i != e; ++i) {
|
|
if (i >= AddRecOps.size()) {
|
|
AddRecOps.append(OtherAddRec->op_begin()+i,
|
|
OtherAddRec->op_end());
|
|
break;
|
|
}
|
|
AddRecOps[i] = getAddExpr(AddRecOps[i],
|
|
OtherAddRec->getOperand(i));
|
|
}
|
|
Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
|
|
}
|
|
// Step size has changed, so we cannot guarantee no self-wraparound.
|
|
Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
|
|
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.
|
|
FoldingSetNodeID ID;
|
|
ID.AddInteger(scAddExpr);
|
|
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
|
|
ID.AddPointer(Ops[i]);
|
|
void *IP = 0;
|
|
SCEVAddExpr *S =
|
|
static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
|
|
if (!S) {
|
|
const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
|
|
std::uninitialized_copy(Ops.begin(), Ops.end(), O);
|
|
S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
|
|
O, Ops.size());
|
|
UniqueSCEVs.InsertNode(S, IP);
|
|
}
|
|
S->setNoWrapFlags(Flags);
|
|
return S;
|
|
}
|
|
|
|
static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
|
|
uint64_t k = i*j;
|
|
if (j > 1 && k / j != i) Overflow = true;
|
|
return k;
|
|
}
|
|
|
|
/// Compute the result of "n choose k", the binomial coefficient. If an
|
|
/// intermediate computation overflows, Overflow will be set and the return will
|
|
/// be garbage. Overflow is not cleared on absence of overflow.
|
|
static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
|
|
// We use the multiplicative formula:
|
|
// n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
|
|
// At each iteration, we take the n-th term of the numeral and divide by the
|
|
// (k-n)th term of the denominator. This division will always produce an
|
|
// integral result, and helps reduce the chance of overflow in the
|
|
// intermediate computations. However, we can still overflow even when the
|
|
// final result would fit.
|
|
|
|
if (n == 0 || n == k) return 1;
|
|
if (k > n) return 0;
|
|
|
|
if (k > n/2)
|
|
k = n-k;
|
|
|
|
uint64_t r = 1;
|
|
for (uint64_t i = 1; i <= k; ++i) {
|
|
r = umul_ov(r, n-(i-1), Overflow);
|
|
r /= i;
|
|
}
|
|
return r;
|
|
}
|
|
|
|
/// getMulExpr - Get a canonical multiply expression, or something simpler if
|
|
/// possible.
|
|
const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
|
|
SCEV::NoWrapFlags Flags) {
|
|
assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
|
|
"only nuw or nsw allowed");
|
|
assert(!Ops.empty() && "Cannot get empty mul!");
|
|
if (Ops.size() == 1) return Ops[0];
|
|
#ifndef NDEBUG
|
|
Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
|
|
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
|
|
assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
|
|
"SCEVMulExpr operand types don't match!");
|
|
#endif
|
|
|
|
// If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
|
|
// And vice-versa.
|
|
int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
|
|
SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
|
|
if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
|
|
bool All = true;
|
|
for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
|
|
E = Ops.end(); I != E; ++I)
|
|
if (!isKnownNonNegative(*I)) {
|
|
All = false;
|
|
break;
|
|
}
|
|
if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
|
|
}
|
|
|
|
// Sort by complexity, this groups all similar expression types together.
|
|
GroupByComplexity(Ops, LI);
|
|
|
|
// If there are any constants, fold them together.
|
|
unsigned Idx = 0;
|
|
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
|
|
|
|
// C1*(C2+V) -> C1*C2 + C1*V
|
|
if (Ops.size() == 2)
|
|
if (const 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 (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
|
|
// We found two constants, fold them together!
|
|
ConstantInt *Fold = ConstantInt::get(getContext(),
|
|
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];
|
|
} else if (Ops[0]->isAllOnesValue()) {
|
|
// If we have a mul by -1 of an add, try distributing the -1 among the
|
|
// add operands.
|
|
if (Ops.size() == 2) {
|
|
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
|
|
SmallVector<const SCEV *, 4> NewOps;
|
|
bool AnyFolded = false;
|
|
for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
|
|
E = Add->op_end(); I != E; ++I) {
|
|
const SCEV *Mul = getMulExpr(Ops[0], *I);
|
|
if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
|
|
NewOps.push_back(Mul);
|
|
}
|
|
if (AnyFolded)
|
|
return getAddExpr(NewOps);
|
|
}
|
|
else if (const SCEVAddRecExpr *
|
|
AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
|
|
// Negation preserves a recurrence's no self-wrap property.
|
|
SmallVector<const SCEV *, 4> Operands;
|
|
for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
|
|
E = AddRec->op_end(); I != E; ++I) {
|
|
Operands.push_back(getMulExpr(Ops[0], *I));
|
|
}
|
|
return getAddRecExpr(Operands, AddRec->getLoop(),
|
|
AddRec->getNoWrapFlags(SCEV::FlagNW));
|
|
}
|
|
}
|
|
}
|
|
|
|
if (Ops.size() == 1)
|
|
return Ops[0];
|
|
}
|
|
|
|
// Skip over the add expression until we get to a multiply.
|
|
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
|
|
++Idx;
|
|
|
|
// If there are mul operands inline them all into this expression.
|
|
if (Idx < Ops.size()) {
|
|
bool DeletedMul = false;
|
|
while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
|
|
// If we have an mul, expand the mul operands onto the end of the operands
|
|
// list.
|
|
Ops.erase(Ops.begin()+Idx);
|
|
Ops.append(Mul->op_begin(), Mul->op_end());
|
|
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 acquired.
|
|
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.
|
|
SmallVector<const SCEV *, 8> LIOps;
|
|
const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
|
|
const Loop *AddRecLoop = AddRec->getLoop();
|
|
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
|
|
if (isLoopInvariant(Ops[i], AddRecLoop)) {
|
|
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}
|
|
SmallVector<const SCEV *, 4> NewOps;
|
|
NewOps.reserve(AddRec->getNumOperands());
|
|
const SCEV *Scale = getMulExpr(LIOps);
|
|
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
|
|
NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
|
|
|
|
// Build the new addrec. Propagate the NUW and NSW flags if both the
|
|
// outer mul and the inner addrec are guaranteed to have no overflow.
|
|
//
|
|
// No self-wrap cannot be guaranteed after changing the step size, but
|
|
// will be inferred if either NUW or NSW is true.
|
|
Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
|
|
const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
|
|
|
|
// 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-invariant 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 (AddRecLoop != cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop())
|
|
continue;
|
|
|
|
// {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
|
|
// = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
|
|
// choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
|
|
// ]]],+,...up to x=2n}.
|
|
// Note that the arguments to choose() are always integers with values
|
|
// known at compile time, never SCEV objects.
|
|
//
|
|
// The implementation avoids pointless extra computations when the two
|
|
// addrec's are of different length (mathematically, it's equivalent to
|
|
// an infinite stream of zeros on the right).
|
|
bool OpsModified = false;
|
|
for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
|
|
++OtherIdx) {
|
|
const SCEVAddRecExpr *OtherAddRec =
|
|
dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
|
|
if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
|
|
continue;
|
|
|
|
bool Overflow = false;
|
|
Type *Ty = AddRec->getType();
|
|
bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
|
|
SmallVector<const SCEV*, 7> AddRecOps;
|
|
for (int x = 0, xe = AddRec->getNumOperands() +
|
|
OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
|
|
const SCEV *Term = getConstant(Ty, 0);
|
|
for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
|
|
uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
|
|
for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
|
|
ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
|
|
z < ze && !Overflow; ++z) {
|
|
uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
|
|
uint64_t Coeff;
|
|
if (LargerThan64Bits)
|
|
Coeff = umul_ov(Coeff1, Coeff2, Overflow);
|
|
else
|
|
Coeff = Coeff1*Coeff2;
|
|
const SCEV *CoeffTerm = getConstant(Ty, Coeff);
|
|
const SCEV *Term1 = AddRec->getOperand(y-z);
|
|
const SCEV *Term2 = OtherAddRec->getOperand(z);
|
|
Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
|
|
}
|
|
}
|
|
AddRecOps.push_back(Term);
|
|
}
|
|
if (!Overflow) {
|
|
const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
|
|
SCEV::FlagAnyWrap);
|
|
if (Ops.size() == 2) return NewAddRec;
|
|
Ops[Idx] = NewAddRec;
|
|
Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
|
|
OpsModified = true;
|
|
AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
|
|
if (!AddRec)
|
|
break;
|
|
}
|
|
}
|
|
if (OpsModified)
|
|
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.
|
|
FoldingSetNodeID ID;
|
|
ID.AddInteger(scMulExpr);
|
|
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
|
|
ID.AddPointer(Ops[i]);
|
|
void *IP = 0;
|
|
SCEVMulExpr *S =
|
|
static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
|
|
if (!S) {
|
|
const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
|
|
std::uninitialized_copy(Ops.begin(), Ops.end(), O);
|
|
S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
|
|
O, Ops.size());
|
|
UniqueSCEVs.InsertNode(S, IP);
|
|
}
|
|
S->setNoWrapFlags(Flags);
|
|
return S;
|
|
}
|
|
|
|
/// getUDivExpr - Get a canonical unsigned division expression, or something
|
|
/// simpler if possible.
|
|
const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
|
|
const SCEV *RHS) {
|
|
assert(getEffectiveSCEVType(LHS->getType()) ==
|
|
getEffectiveSCEVType(RHS->getType()) &&
|
|
"SCEVUDivExpr operand types don't match!");
|
|
|
|
if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
|
|
if (RHSC->getValue()->equalsInt(1))
|
|
return LHS; // X udiv 1 --> x
|
|
// If the denominator is zero, the result of the udiv is undefined. Don't
|
|
// try to analyze it, because the resolution chosen here may differ from
|
|
// the resolution chosen in other parts of the compiler.
|
|
if (!RHSC->getValue()->isZero()) {
|
|
// Determine if the division can be folded into the operands of
|
|
// its operands.
|
|
// TODO: Generalize this to non-constants by using known-bits information.
|
|
Type *Ty = LHS->getType();
|
|
unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
|
|
unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
|
|
// For non-power-of-two values, effectively round the value up to the
|
|
// nearest power of two.
|
|
if (!RHSC->getValue()->getValue().isPowerOf2())
|
|
++MaxShiftAmt;
|
|
IntegerType *ExtTy =
|
|
IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
|
|
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
|
|
if (const SCEVConstant *Step =
|
|
dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
|
|
// {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
|
|
const APInt &StepInt = Step->getValue()->getValue();
|
|
const APInt &DivInt = RHSC->getValue()->getValue();
|
|
if (!StepInt.urem(DivInt) &&
|
|
getZeroExtendExpr(AR, ExtTy) ==
|
|
getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
|
|
getZeroExtendExpr(Step, ExtTy),
|
|
AR->getLoop(), SCEV::FlagAnyWrap)) {
|
|
SmallVector<const SCEV *, 4> Operands;
|
|
for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
|
|
Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
|
|
return getAddRecExpr(Operands, AR->getLoop(),
|
|
SCEV::FlagNW);
|
|
}
|
|
/// Get a canonical UDivExpr for a recurrence.
|
|
/// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
|
|
// We can currently only fold X%N if X is constant.
|
|
const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
|
|
if (StartC && !DivInt.urem(StepInt) &&
|
|
getZeroExtendExpr(AR, ExtTy) ==
|
|
getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
|
|
getZeroExtendExpr(Step, ExtTy),
|
|
AR->getLoop(), SCEV::FlagAnyWrap)) {
|
|
const APInt &StartInt = StartC->getValue()->getValue();
|
|
const APInt &StartRem = StartInt.urem(StepInt);
|
|
if (StartRem != 0)
|
|
LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
|
|
AR->getLoop(), SCEV::FlagNW);
|
|
}
|
|
}
|
|
// (A*B)/C --> A*(B/C) if safe and B/C can be folded.
|
|
if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
|
|
SmallVector<const SCEV *, 4> Operands;
|
|
for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
|
|
Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
|
|
if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
|
|
// Find an operand that's safely divisible.
|
|
for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
|
|
const SCEV *Op = M->getOperand(i);
|
|
const SCEV *Div = getUDivExpr(Op, RHSC);
|
|
if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
|
|
Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
|
|
M->op_end());
|
|
Operands[i] = Div;
|
|
return getMulExpr(Operands);
|
|
}
|
|
}
|
|
}
|
|
// (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
|
|
if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
|
|
SmallVector<const SCEV *, 4> Operands;
|
|
for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
|
|
Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
|
|
if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
|
|
Operands.clear();
|
|
for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
|
|
const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
|
|
if (isa<SCEVUDivExpr>(Op) ||
|
|
getMulExpr(Op, RHS) != A->getOperand(i))
|
|
break;
|
|
Operands.push_back(Op);
|
|
}
|
|
if (Operands.size() == A->getNumOperands())
|
|
return getAddExpr(Operands);
|
|
}
|
|
}
|
|
|
|
// Fold if both operands are constant.
|
|
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
|
|
Constant *LHSCV = LHSC->getValue();
|
|
Constant *RHSCV = RHSC->getValue();
|
|
return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
|
|
RHSCV)));
|
|
}
|
|
}
|
|
}
|
|
|
|
FoldingSetNodeID ID;
|
|
ID.AddInteger(scUDivExpr);
|
|
ID.AddPointer(LHS);
|
|
ID.AddPointer(RHS);
|
|
void *IP = 0;
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
|
|
LHS, RHS);
|
|
UniqueSCEVs.InsertNode(S, IP);
|
|
return S;
|
|
}
|
|
|
|
|
|
/// getAddRecExpr - Get an add recurrence expression for the specified loop.
|
|
/// Simplify the expression as much as possible.
|
|
const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
|
|
const Loop *L,
|
|
SCEV::NoWrapFlags Flags) {
|
|
SmallVector<const SCEV *, 4> Operands;
|
|
Operands.push_back(Start);
|
|
if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
|
|
if (StepChrec->getLoop() == L) {
|
|
Operands.append(StepChrec->op_begin(), StepChrec->op_end());
|
|
return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
|
|
}
|
|
|
|
Operands.push_back(Step);
|
|
return getAddRecExpr(Operands, L, Flags);
|
|
}
|
|
|
|
/// getAddRecExpr - Get an add recurrence expression for the specified loop.
|
|
/// Simplify the expression as much as possible.
|
|
const SCEV *
|
|
ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
|
|
const Loop *L, SCEV::NoWrapFlags Flags) {
|
|
if (Operands.size() == 1) return Operands[0];
|
|
#ifndef NDEBUG
|
|
Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
|
|
for (unsigned i = 1, e = Operands.size(); i != e; ++i)
|
|
assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
|
|
"SCEVAddRecExpr operand types don't match!");
|
|
for (unsigned i = 0, e = Operands.size(); i != e; ++i)
|
|
assert(isLoopInvariant(Operands[i], L) &&
|
|
"SCEVAddRecExpr operand is not loop-invariant!");
|
|
#endif
|
|
|
|
if (Operands.back()->isZero()) {
|
|
Operands.pop_back();
|
|
return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
|
|
}
|
|
|
|
// It's tempting to want to call getMaxBackedgeTakenCount count here and
|
|
// use that information to infer NUW and NSW flags. However, computing a
|
|
// BE count requires calling getAddRecExpr, so we may not yet have a
|
|
// meaningful BE count at this point (and if we don't, we'd be stuck
|
|
// with a SCEVCouldNotCompute as the cached BE count).
|
|
|
|
// If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
|
|
// And vice-versa.
|
|
int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
|
|
SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
|
|
if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
|
|
bool All = true;
|
|
for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
|
|
E = Operands.end(); I != E; ++I)
|
|
if (!isKnownNonNegative(*I)) {
|
|
All = false;
|
|
break;
|
|
}
|
|
if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
|
|
}
|
|
|
|
// Canonicalize nested AddRecs in by nesting them in order of loop depth.
|
|
if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
|
|
const Loop *NestedLoop = NestedAR->getLoop();
|
|
if (L->contains(NestedLoop) ?
|
|
(L->getLoopDepth() < NestedLoop->getLoopDepth()) :
|
|
(!NestedLoop->contains(L) &&
|
|
DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
|
|
SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
|
|
NestedAR->op_end());
|
|
Operands[0] = NestedAR->getStart();
|
|
// AddRecs require their operands be loop-invariant with respect to their
|
|
// loops. Don't perform this transformation if it would break this
|
|
// requirement.
|
|
bool AllInvariant = true;
|
|
for (unsigned i = 0, e = Operands.size(); i != e; ++i)
|
|
if (!isLoopInvariant(Operands[i], L)) {
|
|
AllInvariant = false;
|
|
break;
|
|
}
|
|
if (AllInvariant) {
|
|
// Create a recurrence for the outer loop with the same step size.
|
|
//
|
|
// The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
|
|
// inner recurrence has the same property.
|
|
SCEV::NoWrapFlags OuterFlags =
|
|
maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
|
|
|
|
NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
|
|
AllInvariant = true;
|
|
for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
|
|
if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
|
|
AllInvariant = false;
|
|
break;
|
|
}
|
|
if (AllInvariant) {
|
|
// Ok, both add recurrences are valid after the transformation.
|
|
//
|
|
// The inner recurrence keeps its NW flag but only keeps NUW/NSW if
|
|
// the outer recurrence has the same property.
|
|
SCEV::NoWrapFlags InnerFlags =
|
|
maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
|
|
return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
|
|
}
|
|
}
|
|
// Reset Operands to its original state.
|
|
Operands[0] = NestedAR;
|
|
}
|
|
}
|
|
|
|
// Okay, it looks like we really DO need an addrec expr. Check to see if we
|
|
// already have one, otherwise create a new one.
|
|
FoldingSetNodeID ID;
|
|
ID.AddInteger(scAddRecExpr);
|
|
for (unsigned i = 0, e = Operands.size(); i != e; ++i)
|
|
ID.AddPointer(Operands[i]);
|
|
ID.AddPointer(L);
|
|
void *IP = 0;
|
|
SCEVAddRecExpr *S =
|
|
static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
|
|
if (!S) {
|
|
const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
|
|
std::uninitialized_copy(Operands.begin(), Operands.end(), O);
|
|
S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
|
|
O, Operands.size(), L);
|
|
UniqueSCEVs.InsertNode(S, IP);
|
|
}
|
|
S->setNoWrapFlags(Flags);
|
|
return S;
|
|
}
|
|
|
|
const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
|
|
const SCEV *RHS) {
|
|
SmallVector<const SCEV *, 2> Ops;
|
|
Ops.push_back(LHS);
|
|
Ops.push_back(RHS);
|
|
return getSMaxExpr(Ops);
|
|
}
|
|
|
|
const SCEV *
|
|
ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
|
|
assert(!Ops.empty() && "Cannot get empty smax!");
|
|
if (Ops.size() == 1) return Ops[0];
|
|
#ifndef NDEBUG
|
|
Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
|
|
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
|
|
assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
|
|
"SCEVSMaxExpr operand types don't match!");
|
|
#endif
|
|
|
|
// Sort by complexity, this groups all similar expression types together.
|
|
GroupByComplexity(Ops, LI);
|
|
|
|
// If there are any constants, fold them together.
|
|
unsigned Idx = 0;
|
|
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
|
|
++Idx;
|
|
assert(Idx < Ops.size());
|
|
while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
|
|
// We found two constants, fold them together!
|
|
ConstantInt *Fold = ConstantInt::get(getContext(),
|
|
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 minimum-int, strip it off.
|
|
if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
|
|
Ops.erase(Ops.begin());
|
|
--Idx;
|
|
} else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
|
|
// If we have an smax with a constant maximum-int, it will always be
|
|
// maximum-int.
|
|
return Ops[0];
|
|
}
|
|
|
|
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 (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
|
|
Ops.erase(Ops.begin()+Idx);
|
|
Ops.append(SMax->op_begin(), SMax->op_end());
|
|
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)
|
|
// X smax Y smax Y --> X smax Y
|
|
// X smax Y --> X, if X is always greater than Y
|
|
if (Ops[i] == Ops[i+1] ||
|
|
isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
|
|
Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
|
|
--i; --e;
|
|
} else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
|
|
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.
|
|
FoldingSetNodeID ID;
|
|
ID.AddInteger(scSMaxExpr);
|
|
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
|
|
ID.AddPointer(Ops[i]);
|
|
void *IP = 0;
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
|
|
std::uninitialized_copy(Ops.begin(), Ops.end(), O);
|
|
SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
|
|
O, Ops.size());
|
|
UniqueSCEVs.InsertNode(S, IP);
|
|
return S;
|
|
}
|
|
|
|
const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
|
|
const SCEV *RHS) {
|
|
SmallVector<const SCEV *, 2> Ops;
|
|
Ops.push_back(LHS);
|
|
Ops.push_back(RHS);
|
|
return getUMaxExpr(Ops);
|
|
}
|
|
|
|
const SCEV *
|
|
ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
|
|
assert(!Ops.empty() && "Cannot get empty umax!");
|
|
if (Ops.size() == 1) return Ops[0];
|
|
#ifndef NDEBUG
|
|
Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
|
|
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
|
|
assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
|
|
"SCEVUMaxExpr operand types don't match!");
|
|
#endif
|
|
|
|
// Sort by complexity, this groups all similar expression types together.
|
|
GroupByComplexity(Ops, LI);
|
|
|
|
// If there are any constants, fold them together.
|
|
unsigned Idx = 0;
|
|
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
|
|
++Idx;
|
|
assert(Idx < Ops.size());
|
|
while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
|
|
// We found two constants, fold them together!
|
|
ConstantInt *Fold = ConstantInt::get(getContext(),
|
|
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 minimum-int, strip it off.
|
|
if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
|
|
Ops.erase(Ops.begin());
|
|
--Idx;
|
|
} else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
|
|
// If we have an umax with a constant maximum-int, it will always be
|
|
// maximum-int.
|
|
return Ops[0];
|
|
}
|
|
|
|
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 (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
|
|
Ops.erase(Ops.begin()+Idx);
|
|
Ops.append(UMax->op_begin(), UMax->op_end());
|
|
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)
|
|
// X umax Y umax Y --> X umax Y
|
|
// X umax Y --> X, if X is always greater than Y
|
|
if (Ops[i] == Ops[i+1] ||
|
|
isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
|
|
Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
|
|
--i; --e;
|
|
} else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
|
|
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.
|
|
FoldingSetNodeID ID;
|
|
ID.AddInteger(scUMaxExpr);
|
|
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
|
|
ID.AddPointer(Ops[i]);
|
|
void *IP = 0;
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
|
|
std::uninitialized_copy(Ops.begin(), Ops.end(), O);
|
|
SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
|
|
O, Ops.size());
|
|
UniqueSCEVs.InsertNode(S, IP);
|
|
return S;
|
|
}
|
|
|
|
const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
|
|
const SCEV *RHS) {
|
|
// ~smax(~x, ~y) == smin(x, y).
|
|
return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
|
|
}
|
|
|
|
const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
|
|
const SCEV *RHS) {
|
|
// ~umax(~x, ~y) == umin(x, y)
|
|
return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
|
|
}
|
|
|
|
const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
|
|
// If we have DataLayout, we can bypass creating a target-independent
|
|
// constant expression and then folding it back into a ConstantInt.
|
|
// This is just a compile-time optimization.
|
|
if (TD)
|
|
return getConstant(IntTy, TD->getTypeAllocSize(AllocTy));
|
|
|
|
Constant *C = ConstantExpr::getSizeOf(AllocTy);
|
|
if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
|
|
if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
|
|
C = Folded;
|
|
Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
|
|
assert(Ty == IntTy && "Effective SCEV type doesn't match");
|
|
return getTruncateOrZeroExtend(getSCEV(C), Ty);
|
|
}
|
|
|
|
const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
|
|
StructType *STy,
|
|
unsigned FieldNo) {
|
|
// If we have DataLayout, we can bypass creating a target-independent
|
|
// constant expression and then folding it back into a ConstantInt.
|
|
// This is just a compile-time optimization.
|
|
if (TD) {
|
|
return getConstant(IntTy,
|
|
TD->getStructLayout(STy)->getElementOffset(FieldNo));
|
|
}
|
|
|
|
Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
|
|
if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
|
|
if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
|
|
C = Folded;
|
|
|
|
Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
|
|
return getTruncateOrZeroExtend(getSCEV(C), Ty);
|
|
}
|
|
|
|
const SCEV *ScalarEvolution::getUnknown(Value *V) {
|
|
// Don't attempt to do anything other than create a SCEVUnknown object
|
|
// here. createSCEV only calls getUnknown after checking for all other
|
|
// interesting possibilities, and any other code that calls getUnknown
|
|
// is doing so in order to hide a value from SCEV canonicalization.
|
|
|
|
FoldingSetNodeID ID;
|
|
ID.AddInteger(scUnknown);
|
|
ID.AddPointer(V);
|
|
void *IP = 0;
|
|
if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
|
|
assert(cast<SCEVUnknown>(S)->getValue() == V &&
|
|
"Stale SCEVUnknown in uniquing map!");
|
|
return S;
|
|
}
|
|
SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
|
|
FirstUnknown);
|
|
FirstUnknown = cast<SCEVUnknown>(S);
|
|
UniqueSCEVs.InsertNode(S, IP);
|
|
return S;
|
|
}
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// Basic SCEV Analysis and PHI Idiom Recognition Code
|
|
//
|
|
|
|
/// isSCEVable - Test if values of the given type are analyzable within
|
|
/// the SCEV framework. This primarily includes integer types, and it
|
|
/// can optionally include pointer types if the ScalarEvolution class
|
|
/// has access to target-specific information.
|
|
bool ScalarEvolution::isSCEVable(Type *Ty) const {
|
|
// Integers and pointers are always SCEVable.
|
|
return Ty->isIntegerTy() || Ty->isPointerTy();
|
|
}
|
|
|
|
/// getTypeSizeInBits - Return the size in bits of the specified type,
|
|
/// for which isSCEVable must return true.
|
|
uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
|
|
assert(isSCEVable(Ty) && "Type is not SCEVable!");
|
|
|
|
// If we have a DataLayout, use it!
|
|
if (TD)
|
|
return TD->getTypeSizeInBits(Ty);
|
|
|
|
// Integer types have fixed sizes.
|
|
if (Ty->isIntegerTy())
|
|
return Ty->getPrimitiveSizeInBits();
|
|
|
|
// The only other support type is pointer. Without DataLayout, conservatively
|
|
// assume pointers are 64-bit.
|
|
assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
|
|
return 64;
|
|
}
|
|
|
|
/// getEffectiveSCEVType - Return a type with the same bitwidth as
|
|
/// the given type and which represents how SCEV will treat the given
|
|
/// type, for which isSCEVable must return true. For pointer types,
|
|
/// this is the pointer-sized integer type.
|
|
Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
|
|
assert(isSCEVable(Ty) && "Type is not SCEVable!");
|
|
|
|
if (Ty->isIntegerTy()) {
|
|
return Ty;
|
|
}
|
|
|
|
// The only other support type is pointer.
|
|
assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
|
|
|
|
if (TD)
|
|
return TD->getIntPtrType(Ty);
|
|
|
|
// Without DataLayout, conservatively assume pointers are 64-bit.
|
|
return Type::getInt64Ty(getContext());
|
|
}
|
|
|
|
const SCEV *ScalarEvolution::getCouldNotCompute() {
|
|
return &CouldNotCompute;
|
|
}
|
|
|
|
namespace {
|
|
// Helper class working with SCEVTraversal to figure out if a SCEV contains
|
|
// a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
|
|
// is set iff if find such SCEVUnknown.
|
|
//
|
|
struct FindInvalidSCEVUnknown {
|
|
bool FindOne;
|
|
FindInvalidSCEVUnknown() { FindOne = false; }
|
|
bool follow(const SCEV *S) {
|
|
switch (S->getSCEVType()) {
|
|
case scConstant:
|
|
return false;
|
|
case scUnknown:
|
|
if (!cast<SCEVUnknown>(S)->getValue())
|
|
FindOne = true;
|
|
return false;
|
|
default:
|
|
return true;
|
|
}
|
|
}
|
|
bool isDone() const { return FindOne; }
|
|
};
|
|
}
|
|
|
|
bool ScalarEvolution::checkValidity(const SCEV *S) const {
|
|
FindInvalidSCEVUnknown F;
|
|
SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
|
|
ST.visitAll(S);
|
|
|
|
return !F.FindOne;
|
|
}
|
|
|
|
/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
|
|
/// expression and create a new one.
|
|
const SCEV *ScalarEvolution::getSCEV(Value *V) {
|
|
assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
|
|
|
|
ValueExprMapType::iterator I = ValueExprMap.find_as(V);
|
|
if (I != ValueExprMap.end()) {
|
|
const SCEV *S = I->second;
|
|
if (checkValidity(S))
|
|
return S;
|
|
else
|
|
ValueExprMap.erase(I);
|
|
}
|
|
const SCEV *S = createSCEV(V);
|
|
|
|
// The process of creating a SCEV for V may have caused other SCEVs
|
|
// to have been created, so it's necessary to insert the new entry
|
|
// from scratch, rather than trying to remember the insert position
|
|
// above.
|
|
ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
|
|
return S;
|
|
}
|
|
|
|
/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
|
|
///
|
|
const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
|
|
if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
|
|
return getConstant(
|
|
cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
|
|
|
|
Type *Ty = V->getType();
|
|
Ty = getEffectiveSCEVType(Ty);
|
|
return getMulExpr(V,
|
|
getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
|
|
}
|
|
|
|
/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
|
|
const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
|
|
if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
|
|
return getConstant(
|
|
cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
|
|
|
|
Type *Ty = V->getType();
|
|
Ty = getEffectiveSCEVType(Ty);
|
|
const SCEV *AllOnes =
|
|
getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
|
|
return getMinusSCEV(AllOnes, V);
|
|
}
|
|
|
|
/// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
|
|
const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
|
|
SCEV::NoWrapFlags Flags) {
|
|
assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
|
|
|
|
// Fast path: X - X --> 0.
|
|
if (LHS == RHS)
|
|
return getConstant(LHS->getType(), 0);
|
|
|
|
// X - Y --> X + -Y
|
|
return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
|
|
}
|
|
|
|
/// 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.
|
|
const SCEV *
|
|
ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
|
|
Type *SrcTy = V->getType();
|
|
assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
|
|
(Ty->isIntegerTy() || Ty->isPointerTy()) &&
|
|
"Cannot truncate or zero extend with non-integer arguments!");
|
|
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
|
|
return V; // No conversion
|
|
if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
|
|
return getTruncateExpr(V, Ty);
|
|
return getZeroExtendExpr(V, Ty);
|
|
}
|
|
|
|
/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
|
|
/// input value to the specified type. If the type must be extended, it is sign
|
|
/// extended.
|
|
const SCEV *
|
|
ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
|
|
Type *Ty) {
|
|
Type *SrcTy = V->getType();
|
|
assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
|
|
(Ty->isIntegerTy() || Ty->isPointerTy()) &&
|
|
"Cannot truncate or zero extend with non-integer arguments!");
|
|
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
|
|
return V; // No conversion
|
|
if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
|
|
return getTruncateExpr(V, Ty);
|
|
return getSignExtendExpr(V, Ty);
|
|
}
|
|
|
|
/// getNoopOrZeroExtend - 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. The conversion must not be narrowing.
|
|
const SCEV *
|
|
ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
|
|
Type *SrcTy = V->getType();
|
|
assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
|
|
(Ty->isIntegerTy() || Ty->isPointerTy()) &&
|
|
"Cannot noop or zero extend with non-integer arguments!");
|
|
assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
|
|
"getNoopOrZeroExtend cannot truncate!");
|
|
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
|
|
return V; // No conversion
|
|
return getZeroExtendExpr(V, Ty);
|
|
}
|
|
|
|
/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
|
|
/// input value to the specified type. If the type must be extended, it is sign
|
|
/// extended. The conversion must not be narrowing.
|
|
const SCEV *
|
|
ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
|
|
Type *SrcTy = V->getType();
|
|
assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
|
|
(Ty->isIntegerTy() || Ty->isPointerTy()) &&
|
|
"Cannot noop or sign extend with non-integer arguments!");
|
|
assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
|
|
"getNoopOrSignExtend cannot truncate!");
|
|
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
|
|
return V; // No conversion
|
|
return getSignExtendExpr(V, Ty);
|
|
}
|
|
|
|
/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
|
|
/// the input value to the specified type. If the type must be extended,
|
|
/// it is extended with unspecified bits. The conversion must not be
|
|
/// narrowing.
|
|
const SCEV *
|
|
ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
|
|
Type *SrcTy = V->getType();
|
|
assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
|
|
(Ty->isIntegerTy() || Ty->isPointerTy()) &&
|
|
"Cannot noop or any extend with non-integer arguments!");
|
|
assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
|
|
"getNoopOrAnyExtend cannot truncate!");
|
|
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
|
|
return V; // No conversion
|
|
return getAnyExtendExpr(V, Ty);
|
|
}
|
|
|
|
/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
|
|
/// input value to the specified type. The conversion must not be widening.
|
|
const SCEV *
|
|
ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
|
|
Type *SrcTy = V->getType();
|
|
assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
|
|
(Ty->isIntegerTy() || Ty->isPointerTy()) &&
|
|
"Cannot truncate or noop with non-integer arguments!");
|
|
assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
|
|
"getTruncateOrNoop cannot extend!");
|
|
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
|
|
return V; // No conversion
|
|
return getTruncateExpr(V, Ty);
|
|
}
|
|
|
|
/// getUMaxFromMismatchedTypes - Promote the operands to the wider of
|
|
/// the types using zero-extension, and then perform a umax operation
|
|
/// with them.
|
|
const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
|
|
const SCEV *RHS) {
|
|
const SCEV *PromotedLHS = LHS;
|
|
const SCEV *PromotedRHS = RHS;
|
|
|
|
if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
|
|
PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
|
|
else
|
|
PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
|
|
|
|
return getUMaxExpr(PromotedLHS, PromotedRHS);
|
|
}
|
|
|
|
/// getUMinFromMismatchedTypes - Promote the operands to the wider of
|
|
/// the types using zero-extension, and then perform a umin operation
|
|
/// with them.
|
|
const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
|
|
const SCEV *RHS) {
|
|
const SCEV *PromotedLHS = LHS;
|
|
const SCEV *PromotedRHS = RHS;
|
|
|
|
if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
|
|
PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
|
|
else
|
|
PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
|
|
|
|
return getUMinExpr(PromotedLHS, PromotedRHS);
|
|
}
|
|
|
|
/// getPointerBase - Transitively follow the chain of pointer-type operands
|
|
/// until reaching a SCEV that does not have a single pointer operand. This
|
|
/// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
|
|
/// but corner cases do exist.
|
|
const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
|
|
// A pointer operand may evaluate to a nonpointer expression, such as null.
|
|
if (!V->getType()->isPointerTy())
|
|
return V;
|
|
|
|
if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
|
|
return getPointerBase(Cast->getOperand());
|
|
}
|
|
else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
|
|
const SCEV *PtrOp = 0;
|
|
for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
|
|
I != E; ++I) {
|
|
if ((*I)->getType()->isPointerTy()) {
|
|
// Cannot find the base of an expression with multiple pointer operands.
|
|
if (PtrOp)
|
|
return V;
|
|
PtrOp = *I;
|
|
}
|
|
}
|
|
if (!PtrOp)
|
|
return V;
|
|
return getPointerBase(PtrOp);
|
|
}
|
|
return V;
|
|
}
|
|
|
|
/// PushDefUseChildren - Push users of the given Instruction
|
|
/// onto the given Worklist.
|
|
static void
|
|
PushDefUseChildren(Instruction *I,
|
|
SmallVectorImpl<Instruction *> &Worklist) {
|
|
// Push the def-use children onto the Worklist stack.
|
|
for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
|
|
UI != UE; ++UI)
|
|
Worklist.push_back(cast<Instruction>(*UI));
|
|
}
|
|
|
|
/// ForgetSymbolicValue - This looks up computed SCEV values for all
|
|
/// instructions that depend on the given instruction and removes them from
|
|
/// the ValueExprMapType map if they reference SymName. This is used during PHI
|
|
/// resolution.
|
|
void
|
|
ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
|
|
SmallVector<Instruction *, 16> Worklist;
|
|
PushDefUseChildren(PN, Worklist);
|
|
|
|
SmallPtrSet<Instruction *, 8> Visited;
|
|
Visited.insert(PN);
|
|
while (!Worklist.empty()) {
|
|
Instruction *I = Worklist.pop_back_val();
|
|
if (!Visited.insert(I)) continue;
|
|
|
|
ValueExprMapType::iterator It =
|
|
ValueExprMap.find_as(static_cast<Value *>(I));
|
|
if (It != ValueExprMap.end()) {
|
|
const SCEV *Old = It->second;
|
|
|
|
// Short-circuit the def-use traversal if the symbolic name
|
|
// ceases to appear in expressions.
|
|
if (Old != SymName && !hasOperand(Old, SymName))
|
|
continue;
|
|
|
|
// SCEVUnknown for a PHI either means that it has an unrecognized
|
|
// structure, it's a PHI that's in the progress of being computed
|
|
// by createNodeForPHI, or it's a single-value PHI. In the first case,
|
|
// additional loop trip count information isn't going to change anything.
|
|
// In the second case, createNodeForPHI will perform the necessary
|
|
// updates on its own when it gets to that point. In the third, we do
|
|
// want to forget the SCEVUnknown.
|
|
if (!isa<PHINode>(I) ||
|
|
!isa<SCEVUnknown>(Old) ||
|
|
(I != PN && Old == SymName)) {
|
|
forgetMemoizedResults(Old);
|
|
ValueExprMap.erase(It);
|
|
}
|
|
}
|
|
|
|
PushDefUseChildren(I, Worklist);
|
|
}
|
|
}
|
|
|
|
/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
|
|
/// a loop header, making it a potential recurrence, or it doesn't.
|
|
///
|
|
const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
|
|
if (const Loop *L = LI->getLoopFor(PN->getParent()))
|
|
if (L->getHeader() == PN->getParent()) {
|
|
// The loop may have multiple entrances or multiple exits; we can analyze
|
|
// this phi as an addrec if it has a unique entry value and a unique
|
|
// backedge value.
|
|
Value *BEValueV = 0, *StartValueV = 0;
|
|
for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
|
|
Value *V = PN->getIncomingValue(i);
|
|
if (L->contains(PN->getIncomingBlock(i))) {
|
|
if (!BEValueV) {
|
|
BEValueV = V;
|
|
} else if (BEValueV != V) {
|
|
BEValueV = 0;
|
|
break;
|
|
}
|
|
} else if (!StartValueV) {
|
|
StartValueV = V;
|
|
} else if (StartValueV != V) {
|
|
StartValueV = 0;
|
|
break;
|
|
}
|
|
}
|
|
if (BEValueV && StartValueV) {
|
|
// While we are analyzing this PHI node, handle its value symbolically.
|
|
const SCEV *SymbolicName = getUnknown(PN);
|
|
assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
|
|
"PHI node already processed?");
|
|
ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
|
|
|
|
// Using this symbolic name for the PHI, analyze the value coming around
|
|
// the back-edge.
|
|
const SCEV *BEValue = getSCEV(BEValueV);
|
|
|
|
// 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 (const 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.
|
|
SmallVector<const SCEV *, 8> Ops;
|
|
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
|
|
if (i != FoundIndex)
|
|
Ops.push_back(Add->getOperand(i));
|
|
const SCEV *Accum = 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 (isLoopInvariant(Accum, L) ||
|
|
(isa<SCEVAddRecExpr>(Accum) &&
|
|
cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
|
|
SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
|
|
|
|
// If the increment doesn't overflow, then neither the addrec nor
|
|
// the post-increment will overflow.
|
|
if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
|
|
if (OBO->hasNoUnsignedWrap())
|
|
Flags = setFlags(Flags, SCEV::FlagNUW);
|
|
if (OBO->hasNoSignedWrap())
|
|
Flags = setFlags(Flags, SCEV::FlagNSW);
|
|
} else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
|
|
// If the increment is an inbounds GEP, then we know the address
|
|
// space cannot be wrapped around. We cannot make any guarantee
|
|
// about signed or unsigned overflow because pointers are
|
|
// unsigned but we may have a negative index from the base
|
|
// pointer. We can guarantee that no unsigned wrap occurs if the
|
|
// indices form a positive value.
|
|
if (GEP->isInBounds()) {
|
|
Flags = setFlags(Flags, SCEV::FlagNW);
|
|
|
|
const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
|
|
if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
|
|
Flags = setFlags(Flags, SCEV::FlagNUW);
|
|
}
|
|
} else if (const SubOperator *OBO =
|
|
dyn_cast<SubOperator>(BEValueV)) {
|
|
if (OBO->hasNoUnsignedWrap())
|
|
Flags = setFlags(Flags, SCEV::FlagNUW);
|
|
if (OBO->hasNoSignedWrap())
|
|
Flags = setFlags(Flags, SCEV::FlagNSW);
|
|
}
|
|
|
|
const SCEV *StartVal = getSCEV(StartValueV);
|
|
const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
|
|
|
|
// Since the no-wrap flags are on the increment, they apply to the
|
|
// post-incremented value as well.
|
|
if (isLoopInvariant(Accum, L))
|
|
(void)getAddRecExpr(getAddExpr(StartVal, Accum),
|
|
Accum, L, Flags);
|
|
|
|
// Okay, for the entire analysis of this edge we assumed the PHI
|
|
// to be symbolic. We now need to go back and purge all of the
|
|
// entries for the scalars that use the symbolic expression.
|
|
ForgetSymbolicName(PN, SymbolicName);
|
|
ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
|
|
return PHISCEV;
|
|
}
|
|
}
|
|
} else if (const 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()) {
|
|
const SCEV *StartVal = getSCEV(StartValueV);
|
|
|
|
// If StartVal = j.start - j.stride, we can use StartVal as the
|
|
// initial step of the addrec evolution.
|
|
if (StartVal == getMinusSCEV(AddRec->getOperand(0),
|
|
AddRec->getOperand(1))) {
|
|
// FIXME: For constant StartVal, we should be able to infer
|
|
// no-wrap flags.
|
|
const SCEV *PHISCEV =
|
|
getAddRecExpr(StartVal, AddRec->getOperand(1), L,
|
|
SCEV::FlagAnyWrap);
|
|
|
|
// Okay, for the entire analysis of this edge we assumed the PHI
|
|
// to be symbolic. We now need to go back and purge all of the
|
|
// entries for the scalars that use the symbolic expression.
|
|
ForgetSymbolicName(PN, SymbolicName);
|
|
ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
|
|
return PHISCEV;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// If the PHI has a single incoming value, follow that value, unless the
|
|
// PHI's incoming blocks are in a different loop, in which case doing so
|
|
// risks breaking LCSSA form. Instcombine would normally zap these, but
|
|
// it doesn't have DominatorTree information, so it may miss cases.
|
|
if (Value *V = SimplifyInstruction(PN, TD, TLI, DT))
|
|
if (LI->replacementPreservesLCSSAForm(PN, V))
|
|
return getSCEV(V);
|
|
|
|
// If it's not a loop phi, we can't handle it yet.
|
|
return getUnknown(PN);
|
|
}
|
|
|
|
/// createNodeForGEP - Expand GEP instructions into add and multiply
|
|
/// operations. This allows them to be analyzed by regular SCEV code.
|
|
///
|
|
const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
|
|
Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
|
|
Value *Base = GEP->getOperand(0);
|
|
// Don't attempt to analyze GEPs over unsized objects.
|
|
if (!Base->getType()->getPointerElementType()->isSized())
|
|
return getUnknown(GEP);
|
|
|
|
// Don't blindly transfer the inbounds flag from the GEP instruction to the
|
|
// Add expression, because the Instruction may be guarded by control flow
|
|
// and the no-overflow bits may not be valid for the expression in any
|
|
// context.
|
|
SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
|
|
|
|
const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
|
|
gep_type_iterator GTI = gep_type_begin(GEP);
|
|
for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()),
|
|
E = GEP->op_end();
|
|
I != E; ++I) {
|
|
Value *Index = *I;
|
|
// Compute the (potentially symbolic) offset in bytes for this index.
|
|
if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
|
|
// For a struct, add the member offset.
|
|
unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
|
|
const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
|
|
|
|
// Add the field offset to the running total offset.
|
|
TotalOffset = getAddExpr(TotalOffset, FieldOffset);
|
|
} else {
|
|
// For an array, add the element offset, explicitly scaled.
|
|
const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, *GTI);
|
|
const SCEV *IndexS = getSCEV(Index);
|
|
// Getelementptr indices are signed.
|
|
IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
|
|
|
|
// Multiply the index by the element size to compute the element offset.
|
|
const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, Wrap);
|
|
|
|
// Add the element offset to the running total offset.
|
|
TotalOffset = getAddExpr(TotalOffset, LocalOffset);
|
|
}
|
|
}
|
|
|
|
// Get the SCEV for the GEP base.
|
|
const SCEV *BaseS = getSCEV(Base);
|
|
|
|
// Add the total offset from all the GEP indices to the base.
|
|
return getAddExpr(BaseS, TotalOffset, Wrap);
|
|
}
|
|
|
|
/// 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.
|
|
uint32_t
|
|
ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
|
|
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
|
|
return C->getValue()->getValue().countTrailingZeros();
|
|
|
|
if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
|
|
return std::min(GetMinTrailingZeros(T->getOperand()),
|
|
(uint32_t)getTypeSizeInBits(T->getType()));
|
|
|
|
if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
|
|
uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
|
|
return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
|
|
getTypeSizeInBits(E->getType()) : OpRes;
|
|
}
|
|
|
|
if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
|
|
uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
|
|
return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
|
|
getTypeSizeInBits(E->getType()) : OpRes;
|
|
}
|
|
|
|
if (const 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 (const 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 = getTypeSizeInBits(M->getType());
|
|
for (unsigned i = 1, e = M->getNumOperands();
|
|
SumOpRes != BitWidth && i != e; ++i)
|
|
SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
|
|
BitWidth);
|
|
return SumOpRes;
|
|
}
|
|
|
|
if (const 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 (const 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 (const 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;
|
|
}
|
|
|
|
if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
|
|
// For a SCEVUnknown, ask ValueTracking.
|
|
unsigned BitWidth = getTypeSizeInBits(U->getType());
|
|
APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
|
|
ComputeMaskedBits(U->getValue(), Zeros, Ones);
|
|
return Zeros.countTrailingOnes();
|
|
}
|
|
|
|
// SCEVUDivExpr
|
|
return 0;
|
|
}
|
|
|
|
/// getUnsignedRange - Determine the unsigned range for a particular SCEV.
|
|
///
|
|
ConstantRange
|
|
ScalarEvolution::getUnsignedRange(const SCEV *S) {
|
|
// See if we've computed this range already.
|
|
DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
|
|
if (I != UnsignedRanges.end())
|
|
return I->second;
|
|
|
|
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
|
|
return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
|
|
|
|
unsigned BitWidth = getTypeSizeInBits(S->getType());
|
|
ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
|
|
|
|
// If the value has known zeros, the maximum unsigned value will have those
|
|
// known zeros as well.
|
|
uint32_t TZ = GetMinTrailingZeros(S);
|
|
if (TZ != 0)
|
|
ConservativeResult =
|
|
ConstantRange(APInt::getMinValue(BitWidth),
|
|
APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
|
|
|
|
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
|
|
ConstantRange X = getUnsignedRange(Add->getOperand(0));
|
|
for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
|
|
X = X.add(getUnsignedRange(Add->getOperand(i)));
|
|
return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
|
|
}
|
|
|
|
if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
|
|
ConstantRange X = getUnsignedRange(Mul->getOperand(0));
|
|
for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
|
|
X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
|
|
return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
|
|
}
|
|
|
|
if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
|
|
ConstantRange X = getUnsignedRange(SMax->getOperand(0));
|
|
for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
|
|
X = X.smax(getUnsignedRange(SMax->getOperand(i)));
|
|
return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
|
|
}
|
|
|
|
if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
|
|
ConstantRange X = getUnsignedRange(UMax->getOperand(0));
|
|
for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
|
|
X = X.umax(getUnsignedRange(UMax->getOperand(i)));
|
|
return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
|
|
}
|
|
|
|
if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
|
|
ConstantRange X = getUnsignedRange(UDiv->getLHS());
|
|
ConstantRange Y = getUnsignedRange(UDiv->getRHS());
|
|
return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
|
|
}
|
|
|
|
if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
|
|
ConstantRange X = getUnsignedRange(ZExt->getOperand());
|
|
return setUnsignedRange(ZExt,
|
|
ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
|
|
}
|
|
|
|
if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
|
|
ConstantRange X = getUnsignedRange(SExt->getOperand());
|
|
return setUnsignedRange(SExt,
|
|
ConservativeResult.intersectWith(X.signExtend(BitWidth)));
|
|
}
|
|
|
|
if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
|
|
ConstantRange X = getUnsignedRange(Trunc->getOperand());
|
|
return setUnsignedRange(Trunc,
|
|
ConservativeResult.intersectWith(X.truncate(BitWidth)));
|
|
}
|
|
|
|
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
|
|
// If there's no unsigned wrap, the value will never be less than its
|
|
// initial value.
|
|
if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
|
|
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
|
|
if (!C->getValue()->isZero())
|
|
ConservativeResult =
|
|
ConservativeResult.intersectWith(
|
|
ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
|
|
|
|
// TODO: non-affine addrec
|
|
if (AddRec->isAffine()) {
|
|
Type *Ty = AddRec->getType();
|
|
const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
|
|
if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
|
|
getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
|
|
MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
|
|
|
|
const SCEV *Start = AddRec->getStart();
|
|
const SCEV *Step = AddRec->getStepRecurrence(*this);
|
|
|
|
ConstantRange StartRange = getUnsignedRange(Start);
|
|
ConstantRange StepRange = getSignedRange(Step);
|
|
ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
|
|
ConstantRange EndRange =
|
|
StartRange.add(MaxBECountRange.multiply(StepRange));
|
|
|
|
// Check for overflow. This must be done with ConstantRange arithmetic
|
|
// because we could be called from within the ScalarEvolution overflow
|
|
// checking code.
|
|
ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
|
|
ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
|
|
ConstantRange ExtMaxBECountRange =
|
|
MaxBECountRange.zextOrTrunc(BitWidth*2+1);
|
|
ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
|
|
if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
|
|
ExtEndRange)
|
|
return setUnsignedRange(AddRec, ConservativeResult);
|
|
|
|
APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
|
|
EndRange.getUnsignedMin());
|
|
APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
|
|
EndRange.getUnsignedMax());
|
|
if (Min.isMinValue() && Max.isMaxValue())
|
|
return setUnsignedRange(AddRec, ConservativeResult);
|
|
return setUnsignedRange(AddRec,
|
|
ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
|
|
}
|
|
}
|
|
|
|
return setUnsignedRange(AddRec, ConservativeResult);
|
|
}
|
|
|
|
if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
|
|
// For a SCEVUnknown, ask ValueTracking.
|
|
APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
|
|
ComputeMaskedBits(U->getValue(), Zeros, Ones, TD);
|
|
if (Ones == ~Zeros + 1)
|
|
return setUnsignedRange(U, ConservativeResult);
|
|
return setUnsignedRange(U,
|
|
ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
|
|
}
|
|
|
|
return setUnsignedRange(S, ConservativeResult);
|
|
}
|
|
|
|
/// getSignedRange - Determine the signed range for a particular SCEV.
|
|
///
|
|
ConstantRange
|
|
ScalarEvolution::getSignedRange(const SCEV *S) {
|
|
// See if we've computed this range already.
|
|
DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
|
|
if (I != SignedRanges.end())
|
|
return I->second;
|
|
|
|
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
|
|
return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
|
|
|
|
unsigned BitWidth = getTypeSizeInBits(S->getType());
|
|
ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
|
|
|
|
// If the value has known zeros, the maximum signed value will have those
|
|
// known zeros as well.
|
|
uint32_t TZ = GetMinTrailingZeros(S);
|
|
if (TZ != 0)
|
|
ConservativeResult =
|
|
ConstantRange(APInt::getSignedMinValue(BitWidth),
|
|
APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
|
|
|
|
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
|
|
ConstantRange X = getSignedRange(Add->getOperand(0));
|
|
for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
|
|
X = X.add(getSignedRange(Add->getOperand(i)));
|
|
return setSignedRange(Add, ConservativeResult.intersectWith(X));
|
|
}
|
|
|
|
if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
|
|
ConstantRange X = getSignedRange(Mul->getOperand(0));
|
|
for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
|
|
X = X.multiply(getSignedRange(Mul->getOperand(i)));
|
|
return setSignedRange(Mul, ConservativeResult.intersectWith(X));
|
|
}
|
|
|
|
if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
|
|
ConstantRange X = getSignedRange(SMax->getOperand(0));
|
|
for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
|
|
X = X.smax(getSignedRange(SMax->getOperand(i)));
|
|
return setSignedRange(SMax, ConservativeResult.intersectWith(X));
|
|
}
|
|
|
|
if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
|
|
ConstantRange X = getSignedRange(UMax->getOperand(0));
|
|
for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
|
|
X = X.umax(getSignedRange(UMax->getOperand(i)));
|
|
return setSignedRange(UMax, ConservativeResult.intersectWith(X));
|
|
}
|
|
|
|
if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
|
|
ConstantRange X = getSignedRange(UDiv->getLHS());
|
|
ConstantRange Y = getSignedRange(UDiv->getRHS());
|
|
return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
|
|
}
|
|
|
|
if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
|
|
ConstantRange X = getSignedRange(ZExt->getOperand());
|
|
return setSignedRange(ZExt,
|
|
ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
|
|
}
|
|
|
|
if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
|
|
ConstantRange X = getSignedRange(SExt->getOperand());
|
|
return setSignedRange(SExt,
|
|
ConservativeResult.intersectWith(X.signExtend(BitWidth)));
|
|
}
|
|
|
|
if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
|
|
ConstantRange X = getSignedRange(Trunc->getOperand());
|
|
return setSignedRange(Trunc,
|
|
ConservativeResult.intersectWith(X.truncate(BitWidth)));
|
|
}
|
|
|
|
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
|
|
// If there's no signed wrap, and all the operands have the same sign or
|
|
// zero, the value won't ever change sign.
|
|
if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
|
|
bool AllNonNeg = true;
|
|
bool AllNonPos = true;
|
|
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
|
|
if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
|
|
if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
|
|
}
|
|
if (AllNonNeg)
|
|
ConservativeResult = ConservativeResult.intersectWith(
|
|
ConstantRange(APInt(BitWidth, 0),
|
|
APInt::getSignedMinValue(BitWidth)));
|
|
else if (AllNonPos)
|
|
ConservativeResult = ConservativeResult.intersectWith(
|
|
ConstantRange(APInt::getSignedMinValue(BitWidth),
|
|
APInt(BitWidth, 1)));
|
|
}
|
|
|
|
// TODO: non-affine addrec
|
|
if (AddRec->isAffine()) {
|
|
Type *Ty = AddRec->getType();
|
|
const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
|
|
if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
|
|
getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
|
|
MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
|
|
|
|
const SCEV *Start = AddRec->getStart();
|
|
const SCEV *Step = AddRec->getStepRecurrence(*this);
|
|
|
|
ConstantRange StartRange = getSignedRange(Start);
|
|
ConstantRange StepRange = getSignedRange(Step);
|
|
ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
|
|
ConstantRange EndRange =
|
|
StartRange.add(MaxBECountRange.multiply(StepRange));
|
|
|
|
// Check for overflow. This must be done with ConstantRange arithmetic
|
|
// because we could be called from within the ScalarEvolution overflow
|
|
// checking code.
|
|
ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
|
|
ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
|
|
ConstantRange ExtMaxBECountRange =
|
|
MaxBECountRange.zextOrTrunc(BitWidth*2+1);
|
|
ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
|
|
if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
|
|
ExtEndRange)
|
|
return setSignedRange(AddRec, ConservativeResult);
|
|
|
|
APInt Min = APIntOps::smin(StartRange.getSignedMin(),
|
|
EndRange.getSignedMin());
|
|
APInt Max = APIntOps::smax(StartRange.getSignedMax(),
|
|
EndRange.getSignedMax());
|
|
if (Min.isMinSignedValue() && Max.isMaxSignedValue())
|
|
return setSignedRange(AddRec, ConservativeResult);
|
|
return setSignedRange(AddRec,
|
|
ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
|
|
}
|
|
}
|
|
|
|
return setSignedRange(AddRec, ConservativeResult);
|
|
}
|
|
|
|
if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
|
|
// For a SCEVUnknown, ask ValueTracking.
|
|
if (!U->getValue()->getType()->isIntegerTy() && !TD)
|
|
return setSignedRange(U, ConservativeResult);
|
|
unsigned NS = ComputeNumSignBits(U->getValue(), TD);
|
|
if (NS <= 1)
|
|
return setSignedRange(U, ConservativeResult);
|
|
return setSignedRange(U, ConservativeResult.intersectWith(
|
|
ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
|
|
APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
|
|
}
|
|
|
|
return setSignedRange(S, ConservativeResult);
|
|
}
|
|
|
|
/// createSCEV - We know that there is no SCEV for the specified value.
|
|
/// Analyze the expression.
|
|
///
|
|
const SCEV *ScalarEvolution::createSCEV(Value *V) {
|
|
if (!isSCEVable(V->getType()))
|
|
return getUnknown(V);
|
|
|
|
unsigned Opcode = Instruction::UserOp1;
|
|
if (Instruction *I = dyn_cast<Instruction>(V)) {
|
|
Opcode = I->getOpcode();
|
|
|
|
// Don't attempt to analyze instructions in blocks that aren't
|
|
// reachable. Such instructions don't matter, and they aren't required
|
|
// to obey basic rules for definitions dominating uses which this
|
|
// analysis depends on.
|
|
if (!DT->isReachableFromEntry(I->getParent()))
|
|
return getUnknown(V);
|
|
} else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
|
|
Opcode = CE->getOpcode();
|
|
else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
|
|
return getConstant(CI);
|
|
else if (isa<ConstantPointerNull>(V))
|
|
return getConstant(V->getType(), 0);
|
|
else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
|
|
return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
|
|
else
|
|
return getUnknown(V);
|
|
|
|
Operator *U = cast<Operator>(V);
|
|
switch (Opcode) {
|
|
case Instruction::Add: {
|
|
// The simple thing to do would be to just call getSCEV on both operands
|
|
// and call getAddExpr with the result. However if we're looking at a
|
|
// bunch of things all added together, this can be quite inefficient,
|
|
// because it leads to N-1 getAddExpr calls for N ultimate operands.
|
|
// Instead, gather up all the operands and make a single getAddExpr call.
|
|
// LLVM IR canonical form means we need only traverse the left operands.
|
|
//
|
|
// Don't apply this instruction's NSW or NUW flags to the new
|
|
// expression. The instruction may be guarded by control flow that the
|
|
// no-wrap behavior depends on. Non-control-equivalent instructions can be
|
|
// mapped to the same SCEV expression, and it would be incorrect to transfer
|
|
// NSW/NUW semantics to those operations.
|
|
SmallVector<const SCEV *, 4> AddOps;
|
|
AddOps.push_back(getSCEV(U->getOperand(1)));
|
|
for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
|
|
unsigned Opcode = Op->getValueID() - Value::InstructionVal;
|
|
if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
|
|
break;
|
|
U = cast<Operator>(Op);
|
|
const SCEV *Op1 = getSCEV(U->getOperand(1));
|
|
if (Opcode == Instruction::Sub)
|
|
AddOps.push_back(getNegativeSCEV(Op1));
|
|
else
|
|
AddOps.push_back(Op1);
|
|
}
|
|
AddOps.push_back(getSCEV(U->getOperand(0)));
|
|
return getAddExpr(AddOps);
|
|
}
|
|
case Instruction::Mul: {
|
|
// Don't transfer NSW/NUW for the same reason as AddExpr.
|
|
SmallVector<const SCEV *, 4> MulOps;
|
|
MulOps.push_back(getSCEV(U->getOperand(1)));
|
|
for (Value *Op = U->getOperand(0);
|
|
Op->getValueID() == Instruction::Mul + Value::InstructionVal;
|
|
Op = U->getOperand(0)) {
|
|
U = cast<Operator>(Op);
|
|
MulOps.push_back(getSCEV(U->getOperand(1)));
|
|
}
|
|
MulOps.push_back(getSCEV(U->getOperand(0)));
|
|
return getMulExpr(MulOps);
|
|
}
|
|
case Instruction::UDiv:
|
|
return getUDivExpr(getSCEV(U->getOperand(0)),
|
|
getSCEV(U->getOperand(1)));
|
|
case Instruction::Sub:
|
|
return getMinusSCEV(getSCEV(U->getOperand(0)),
|
|
getSCEV(U->getOperand(1)));
|
|
case Instruction::And:
|
|
// For an expression like x&255 that merely masks off the high bits,
|
|
// use zext(trunc(x)) as the SCEV expression.
|
|
if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
|
|
if (CI->isNullValue())
|
|
return getSCEV(U->getOperand(1));
|
|
if (CI->isAllOnesValue())
|
|
return getSCEV(U->getOperand(0));
|
|
const APInt &A = CI->getValue();
|
|
|
|
// Instcombine's ShrinkDemandedConstant may strip bits out of
|
|
// constants, obscuring what would otherwise be a low-bits mask.
|
|
// Use ComputeMaskedBits to compute what ShrinkDemandedConstant
|
|
// knew about to reconstruct a low-bits mask value.
|
|
unsigned LZ = A.countLeadingZeros();
|
|
unsigned BitWidth = A.getBitWidth();
|
|
APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
|
|
ComputeMaskedBits(U->getOperand(0), KnownZero, KnownOne, TD);
|
|
|
|
APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
|
|
|
|
if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
|
|
return
|
|
getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
|
|
IntegerType::get(getContext(), BitWidth - LZ)),
|
|
U->getType());
|
|
}
|
|
break;
|
|
|
|
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>(U->getOperand(1))) {
|
|
const SCEV *LHS = getSCEV(U->getOperand(0));
|
|
const APInt &CIVal = CI->getValue();
|
|
if (GetMinTrailingZeros(LHS) >=
|
|
(CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
|
|
// Build a plain add SCEV.
|
|
const SCEV *S = getAddExpr(LHS, getSCEV(CI));
|
|
// If the LHS of the add was an addrec and it has no-wrap flags,
|
|
// transfer the no-wrap flags, since an or won't introduce a wrap.
|
|
if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
|
|
const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
|
|
const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
|
|
OldAR->getNoWrapFlags());
|
|
}
|
|
return S;
|
|
}
|
|
}
|
|
break;
|
|
case Instruction::Xor:
|
|
if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
|
|
// 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 (CI->getValue().isSignBit())
|
|
return getAddExpr(getSCEV(U->getOperand(0)),
|
|
getSCEV(U->getOperand(1)));
|
|
|
|
// If the RHS of xor is -1, then this is a not operation.
|
|
if (CI->isAllOnesValue())
|
|
return getNotSCEV(getSCEV(U->getOperand(0)));
|
|
|
|
// Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
|
|
// This is a variant of the check for xor with -1, and it handles
|
|
// the case where instcombine has trimmed non-demanded bits out
|
|
// of an xor with -1.
|
|
if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
|
|
if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
|
|
if (BO->getOpcode() == Instruction::And &&
|
|
LCI->getValue() == CI->getValue())
|
|
if (const SCEVZeroExtendExpr *Z =
|
|
dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
|
|
Type *UTy = U->getType();
|
|
const SCEV *Z0 = Z->getOperand();
|
|
Type *Z0Ty = Z0->getType();
|
|
unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
|
|
|
|
// If C is a low-bits mask, the zero extend is serving to
|
|
// mask off the high bits. Complement the operand and
|
|
// re-apply the zext.
|
|
if (APIntOps::isMask(Z0TySize, CI->getValue()))
|
|
return getZeroExtendExpr(getNotSCEV(Z0), UTy);
|
|
|
|
// If C is a single bit, it may be in the sign-bit position
|
|
// before the zero-extend. In this case, represent the xor
|
|
// using an add, which is equivalent, and re-apply the zext.
|
|
APInt Trunc = CI->getValue().trunc(Z0TySize);
|
|
if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
|
|
Trunc.isSignBit())
|
|
return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
|
|
UTy);
|
|
}
|
|
}
|
|
break;
|
|
|
|
case Instruction::Shl:
|
|
// Turn shift left of a constant amount into a multiply.
|
|
if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
|
|
uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
|
|
|
|
// If the shift count is not less than the bitwidth, the result of
|
|
// the shift is undefined. Don't try to analyze it, because the
|
|
// resolution chosen here may differ from the resolution chosen in
|
|
// other parts of the compiler.
|
|
if (SA->getValue().uge(BitWidth))
|
|
break;
|
|
|
|
Constant *X = ConstantInt::get(getContext(),
|
|
APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
|
|
return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
|
|
}
|
|
break;
|
|
|
|
case Instruction::LShr:
|
|
// Turn logical shift right of a constant into a unsigned divide.
|
|
if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
|
|
uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
|
|
|
|
// If the shift count is not less than the bitwidth, the result of
|
|
// the shift is undefined. Don't try to analyze it, because the
|
|
// resolution chosen here may differ from the resolution chosen in
|
|
// other parts of the compiler.
|
|
if (SA->getValue().uge(BitWidth))
|
|
break;
|
|
|
|
Constant *X = ConstantInt::get(getContext(),
|
|
APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
|
|
return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
|
|
}
|
|
break;
|
|
|
|
case Instruction::AShr:
|
|
// For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
|
|
if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
|
|
if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
|
|
if (L->getOpcode() == Instruction::Shl &&
|
|
L->getOperand(1) == U->getOperand(1)) {
|
|
uint64_t BitWidth = getTypeSizeInBits(U->getType());
|
|
|
|
// If the shift count is not less than the bitwidth, the result of
|
|
// the shift is undefined. Don't try to analyze it, because the
|
|
// resolution chosen here may differ from the resolution chosen in
|
|
// other parts of the compiler.
|
|
if (CI->getValue().uge(BitWidth))
|
|
break;
|
|
|
|
uint64_t Amt = BitWidth - CI->getZExtValue();
|
|
if (Amt == BitWidth)
|
|
return getSCEV(L->getOperand(0)); // shift by zero --> noop
|
|
return
|
|
getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
|
|
IntegerType::get(getContext(),
|
|
Amt)),
|
|
U->getType());
|
|
}
|
|
break;
|
|
|
|
case Instruction::Trunc:
|
|
return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
|
|
|
|
case Instruction::ZExt:
|
|
return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
|
|
|
|
case Instruction::SExt:
|
|
return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
|
|
|
|
case Instruction::BitCast:
|
|
// BitCasts are no-op casts so we just eliminate the cast.
|
|
if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
|
|
return getSCEV(U->getOperand(0));
|
|
break;
|
|
|
|
// It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
|
|
// lead to pointer expressions which cannot safely be expanded to GEPs,
|
|
// because ScalarEvolution doesn't respect the GEP aliasing rules when
|
|
// simplifying integer expressions.
|
|
|
|
case Instruction::GetElementPtr:
|
|
return createNodeForGEP(cast<GEPOperator>(U));
|
|
|
|
case Instruction::PHI:
|
|
return createNodeForPHI(cast<PHINode>(U));
|
|
|
|
case Instruction::Select:
|
|
// This could be a smax or umax that was lowered earlier.
|
|
// Try to recover it.
|
|
if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->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:
|
|
// a >s b ? a+x : b+x -> smax(a, b)+x
|
|
// a >s b ? b+x : a+x -> smin(a, b)+x
|
|
if (LHS->getType() == U->getType()) {
|
|
const SCEV *LS = getSCEV(LHS);
|
|
const SCEV *RS = getSCEV(RHS);
|
|
const SCEV *LA = getSCEV(U->getOperand(1));
|
|
const SCEV *RA = getSCEV(U->getOperand(2));
|
|
const SCEV *LDiff = getMinusSCEV(LA, LS);
|
|
const SCEV *RDiff = getMinusSCEV(RA, RS);
|
|
if (LDiff == RDiff)
|
|
return getAddExpr(getSMaxExpr(LS, RS), LDiff);
|
|
LDiff = getMinusSCEV(LA, RS);
|
|
RDiff = getMinusSCEV(RA, LS);
|
|
if (LDiff == RDiff)
|
|
return getAddExpr(getSMinExpr(LS, RS), LDiff);
|
|
}
|
|
break;
|
|
case ICmpInst::ICMP_ULT:
|
|
case ICmpInst::ICMP_ULE:
|
|
std::swap(LHS, RHS);
|
|
// fall through
|
|
case ICmpInst::ICMP_UGT:
|
|
case ICmpInst::ICMP_UGE:
|
|
// a >u b ? a+x : b+x -> umax(a, b)+x
|
|
// a >u b ? b+x : a+x -> umin(a, b)+x
|
|
if (LHS->getType() == U->getType()) {
|
|
const SCEV *LS = getSCEV(LHS);
|
|
const SCEV *RS = getSCEV(RHS);
|
|
const SCEV *LA = getSCEV(U->getOperand(1));
|
|
const SCEV *RA = getSCEV(U->getOperand(2));
|
|
const SCEV *LDiff = getMinusSCEV(LA, LS);
|
|
const SCEV *RDiff = getMinusSCEV(RA, RS);
|
|
if (LDiff == RDiff)
|
|
return getAddExpr(getUMaxExpr(LS, RS), LDiff);
|
|
LDiff = getMinusSCEV(LA, RS);
|
|
RDiff = getMinusSCEV(RA, LS);
|
|
if (LDiff == RDiff)
|
|
return getAddExpr(getUMinExpr(LS, RS), LDiff);
|
|
}
|
|
break;
|
|
case ICmpInst::ICMP_NE:
|
|
// n != 0 ? n+x : 1+x -> umax(n, 1)+x
|
|
if (LHS->getType() == U->getType() &&
|
|
isa<ConstantInt>(RHS) &&
|
|
cast<ConstantInt>(RHS)->isZero()) {
|
|
const SCEV *One = getConstant(LHS->getType(), 1);
|
|
const SCEV *LS = getSCEV(LHS);
|
|
const SCEV *LA = getSCEV(U->getOperand(1));
|
|
const SCEV *RA = getSCEV(U->getOperand(2));
|
|
const SCEV *LDiff = getMinusSCEV(LA, LS);
|
|
const SCEV *RDiff = getMinusSCEV(RA, One);
|
|
if (LDiff == RDiff)
|
|
return getAddExpr(getUMaxExpr(One, LS), LDiff);
|
|
}
|
|
break;
|
|
case ICmpInst::ICMP_EQ:
|
|
// n == 0 ? 1+x : n+x -> umax(n, 1)+x
|
|
if (LHS->getType() == U->getType() &&
|
|
isa<ConstantInt>(RHS) &&
|
|
cast<ConstantInt>(RHS)->isZero()) {
|
|
const SCEV *One = getConstant(LHS->getType(), 1);
|
|
const SCEV *LS = getSCEV(LHS);
|
|
const SCEV *LA = getSCEV(U->getOperand(1));
|
|
const SCEV *RA = getSCEV(U->getOperand(2));
|
|
const SCEV *LDiff = getMinusSCEV(LA, One);
|
|
const SCEV *RDiff = getMinusSCEV(RA, LS);
|
|
if (LDiff == RDiff)
|
|
return getAddExpr(getUMaxExpr(One, LS), LDiff);
|
|
}
|
|
break;
|
|
default:
|
|
break;
|
|
}
|
|
}
|
|
|
|
default: // We cannot analyze this expression.
|
|
break;
|
|
}
|
|
|
|
return getUnknown(V);
|
|
}
|
|
|
|
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// Iteration Count Computation Code
|
|
//
|
|
|
|
/// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
|
|
/// normal unsigned value. Returns 0 if the trip count is unknown or not
|
|
/// constant. Will also return 0 if the maximum trip count is very large (>=
|
|
/// 2^32).
|
|
///
|
|
/// This "trip count" assumes that control exits via ExitingBlock. More
|
|
/// precisely, it is the number of times that control may reach ExitingBlock
|
|
/// before taking the branch. For loops with multiple exits, it may not be the
|
|
/// number times that the loop header executes because the loop may exit
|
|
/// prematurely via another branch.
|
|
///
|
|
/// FIXME: We conservatively call getBackedgeTakenCount(L) instead of
|
|
/// getExitCount(L, ExitingBlock) to compute a safe trip count considering all
|
|
/// loop exits. getExitCount() may return an exact count for this branch
|
|
/// assuming no-signed-wrap. The number of well-defined iterations may actually
|
|
/// be higher than this trip count if this exit test is skipped and the loop
|
|
/// exits via a different branch. Ideally, getExitCount() would know whether it
|
|
/// depends on a NSW assumption, and we would only fall back to a conservative
|
|
/// trip count in that case.
|
|
unsigned ScalarEvolution::
|
|
getSmallConstantTripCount(Loop *L, BasicBlock * /*ExitingBlock*/) {
|
|
const SCEVConstant *ExitCount =
|
|
dyn_cast<SCEVConstant>(getBackedgeTakenCount(L));
|
|
if (!ExitCount)
|
|
return 0;
|
|
|
|
ConstantInt *ExitConst = ExitCount->getValue();
|
|
|
|
// Guard against huge trip counts.
|
|
if (ExitConst->getValue().getActiveBits() > 32)
|
|
return 0;
|
|
|
|
// In case of integer overflow, this returns 0, which is correct.
|
|
return ((unsigned)ExitConst->getZExtValue()) + 1;
|
|
}
|
|
|
|
/// getSmallConstantTripMultiple - Returns the largest constant divisor of the
|
|
/// trip count of this loop as a normal unsigned value, if possible. This
|
|
/// means that the actual trip count is always a multiple of the returned
|
|
/// value (don't forget the trip count could very well be zero as well!).
|
|
///
|
|
/// Returns 1 if the trip count is unknown or not guaranteed to be the
|
|
/// multiple of a constant (which is also the case if the trip count is simply
|
|
/// constant, use getSmallConstantTripCount for that case), Will also return 1
|
|
/// if the trip count is very large (>= 2^32).
|
|
///
|
|
/// As explained in the comments for getSmallConstantTripCount, this assumes
|
|
/// that control exits the loop via ExitingBlock.
|
|
unsigned ScalarEvolution::
|
|
getSmallConstantTripMultiple(Loop *L, BasicBlock * /*ExitingBlock*/) {
|
|
const SCEV *ExitCount = getBackedgeTakenCount(L);
|
|
if (ExitCount == getCouldNotCompute())
|
|
return 1;
|
|
|
|
// Get the trip count from the BE count by adding 1.
|
|
const SCEV *TCMul = getAddExpr(ExitCount,
|
|
getConstant(ExitCount->getType(), 1));
|
|
// FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
|
|
// to factor simple cases.
|
|
if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
|
|
TCMul = Mul->getOperand(0);
|
|
|
|
const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
|
|
if (!MulC)
|
|
return 1;
|
|
|
|
ConstantInt *Result = MulC->getValue();
|
|
|
|
// Guard against huge trip counts (this requires checking
|
|
// for zero to handle the case where the trip count == -1 and the
|
|
// addition wraps).
|
|
if (!Result || Result->getValue().getActiveBits() > 32 ||
|
|
Result->getValue().getActiveBits() == 0)
|
|
return 1;
|
|
|
|
return (unsigned)Result->getZExtValue();
|
|
}
|
|
|
|
// getExitCount - Get the expression for the number of loop iterations for which
|
|
// this loop is guaranteed not to exit via ExitingBlock. Otherwise return
|
|
// SCEVCouldNotCompute.
|
|
const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
|
|
return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
|
|
}
|
|
|
|
/// getBackedgeTakenCount - If the specified loop has a predictable
|
|
/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
|
|
/// object. The backedge-taken count is the number of times the loop header
|
|
/// will be branched to from within the loop. This is one less than the
|
|
/// trip count of the loop, since it doesn't count the first iteration,
|
|
/// when the header is branched to from outside the loop.
|
|
///
|
|
/// Note that it is not valid to call this method on a loop without a
|
|
/// loop-invariant backedge-taken count (see
|
|
/// hasLoopInvariantBackedgeTakenCount).
|
|
///
|
|
const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
|
|
return getBackedgeTakenInfo(L).getExact(this);
|
|
}
|
|
|
|
/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
|
|
/// return the least SCEV value that is known never to be less than the
|
|
/// actual backedge taken count.
|
|
const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
|
|
return getBackedgeTakenInfo(L).getMax(this);
|
|
}
|
|
|
|
/// PushLoopPHIs - Push PHI nodes in the header of the given loop
|
|
/// onto the given Worklist.
|
|
static void
|
|
PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
|
|
BasicBlock *Header = L->getHeader();
|
|
|
|
// Push all Loop-header PHIs onto the Worklist stack.
|
|
for (BasicBlock::iterator I = Header->begin();
|
|
PHINode *PN = dyn_cast<PHINode>(I); ++I)
|
|
Worklist.push_back(PN);
|
|
}
|
|
|
|
const ScalarEvolution::BackedgeTakenInfo &
|
|
ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
|
|
// Initially insert an invalid entry for this loop. If the insertion
|
|
// succeeds, proceed to actually compute a backedge-taken count and
|
|
// update the value. The temporary CouldNotCompute value tells SCEV
|
|
// code elsewhere that it shouldn't attempt to request a new
|
|
// backedge-taken count, which could result in infinite recursion.
|
|
std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
|
|
BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
|
|
if (!Pair.second)
|
|
return Pair.first->second;
|
|
|
|
// ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
|
|
// into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
|
|
// must be cleared in this scope.
|
|
BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
|
|
|
|
if (Result.getExact(this) != getCouldNotCompute()) {
|
|
assert(isLoopInvariant(Result.getExact(this), L) &&
|
|
isLoopInvariant(Result.getMax(this), L) &&
|
|
"Computed backedge-taken count isn't loop invariant for loop!");
|
|
++NumTripCountsComputed;
|
|
}
|
|
else if (Result.getMax(this) == getCouldNotCompute() &&
|
|
isa<PHINode>(L->getHeader()->begin())) {
|
|
// Only count loops that have phi nodes as not being computable.
|
|
++NumTripCountsNotComputed;
|
|
}
|
|
|
|
// Now that we know more about the trip count for this loop, forget any
|
|
// existing SCEV values for PHI nodes in this loop since they are only
|
|
// conservative estimates made without the benefit of trip count
|
|
// information. This is similar to the code in forgetLoop, except that
|
|
// it handles SCEVUnknown PHI nodes specially.
|
|
if (Result.hasAnyInfo()) {
|
|
SmallVector<Instruction *, 16> Worklist;
|
|
PushLoopPHIs(L, Worklist);
|
|
|
|
SmallPtrSet<Instruction *, 8> Visited;
|
|
while (!Worklist.empty()) {
|
|
Instruction *I = Worklist.pop_back_val();
|
|
if (!Visited.insert(I)) continue;
|
|
|
|
ValueExprMapType::iterator It =
|
|
ValueExprMap.find_as(static_cast<Value *>(I));
|
|
if (It != ValueExprMap.end()) {
|
|
const SCEV *Old = It->second;
|
|
|
|
// SCEVUnknown for a PHI either means that it has an unrecognized
|
|
// structure, or it's a PHI that's in the progress of being computed
|
|
// by createNodeForPHI. In the former case, additional loop trip
|
|
// count information isn't going to change anything. In the later
|
|
// case, createNodeForPHI will perform the necessary updates on its
|
|
// own when it gets to that point.
|
|
if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
|
|
forgetMemoizedResults(Old);
|
|
ValueExprMap.erase(It);
|
|
}
|
|
if (PHINode *PN = dyn_cast<PHINode>(I))
|
|
ConstantEvolutionLoopExitValue.erase(PN);
|
|
}
|
|
|
|
PushDefUseChildren(I, Worklist);
|
|
}
|
|
}
|
|
|
|
// Re-lookup the insert position, since the call to
|
|
// ComputeBackedgeTakenCount above could result in a
|
|
// recusive call to getBackedgeTakenInfo (on a different
|
|
// loop), which would invalidate the iterator computed
|
|
// earlier.
|
|
return BackedgeTakenCounts.find(L)->second = Result;
|
|
}
|
|
|
|
/// forgetLoop - This method should be called by the client when it has
|
|
/// changed a loop in a way that may effect ScalarEvolution's ability to
|
|
/// compute a trip count, or if the loop is deleted.
|
|
void ScalarEvolution::forgetLoop(const Loop *L) {
|
|
// Drop any stored trip count value.
|
|
DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
|
|
BackedgeTakenCounts.find(L);
|
|
if (BTCPos != BackedgeTakenCounts.end()) {
|
|
BTCPos->second.clear();
|
|
BackedgeTakenCounts.erase(BTCPos);
|
|
}
|
|
|
|
// Drop information about expressions based on loop-header PHIs.
|
|
SmallVector<Instruction *, 16> Worklist;
|
|
PushLoopPHIs(L, Worklist);
|
|
|
|
SmallPtrSet<Instruction *, 8> Visited;
|
|
while (!Worklist.empty()) {
|
|
Instruction *I = Worklist.pop_back_val();
|
|
if (!Visited.insert(I)) continue;
|
|
|
|
ValueExprMapType::iterator It =
|
|
ValueExprMap.find_as(static_cast<Value *>(I));
|
|
if (It != ValueExprMap.end()) {
|
|
forgetMemoizedResults(It->second);
|
|
ValueExprMap.erase(It);
|
|
if (PHINode *PN = dyn_cast<PHINode>(I))
|
|
ConstantEvolutionLoopExitValue.erase(PN);
|
|
}
|
|
|
|
PushDefUseChildren(I, Worklist);
|
|
}
|
|
|
|
// Forget all contained loops too, to avoid dangling entries in the
|
|
// ValuesAtScopes map.
|
|
for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
|
|
forgetLoop(*I);
|
|
}
|
|
|
|
/// forgetValue - This method should be called by the client when it has
|
|
/// changed a value in a way that may effect its value, or which may
|
|
/// disconnect it from a def-use chain linking it to a loop.
|
|
void ScalarEvolution::forgetValue(Value *V) {
|
|
Instruction *I = dyn_cast<Instruction>(V);
|
|
if (!I) return;
|
|
|
|
// Drop information about expressions based on loop-header PHIs.
|
|
SmallVector<Instruction *, 16> Worklist;
|
|
Worklist.push_back(I);
|
|
|
|
SmallPtrSet<Instruction *, 8> Visited;
|
|
while (!Worklist.empty()) {
|
|
I = Worklist.pop_back_val();
|
|
if (!Visited.insert(I)) continue;
|
|
|
|
ValueExprMapType::iterator It =
|
|
ValueExprMap.find_as(static_cast<Value *>(I));
|
|
if (It != ValueExprMap.end()) {
|
|
forgetMemoizedResults(It->second);
|
|
ValueExprMap.erase(It);
|
|
if (PHINode *PN = dyn_cast<PHINode>(I))
|
|
ConstantEvolutionLoopExitValue.erase(PN);
|
|
}
|
|
|
|
PushDefUseChildren(I, Worklist);
|
|
}
|
|
}
|
|
|
|
/// getExact - Get the exact loop backedge taken count considering all loop
|
|
/// exits. A computable result can only be return for loops with a single exit.
|
|
/// Returning the minimum taken count among all exits is incorrect because one
|
|
/// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
|
|
/// the limit of each loop test is never skipped. This is a valid assumption as
|
|
/// long as the loop exits via that test. For precise results, it is the
|
|
/// caller's responsibility to specify the relevant loop exit using
|
|
/// getExact(ExitingBlock, SE).
|
|
const SCEV *
|
|
ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
|
|
// If any exits were not computable, the loop is not computable.
|
|
if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
|
|
|
|
// We need exactly one computable exit.
|
|
if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
|
|
assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
|
|
|
|
const SCEV *BECount = 0;
|
|
for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
|
|
ENT != 0; ENT = ENT->getNextExit()) {
|
|
|
|
assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
|
|
|
|
if (!BECount)
|
|
BECount = ENT->ExactNotTaken;
|
|
else if (BECount != ENT->ExactNotTaken)
|
|
return SE->getCouldNotCompute();
|
|
}
|
|
assert(BECount && "Invalid not taken count for loop exit");
|
|
return BECount;
|
|
}
|
|
|
|
/// getExact - Get the exact not taken count for this loop exit.
|
|
const SCEV *
|
|
ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
|
|
ScalarEvolution *SE) const {
|
|
for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
|
|
ENT != 0; ENT = ENT->getNextExit()) {
|
|
|
|
if (ENT->ExitingBlock == ExitingBlock)
|
|
return ENT->ExactNotTaken;
|
|
}
|
|
return SE->getCouldNotCompute();
|
|
}
|
|
|
|
/// getMax - Get the max backedge taken count for the loop.
|
|
const SCEV *
|
|
ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
|
|
return Max ? Max : SE->getCouldNotCompute();
|
|
}
|
|
|
|
bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
|
|
ScalarEvolution *SE) const {
|
|
if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
|
|
return true;
|
|
|
|
if (!ExitNotTaken.ExitingBlock)
|
|
return false;
|
|
|
|
for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
|
|
ENT != 0; ENT = ENT->getNextExit()) {
|
|
|
|
if (ENT->ExactNotTaken != SE->getCouldNotCompute()
|
|
&& SE->hasOperand(ENT->ExactNotTaken, S)) {
|
|
return true;
|
|
}
|
|
}
|
|
return false;
|
|
}
|
|
|
|
/// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
|
|
/// computable exit into a persistent ExitNotTakenInfo array.
|
|
ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
|
|
SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
|
|
bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
|
|
|
|
if (!Complete)
|
|
ExitNotTaken.setIncomplete();
|
|
|
|
unsigned NumExits = ExitCounts.size();
|
|
if (NumExits == 0) return;
|
|
|
|
ExitNotTaken.ExitingBlock = ExitCounts[0].first;
|
|
ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
|
|
if (NumExits == 1) return;
|
|
|
|
// Handle the rare case of multiple computable exits.
|
|
ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
|
|
|
|
ExitNotTakenInfo *PrevENT = &ExitNotTaken;
|
|
for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
|
|
PrevENT->setNextExit(ENT);
|
|
ENT->ExitingBlock = ExitCounts[i].first;
|
|
ENT->ExactNotTaken = ExitCounts[i].second;
|
|
}
|
|
}
|
|
|
|
/// clear - Invalidate this result and free the ExitNotTakenInfo array.
|
|
void ScalarEvolution::BackedgeTakenInfo::clear() {
|
|
ExitNotTaken.ExitingBlock = 0;
|
|
ExitNotTaken.ExactNotTaken = 0;
|
|
delete[] ExitNotTaken.getNextExit();
|
|
}
|
|
|
|
/// ComputeBackedgeTakenCount - Compute the number of times the backedge
|
|
/// of the specified loop will execute.
|
|
ScalarEvolution::BackedgeTakenInfo
|
|
ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
|
|
SmallVector<BasicBlock *, 8> ExitingBlocks;
|
|
L->getExitingBlocks(ExitingBlocks);
|
|
|
|
// Examine all exits and pick the most conservative values.
|
|
const SCEV *MaxBECount = getCouldNotCompute();
|
|
bool CouldComputeBECount = true;
|
|
SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
|
|
for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
|
|
ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]);
|
|
if (EL.Exact == getCouldNotCompute())
|
|
// We couldn't compute an exact value for this exit, so
|
|
// we won't be able to compute an exact value for the loop.
|
|
CouldComputeBECount = false;
|
|
else
|
|
ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact));
|
|
|
|
if (MaxBECount == getCouldNotCompute())
|
|
MaxBECount = EL.Max;
|
|
else if (EL.Max != getCouldNotCompute()) {
|
|
// We cannot take the "min" MaxBECount, because non-unit stride loops may
|
|
// skip some loop tests. Taking the max over the exits is sufficiently
|
|
// conservative. TODO: We could do better taking into consideration
|
|
// that (1) the loop has unit stride (2) the last loop test is
|
|
// less-than/greater-than (3) any loop test is less-than/greater-than AND
|
|
// falls-through some constant times less then the other tests.
|
|
MaxBECount = getUMaxFromMismatchedTypes(MaxBECount, EL.Max);
|
|
}
|
|
}
|
|
|
|
return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
|
|
}
|
|
|
|
/// ComputeExitLimit - Compute the number of times the backedge of the specified
|
|
/// loop will execute if it exits via the specified block.
|
|
ScalarEvolution::ExitLimit
|
|
ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
|
|
|
|
// Okay, we've chosen an exiting block. See what condition causes us to
|
|
// exit at this block.
|
|
//
|
|
// FIXME: we should be able to handle switch instructions (with a single exit)
|
|
BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
|
|
if (ExitBr == 0) return getCouldNotCompute();
|
|
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.
|
|
//
|
|
// If both of those tests fail, walk up the unique predecessor chain to the
|
|
// header, stopping if there is an edge that doesn't exit the loop. If the
|
|
// header is reached, the execution count of the branch will be equal to the
|
|
// trip count of the loop.
|
|
//
|
|
// 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()) {
|
|
// The simple checks failed, try climbing the unique predecessor chain
|
|
// up to the header.
|
|
bool Ok = false;
|
|
for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
|
|
BasicBlock *Pred = BB->getUniquePredecessor();
|
|
if (!Pred)
|
|
return getCouldNotCompute();
|
|
TerminatorInst *PredTerm = Pred->getTerminator();
|
|
for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
|
|
BasicBlock *PredSucc = PredTerm->getSuccessor(i);
|
|
if (PredSucc == BB)
|
|
continue;
|
|
// If the predecessor has a successor that isn't BB and isn't
|
|
// outside the loop, assume the worst.
|
|
if (L->contains(PredSucc))
|
|
return getCouldNotCompute();
|
|
}
|
|
if (Pred == L->getHeader()) {
|
|
Ok = true;
|
|
break;
|
|
}
|
|
BB = Pred;
|
|
}
|
|
if (!Ok)
|
|
return getCouldNotCompute();
|
|
}
|
|
|
|
// Proceed to the next level to examine the exit condition expression.
|
|
return ComputeExitLimitFromCond(L, ExitBr->getCondition(),
|
|
ExitBr->getSuccessor(0),
|
|
ExitBr->getSuccessor(1),
|
|
/*IsSubExpr=*/false);
|
|
}
|
|
|
|
/// ComputeExitLimitFromCond - Compute the number of times the
|
|
/// backedge of the specified loop will execute if its exit condition
|
|
/// were a conditional branch of ExitCond, TBB, and FBB.
|
|
///
|
|
/// @param IsSubExpr is true if ExitCond does not directly control the exit
|
|
/// branch. In this case, we cannot assume that the loop only exits when the
|
|
/// condition is true and cannot infer that failing to meet the condition prior
|
|
/// to integer wraparound results in undefined behavior.
|
|
ScalarEvolution::ExitLimit
|
|
ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
|
|
Value *ExitCond,
|
|
BasicBlock *TBB,
|
|
BasicBlock *FBB,
|
|
bool IsSubExpr) {
|
|
// Check if the controlling expression for this loop is an And or Or.
|
|
if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
|
|
if (BO->getOpcode() == Instruction::And) {
|
|
// Recurse on the operands of the and.
|
|
bool EitherMayExit = L->contains(TBB);
|
|
ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
|
|
IsSubExpr || EitherMayExit);
|
|
ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
|
|
IsSubExpr || EitherMayExit);
|
|
const SCEV *BECount = getCouldNotCompute();
|
|
const SCEV *MaxBECount = getCouldNotCompute();
|
|
if (EitherMayExit) {
|
|
// Both conditions must be true for the loop to continue executing.
|
|
// Choose the less conservative count.
|
|
if (EL0.Exact == getCouldNotCompute() ||
|
|
EL1.Exact == getCouldNotCompute())
|
|
BECount = getCouldNotCompute();
|
|
else
|
|
BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
|
|
if (EL0.Max == getCouldNotCompute())
|
|
MaxBECount = EL1.Max;
|
|
else if (EL1.Max == getCouldNotCompute())
|
|
MaxBECount = EL0.Max;
|
|
else
|
|
MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
|
|
} else {
|
|
// Both conditions must be true at the same time for the loop to exit.
|
|
// For now, be conservative.
|
|
assert(L->contains(FBB) && "Loop block has no successor in loop!");
|
|
if (EL0.Max == EL1.Max)
|
|
MaxBECount = EL0.Max;
|
|
if (EL0.Exact == EL1.Exact)
|
|
BECount = EL0.Exact;
|
|
}
|
|
|
|
return ExitLimit(BECount, MaxBECount);
|
|
}
|
|
if (BO->getOpcode() == Instruction::Or) {
|
|
// Recurse on the operands of the or.
|
|
bool EitherMayExit = L->contains(FBB);
|
|
ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
|
|
IsSubExpr || EitherMayExit);
|
|
ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
|
|
IsSubExpr || EitherMayExit);
|
|
const SCEV *BECount = getCouldNotCompute();
|
|
const SCEV *MaxBECount = getCouldNotCompute();
|
|
if (EitherMayExit) {
|
|
// Both conditions must be false for the loop to continue executing.
|
|
// Choose the less conservative count.
|
|
if (EL0.Exact == getCouldNotCompute() ||
|
|
EL1.Exact == getCouldNotCompute())
|
|
BECount = getCouldNotCompute();
|
|
else
|
|
BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
|
|
if (EL0.Max == getCouldNotCompute())
|
|
MaxBECount = EL1.Max;
|
|
else if (EL1.Max == getCouldNotCompute())
|
|
MaxBECount = EL0.Max;
|
|
else
|
|
MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
|
|
} else {
|
|
// Both conditions must be false at the same time for the loop to exit.
|
|
// For now, be conservative.
|
|
assert(L->contains(TBB) && "Loop block has no successor in loop!");
|
|
if (EL0.Max == EL1.Max)
|
|
MaxBECount = EL0.Max;
|
|
if (EL0.Exact == EL1.Exact)
|
|
BECount = EL0.Exact;
|
|
}
|
|
|
|
return ExitLimit(BECount, MaxBECount);
|
|
}
|
|
}
|
|
|
|
// With an icmp, it may be feasible to compute an exact backedge-taken count.
|
|
// Proceed to the next level to examine the icmp.
|
|
if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
|
|
return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, IsSubExpr);
|
|
|
|
// Check for a constant condition. These are normally stripped out by
|
|
// SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
|
|
// preserve the CFG and is temporarily leaving constant conditions
|
|
// in place.
|
|
if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
|
|
if (L->contains(FBB) == !CI->getZExtValue())
|
|
// The backedge is always taken.
|
|
return getCouldNotCompute();
|
|
else
|
|
// The backedge is never taken.
|
|
return getConstant(CI->getType(), 0);
|
|
}
|
|
|
|
// If it's not an integer or pointer comparison then compute it the hard way.
|
|
return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
|
|
}
|
|
|
|
/// ComputeExitLimitFromICmp - Compute the number of times the
|
|
/// backedge of the specified loop will execute if its exit condition
|
|
/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
|
|
ScalarEvolution::ExitLimit
|
|
ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
|
|
ICmpInst *ExitCond,
|
|
BasicBlock *TBB,
|
|
BasicBlock *FBB,
|
|
bool IsSubExpr) {
|
|
|
|
// If the condition was exit on true, convert the condition to exit on false
|
|
ICmpInst::Predicate Cond;
|
|
if (!L->contains(FBB))
|
|
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))) {
|
|
ExitLimit ItCnt =
|
|
ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
|
|
if (ItCnt.hasAnyInfo())
|
|
return ItCnt;
|
|
}
|
|
|
|
const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
|
|
const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
|
|
|
|
// Try to evaluate any dependencies out of the loop.
|
|
LHS = getSCEVAtScope(LHS, L);
|
|
RHS = getSCEVAtScope(RHS, L);
|
|
|
|
// At this point, we would like to compute how many iterations of the
|
|
// loop the predicate will return true for these inputs.
|
|
if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
|
|
// If there is a loop-invariant, force it into the RHS.
|
|
std::swap(LHS, RHS);
|
|
Cond = ICmpInst::getSwappedPredicate(Cond);
|
|
}
|
|
|
|
// Simplify the operands before analyzing them.
|
|
(void)SimplifyICmpOperands(Cond, LHS, RHS);
|
|
|
|
// If we have a comparison of a chrec against a constant, try to use value
|
|
// ranges to answer this query.
|
|
if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
|
|
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
|
|
if (AddRec->getLoop() == L) {
|
|
// Form the constant range.
|
|
ConstantRange CompRange(
|
|
ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
|
|
|
|
const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
|
|
if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
|
|
}
|
|
|
|
switch (Cond) {
|
|
case ICmpInst::ICMP_NE: { // while (X != Y)
|
|
// Convert to: while (X-Y != 0)
|
|
ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, IsSubExpr);
|
|
if (EL.hasAnyInfo()) return EL;
|
|
break;
|
|
}
|
|
case ICmpInst::ICMP_EQ: { // while (X == Y)
|
|
// Convert to: while (X-Y == 0)
|
|
ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
|
|
if (EL.hasAnyInfo()) return EL;
|
|
break;
|
|
}
|
|
case ICmpInst::ICMP_SLT:
|
|
case ICmpInst::ICMP_ULT: { // while (X < Y)
|
|
bool IsSigned = Cond == ICmpInst::ICMP_SLT;
|
|
ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, IsSubExpr);
|
|
if (EL.hasAnyInfo()) return EL;
|
|
break;
|
|
}
|
|
case ICmpInst::ICMP_SGT:
|
|
case ICmpInst::ICMP_UGT: { // while (X > Y)
|
|
bool IsSigned = Cond == ICmpInst::ICMP_SGT;
|
|
ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, IsSubExpr);
|
|
if (EL.hasAnyInfo()) return EL;
|
|
break;
|
|
}
|
|
default:
|
|
#if 0
|
|
dbgs() << "ComputeBackedgeTakenCount ";
|
|
if (ExitCond->getOperand(0)->getType()->isUnsigned())
|
|
dbgs() << "[unsigned] ";
|
|
dbgs() << *LHS << " "
|
|
<< Instruction::getOpcodeName(Instruction::ICmp)
|
|
<< " " << *RHS << "\n";
|
|
#endif
|
|
break;
|
|
}
|
|
return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
|
|
}
|
|
|
|
static ConstantInt *
|
|
EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
|
|
ScalarEvolution &SE) {
|
|
const SCEV *InVal = SE.getConstant(C);
|
|
const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
|
|
assert(isa<SCEVConstant>(Val) &&
|
|
"Evaluation of SCEV at constant didn't fold correctly?");
|
|
return cast<SCEVConstant>(Val)->getValue();
|
|
}
|
|
|
|
/// ComputeLoadConstantCompareExitLimit - Given an exit condition of
|
|
/// 'icmp op load X, cst', try to see if we can compute the backedge
|
|
/// execution count.
|
|
ScalarEvolution::ExitLimit
|
|
ScalarEvolution::ComputeLoadConstantCompareExitLimit(
|
|
LoadInst *LI,
|
|
Constant *RHS,
|
|
const Loop *L,
|
|
ICmpInst::Predicate predicate) {
|
|
|
|
if (LI->isVolatile()) return getCouldNotCompute();
|
|
|
|
// Check to see if the loaded pointer is a getelementptr of a global.
|
|
// TODO: Use SCEV instead of manually grubbing with GEPs.
|
|
GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
|
|
if (!GEP) return getCouldNotCompute();
|
|
|
|
// 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->hasDefinitiveInitializer() ||
|
|
GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
|
|
!cast<Constant>(GEP->getOperand(1))->isNullValue())
|
|
return getCouldNotCompute();
|
|
|
|
// Okay, we allow one non-constant index into the GEP instruction.
|
|
Value *VarIdx = 0;
|
|
std::vector<Constant*> 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 getCouldNotCompute(); // Multiple non-constant idx's.
|
|
VarIdx = GEP->getOperand(i);
|
|
VarIdxNum = i-2;
|
|
Indexes.push_back(0);
|
|
}
|
|
|
|
// Loop-invariant loads may be a byproduct of loop optimization. Skip them.
|
|
if (!VarIdx)
|
|
return getCouldNotCompute();
|
|
|
|
// 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.
|
|
const SCEV *Idx = getSCEV(VarIdx);
|
|
Idx = getSCEVAtScope(Idx, L);
|
|
|
|
// We can only recognize very limited forms of loop index expressions, in
|
|
// particular, only affine AddRec's like {C1,+,C2}.
|
|
const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
|
|
if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
|
|
!isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
|
|
!isa<SCEVConstant>(IdxExpr->getOperand(1)))
|
|
return getCouldNotCompute();
|
|
|
|
unsigned MaxSteps = MaxBruteForceIterations;
|
|
for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
|
|
ConstantInt *ItCst = ConstantInt::get(
|
|
cast<IntegerType>(IdxExpr->getType()), IterationNum);
|
|
ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
|
|
|
|
// Form the GEP offset.
|
|
Indexes[VarIdxNum] = Val;
|
|
|
|
Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
|
|
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
|
|
dbgs() << "\n***\n*** Computed loop count " << *ItCst
|
|
<< "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
|
|
<< "***\n";
|
|
#endif
|
|
++NumArrayLenItCounts;
|
|
return getConstant(ItCst); // Found terminating iteration!
|
|
}
|
|
}
|
|
return getCouldNotCompute();
|
|
}
|
|
|
|
|
|
/// 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) ||
|
|
isa<LoadInst>(I))
|
|
return true;
|
|
|
|
if (const CallInst *CI = dyn_cast<CallInst>(I))
|
|
if (const Function *F = CI->getCalledFunction())
|
|
return canConstantFoldCallTo(F);
|
|
return false;
|
|
}
|
|
|
|
/// Determine whether this instruction can constant evolve within this loop
|
|
/// assuming its operands can all constant evolve.
|
|
static bool canConstantEvolve(Instruction *I, const Loop *L) {
|
|
// An instruction outside of the loop can't be derived from a loop PHI.
|
|
if (!L->contains(I)) return false;
|
|
|
|
if (isa<PHINode>(I)) {
|
|
if (L->getHeader() == I->getParent())
|
|
return true;
|
|
else
|
|
// We don't currently keep track of the control flow needed to evaluate
|
|
// PHIs, so we cannot handle PHIs inside of loops.
|
|
return false;
|
|
}
|
|
|
|
// If we won't be able to constant fold this expression even if the operands
|
|
// are constants, bail early.
|
|
return CanConstantFold(I);
|
|
}
|
|
|
|
/// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
|
|
/// recursing through each instruction operand until reaching a loop header phi.
|
|
static PHINode *
|
|
getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
|
|
DenseMap<Instruction *, PHINode *> &PHIMap) {
|
|
|
|
// Otherwise, we can evaluate this instruction if all of its operands are
|
|
// constant or derived from a PHI node themselves.
|
|
PHINode *PHI = 0;
|
|
for (Instruction::op_iterator OpI = UseInst->op_begin(),
|
|
OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
|
|
|
|
if (isa<Constant>(*OpI)) continue;
|
|
|
|
Instruction *OpInst = dyn_cast<Instruction>(*OpI);
|
|
if (!OpInst || !canConstantEvolve(OpInst, L)) return 0;
|
|
|
|
PHINode *P = dyn_cast<PHINode>(OpInst);
|
|
if (!P)
|
|
// If this operand is already visited, reuse the prior result.
|
|
// We may have P != PHI if this is the deepest point at which the
|
|
// inconsistent paths meet.
|
|
P = PHIMap.lookup(OpInst);
|
|
if (!P) {
|
|
// Recurse and memoize the results, whether a phi is found or not.
|
|
// This recursive call invalidates pointers into PHIMap.
|
|
P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
|
|
PHIMap[OpInst] = P;
|
|
}
|
|
if (P == 0) return 0; // Not evolving from PHI
|
|
if (PHI && PHI != P) return 0; // Evolving from multiple different PHIs.
|
|
PHI = P;
|
|
}
|
|
// This is a expression evolving from a constant PHI!
|
|
return PHI;
|
|
}
|
|
|
|
/// 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) {
|
|
Instruction *I = dyn_cast<Instruction>(V);
|
|
if (I == 0 || !canConstantEvolve(I, L)) return 0;
|
|
|
|
if (PHINode *PN = dyn_cast<PHINode>(I)) {
|
|
return PN;
|
|
}
|
|
|
|
// Record non-constant instructions contained by the loop.
|
|
DenseMap<Instruction *, PHINode *> PHIMap;
|
|
return getConstantEvolvingPHIOperands(I, L, PHIMap);
|
|
}
|
|
|
|
/// 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, const Loop *L,
|
|
DenseMap<Instruction *, Constant *> &Vals,
|
|
const DataLayout *TD,
|
|
const TargetLibraryInfo *TLI) {
|
|
// Convenient constant check, but redundant for recursive calls.
|
|
if (Constant *C = dyn_cast<Constant>(V)) return C;
|
|
Instruction *I = dyn_cast<Instruction>(V);
|
|
if (!I) return 0;
|
|
|
|
if (Constant *C = Vals.lookup(I)) return C;
|
|
|
|
// An instruction inside the loop depends on a value outside the loop that we
|
|
// weren't given a mapping for, or a value such as a call inside the loop.
|
|
if (!canConstantEvolve(I, L)) return 0;
|
|
|
|
// An unmapped PHI can be due to a branch or another loop inside this loop,
|
|
// or due to this not being the initial iteration through a loop where we
|
|
// couldn't compute the evolution of this particular PHI last time.
|
|
if (isa<PHINode>(I)) return 0;
|
|
|
|
std::vector<Constant*> Operands(I->getNumOperands());
|
|
|
|
for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
|
|
Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
|
|
if (!Operand) {
|
|
Operands[i] = dyn_cast<Constant>(I->getOperand(i));
|
|
if (!Operands[i]) return 0;
|
|
continue;
|
|
}
|
|
Constant *C = EvaluateExpression(Operand, L, Vals, TD, TLI);
|
|
Vals[Operand] = C;
|
|
if (!C) return 0;
|
|
Operands[i] = C;
|
|
}
|
|
|
|
if (CmpInst *CI = dyn_cast<CmpInst>(I))
|
|
return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
|
|
Operands[1], TD, TLI);
|
|
if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
|
|
if (!LI->isVolatile())
|
|
return ConstantFoldLoadFromConstPtr(Operands[0], TD);
|
|
}
|
|
return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, TD,
|
|
TLI);
|
|
}
|
|
|
|
/// 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 *
|
|
ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
|
|
const APInt &BEs,
|
|
const Loop *L) {
|
|
DenseMap<PHINode*, Constant*>::const_iterator I =
|
|
ConstantEvolutionLoopExitValue.find(PN);
|
|
if (I != ConstantEvolutionLoopExitValue.end())
|
|
return I->second;
|
|
|
|
if (BEs.ugt(MaxBruteForceIterations))
|
|
return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
|
|
|
|
Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
|
|
|
|
DenseMap<Instruction *, Constant *> CurrentIterVals;
|
|
BasicBlock *Header = L->getHeader();
|
|
assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
|
|
|
|
// 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));
|
|
PHINode *PHI = 0;
|
|
for (BasicBlock::iterator I = Header->begin();
|
|
(PHI = dyn_cast<PHINode>(I)); ++I) {
|
|
Constant *StartCST =
|
|
dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
|
|
if (StartCST == 0) continue;
|
|
CurrentIterVals[PHI] = StartCST;
|
|
}
|
|
if (!CurrentIterVals.count(PN))
|
|
return RetVal = 0;
|
|
|
|
Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
|
|
|
|
// Execute the loop symbolically to determine the exit value.
|
|
if (BEs.getActiveBits() >= 32)
|
|
return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
|
|
|
|
unsigned NumIterations = BEs.getZExtValue(); // must be in range
|
|
unsigned IterationNum = 0;
|
|
for (; ; ++IterationNum) {
|
|
if (IterationNum == NumIterations)
|
|
return RetVal = CurrentIterVals[PN]; // Got exit value!
|
|
|
|
// Compute the value of the PHIs for the next iteration.
|
|
// EvaluateExpression adds non-phi values to the CurrentIterVals map.
|
|
DenseMap<Instruction *, Constant *> NextIterVals;
|
|
Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD,
|
|
TLI);
|
|
if (NextPHI == 0)
|
|
return 0; // Couldn't evaluate!
|
|
NextIterVals[PN] = NextPHI;
|
|
|
|
bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
|
|
|
|
// Also evaluate the other PHI nodes. However, we don't get to stop if we
|
|
// cease to be able to evaluate one of them or if they stop evolving,
|
|
// because that doesn't necessarily prevent us from computing PN.
|
|
SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
|
|
for (DenseMap<Instruction *, Constant *>::const_iterator
|
|
I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
|
|
PHINode *PHI = dyn_cast<PHINode>(I->first);
|
|
if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
|
|
PHIsToCompute.push_back(std::make_pair(PHI, I->second));
|
|
}
|
|
// We use two distinct loops because EvaluateExpression may invalidate any
|
|
// iterators into CurrentIterVals.
|
|
for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
|
|
I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
|
|
PHINode *PHI = I->first;
|
|
Constant *&NextPHI = NextIterVals[PHI];
|
|
if (!NextPHI) { // Not already computed.
|
|
Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
|
|
NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
|
|
}
|
|
if (NextPHI != I->second)
|
|
StoppedEvolving = false;
|
|
}
|
|
|
|
// If all entries in CurrentIterVals == NextIterVals then we can stop
|
|
// iterating, the loop can't continue to change.
|
|
if (StoppedEvolving)
|
|
return RetVal = CurrentIterVals[PN];
|
|
|
|
CurrentIterVals.swap(NextIterVals);
|
|
}
|
|
}
|
|
|
|
/// ComputeExitCountExhaustively - If the loop 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 getCouldNotCompute().
|
|
const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
|
|
Value *Cond,
|
|
bool ExitWhen) {
|
|
PHINode *PN = getConstantEvolvingPHI(Cond, L);
|
|
if (PN == 0) return getCouldNotCompute();
|
|
|
|
// If the loop is canonicalized, the PHI will have exactly two entries.
|
|
// That's the only form we support here.
|
|
if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
|
|
|
|
DenseMap<Instruction *, Constant *> CurrentIterVals;
|
|
BasicBlock *Header = L->getHeader();
|
|
assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
|
|
|
|
// 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));
|
|
PHINode *PHI = 0;
|
|
for (BasicBlock::iterator I = Header->begin();
|
|
(PHI = dyn_cast<PHINode>(I)); ++I) {
|
|
Constant *StartCST =
|
|
dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
|
|
if (StartCST == 0) continue;
|
|
CurrentIterVals[PHI] = StartCST;
|
|
}
|
|
if (!CurrentIterVals.count(PN))
|
|
return getCouldNotCompute();
|
|
|
|
// 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 MaxIterations = MaxBruteForceIterations; // Limit analysis.
|
|
for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
|
|
ConstantInt *CondVal =
|
|
dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
|
|
TD, TLI));
|
|
|
|
// Couldn't symbolically evaluate.
|
|
if (!CondVal) return getCouldNotCompute();
|
|
|
|
if (CondVal->getValue() == uint64_t(ExitWhen)) {
|
|
++NumBruteForceTripCountsComputed;
|
|
return getConstant(Type::getInt32Ty(getContext()), IterationNum);
|
|
}
|
|
|
|
// Update all the PHI nodes for the next iteration.
|
|
DenseMap<Instruction *, Constant *> NextIterVals;
|
|
|
|
// Create a list of which PHIs we need to compute. We want to do this before
|
|
// calling EvaluateExpression on them because that may invalidate iterators
|
|
// into CurrentIterVals.
|
|
SmallVector<PHINode *, 8> PHIsToCompute;
|
|
for (DenseMap<Instruction *, Constant *>::const_iterator
|
|
I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
|
|
PHINode *PHI = dyn_cast<PHINode>(I->first);
|
|
if (!PHI || PHI->getParent() != Header) continue;
|
|
PHIsToCompute.push_back(PHI);
|
|
}
|
|
for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
|
|
E = PHIsToCompute.end(); I != E; ++I) {
|
|
PHINode *PHI = *I;
|
|
Constant *&NextPHI = NextIterVals[PHI];
|
|
if (NextPHI) continue; // Already computed!
|
|
|
|
Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
|
|
NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
|
|
}
|
|
CurrentIterVals.swap(NextIterVals);
|
|
}
|
|
|
|
// Too many iterations were needed to evaluate.
|
|
return getCouldNotCompute();
|
|
}
|
|
|
|
/// getSCEVAtScope - Return a SCEV expression for the specified value
|
|
/// at the specified scope in the program. The L value specifies a loop
|
|
/// nest to evaluate the expression at, where null is the top-level or a
|
|
/// specified loop is immediately inside of the loop.
|
|
///
|
|
/// This method can be used to compute the exit value for a variable defined
|
|
/// in a loop by querying what the value will hold in the parent loop.
|
|
///
|
|
/// In the case that a relevant loop exit value cannot be computed, the
|
|
/// original value V is returned.
|
|
const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
|
|
// Check to see if we've folded this expression at this loop before.
|
|
SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
|
|
for (unsigned u = 0; u < Values.size(); u++) {
|
|
if (Values[u].first == L)
|
|
return Values[u].second ? Values[u].second : V;
|
|
}
|
|
Values.push_back(std::make_pair(L, static_cast<const SCEV *>(0)));
|
|
// Otherwise compute it.
|
|
const SCEV *C = computeSCEVAtScope(V, L);
|
|
SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
|
|
for (unsigned u = Values2.size(); u > 0; u--) {
|
|
if (Values2[u - 1].first == L) {
|
|
Values2[u - 1].second = C;
|
|
break;
|
|
}
|
|
}
|
|
return C;
|
|
}
|
|
|
|
/// This builds up a Constant using the ConstantExpr interface. That way, we
|
|
/// will return Constants for objects which aren't represented by a
|
|
/// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
|
|
/// Returns NULL if the SCEV isn't representable as a Constant.
|
|
static Constant *BuildConstantFromSCEV(const SCEV *V) {
|
|
switch (V->getSCEVType()) {
|
|
default: // TODO: smax, umax.
|
|
case scCouldNotCompute:
|
|
case scAddRecExpr:
|
|
break;
|
|
case scConstant:
|
|
return cast<SCEVConstant>(V)->getValue();
|
|
case scUnknown:
|
|
return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
|
|
case scSignExtend: {
|
|
const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
|
|
if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
|
|
return ConstantExpr::getSExt(CastOp, SS->getType());
|
|
break;
|
|
}
|
|
case scZeroExtend: {
|
|
const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
|
|
if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
|
|
return ConstantExpr::getZExt(CastOp, SZ->getType());
|
|
break;
|
|
}
|
|
case scTruncate: {
|
|
const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
|
|
if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
|
|
return ConstantExpr::getTrunc(CastOp, ST->getType());
|
|
break;
|
|
}
|
|
case scAddExpr: {
|
|
const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
|
|
if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
|
|
if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
|
|
unsigned AS = PTy->getAddressSpace();
|
|
Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
|
|
C = ConstantExpr::getBitCast(C, DestPtrTy);
|
|
}
|
|
for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
|
|
Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
|
|
if (!C2) return 0;
|
|
|
|
// First pointer!
|
|
if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
|
|
unsigned AS = C2->getType()->getPointerAddressSpace();
|
|
std::swap(C, C2);
|
|
Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
|
|
// The offsets have been converted to bytes. We can add bytes to an
|
|
// i8* by GEP with the byte count in the first index.
|
|
C = ConstantExpr::getBitCast(C, DestPtrTy);
|
|
}
|
|
|
|
// Don't bother trying to sum two pointers. We probably can't
|
|
// statically compute a load that results from it anyway.
|
|
if (C2->getType()->isPointerTy())
|
|
return 0;
|
|
|
|
if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
|
|
if (PTy->getElementType()->isStructTy())
|
|
C2 = ConstantExpr::getIntegerCast(
|
|
C2, Type::getInt32Ty(C->getContext()), true);
|
|
C = ConstantExpr::getGetElementPtr(C, C2);
|
|
} else
|
|
C = ConstantExpr::getAdd(C, C2);
|
|
}
|
|
return C;
|
|
}
|
|
break;
|
|
}
|
|
case scMulExpr: {
|
|
const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
|
|
if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
|
|
// Don't bother with pointers at all.
|
|
if (C->getType()->isPointerTy()) return 0;
|
|
for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
|
|
Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
|
|
if (!C2 || C2->getType()->isPointerTy()) return 0;
|
|
C = ConstantExpr::getMul(C, C2);
|
|
}
|
|
return C;
|
|
}
|
|
break;
|
|
}
|
|
case scUDivExpr: {
|
|
const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
|
|
if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
|
|
if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
|
|
if (LHS->getType() == RHS->getType())
|
|
return ConstantExpr::getUDiv(LHS, RHS);
|
|
break;
|
|
}
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
|
|
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 (const 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 backedge-taken
|
|
// count. If so, we may be able to force computation of the exit
|
|
// value.
|
|
const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
|
|
if (const SCEVConstant *BTCC =
|
|
dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
|
|
// 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,
|
|
BTCC->getValue()->getValue(),
|
|
LI);
|
|
if (RV) return getSCEV(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)) {
|
|
SmallVector<Constant *, 4> Operands;
|
|
bool MadeImprovement = false;
|
|
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);
|
|
continue;
|
|
}
|
|
|
|
// If any of the operands is non-constant and if they are
|
|
// non-integer and non-pointer, don't even try to analyze them
|
|
// with scev techniques.
|
|
if (!isSCEVable(Op->getType()))
|
|
return V;
|
|
|
|
const SCEV *OrigV = getSCEV(Op);
|
|
const SCEV *OpV = getSCEVAtScope(OrigV, L);
|
|
MadeImprovement |= OrigV != OpV;
|
|
|
|
Constant *C = BuildConstantFromSCEV(OpV);
|
|
if (!C) return V;
|
|
if (C->getType() != Op->getType())
|
|
C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
|
|
Op->getType(),
|
|
false),
|
|
C, Op->getType());
|
|
Operands.push_back(C);
|
|
}
|
|
|
|
// Check to see if getSCEVAtScope actually made an improvement.
|
|
if (MadeImprovement) {
|
|
Constant *C = 0;
|
|
if (const CmpInst *CI = dyn_cast<CmpInst>(I))
|
|
C = ConstantFoldCompareInstOperands(CI->getPredicate(),
|
|
Operands[0], Operands[1], TD,
|
|
TLI);
|
|
else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
|
|
if (!LI->isVolatile())
|
|
C = ConstantFoldLoadFromConstPtr(Operands[0], TD);
|
|
} else
|
|
C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
|
|
Operands, TD, TLI);
|
|
if (!C) return V;
|
|
return getSCEV(C);
|
|
}
|
|
}
|
|
}
|
|
|
|
// This is some other type of SCEVUnknown, just return it.
|
|
return V;
|
|
}
|
|
|
|
if (const 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) {
|
|
const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
|
|
if (OpAtScope != Comm->getOperand(i)) {
|
|
// Okay, at least one of these operands is loop variant but might be
|
|
// foldable. Build a new instance of the folded commutative expression.
|
|
SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
|
|
Comm->op_begin()+i);
|
|
NewOps.push_back(OpAtScope);
|
|
|
|
for (++i; i != e; ++i) {
|
|
OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
|
|
NewOps.push_back(OpAtScope);
|
|
}
|
|
if (isa<SCEVAddExpr>(Comm))
|
|
return getAddExpr(NewOps);
|
|
if (isa<SCEVMulExpr>(Comm))
|
|
return getMulExpr(NewOps);
|
|
if (isa<SCEVSMaxExpr>(Comm))
|
|
return getSMaxExpr(NewOps);
|
|
if (isa<SCEVUMaxExpr>(Comm))
|
|
return getUMaxExpr(NewOps);
|
|
llvm_unreachable("Unknown commutative SCEV type!");
|
|
}
|
|
}
|
|
// If we got here, all operands are loop invariant.
|
|
return Comm;
|
|
}
|
|
|
|
if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
|
|
const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
|
|
const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
|
|
if (LHS == Div->getLHS() && RHS == Div->getRHS())
|
|
return Div; // must be loop invariant
|
|
return 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 (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
|
|
// First, attempt to evaluate each operand.
|
|
// Avoid performing the look-up in the common case where the specified
|
|
// expression has no loop-variant portions.
|
|
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
|
|
const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
|
|
if (OpAtScope == AddRec->getOperand(i))
|
|
continue;
|
|
|
|
// Okay, at least one of these operands is loop variant but might be
|
|
// foldable. Build a new instance of the folded commutative expression.
|
|
SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
|
|
AddRec->op_begin()+i);
|
|
NewOps.push_back(OpAtScope);
|
|
for (++i; i != e; ++i)
|
|
NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
|
|
|
|
const SCEV *FoldedRec =
|
|
getAddRecExpr(NewOps, AddRec->getLoop(),
|
|
AddRec->getNoWrapFlags(SCEV::FlagNW));
|
|
AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
|
|
// The addrec may be folded to a nonrecurrence, for example, if the
|
|
// induction variable is multiplied by zero after constant folding. Go
|
|
// ahead and return the folded value.
|
|
if (!AddRec)
|
|
return FoldedRec;
|
|
break;
|
|
}
|
|
|
|
// If the scope is outside the addrec's loop, evaluate it by using the
|
|
// loop exit value of the addrec.
|
|
if (!AddRec->getLoop()->contains(L)) {
|
|
// To evaluate this recurrence, we need to know how many times the AddRec
|
|
// loop iterates. Compute this now.
|
|
const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
|
|
if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
|
|
|
|
// Then, evaluate the AddRec.
|
|
return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
|
|
}
|
|
|
|
return AddRec;
|
|
}
|
|
|
|
if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
|
|
const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
|
|
if (Op == Cast->getOperand())
|
|
return Cast; // must be loop invariant
|
|
return getZeroExtendExpr(Op, Cast->getType());
|
|
}
|
|
|
|
if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
|
|
const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
|
|
if (Op == Cast->getOperand())
|
|
return Cast; // must be loop invariant
|
|
return getSignExtendExpr(Op, Cast->getType());
|
|
}
|
|
|
|
if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
|
|
const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
|
|
if (Op == Cast->getOperand())
|
|
return Cast; // must be loop invariant
|
|
return getTruncateExpr(Op, Cast->getType());
|
|
}
|
|
|
|
llvm_unreachable("Unknown SCEV type!");
|
|
}
|
|
|
|
/// getSCEVAtScope - This is a convenience function which does
|
|
/// getSCEVAtScope(getSCEV(V), L).
|
|
const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
|
|
return getSCEVAtScope(getSCEV(V), L);
|
|
}
|
|
|
|
/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
|
|
/// following equation:
|
|
///
|
|
/// A * X = B (mod N)
|
|
///
|
|
/// where N = 2^BW and BW is the common bit width of A and B. The signedness of
|
|
/// A and B isn't important.
|
|
///
|
|
/// If the equation does not have a solution, SCEVCouldNotCompute is returned.
|
|
static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
|
|
ScalarEvolution &SE) {
|
|
uint32_t BW = A.getBitWidth();
|
|
assert(BW == B.getBitWidth() && "Bit widths must be the same.");
|
|
assert(A != 0 && "A must be non-zero.");
|
|
|
|
// 1. D = gcd(A, N)
|
|
//
|
|
// The gcd of A and N may have only one prime factor: 2. The number of
|
|
// trailing zeros in A is its multiplicity
|
|
uint32_t Mult2 = A.countTrailingZeros();
|
|
// D = 2^Mult2
|
|
|
|
// 2. Check if B is divisible by D.
|
|
//
|
|
// B is divisible by D if and only if the multiplicity of prime factor 2 for B
|
|
// is not less than multiplicity of this prime factor for D.
|
|
if (B.countTrailingZeros() < Mult2)
|
|
return SE.getCouldNotCompute();
|
|
|
|
// 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
|
|
// modulo (N / D).
|
|
//
|
|
// (N / D) may need BW+1 bits in its representation. Hence, we'll use this
|
|
// bit width during computations.
|
|
APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
|
|
APInt Mod(BW + 1, 0);
|
|
Mod.setBit(BW - Mult2); // Mod = N / D
|
|
APInt I = AD.multiplicativeInverse(Mod);
|
|
|
|
// 4. Compute the minimum unsigned root of the equation:
|
|
// I * (B / D) mod (N / D)
|
|
APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
|
|
|
|
// The result is guaranteed to be less than 2^BW so we may truncate it to BW
|
|
// bits.
|
|
return SE.getConstant(Result.trunc(BW));
|
|
}
|
|
|
|
/// 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<const SCEV *,const SCEV *>
|
|
SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
|
|
assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
|
|
const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
|
|
const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
|
|
const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
|
|
|
|
// We currently can only solve this if the coefficients are constants.
|
|
if (!LC || !MC || !NC) {
|
|
const SCEV *CNC = SE.getCouldNotCompute();
|
|
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);
|
|
|
|
if (SqrtTerm.isNegative()) {
|
|
// The loop is provably infinite.
|
|
const SCEV *CNC = SE.getCouldNotCompute();
|
|
return std::make_pair(CNC, CNC);
|
|
}
|
|
|
|
// 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);
|
|
if (TwoA.isMinValue()) {
|
|
const SCEV *CNC = SE.getCouldNotCompute();
|
|
return std::make_pair(CNC, CNC);
|
|
}
|
|
|
|
LLVMContext &Context = SE.getContext();
|
|
|
|
ConstantInt *Solution1 =
|
|
ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
|
|
ConstantInt *Solution2 =
|
|
ConstantInt::get(Context, (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 CouldNotCompute.
|
|
///
|
|
/// This is only used for loops with a "x != y" exit test. The exit condition is
|
|
/// now expressed as a single expression, V = x-y. So the exit test is
|
|
/// effectively V != 0. We know and take advantage of the fact that this
|
|
/// expression only being used in a comparison by zero context.
|
|
ScalarEvolution::ExitLimit
|
|
ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr) {
|
|
// If the value is a constant
|
|
if (const 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 getCouldNotCompute(); // Otherwise it will loop infinitely.
|
|
}
|
|
|
|
const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
|
|
if (!AddRec || AddRec->getLoop() != L)
|
|
return getCouldNotCompute();
|
|
|
|
// If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
|
|
// the quadratic equation to solve it.
|
|
if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
|
|
std::pair<const SCEV *,const SCEV *> Roots =
|
|
SolveQuadraticEquation(AddRec, *this);
|
|
const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
|
|
const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
|
|
if (R1 && R2) {
|
|
#if 0
|
|
dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
|
|
<< " sol#2: " << *R2 << "\n";
|
|
#endif
|
|
// Pick the smallest positive root value.
|
|
if (ConstantInt *CB =
|
|
dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::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.
|
|
const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
|
|
if (Val->isZero())
|
|
return R1; // We found a quadratic root!
|
|
}
|
|
}
|
|
return getCouldNotCompute();
|
|
}
|
|
|
|
// Otherwise we can only handle this if it is affine.
|
|
if (!AddRec->isAffine())
|
|
return getCouldNotCompute();
|
|
|
|
// If this is an affine expression, the execution count of this branch is
|
|
// the minimum unsigned root of the following equation:
|
|
//
|
|
// Start + Step*N = 0 (mod 2^BW)
|
|
//
|
|
// equivalent to:
|
|
//
|
|
// Step*N = -Start (mod 2^BW)
|
|
//
|
|
// where BW is the common bit width of Start and Step.
|
|
|
|
// Get the initial value for the loop.
|
|
const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
|
|
const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
|
|
|
|
// For now we handle only constant steps.
|
|
//
|
|
// TODO: Handle a nonconstant Step given AddRec<NUW>. If the
|
|
// AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
|
|
// to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
|
|
// We have not yet seen any such cases.
|
|
const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
|
|
if (StepC == 0 || StepC->getValue()->equalsInt(0))
|
|
return getCouldNotCompute();
|
|
|
|
// For positive steps (counting up until unsigned overflow):
|
|
// N = -Start/Step (as unsigned)
|
|
// For negative steps (counting down to zero):
|
|
// N = Start/-Step
|
|
// First compute the unsigned distance from zero in the direction of Step.
|
|
bool CountDown = StepC->getValue()->getValue().isNegative();
|
|
const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
|
|
|
|
// Handle unitary steps, which cannot wraparound.
|
|
// 1*N = -Start; -1*N = Start (mod 2^BW), so:
|
|
// N = Distance (as unsigned)
|
|
if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
|
|
ConstantRange CR = getUnsignedRange(Start);
|
|
const SCEV *MaxBECount;
|
|
if (!CountDown && CR.getUnsignedMin().isMinValue())
|
|
// When counting up, the worst starting value is 1, not 0.
|
|
MaxBECount = CR.getUnsignedMax().isMinValue()
|
|
? getConstant(APInt::getMinValue(CR.getBitWidth()))
|
|
: getConstant(APInt::getMaxValue(CR.getBitWidth()));
|
|
else
|
|
MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
|
|
: -CR.getUnsignedMin());
|
|
return ExitLimit(Distance, MaxBECount);
|
|
}
|
|
|
|
// If the recurrence is known not to wraparound, unsigned divide computes the
|
|
// back edge count. (Ideally we would have an "isexact" bit for udiv). We know
|
|
// that the value will either become zero (and thus the loop terminates), that
|
|
// the loop will terminate through some other exit condition first, or that
|
|
// the loop has undefined behavior. This means we can't "miss" the exit
|
|
// value, even with nonunit stride.
|
|
//
|
|
// This is only valid for expressions that directly compute the loop exit. It
|
|
// is invalid for subexpressions in which the loop may exit through this
|
|
// branch even if this subexpression is false. In that case, the trip count
|
|
// computed by this udiv could be smaller than the number of well-defined
|
|
// iterations.
|
|
if (!IsSubExpr && AddRec->getNoWrapFlags(SCEV::FlagNW))
|
|
return getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
|
|
|
|
// Then, try to solve the above equation provided that Start is constant.
|
|
if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
|
|
return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
|
|
-StartC->getValue()->getValue(),
|
|
*this);
|
|
return getCouldNotCompute();
|
|
}
|
|
|
|
/// HowFarToNonZero - Return the number of times a backedge checking the
|
|
/// specified value for nonzero will execute. If not computable, return
|
|
/// CouldNotCompute
|
|
ScalarEvolution::ExitLimit
|
|
ScalarEvolution::HowFarToNonZero(const 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 (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
|
|
if (!C->getValue()->isNullValue())
|
|
return getConstant(C->getType(), 0);
|
|
return getCouldNotCompute(); // 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 getCouldNotCompute();
|
|
}
|
|
|
|
/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
|
|
/// (which may not be an immediate predecessor) which has exactly one
|
|
/// successor from which BB is reachable, or null if no such block is
|
|
/// found.
|
|
///
|
|
std::pair<BasicBlock *, BasicBlock *>
|
|
ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
|
|
// If the block has a unique predecessor, then there is no path from the
|
|
// predecessor to the block that does not go through the direct edge
|
|
// from the predecessor to the block.
|
|
if (BasicBlock *Pred = BB->getSinglePredecessor())
|
|
return std::make_pair(Pred, BB);
|
|
|
|
// A loop's header is defined to be a block that dominates the loop.
|
|
// If the header has a unique predecessor outside the loop, it must be
|
|
// a block that has exactly one successor that can reach the loop.
|
|
if (Loop *L = LI->getLoopFor(BB))
|
|
return std::make_pair(L->getLoopPredecessor(), L->getHeader());
|
|
|
|
return std::pair<BasicBlock *, BasicBlock *>();
|
|
}
|
|
|
|
/// HasSameValue - SCEV structural equivalence is usually sufficient for
|
|
/// testing whether two expressions are equal, however for the purposes of
|
|
/// looking for a condition guarding a loop, it can be useful to be a little
|
|
/// more general, since a front-end may have replicated the controlling
|
|
/// expression.
|
|
///
|
|
static bool HasSameValue(const SCEV *A, const SCEV *B) {
|
|
// Quick check to see if they are the same SCEV.
|
|
if (A == B) return true;
|
|
|
|
// Otherwise, if they're both SCEVUnknown, it's possible that they hold
|
|
// two different instructions with the same value. Check for this case.
|
|
if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
|
|
if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
|
|
if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
|
|
if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
|
|
if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
|
|
return true;
|
|
|
|
// Otherwise assume they may have a different value.
|
|
return false;
|
|
}
|
|
|
|
/// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
|
|
/// predicate Pred. Return true iff any changes were made.
|
|
///
|
|
bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
|
|
const SCEV *&LHS, const SCEV *&RHS,
|
|
unsigned Depth) {
|
|
bool Changed = false;
|
|
|
|
// If we hit the max recursion limit bail out.
|
|
if (Depth >= 3)
|
|
return false;
|
|
|
|
// Canonicalize a constant to the right side.
|
|
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
|
|
// Check for both operands constant.
|
|
if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
|
|
if (ConstantExpr::getICmp(Pred,
|
|
LHSC->getValue(),
|
|
RHSC->getValue())->isNullValue())
|
|
goto trivially_false;
|
|
else
|
|
goto trivially_true;
|
|
}
|
|
// Otherwise swap the operands to put the constant on the right.
|
|
std::swap(LHS, RHS);
|
|
Pred = ICmpInst::getSwappedPredicate(Pred);
|
|
Changed = true;
|
|
}
|
|
|
|
// If we're comparing an addrec with a value which is loop-invariant in the
|
|
// addrec's loop, put the addrec on the left. Also make a dominance check,
|
|
// as both operands could be addrecs loop-invariant in each other's loop.
|
|
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
|
|
const Loop *L = AR->getLoop();
|
|
if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
|
|
std::swap(LHS, RHS);
|
|
Pred = ICmpInst::getSwappedPredicate(Pred);
|
|
Changed = true;
|
|
}
|
|
}
|
|
|
|
// If there's a constant operand, canonicalize comparisons with boundary
|
|
// cases, and canonicalize *-or-equal comparisons to regular comparisons.
|
|
if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
|
|
const APInt &RA = RC->getValue()->getValue();
|
|
switch (Pred) {
|
|
default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
|
|
case ICmpInst::ICMP_EQ:
|
|
case ICmpInst::ICMP_NE:
|
|
// Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
|
|
if (!RA)
|
|
if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
|
|
if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
|
|
if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
|
|
ME->getOperand(0)->isAllOnesValue()) {
|
|
RHS = AE->getOperand(1);
|
|
LHS = ME->getOperand(1);
|
|
Changed = true;
|
|
}
|
|
break;
|
|
case ICmpInst::ICMP_UGE:
|
|
if ((RA - 1).isMinValue()) {
|
|
Pred = ICmpInst::ICMP_NE;
|
|
RHS = getConstant(RA - 1);
|
|
Changed = true;
|
|
break;
|
|
}
|
|
if (RA.isMaxValue()) {
|
|
Pred = ICmpInst::ICMP_EQ;
|
|
Changed = true;
|
|
break;
|
|
}
|
|
if (RA.isMinValue()) goto trivially_true;
|
|
|
|
Pred = ICmpInst::ICMP_UGT;
|
|
RHS = getConstant(RA - 1);
|
|
Changed = true;
|
|
break;
|
|
case ICmpInst::ICMP_ULE:
|
|
if ((RA + 1).isMaxValue()) {
|
|
Pred = ICmpInst::ICMP_NE;
|
|
RHS = getConstant(RA + 1);
|
|
Changed = true;
|
|
break;
|
|
}
|
|
if (RA.isMinValue()) {
|
|
Pred = ICmpInst::ICMP_EQ;
|
|
Changed = true;
|
|
break;
|
|
}
|
|
if (RA.isMaxValue()) goto trivially_true;
|
|
|
|
Pred = ICmpInst::ICMP_ULT;
|
|
RHS = getConstant(RA + 1);
|
|
Changed = true;
|
|
break;
|
|
case ICmpInst::ICMP_SGE:
|
|
if ((RA - 1).isMinSignedValue()) {
|
|
Pred = ICmpInst::ICMP_NE;
|
|
RHS = getConstant(RA - 1);
|
|
Changed = true;
|
|
break;
|
|
}
|
|
if (RA.isMaxSignedValue()) {
|
|
Pred = ICmpInst::ICMP_EQ;
|
|
Changed = true;
|
|
break;
|
|
}
|
|
if (RA.isMinSignedValue()) goto trivially_true;
|
|
|
|
Pred = ICmpInst::ICMP_SGT;
|
|
RHS = getConstant(RA - 1);
|
|
Changed = true;
|
|
break;
|
|
case ICmpInst::ICMP_SLE:
|
|
if ((RA + 1).isMaxSignedValue()) {
|
|
Pred = ICmpInst::ICMP_NE;
|
|
RHS = getConstant(RA + 1);
|
|
Changed = true;
|
|
break;
|
|
}
|
|
if (RA.isMinSignedValue()) {
|
|
Pred = ICmpInst::ICMP_EQ;
|
|
Changed = true;
|
|
break;
|
|
}
|
|
if (RA.isMaxSignedValue()) goto trivially_true;
|
|
|
|
Pred = ICmpInst::ICMP_SLT;
|
|
RHS = getConstant(RA + 1);
|
|
Changed = true;
|
|
break;
|
|
case ICmpInst::ICMP_UGT:
|
|
if (RA.isMinValue()) {
|
|
Pred = ICmpInst::ICMP_NE;
|
|
Changed = true;
|
|
break;
|
|
}
|
|
if ((RA + 1).isMaxValue()) {
|
|
Pred = ICmpInst::ICMP_EQ;
|
|
RHS = getConstant(RA + 1);
|
|
Changed = true;
|
|
break;
|
|
}
|
|
if (RA.isMaxValue()) goto trivially_false;
|
|
break;
|
|
case ICmpInst::ICMP_ULT:
|
|
if (RA.isMaxValue()) {
|
|
Pred = ICmpInst::ICMP_NE;
|
|
Changed = true;
|
|
break;
|
|
}
|
|
if ((RA - 1).isMinValue()) {
|
|
Pred = ICmpInst::ICMP_EQ;
|
|
RHS = getConstant(RA - 1);
|
|
Changed = true;
|
|
break;
|
|
}
|
|
if (RA.isMinValue()) goto trivially_false;
|
|
break;
|
|
case ICmpInst::ICMP_SGT:
|
|
if (RA.isMinSignedValue()) {
|
|
Pred = ICmpInst::ICMP_NE;
|
|
Changed = true;
|
|
break;
|
|
}
|
|
if ((RA + 1).isMaxSignedValue()) {
|
|
Pred = ICmpInst::ICMP_EQ;
|
|
RHS = getConstant(RA + 1);
|
|
Changed = true;
|
|
break;
|
|
}
|
|
if (RA.isMaxSignedValue()) goto trivially_false;
|
|
break;
|
|
case ICmpInst::ICMP_SLT:
|
|
if (RA.isMaxSignedValue()) {
|
|
Pred = ICmpInst::ICMP_NE;
|
|
Changed = true;
|
|
break;
|
|
}
|
|
if ((RA - 1).isMinSignedValue()) {
|
|
Pred = ICmpInst::ICMP_EQ;
|
|
RHS = getConstant(RA - 1);
|
|
Changed = true;
|
|
break;
|
|
}
|
|
if (RA.isMinSignedValue()) goto trivially_false;
|
|
break;
|
|
}
|
|
}
|
|
|
|
// Check for obvious equality.
|
|
if (HasSameValue(LHS, RHS)) {
|
|
if (ICmpInst::isTrueWhenEqual(Pred))
|
|
goto trivially_true;
|
|
if (ICmpInst::isFalseWhenEqual(Pred))
|
|
goto trivially_false;
|
|
}
|
|
|
|
// If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
|
|
// adding or subtracting 1 from one of the operands.
|
|
switch (Pred) {
|
|
case ICmpInst::ICMP_SLE:
|
|
if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
|
|
RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
|
|
SCEV::FlagNSW);
|
|
Pred = ICmpInst::ICMP_SLT;
|
|
Changed = true;
|
|
} else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
|
|
LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
|
|
SCEV::FlagNSW);
|
|
Pred = ICmpInst::ICMP_SLT;
|
|
Changed = true;
|
|
}
|
|
break;
|
|
case ICmpInst::ICMP_SGE:
|
|
if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
|
|
RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
|
|
SCEV::FlagNSW);
|
|
Pred = ICmpInst::ICMP_SGT;
|
|
Changed = true;
|
|
} else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
|
|
LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
|
|
SCEV::FlagNSW);
|
|
Pred = ICmpInst::ICMP_SGT;
|
|
Changed = true;
|
|
}
|
|
break;
|
|
case ICmpInst::ICMP_ULE:
|
|
if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
|
|
RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
|
|
SCEV::FlagNUW);
|
|
Pred = ICmpInst::ICMP_ULT;
|
|
Changed = true;
|
|
} else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
|
|
LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
|
|
SCEV::FlagNUW);
|
|
Pred = ICmpInst::ICMP_ULT;
|
|
Changed = true;
|
|
}
|
|
break;
|
|
case ICmpInst::ICMP_UGE:
|
|
if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
|
|
RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
|
|
SCEV::FlagNUW);
|
|
Pred = ICmpInst::ICMP_UGT;
|
|
Changed = true;
|
|
} else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
|
|
LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
|
|
SCEV::FlagNUW);
|
|
Pred = ICmpInst::ICMP_UGT;
|
|
Changed = true;
|
|
}
|
|
break;
|
|
default:
|
|
break;
|
|
}
|
|
|
|
// TODO: More simplifications are possible here.
|
|
|
|
// Recursively simplify until we either hit a recursion limit or nothing
|
|
// changes.
|
|
if (Changed)
|
|
return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
|
|
|
|
return Changed;
|
|
|
|
trivially_true:
|
|
// Return 0 == 0.
|
|
LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
|
|
Pred = ICmpInst::ICMP_EQ;
|
|
return true;
|
|
|
|
trivially_false:
|
|
// Return 0 != 0.
|
|
LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
|
|
Pred = ICmpInst::ICMP_NE;
|
|
return true;
|
|
}
|
|
|
|
bool ScalarEvolution::isKnownNegative(const SCEV *S) {
|
|
return getSignedRange(S).getSignedMax().isNegative();
|
|
}
|
|
|
|
bool ScalarEvolution::isKnownPositive(const SCEV *S) {
|
|
return getSignedRange(S).getSignedMin().isStrictlyPositive();
|
|
}
|
|
|
|
bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
|
|
return !getSignedRange(S).getSignedMin().isNegative();
|
|
}
|
|
|
|
bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
|
|
return !getSignedRange(S).getSignedMax().isStrictlyPositive();
|
|
}
|
|
|
|
bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
|
|
return isKnownNegative(S) || isKnownPositive(S);
|
|
}
|
|
|
|
bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
|
|
const SCEV *LHS, const SCEV *RHS) {
|
|
// Canonicalize the inputs first.
|
|
(void)SimplifyICmpOperands(Pred, LHS, RHS);
|
|
|
|
// If LHS or RHS is an addrec, check to see if the condition is true in
|
|
// every iteration of the loop.
|
|
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
|
|
if (isLoopEntryGuardedByCond(
|
|
AR->getLoop(), Pred, AR->getStart(), RHS) &&
|
|
isLoopBackedgeGuardedByCond(
|
|
AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
|
|
return true;
|
|
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
|
|
if (isLoopEntryGuardedByCond(
|
|
AR->getLoop(), Pred, LHS, AR->getStart()) &&
|
|
isLoopBackedgeGuardedByCond(
|
|
AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
|
|
return true;
|
|
|
|
// Otherwise see what can be done with known constant ranges.
|
|
return isKnownPredicateWithRanges(Pred, LHS, RHS);
|
|
}
|
|
|
|
bool
|
|
ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
|
|
const SCEV *LHS, const SCEV *RHS) {
|
|
if (HasSameValue(LHS, RHS))
|
|
return ICmpInst::isTrueWhenEqual(Pred);
|
|
|
|
// This code is split out from isKnownPredicate because it is called from
|
|
// within isLoopEntryGuardedByCond.
|
|
switch (Pred) {
|
|
default:
|
|
llvm_unreachable("Unexpected ICmpInst::Predicate value!");
|
|
case ICmpInst::ICMP_SGT:
|
|
Pred = ICmpInst::ICMP_SLT;
|
|
std::swap(LHS, RHS);
|
|
case ICmpInst::ICMP_SLT: {
|
|
ConstantRange LHSRange = getSignedRange(LHS);
|
|
ConstantRange RHSRange = getSignedRange(RHS);
|
|
if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
|
|
return true;
|
|
if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
|
|
return false;
|
|
break;
|
|
}
|
|
case ICmpInst::ICMP_SGE:
|
|
Pred = ICmpInst::ICMP_SLE;
|
|
std::swap(LHS, RHS);
|
|
case ICmpInst::ICMP_SLE: {
|
|
ConstantRange LHSRange = getSignedRange(LHS);
|
|
ConstantRange RHSRange = getSignedRange(RHS);
|
|
if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
|
|
return true;
|
|
if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
|
|
return false;
|
|
break;
|
|
}
|
|
case ICmpInst::ICMP_UGT:
|
|
Pred = ICmpInst::ICMP_ULT;
|
|
std::swap(LHS, RHS);
|
|
case ICmpInst::ICMP_ULT: {
|
|
ConstantRange LHSRange = getUnsignedRange(LHS);
|
|
ConstantRange RHSRange = getUnsignedRange(RHS);
|
|
if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
|
|
return true;
|
|
if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
|
|
return false;
|
|
break;
|
|
}
|
|
case ICmpInst::ICMP_UGE:
|
|
Pred = ICmpInst::ICMP_ULE;
|
|
std::swap(LHS, RHS);
|
|
case ICmpInst::ICMP_ULE: {
|
|
ConstantRange LHSRange = getUnsignedRange(LHS);
|
|
ConstantRange RHSRange = getUnsignedRange(RHS);
|
|
if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
|
|
return true;
|
|
if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
|
|
return false;
|
|
break;
|
|
}
|
|
case ICmpInst::ICMP_NE: {
|
|
if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
|
|
return true;
|
|
if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
|
|
return true;
|
|
|
|
const SCEV *Diff = getMinusSCEV(LHS, RHS);
|
|
if (isKnownNonZero(Diff))
|
|
return true;
|
|
break;
|
|
}
|
|
case ICmpInst::ICMP_EQ:
|
|
// The check at the top of the function catches the case where
|
|
// the values are known to be equal.
|
|
break;
|
|
}
|
|
return false;
|
|
}
|
|
|
|
/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
|
|
/// protected by a conditional between LHS and RHS. This is used to
|
|
/// to eliminate casts.
|
|
bool
|
|
ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
|
|
ICmpInst::Predicate Pred,
|
|
const SCEV *LHS, const SCEV *RHS) {
|
|
// Interpret a null as meaning no loop, where there is obviously no guard
|
|
// (interprocedural conditions notwithstanding).
|
|
if (!L) return true;
|
|
|
|
BasicBlock *Latch = L->getLoopLatch();
|
|
if (!Latch)
|
|
return false;
|
|
|
|
BranchInst *LoopContinuePredicate =
|
|
dyn_cast<BranchInst>(Latch->getTerminator());
|
|
if (!LoopContinuePredicate ||
|
|
LoopContinuePredicate->isUnconditional())
|
|
return false;
|
|
|
|
return isImpliedCond(Pred, LHS, RHS,
|
|
LoopContinuePredicate->getCondition(),
|
|
LoopContinuePredicate->getSuccessor(0) != L->getHeader());
|
|
}
|
|
|
|
/// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
|
|
/// by a conditional between LHS and RHS. This is used to help avoid max
|
|
/// expressions in loop trip counts, and to eliminate casts.
|
|
bool
|
|
ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
|
|
ICmpInst::Predicate Pred,
|
|
const SCEV *LHS, const SCEV *RHS) {
|
|
// Interpret a null as meaning no loop, where there is obviously no guard
|
|
// (interprocedural conditions notwithstanding).
|
|
if (!L) return false;
|
|
|
|
// Starting at the loop predecessor, climb up the predecessor chain, as long
|
|
// as there are predecessors that can be found that have unique successors
|
|
// leading to the original header.
|
|
for (std::pair<BasicBlock *, BasicBlock *>
|
|
Pair(L->getLoopPredecessor(), L->getHeader());
|
|
Pair.first;
|
|
Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
|
|
|
|
BranchInst *LoopEntryPredicate =
|
|
dyn_cast<BranchInst>(Pair.first->getTerminator());
|
|
if (!LoopEntryPredicate ||
|
|
LoopEntryPredicate->isUnconditional())
|
|
continue;
|
|
|
|
if (isImpliedCond(Pred, LHS, RHS,
|
|
LoopEntryPredicate->getCondition(),
|
|
LoopEntryPredicate->getSuccessor(0) != Pair.second))
|
|
return true;
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
/// RAII wrapper to prevent recursive application of isImpliedCond.
|
|
/// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
|
|
/// currently evaluating isImpliedCond.
|
|
struct MarkPendingLoopPredicate {
|
|
Value *Cond;
|
|
DenseSet<Value*> &LoopPreds;
|
|
bool Pending;
|
|
|
|
MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
|
|
: Cond(C), LoopPreds(LP) {
|
|
Pending = !LoopPreds.insert(Cond).second;
|
|
}
|
|
~MarkPendingLoopPredicate() {
|
|
if (!Pending)
|
|
LoopPreds.erase(Cond);
|
|
}
|
|
};
|
|
|
|
/// isImpliedCond - Test whether the condition described by Pred, LHS,
|
|
/// and RHS is true whenever the given Cond value evaluates to true.
|
|
bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
|
|
const SCEV *LHS, const SCEV *RHS,
|
|
Value *FoundCondValue,
|
|
bool Inverse) {
|
|
MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
|
|
if (Mark.Pending)
|
|
return false;
|
|
|
|
// Recursively handle And and Or conditions.
|
|
if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
|
|
if (BO->getOpcode() == Instruction::And) {
|
|
if (!Inverse)
|
|
return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
|
|
isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
|
|
} else if (BO->getOpcode() == Instruction::Or) {
|
|
if (Inverse)
|
|
return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
|
|
isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
|
|
}
|
|
}
|
|
|
|
ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
|
|
if (!ICI) return false;
|
|
|
|
// Bail if the ICmp's operands' types are wider than the needed type
|
|
// before attempting to call getSCEV on them. This avoids infinite
|
|
// recursion, since the analysis of widening casts can require loop
|
|
// exit condition information for overflow checking, which would
|
|
// lead back here.
|
|
if (getTypeSizeInBits(LHS->getType()) <
|
|
getTypeSizeInBits(ICI->getOperand(0)->getType()))
|
|
return false;
|
|
|
|
// Now that we found a conditional branch that dominates the loop or controls
|
|
// the loop latch. Check to see if it is the comparison we are looking for.
|
|
ICmpInst::Predicate FoundPred;
|
|
if (Inverse)
|
|
FoundPred = ICI->getInversePredicate();
|
|
else
|
|
FoundPred = ICI->getPredicate();
|
|
|
|
const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
|
|
const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
|
|
|
|
// Balance the types. The case where FoundLHS' type is wider than
|
|
// LHS' type is checked for above.
|
|
if (getTypeSizeInBits(LHS->getType()) >
|
|
getTypeSizeInBits(FoundLHS->getType())) {
|
|
if (CmpInst::isSigned(Pred)) {
|
|
FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
|
|
FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
|
|
} else {
|
|
FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
|
|
FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
|
|
}
|
|
}
|
|
|
|
// Canonicalize the query to match the way instcombine will have
|
|
// canonicalized the comparison.
|
|
if (SimplifyICmpOperands(Pred, LHS, RHS))
|
|
if (LHS == RHS)
|
|
return CmpInst::isTrueWhenEqual(Pred);
|
|
if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
|
|
if (FoundLHS == FoundRHS)
|
|
return CmpInst::isFalseWhenEqual(FoundPred);
|
|
|
|
// Check to see if we can make the LHS or RHS match.
|
|
if (LHS == FoundRHS || RHS == FoundLHS) {
|
|
if (isa<SCEVConstant>(RHS)) {
|
|
std::swap(FoundLHS, FoundRHS);
|
|
FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
|
|
} else {
|
|
std::swap(LHS, RHS);
|
|
Pred = ICmpInst::getSwappedPredicate(Pred);
|
|
}
|
|
}
|
|
|
|
// Check whether the found predicate is the same as the desired predicate.
|
|
if (FoundPred == Pred)
|
|
return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
|
|
|
|
// Check whether swapping the found predicate makes it the same as the
|
|
// desired predicate.
|
|
if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
|
|
if (isa<SCEVConstant>(RHS))
|
|
return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
|
|
else
|
|
return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
|
|
RHS, LHS, FoundLHS, FoundRHS);
|
|
}
|
|
|
|
// Check whether the actual condition is beyond sufficient.
|
|
if (FoundPred == ICmpInst::ICMP_EQ)
|
|
if (ICmpInst::isTrueWhenEqual(Pred))
|
|
if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
|
|
return true;
|
|
if (Pred == ICmpInst::ICMP_NE)
|
|
if (!ICmpInst::isTrueWhenEqual(FoundPred))
|
|
if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
|
|
return true;
|
|
|
|
// Otherwise assume the worst.
|
|
return false;
|
|
}
|
|
|
|
/// isImpliedCondOperands - Test whether the condition described by Pred,
|
|
/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
|
|
/// and FoundRHS is true.
|
|
bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
|
|
const SCEV *LHS, const SCEV *RHS,
|
|
const SCEV *FoundLHS,
|
|
const SCEV *FoundRHS) {
|
|
return isImpliedCondOperandsHelper(Pred, LHS, RHS,
|
|
FoundLHS, FoundRHS) ||
|
|
// ~x < ~y --> x > y
|
|
isImpliedCondOperandsHelper(Pred, LHS, RHS,
|
|
getNotSCEV(FoundRHS),
|
|
getNotSCEV(FoundLHS));
|
|
}
|
|
|
|
/// isImpliedCondOperandsHelper - Test whether the condition described by
|
|
/// Pred, LHS, and RHS is true whenever the condition described by Pred,
|
|
/// FoundLHS, and FoundRHS is true.
|
|
bool
|
|
ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
|
|
const SCEV *LHS, const SCEV *RHS,
|
|
const SCEV *FoundLHS,
|
|
const SCEV *FoundRHS) {
|
|
switch (Pred) {
|
|
default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
|
|
case ICmpInst::ICMP_EQ:
|
|
case ICmpInst::ICMP_NE:
|
|
if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
|
|
return true;
|
|
break;
|
|
case ICmpInst::ICMP_SLT:
|
|
case ICmpInst::ICMP_SLE:
|
|
if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
|
|
isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
|
|
return true;
|
|
break;
|
|
case ICmpInst::ICMP_SGT:
|
|
case ICmpInst::ICMP_SGE:
|
|
if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
|
|
isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
|
|
return true;
|
|
break;
|
|
case ICmpInst::ICMP_ULT:
|
|
case ICmpInst::ICMP_ULE:
|
|
if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
|
|
isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
|
|
return true;
|
|
break;
|
|
case ICmpInst::ICMP_UGT:
|
|
case ICmpInst::ICMP_UGE:
|
|
if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
|
|
isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
|
|
return true;
|
|
break;
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
// Verify if an linear IV with positive stride can overflow when in a
|
|
// less-than comparison, knowing the invariant term of the comparison, the
|
|
// stride and the knowledge of NSW/NUW flags on the recurrence.
|
|
bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
|
|
bool IsSigned, bool NoWrap) {
|
|
if (NoWrap) return false;
|
|
|
|
unsigned BitWidth = getTypeSizeInBits(RHS->getType());
|
|
const SCEV *One = getConstant(Stride->getType(), 1);
|
|
|
|
if (IsSigned) {
|
|
APInt MaxRHS = getSignedRange(RHS).getSignedMax();
|
|
APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
|
|
APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
|
|
.getSignedMax();
|
|
|
|
// SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
|
|
return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
|
|
}
|
|
|
|
APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
|
|
APInt MaxValue = APInt::getMaxValue(BitWidth);
|
|
APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
|
|
.getUnsignedMax();
|
|
|
|
// UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
|
|
return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
|
|
}
|
|
|
|
// Verify if an linear IV with negative stride can overflow when in a
|
|
// greater-than comparison, knowing the invariant term of the comparison,
|
|
// the stride and the knowledge of NSW/NUW flags on the recurrence.
|
|
bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
|
|
bool IsSigned, bool NoWrap) {
|
|
if (NoWrap) return false;
|
|
|
|
unsigned BitWidth = getTypeSizeInBits(RHS->getType());
|
|
const SCEV *One = getConstant(Stride->getType(), 1);
|
|
|
|
if (IsSigned) {
|
|
APInt MinRHS = getSignedRange(RHS).getSignedMin();
|
|
APInt MinValue = APInt::getSignedMinValue(BitWidth);
|
|
APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
|
|
.getSignedMax();
|
|
|
|
// SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
|
|
return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
|
|
}
|
|
|
|
APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
|
|
APInt MinValue = APInt::getMinValue(BitWidth);
|
|
APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
|
|
.getUnsignedMax();
|
|
|
|
// UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
|
|
return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
|
|
}
|
|
|
|
// Compute the backedge taken count knowing the interval difference, the
|
|
// stride and presence of the equality in the comparison.
|
|
const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
|
|
bool Equality) {
|
|
const SCEV *One = getConstant(Step->getType(), 1);
|
|
Delta = Equality ? getAddExpr(Delta, Step)
|
|
: getAddExpr(Delta, getMinusSCEV(Step, One));
|
|
return getUDivExpr(Delta, Step);
|
|
}
|
|
|
|
/// HowManyLessThans - Return the number of times a backedge containing the
|
|
/// specified less-than comparison will execute. If not computable, return
|
|
/// CouldNotCompute.
|
|
///
|
|
/// @param IsSubExpr is true when the LHS < RHS condition does not directly
|
|
/// control the branch. In this case, we can only compute an iteration count for
|
|
/// a subexpression that cannot overflow before evaluating true.
|
|
ScalarEvolution::ExitLimit
|
|
ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
|
|
const Loop *L, bool IsSigned,
|
|
bool IsSubExpr) {
|
|
// We handle only IV < Invariant
|
|
if (!isLoopInvariant(RHS, L))
|
|
return getCouldNotCompute();
|
|
|
|
const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
|
|
|
|
// Avoid weird loops
|
|
if (!IV || IV->getLoop() != L || !IV->isAffine())
|
|
return getCouldNotCompute();
|
|
|
|
bool NoWrap = !IsSubExpr &&
|
|
IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
|
|
|
|
const SCEV *Stride = IV->getStepRecurrence(*this);
|
|
|
|
// Avoid negative or zero stride values
|
|
if (!isKnownPositive(Stride))
|
|
return getCouldNotCompute();
|
|
|
|
// Avoid proven overflow cases: this will ensure that the backedge taken count
|
|
// will not generate any unsigned overflow. Relaxed no-overflow conditions
|
|
// exploit NoWrapFlags, allowing to optimize in presence of undefined
|
|
// behaviors like the case of C language.
|
|
if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
|
|
return getCouldNotCompute();
|
|
|
|
ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
|
|
: ICmpInst::ICMP_ULT;
|
|
const SCEV *Start = IV->getStart();
|
|
const SCEV *End = RHS;
|
|
if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS))
|
|
End = IsSigned ? getSMaxExpr(RHS, Start)
|
|
: getUMaxExpr(RHS, Start);
|
|
|
|
const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
|
|
|
|
APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
|
|
: getUnsignedRange(Start).getUnsignedMin();
|
|
|
|
APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
|
|
: getUnsignedRange(Stride).getUnsignedMin();
|
|
|
|
unsigned BitWidth = getTypeSizeInBits(LHS->getType());
|
|
APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
|
|
: APInt::getMaxValue(BitWidth) - (MinStride - 1);
|
|
|
|
// Although End can be a MAX expression we estimate MaxEnd considering only
|
|
// the case End = RHS. This is safe because in the other case (End - Start)
|
|
// is zero, leading to a zero maximum backedge taken count.
|
|
APInt MaxEnd =
|
|
IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
|
|
: APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
|
|
|
|
const SCEV *MaxBECount = getCouldNotCompute();
|
|
if (isa<SCEVConstant>(BECount))
|
|
MaxBECount = BECount;
|
|
else
|
|
MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
|
|
getConstant(MinStride), false);
|
|
|
|
if (isa<SCEVCouldNotCompute>(MaxBECount))
|
|
MaxBECount = BECount;
|
|
|
|
return ExitLimit(BECount, MaxBECount);
|
|
}
|
|
|
|
ScalarEvolution::ExitLimit
|
|
ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
|
|
const Loop *L, bool IsSigned,
|
|
bool IsSubExpr) {
|
|
// We handle only IV > Invariant
|
|
if (!isLoopInvariant(RHS, L))
|
|
return getCouldNotCompute();
|
|
|
|
const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
|
|
|
|
// Avoid weird loops
|
|
if (!IV || IV->getLoop() != L || !IV->isAffine())
|
|
return getCouldNotCompute();
|
|
|
|
bool NoWrap = !IsSubExpr &&
|
|
IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
|
|
|
|
const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
|
|
|
|
// Avoid negative or zero stride values
|
|
if (!isKnownPositive(Stride))
|
|
return getCouldNotCompute();
|
|
|
|
// Avoid proven overflow cases: this will ensure that the backedge taken count
|
|
// will not generate any unsigned overflow. Relaxed no-overflow conditions
|
|
// exploit NoWrapFlags, allowing to optimize in presence of undefined
|
|
// behaviors like the case of C language.
|
|
if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
|
|
return getCouldNotCompute();
|
|
|
|
ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
|
|
: ICmpInst::ICMP_UGT;
|
|
|
|
const SCEV *Start = IV->getStart();
|
|
const SCEV *End = RHS;
|
|
if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS))
|
|
End = IsSigned ? getSMinExpr(RHS, Start)
|
|
: getUMinExpr(RHS, Start);
|
|
|
|
const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
|
|
|
|
APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
|
|
: getUnsignedRange(Start).getUnsignedMax();
|
|
|
|
APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
|
|
: getUnsignedRange(Stride).getUnsignedMin();
|
|
|
|
unsigned BitWidth = getTypeSizeInBits(LHS->getType());
|
|
APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
|
|
: APInt::getMinValue(BitWidth) + (MinStride - 1);
|
|
|
|
// Although End can be a MIN expression we estimate MinEnd considering only
|
|
// the case End = RHS. This is safe because in the other case (Start - End)
|
|
// is zero, leading to a zero maximum backedge taken count.
|
|
APInt MinEnd =
|
|
IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
|
|
: APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
|
|
|
|
|
|
const SCEV *MaxBECount = getCouldNotCompute();
|
|
if (isa<SCEVConstant>(BECount))
|
|
MaxBECount = BECount;
|
|
else
|
|
MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
|
|
getConstant(MinStride), false);
|
|
|
|
if (isa<SCEVCouldNotCompute>(MaxBECount))
|
|
MaxBECount = BECount;
|
|
|
|
return ExitLimit(BECount, MaxBECount);
|
|
}
|
|
|
|
/// 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.
|
|
const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
|
|
ScalarEvolution &SE) const {
|
|
if (Range.isFullSet()) // Infinite loop.
|
|
return SE.getCouldNotCompute();
|
|
|
|
// If the start is a non-zero constant, shift the range to simplify things.
|
|
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
|
|
if (!SC->getValue()->isZero()) {
|
|
SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
|
|
Operands[0] = SE.getConstant(SC->getType(), 0);
|
|
const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
|
|
getNoWrapFlags(FlagNW));
|
|
if (const SCEVAddRecExpr *ShiftedAddRec =
|
|
dyn_cast<SCEVAddRecExpr>(Shifted))
|
|
return ShiftedAddRec->getNumIterationsInRange(
|
|
Range.subtract(SC->getValue()->getValue()), SE);
|
|
// This is strange and shouldn't happen.
|
|
return SE.getCouldNotCompute();
|
|
}
|
|
|
|
// 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 SE.getCouldNotCompute();
|
|
|
|
|
|
// 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.
|
|
unsigned BitWidth = SE.getTypeSizeInBits(getType());
|
|
if (!Range.contains(APInt(BitWidth, 0)))
|
|
return SE.getConstant(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(BitWidth,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(SE.getContext(), 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 SE.getCouldNotCompute(); // Something strange happened
|
|
|
|
// Ensure that the previous value is in the range. This is a sanity check.
|
|
assert(Range.contains(
|
|
EvaluateConstantChrecAtConstant(this,
|
|
ConstantInt::get(SE.getContext(), 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.
|
|
SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
|
|
NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
|
|
const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
|
|
// getNoWrapFlags(FlagNW)
|
|
FlagAnyWrap);
|
|
|
|
// Next, solve the constructed addrec
|
|
std::pair<const SCEV *,const SCEV *> Roots =
|
|
SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
|
|
const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
|
|
const 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(SE.getContext(), R1->getValue()->getValue()+1);
|
|
|
|
R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
|
|
if (!Range.contains(R1Val->getValue()))
|
|
return SE.getConstant(NextVal);
|
|
return SE.getCouldNotCompute(); // 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(SE.getContext(), R1->getValue()->getValue()-1);
|
|
R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
|
|
if (Range.contains(R1Val->getValue()))
|
|
return R1;
|
|
return SE.getCouldNotCompute(); // Something strange happened
|
|
}
|
|
}
|
|
}
|
|
|
|
return SE.getCouldNotCompute();
|
|
}
|
|
|
|
static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
|
|
APInt A = C1->getValue()->getValue().abs();
|
|
APInt B = C2->getValue()->getValue().abs();
|
|
uint32_t ABW = A.getBitWidth();
|
|
uint32_t BBW = B.getBitWidth();
|
|
|
|
if (ABW > BBW)
|
|
B = B.zext(ABW);
|
|
else if (ABW < BBW)
|
|
A = A.zext(BBW);
|
|
|
|
return APIntOps::GreatestCommonDivisor(A, B);
|
|
}
|
|
|
|
static const APInt srem(const SCEVConstant *C1, const SCEVConstant *C2) {
|
|
APInt A = C1->getValue()->getValue();
|
|
APInt B = C2->getValue()->getValue();
|
|
uint32_t ABW = A.getBitWidth();
|
|
uint32_t BBW = B.getBitWidth();
|
|
|
|
if (ABW > BBW)
|
|
B = B.sext(ABW);
|
|
else if (ABW < BBW)
|
|
A = A.sext(BBW);
|
|
|
|
return APIntOps::srem(A, B);
|
|
}
|
|
|
|
static const APInt sdiv(const SCEVConstant *C1, const SCEVConstant *C2) {
|
|
APInt A = C1->getValue()->getValue();
|
|
APInt B = C2->getValue()->getValue();
|
|
uint32_t ABW = A.getBitWidth();
|
|
uint32_t BBW = B.getBitWidth();
|
|
|
|
if (ABW > BBW)
|
|
B = B.sext(ABW);
|
|
else if (ABW < BBW)
|
|
A = A.sext(BBW);
|
|
|
|
return APIntOps::sdiv(A, B);
|
|
}
|
|
|
|
namespace {
|
|
struct SCEVGCD : public SCEVVisitor<SCEVGCD, const SCEV *> {
|
|
public:
|
|
// Pattern match Step into Start. When Step is a multiply expression, find
|
|
// the largest subexpression of Step that appears in Start. When Start is an
|
|
// add expression, try to match Step in the subexpressions of Start, non
|
|
// matching subexpressions are returned under Remainder.
|
|
static const SCEV *findGCD(ScalarEvolution &SE, const SCEV *Start,
|
|
const SCEV *Step, const SCEV **Remainder) {
|
|
assert(Remainder && "Remainder should not be NULL");
|
|
SCEVGCD R(SE, Step, SE.getConstant(Step->getType(), 0));
|
|
const SCEV *Res = R.visit(Start);
|
|
*Remainder = R.Remainder;
|
|
return Res;
|
|
}
|
|
|
|
SCEVGCD(ScalarEvolution &S, const SCEV *G, const SCEV *R)
|
|
: SE(S), GCD(G), Remainder(R) {
|
|
Zero = SE.getConstant(GCD->getType(), 0);
|
|
One = SE.getConstant(GCD->getType(), 1);
|
|
}
|
|
|
|
const SCEV *visitConstant(const SCEVConstant *Constant) {
|
|
if (GCD == Constant || Constant == Zero)
|
|
return GCD;
|
|
|
|
if (const SCEVConstant *CGCD = dyn_cast<SCEVConstant>(GCD)) {
|
|
const SCEV *Res = SE.getConstant(gcd(Constant, CGCD));
|
|
if (Res != One)
|
|
return Res;
|
|
|
|
Remainder = SE.getConstant(srem(Constant, CGCD));
|
|
Constant = cast<SCEVConstant>(SE.getMinusSCEV(Constant, Remainder));
|
|
Res = SE.getConstant(gcd(Constant, CGCD));
|
|
return Res;
|
|
}
|
|
|
|
// When GCD is not a constant, it could be that the GCD is an Add, Mul,
|
|
// AddRec, etc., in which case we want to find out how many times the
|
|
// Constant divides the GCD: we then return that as the new GCD.
|
|
const SCEV *Rem = Zero;
|
|
const SCEV *Res = findGCD(SE, GCD, Constant, &Rem);
|
|
|
|
if (Res == One || Rem != Zero) {
|
|
Remainder = Constant;
|
|
return One;
|
|
}
|
|
|
|
assert(isa<SCEVConstant>(Res) && "Res should be a constant");
|
|
Remainder = SE.getConstant(srem(Constant, cast<SCEVConstant>(Res)));
|
|
return Res;
|
|
}
|
|
|
|
const SCEV *visitTruncateExpr(const SCEVTruncateExpr *Expr) {
|
|
if (GCD != Expr)
|
|
Remainder = Expr;
|
|
return GCD;
|
|
}
|
|
|
|
const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
|
|
if (GCD != Expr)
|
|
Remainder = Expr;
|
|
return GCD;
|
|
}
|
|
|
|
const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
|
|
if (GCD != Expr)
|
|
Remainder = Expr;
|
|
return GCD;
|
|
}
|
|
|
|
const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
|
|
if (GCD == Expr)
|
|
return GCD;
|
|
|
|
for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
|
|
const SCEV *Rem = Zero;
|
|
const SCEV *Res = findGCD(SE, Expr->getOperand(e - 1 - i), GCD, &Rem);
|
|
|
|
// FIXME: There may be ambiguous situations: for instance,
|
|
// GCD(-4 + (3 * %m), 2 * %m) where 2 divides -4 and %m divides (3 * %m).
|
|
// The order in which the AddExpr is traversed computes a different GCD
|
|
// and Remainder.
|
|
if (Res != One)
|
|
GCD = Res;
|
|
if (Rem != Zero)
|
|
Remainder = SE.getAddExpr(Remainder, Rem);
|
|
}
|
|
|
|
return GCD;
|
|
}
|
|
|
|
const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
|
|
if (GCD == Expr)
|
|
return GCD;
|
|
|
|
for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
|
|
if (Expr->getOperand(i) == GCD)
|
|
return GCD;
|
|
}
|
|
|
|
// If we have not returned yet, it means that GCD is not part of Expr.
|
|
const SCEV *PartialGCD = One;
|
|
for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
|
|
const SCEV *Rem = Zero;
|
|
const SCEV *Res = findGCD(SE, Expr->getOperand(i), GCD, &Rem);
|
|
if (Rem != Zero)
|
|
// GCD does not divide Expr->getOperand(i).
|
|
continue;
|
|
|
|
if (Res == GCD)
|
|
return GCD;
|
|
PartialGCD = SE.getMulExpr(PartialGCD, Res);
|
|
if (PartialGCD == GCD)
|
|
return GCD;
|
|
}
|
|
|
|
if (PartialGCD != One)
|
|
return PartialGCD;
|
|
|
|
Remainder = Expr;
|
|
const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(GCD);
|
|
if (!Mul)
|
|
return PartialGCD;
|
|
|
|
// When the GCD is a multiply expression, try to decompose it:
|
|
// this occurs when Step does not divide the Start expression
|
|
// as in: {(-4 + (3 * %m)),+,(2 * %m)}
|
|
for (int i = 0, e = Mul->getNumOperands(); i < e; ++i) {
|
|
const SCEV *Rem = Zero;
|
|
const SCEV *Res = findGCD(SE, Expr, Mul->getOperand(i), &Rem);
|
|
if (Rem == Zero) {
|
|
Remainder = Rem;
|
|
return Res;
|
|
}
|
|
}
|
|
|
|
return PartialGCD;
|
|
}
|
|
|
|
const SCEV *visitUDivExpr(const SCEVUDivExpr *Expr) {
|
|
if (GCD != Expr)
|
|
Remainder = Expr;
|
|
return GCD;
|
|
}
|
|
|
|
const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
|
|
if (GCD == Expr)
|
|
return GCD;
|
|
|
|
if (!Expr->isAffine()) {
|
|
Remainder = Expr;
|
|
return GCD;
|
|
}
|
|
|
|
const SCEV *Rem = Zero;
|
|
const SCEV *Res = findGCD(SE, Expr->getOperand(0), GCD, &Rem);
|
|
if (Rem != Zero)
|
|
Remainder = SE.getAddExpr(Remainder, Rem);
|
|
|
|
Rem = Zero;
|
|
Res = findGCD(SE, Expr->getOperand(1), Res, &Rem);
|
|
if (Rem != Zero) {
|
|
Remainder = Expr;
|
|
return GCD;
|
|
}
|
|
|
|
return Res;
|
|
}
|
|
|
|
const SCEV *visitSMaxExpr(const SCEVSMaxExpr *Expr) {
|
|
if (GCD != Expr)
|
|
Remainder = Expr;
|
|
return GCD;
|
|
}
|
|
|
|
const SCEV *visitUMaxExpr(const SCEVUMaxExpr *Expr) {
|
|
if (GCD != Expr)
|
|
Remainder = Expr;
|
|
return GCD;
|
|
}
|
|
|
|
const SCEV *visitUnknown(const SCEVUnknown *Expr) {
|
|
if (GCD != Expr)
|
|
Remainder = Expr;
|
|
return GCD;
|
|
}
|
|
|
|
const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
|
|
return One;
|
|
}
|
|
|
|
private:
|
|
ScalarEvolution &SE;
|
|
const SCEV *GCD, *Remainder, *Zero, *One;
|
|
};
|
|
|
|
struct SCEVDivision : public SCEVVisitor<SCEVDivision, const SCEV *> {
|
|
public:
|
|
// Remove from Start all multiples of Step.
|
|
static const SCEV *divide(ScalarEvolution &SE, const SCEV *Start,
|
|
const SCEV *Step) {
|
|
SCEVDivision D(SE, Step);
|
|
const SCEV *Rem = D.Zero;
|
|
(void)Rem;
|
|
// The division is guaranteed to succeed: Step should divide Start with no
|
|
// remainder.
|
|
assert(Step == SCEVGCD::findGCD(SE, Start, Step, &Rem) && Rem == D.Zero &&
|
|
"Step should divide Start with no remainder.");
|
|
return D.visit(Start);
|
|
}
|
|
|
|
SCEVDivision(ScalarEvolution &S, const SCEV *G) : SE(S), GCD(G) {
|
|
Zero = SE.getConstant(GCD->getType(), 0);
|
|
One = SE.getConstant(GCD->getType(), 1);
|
|
}
|
|
|
|
const SCEV *visitConstant(const SCEVConstant *Constant) {
|
|
if (GCD == Constant)
|
|
return One;
|
|
|
|
if (const SCEVConstant *CGCD = dyn_cast<SCEVConstant>(GCD))
|
|
return SE.getConstant(sdiv(Constant, CGCD));
|
|
return Constant;
|
|
}
|
|
|
|
const SCEV *visitTruncateExpr(const SCEVTruncateExpr *Expr) {
|
|
if (GCD == Expr)
|
|
return One;
|
|
return Expr;
|
|
}
|
|
|
|
const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
|
|
if (GCD == Expr)
|
|
return One;
|
|
return Expr;
|
|
}
|
|
|
|
const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
|
|
if (GCD == Expr)
|
|
return One;
|
|
return Expr;
|
|
}
|
|
|
|
const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
|
|
if (GCD == Expr)
|
|
return One;
|
|
|
|
SmallVector<const SCEV *, 2> Operands;
|
|
for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
|
|
Operands.push_back(divide(SE, Expr->getOperand(i), GCD));
|
|
|
|
if (Operands.size() == 1)
|
|
return Operands[0];
|
|
return SE.getAddExpr(Operands);
|
|
}
|
|
|
|
const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
|
|
if (GCD == Expr)
|
|
return One;
|
|
|
|
bool FoundGCDTerm = false;
|
|
for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
|
|
if (Expr->getOperand(i) == GCD)
|
|
FoundGCDTerm = true;
|
|
|
|
SmallVector<const SCEV *, 2> Operands;
|
|
if (FoundGCDTerm) {
|
|
FoundGCDTerm = false;
|
|
for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
|
|
if (FoundGCDTerm)
|
|
Operands.push_back(Expr->getOperand(i));
|
|
else if (Expr->getOperand(i) == GCD)
|
|
FoundGCDTerm = true;
|
|
else
|
|
Operands.push_back(Expr->getOperand(i));
|
|
}
|
|
} else {
|
|
FoundGCDTerm = false;
|
|
const SCEV *PartialGCD = One;
|
|
for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
|
|
if (PartialGCD == GCD) {
|
|
Operands.push_back(Expr->getOperand(i));
|
|
continue;
|
|
}
|
|
|
|
const SCEV *Rem = Zero;
|
|
const SCEV *Res = SCEVGCD::findGCD(SE, Expr->getOperand(i), GCD, &Rem);
|
|
if (Rem == Zero) {
|
|
PartialGCD = SE.getMulExpr(PartialGCD, Res);
|
|
Operands.push_back(divide(SE, Expr->getOperand(i), GCD));
|
|
} else {
|
|
Operands.push_back(Expr->getOperand(i));
|
|
}
|
|
}
|
|
}
|
|
|
|
if (Operands.size() == 1)
|
|
return Operands[0];
|
|
return SE.getMulExpr(Operands);
|
|
}
|
|
|
|
const SCEV *visitUDivExpr(const SCEVUDivExpr *Expr) {
|
|
if (GCD == Expr)
|
|
return One;
|
|
return Expr;
|
|
}
|
|
|
|
const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
|
|
if (GCD == Expr)
|
|
return One;
|
|
|
|
assert(Expr->isAffine() && "Expr should be affine");
|
|
|
|
const SCEV *Start = divide(SE, Expr->getStart(), GCD);
|
|
const SCEV *Step = divide(SE, Expr->getStepRecurrence(SE), GCD);
|
|
|
|
return SE.getAddRecExpr(Start, Step, Expr->getLoop(),
|
|
Expr->getNoWrapFlags());
|
|
}
|
|
|
|
const SCEV *visitSMaxExpr(const SCEVSMaxExpr *Expr) {
|
|
if (GCD == Expr)
|
|
return One;
|
|
return Expr;
|
|
}
|
|
|
|
const SCEV *visitUMaxExpr(const SCEVUMaxExpr *Expr) {
|
|
if (GCD == Expr)
|
|
return One;
|
|
return Expr;
|
|
}
|
|
|
|
const SCEV *visitUnknown(const SCEVUnknown *Expr) {
|
|
if (GCD == Expr)
|
|
return One;
|
|
return Expr;
|
|
}
|
|
|
|
const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
|
|
return Expr;
|
|
}
|
|
|
|
private:
|
|
ScalarEvolution &SE;
|
|
const SCEV *GCD, *Zero, *One;
|
|
};
|
|
}
|
|
|
|
/// Splits the SCEV into two vectors of SCEVs representing the subscripts and
|
|
/// sizes of an array access. Returns the remainder of the delinearization that
|
|
/// is the offset start of the array. The SCEV->delinearize algorithm computes
|
|
/// the multiples of SCEV coefficients: that is a pattern matching of sub
|
|
/// expressions in the stride and base of a SCEV corresponding to the
|
|
/// computation of a GCD (greatest common divisor) of base and stride. When
|
|
/// SCEV->delinearize fails, it returns the SCEV unchanged.
|
|
///
|
|
/// For example: when analyzing the memory access A[i][j][k] in this loop nest
|
|
///
|
|
/// void foo(long n, long m, long o, double A[n][m][o]) {
|
|
///
|
|
/// for (long i = 0; i < n; i++)
|
|
/// for (long j = 0; j < m; j++)
|
|
/// for (long k = 0; k < o; k++)
|
|
/// A[i][j][k] = 1.0;
|
|
/// }
|
|
///
|
|
/// the delinearization input is the following AddRec SCEV:
|
|
///
|
|
/// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
|
|
///
|
|
/// From this SCEV, we are able to say that the base offset of the access is %A
|
|
/// because it appears as an offset that does not divide any of the strides in
|
|
/// the loops:
|
|
///
|
|
/// CHECK: Base offset: %A
|
|
///
|
|
/// and then SCEV->delinearize determines the size of some of the dimensions of
|
|
/// the array as these are the multiples by which the strides are happening:
|
|
///
|
|
/// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
|
|
///
|
|
/// Note that the outermost dimension remains of UnknownSize because there are
|
|
/// no strides that would help identifying the size of the last dimension: when
|
|
/// the array has been statically allocated, one could compute the size of that
|
|
/// dimension by dividing the overall size of the array by the size of the known
|
|
/// dimensions: %m * %o * 8.
|
|
///
|
|
/// Finally delinearize provides the access functions for the array reference
|
|
/// that does correspond to A[i][j][k] of the above C testcase:
|
|
///
|
|
/// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
|
|
///
|
|
/// The testcases are checking the output of a function pass:
|
|
/// DelinearizationPass that walks through all loads and stores of a function
|
|
/// asking for the SCEV of the memory access with respect to all enclosing
|
|
/// loops, calling SCEV->delinearize on that and printing the results.
|
|
|
|
const SCEV *
|
|
SCEVAddRecExpr::delinearize(ScalarEvolution &SE,
|
|
SmallVectorImpl<const SCEV *> &Subscripts,
|
|
SmallVectorImpl<const SCEV *> &Sizes) const {
|
|
// Early exit in case this SCEV is not an affine multivariate function.
|
|
if (!this->isAffine())
|
|
return this;
|
|
|
|
const SCEV *Start = this->getStart();
|
|
const SCEV *Step = this->getStepRecurrence(SE);
|
|
|
|
// Build the SCEV representation of the cannonical induction variable in the
|
|
// loop of this SCEV.
|
|
const SCEV *Zero = SE.getConstant(this->getType(), 0);
|
|
const SCEV *One = SE.getConstant(this->getType(), 1);
|
|
const SCEV *IV =
|
|
SE.getAddRecExpr(Zero, One, this->getLoop(), this->getNoWrapFlags());
|
|
|
|
DEBUG(dbgs() << "(delinearize: " << *this << "\n");
|
|
|
|
// Currently we fail to delinearize when the stride of this SCEV is 1. We
|
|
// could decide to not fail in this case: we could just return 1 for the size
|
|
// of the subscript, and this same SCEV for the access function.
|
|
if (Step == One) {
|
|
DEBUG(dbgs() << "failed to delinearize " << *this << "\n)\n");
|
|
return this;
|
|
}
|
|
|
|
// Find the GCD and Remainder of the Start and Step coefficients of this SCEV.
|
|
const SCEV *Remainder = NULL;
|
|
const SCEV *GCD = SCEVGCD::findGCD(SE, Start, Step, &Remainder);
|
|
|
|
DEBUG(dbgs() << "GCD: " << *GCD << "\n");
|
|
DEBUG(dbgs() << "Remainder: " << *Remainder << "\n");
|
|
|
|
// Same remark as above: we currently fail the delinearization, although we
|
|
// can very well handle this special case.
|
|
if (GCD == One) {
|
|
DEBUG(dbgs() << "failed to delinearize " << *this << "\n)\n");
|
|
return this;
|
|
}
|
|
|
|
// As findGCD computed Remainder, GCD divides "Start - Remainder." The
|
|
// Quotient is then this SCEV without Remainder, scaled down by the GCD. The
|
|
// Quotient is what will be used in the next subscript delinearization.
|
|
const SCEV *Quotient =
|
|
SCEVDivision::divide(SE, SE.getMinusSCEV(Start, Remainder), GCD);
|
|
DEBUG(dbgs() << "Quotient: " << *Quotient << "\n");
|
|
|
|
const SCEV *Rem;
|
|
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Quotient))
|
|
// Recursively call delinearize on the Quotient until there are no more
|
|
// multiples that can be recognized.
|
|
Rem = AR->delinearize(SE, Subscripts, Sizes);
|
|
else
|
|
Rem = Quotient;
|
|
|
|
// Scale up the cannonical induction variable IV by whatever remains from the
|
|
// Step after division by the GCD: the GCD is the size of all the sub-array.
|
|
if (Step != GCD) {
|
|
Step = SCEVDivision::divide(SE, Step, GCD);
|
|
IV = SE.getMulExpr(IV, Step);
|
|
}
|
|
// The access function in the current subscript is computed as the cannonical
|
|
// induction variable IV (potentially scaled up by the step) and offset by
|
|
// Rem, the offset of delinearization in the sub-array.
|
|
const SCEV *Index = SE.getAddExpr(IV, Rem);
|
|
|
|
// Record the access function and the size of the current subscript.
|
|
Subscripts.push_back(Index);
|
|
Sizes.push_back(GCD);
|
|
|
|
#ifndef NDEBUG
|
|
int Size = Sizes.size();
|
|
DEBUG(dbgs() << "succeeded to delinearize " << *this << "\n");
|
|
DEBUG(dbgs() << "ArrayDecl[UnknownSize]");
|
|
for (int i = 0; i < Size - 1; i++)
|
|
DEBUG(dbgs() << "[" << *Sizes[i] << "]");
|
|
DEBUG(dbgs() << " with elements of " << *Sizes[Size - 1] << " bytes.\n");
|
|
|
|
DEBUG(dbgs() << "ArrayRef");
|
|
for (int i = 0; i < Size; i++)
|
|
DEBUG(dbgs() << "[" << *Subscripts[i] << "]");
|
|
DEBUG(dbgs() << "\n)\n");
|
|
#endif
|
|
|
|
return Remainder;
|
|
}
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// SCEVCallbackVH Class Implementation
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
void ScalarEvolution::SCEVCallbackVH::deleted() {
|
|
assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
|
|
if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
|
|
SE->ConstantEvolutionLoopExitValue.erase(PN);
|
|
SE->ValueExprMap.erase(getValPtr());
|
|
// this now dangles!
|
|
}
|
|
|
|
void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
|
|
assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
|
|
|
|
// Forget all the expressions associated with users of the old value,
|
|
// so that future queries will recompute the expressions using the new
|
|
// value.
|
|
Value *Old = getValPtr();
|
|
SmallVector<User *, 16> Worklist;
|
|
SmallPtrSet<User *, 8> Visited;
|
|
for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
|
|
UI != UE; ++UI)
|
|
Worklist.push_back(*UI);
|
|
while (!Worklist.empty()) {
|
|
User *U = Worklist.pop_back_val();
|
|
// Deleting the Old value will cause this to dangle. Postpone
|
|
// that until everything else is done.
|
|
if (U == Old)
|
|
continue;
|
|
if (!Visited.insert(U))
|
|
continue;
|
|
if (PHINode *PN = dyn_cast<PHINode>(U))
|
|
SE->ConstantEvolutionLoopExitValue.erase(PN);
|
|
SE->ValueExprMap.erase(U);
|
|
for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
|
|
UI != UE; ++UI)
|
|
Worklist.push_back(*UI);
|
|
}
|
|
// Delete the Old value.
|
|
if (PHINode *PN = dyn_cast<PHINode>(Old))
|
|
SE->ConstantEvolutionLoopExitValue.erase(PN);
|
|
SE->ValueExprMap.erase(Old);
|
|
// this now dangles!
|
|
}
|
|
|
|
ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
|
|
: CallbackVH(V), SE(se) {}
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// ScalarEvolution Class Implementation
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
ScalarEvolution::ScalarEvolution()
|
|
: FunctionPass(ID), ValuesAtScopes(64), LoopDispositions(64), BlockDispositions(64), FirstUnknown(0) {
|
|
initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
|
|
}
|
|
|
|
bool ScalarEvolution::runOnFunction(Function &F) {
|
|
this->F = &F;
|
|
LI = &getAnalysis<LoopInfo>();
|
|
TD = getAnalysisIfAvailable<DataLayout>();
|
|
TLI = &getAnalysis<TargetLibraryInfo>();
|
|
DT = &getAnalysis<DominatorTree>();
|
|
return false;
|
|
}
|
|
|
|
void ScalarEvolution::releaseMemory() {
|
|
// Iterate through all the SCEVUnknown instances and call their
|
|
// destructors, so that they release their references to their values.
|
|
for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
|
|
U->~SCEVUnknown();
|
|
FirstUnknown = 0;
|
|
|
|
ValueExprMap.clear();
|
|
|
|
// Free any extra memory created for ExitNotTakenInfo in the unlikely event
|
|
// that a loop had multiple computable exits.
|
|
for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
|
|
BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
|
|
I != E; ++I) {
|
|
I->second.clear();
|
|
}
|
|
|
|
assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
|
|
|
|
BackedgeTakenCounts.clear();
|
|
ConstantEvolutionLoopExitValue.clear();
|
|
ValuesAtScopes.clear();
|
|
LoopDispositions.clear();
|
|
BlockDispositions.clear();
|
|
UnsignedRanges.clear();
|
|
SignedRanges.clear();
|
|
UniqueSCEVs.clear();
|
|
SCEVAllocator.Reset();
|
|
}
|
|
|
|
void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
|
|
AU.setPreservesAll();
|
|
AU.addRequiredTransitive<LoopInfo>();
|
|
AU.addRequiredTransitive<DominatorTree>();
|
|
AU.addRequired<TargetLibraryInfo>();
|
|
}
|
|
|
|
bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
|
|
return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
|
|
}
|
|
|
|
static void PrintLoopInfo(raw_ostream &OS, 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 ";
|
|
WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
|
|
OS << ": ";
|
|
|
|
SmallVector<BasicBlock *, 8> ExitBlocks;
|
|
L->getExitBlocks(ExitBlocks);
|
|
if (ExitBlocks.size() != 1)
|
|
OS << "<multiple exits> ";
|
|
|
|
if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
|
|
OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
|
|
} else {
|
|
OS << "Unpredictable backedge-taken count. ";
|
|
}
|
|
|
|
OS << "\n"
|
|
"Loop ";
|
|
WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
|
|
OS << ": ";
|
|
|
|
if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
|
|
OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
|
|
} else {
|
|
OS << "Unpredictable max backedge-taken count. ";
|
|
}
|
|
|
|
OS << "\n";
|
|
}
|
|
|
|
void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
|
|
// ScalarEvolution's implementation of the print method is to print
|
|
// out SCEV values of all instructions that are interesting. Doing
|
|
// this potentially causes it to create new SCEV objects though,
|
|
// which technically conflicts with the const qualifier. This isn't
|
|
// observable from outside the class though, so casting away the
|
|
// const isn't dangerous.
|
|
ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
|
|
|
|
OS << "Classifying expressions for: ";
|
|
WriteAsOperand(OS, F, /*PrintType=*/false);
|
|
OS << "\n";
|
|
for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
|
|
if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
|
|
OS << *I << '\n';
|
|
OS << " --> ";
|
|
const SCEV *SV = SE.getSCEV(&*I);
|
|
SV->print(OS);
|
|
|
|
const Loop *L = LI->getLoopFor((*I).getParent());
|
|
|
|
const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
|
|
if (AtUse != SV) {
|
|
OS << " --> ";
|
|
AtUse->print(OS);
|
|
}
|
|
|
|
if (L) {
|
|
OS << "\t\t" "Exits: ";
|
|
const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
|
|
if (!SE.isLoopInvariant(ExitValue, L)) {
|
|
OS << "<<Unknown>>";
|
|
} else {
|
|
OS << *ExitValue;
|
|
}
|
|
}
|
|
|
|
OS << "\n";
|
|
}
|
|
|
|
OS << "Determining loop execution counts for: ";
|
|
WriteAsOperand(OS, F, /*PrintType=*/false);
|
|
OS << "\n";
|
|
for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
|
|
PrintLoopInfo(OS, &SE, *I);
|
|
}
|
|
|
|
ScalarEvolution::LoopDisposition
|
|
ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
|
|
SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values = LoopDispositions[S];
|
|
for (unsigned u = 0; u < Values.size(); u++) {
|
|
if (Values[u].first == L)
|
|
return Values[u].second;
|
|
}
|
|
Values.push_back(std::make_pair(L, LoopVariant));
|
|
LoopDisposition D = computeLoopDisposition(S, L);
|
|
SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values2 = LoopDispositions[S];
|
|
for (unsigned u = Values2.size(); u > 0; u--) {
|
|
if (Values2[u - 1].first == L) {
|
|
Values2[u - 1].second = D;
|
|
break;
|
|
}
|
|
}
|
|
return D;
|
|
}
|
|
|
|
ScalarEvolution::LoopDisposition
|
|
ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
|
|
switch (S->getSCEVType()) {
|
|
case scConstant:
|
|
return LoopInvariant;
|
|
case scTruncate:
|
|
case scZeroExtend:
|
|
case scSignExtend:
|
|
return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
|
|
case scAddRecExpr: {
|
|
const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
|
|
|
|
// If L is the addrec's loop, it's computable.
|
|
if (AR->getLoop() == L)
|
|
return LoopComputable;
|
|
|
|
// Add recurrences are never invariant in the function-body (null loop).
|
|
if (!L)
|
|
return LoopVariant;
|
|
|
|
// This recurrence is variant w.r.t. L if L contains AR's loop.
|
|
if (L->contains(AR->getLoop()))
|
|
return LoopVariant;
|
|
|
|
// This recurrence is invariant w.r.t. L if AR's loop contains L.
|
|
if (AR->getLoop()->contains(L))
|
|
return LoopInvariant;
|
|
|
|
// This recurrence is variant w.r.t. L if any of its operands
|
|
// are variant.
|
|
for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
|
|
I != E; ++I)
|
|
if (!isLoopInvariant(*I, L))
|
|
return LoopVariant;
|
|
|
|
// Otherwise it's loop-invariant.
|
|
return LoopInvariant;
|
|
}
|
|
case scAddExpr:
|
|
case scMulExpr:
|
|
case scUMaxExpr:
|
|
case scSMaxExpr: {
|
|
const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
|
|
bool HasVarying = false;
|
|
for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
|
|
I != E; ++I) {
|
|
LoopDisposition D = getLoopDisposition(*I, L);
|
|
if (D == LoopVariant)
|
|
return LoopVariant;
|
|
if (D == LoopComputable)
|
|
HasVarying = true;
|
|
}
|
|
return HasVarying ? LoopComputable : LoopInvariant;
|
|
}
|
|
case scUDivExpr: {
|
|
const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
|
|
LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
|
|
if (LD == LoopVariant)
|
|
return LoopVariant;
|
|
LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
|
|
if (RD == LoopVariant)
|
|
return LoopVariant;
|
|
return (LD == LoopInvariant && RD == LoopInvariant) ?
|
|
LoopInvariant : LoopComputable;
|
|
}
|
|
case scUnknown:
|
|
// All non-instruction values are loop invariant. All instructions are loop
|
|
// invariant if they are not contained in the specified loop.
|
|
// Instructions are never considered invariant in the function body
|
|
// (null loop) because they are defined within the "loop".
|
|
if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
|
|
return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
|
|
return LoopInvariant;
|
|
case scCouldNotCompute:
|
|
llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
|
|
default: llvm_unreachable("Unknown SCEV kind!");
|
|
}
|
|
}
|
|
|
|
bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
|
|
return getLoopDisposition(S, L) == LoopInvariant;
|
|
}
|
|
|
|
bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
|
|
return getLoopDisposition(S, L) == LoopComputable;
|
|
}
|
|
|
|
ScalarEvolution::BlockDisposition
|
|
ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
|
|
SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values = BlockDispositions[S];
|
|
for (unsigned u = 0; u < Values.size(); u++) {
|
|
if (Values[u].first == BB)
|
|
return Values[u].second;
|
|
}
|
|
Values.push_back(std::make_pair(BB, DoesNotDominateBlock));
|
|
BlockDisposition D = computeBlockDisposition(S, BB);
|
|
SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values2 = BlockDispositions[S];
|
|
for (unsigned u = Values2.size(); u > 0; u--) {
|
|
if (Values2[u - 1].first == BB) {
|
|
Values2[u - 1].second = D;
|
|
break;
|
|
}
|
|
}
|
|
return D;
|
|
}
|
|
|
|
ScalarEvolution::BlockDisposition
|
|
ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
|
|
switch (S->getSCEVType()) {
|
|
case scConstant:
|
|
return ProperlyDominatesBlock;
|
|
case scTruncate:
|
|
case scZeroExtend:
|
|
case scSignExtend:
|
|
return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
|
|
case scAddRecExpr: {
|
|
// This uses a "dominates" query instead of "properly dominates" query
|
|
// to test for proper dominance too, because the instruction which
|
|
// produces the addrec's value is a PHI, and a PHI effectively properly
|
|
// dominates its entire containing block.
|
|
const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
|
|
if (!DT->dominates(AR->getLoop()->getHeader(), BB))
|
|
return DoesNotDominateBlock;
|
|
}
|
|
// FALL THROUGH into SCEVNAryExpr handling.
|
|
case scAddExpr:
|
|
case scMulExpr:
|
|
case scUMaxExpr:
|
|
case scSMaxExpr: {
|
|
const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
|
|
bool Proper = true;
|
|
for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
|
|
I != E; ++I) {
|
|
BlockDisposition D = getBlockDisposition(*I, BB);
|
|
if (D == DoesNotDominateBlock)
|
|
return DoesNotDominateBlock;
|
|
if (D == DominatesBlock)
|
|
Proper = false;
|
|
}
|
|
return Proper ? ProperlyDominatesBlock : DominatesBlock;
|
|
}
|
|
case scUDivExpr: {
|
|
const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
|
|
const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
|
|
BlockDisposition LD = getBlockDisposition(LHS, BB);
|
|
if (LD == DoesNotDominateBlock)
|
|
return DoesNotDominateBlock;
|
|
BlockDisposition RD = getBlockDisposition(RHS, BB);
|
|
if (RD == DoesNotDominateBlock)
|
|
return DoesNotDominateBlock;
|
|
return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
|
|
ProperlyDominatesBlock : DominatesBlock;
|
|
}
|
|
case scUnknown:
|
|
if (Instruction *I =
|
|
dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
|
|
if (I->getParent() == BB)
|
|
return DominatesBlock;
|
|
if (DT->properlyDominates(I->getParent(), BB))
|
|
return ProperlyDominatesBlock;
|
|
return DoesNotDominateBlock;
|
|
}
|
|
return ProperlyDominatesBlock;
|
|
case scCouldNotCompute:
|
|
llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
|
|
default:
|
|
llvm_unreachable("Unknown SCEV kind!");
|
|
}
|
|
}
|
|
|
|
bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
|
|
return getBlockDisposition(S, BB) >= DominatesBlock;
|
|
}
|
|
|
|
bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
|
|
return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
|
|
}
|
|
|
|
namespace {
|
|
// Search for a SCEV expression node within an expression tree.
|
|
// Implements SCEVTraversal::Visitor.
|
|
struct SCEVSearch {
|
|
const SCEV *Node;
|
|
bool IsFound;
|
|
|
|
SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
|
|
|
|
bool follow(const SCEV *S) {
|
|
IsFound |= (S == Node);
|
|
return !IsFound;
|
|
}
|
|
bool isDone() const { return IsFound; }
|
|
};
|
|
}
|
|
|
|
bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
|
|
SCEVSearch Search(Op);
|
|
visitAll(S, Search);
|
|
return Search.IsFound;
|
|
}
|
|
|
|
void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
|
|
ValuesAtScopes.erase(S);
|
|
LoopDispositions.erase(S);
|
|
BlockDispositions.erase(S);
|
|
UnsignedRanges.erase(S);
|
|
SignedRanges.erase(S);
|
|
|
|
for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
|
|
BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
|
|
BackedgeTakenInfo &BEInfo = I->second;
|
|
if (BEInfo.hasOperand(S, this)) {
|
|
BEInfo.clear();
|
|
BackedgeTakenCounts.erase(I++);
|
|
}
|
|
else
|
|
++I;
|
|
}
|
|
}
|
|
|
|
typedef DenseMap<const Loop *, std::string> VerifyMap;
|
|
|
|
/// replaceSubString - Replaces all occurences of From in Str with To.
|
|
static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
|
|
size_t Pos = 0;
|
|
while ((Pos = Str.find(From, Pos)) != std::string::npos) {
|
|
Str.replace(Pos, From.size(), To.data(), To.size());
|
|
Pos += To.size();
|
|
}
|
|
}
|
|
|
|
/// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
|
|
static void
|
|
getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
|
|
for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
|
|
getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
|
|
|
|
std::string &S = Map[L];
|
|
if (S.empty()) {
|
|
raw_string_ostream OS(S);
|
|
SE.getBackedgeTakenCount(L)->print(OS);
|
|
|
|
// false and 0 are semantically equivalent. This can happen in dead loops.
|
|
replaceSubString(OS.str(), "false", "0");
|
|
// Remove wrap flags, their use in SCEV is highly fragile.
|
|
// FIXME: Remove this when SCEV gets smarter about them.
|
|
replaceSubString(OS.str(), "<nw>", "");
|
|
replaceSubString(OS.str(), "<nsw>", "");
|
|
replaceSubString(OS.str(), "<nuw>", "");
|
|
}
|
|
}
|
|
}
|
|
|
|
void ScalarEvolution::verifyAnalysis() const {
|
|
if (!VerifySCEV)
|
|
return;
|
|
|
|
ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
|
|
|
|
// Gather stringified backedge taken counts for all loops using SCEV's caches.
|
|
// FIXME: It would be much better to store actual values instead of strings,
|
|
// but SCEV pointers will change if we drop the caches.
|
|
VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
|
|
for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
|
|
getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
|
|
|
|
// Gather stringified backedge taken counts for all loops without using
|
|
// SCEV's caches.
|
|
SE.releaseMemory();
|
|
for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
|
|
getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
|
|
|
|
// Now compare whether they're the same with and without caches. This allows
|
|
// verifying that no pass changed the cache.
|
|
assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
|
|
"New loops suddenly appeared!");
|
|
|
|
for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
|
|
OldE = BackedgeDumpsOld.end(),
|
|
NewI = BackedgeDumpsNew.begin();
|
|
OldI != OldE; ++OldI, ++NewI) {
|
|
assert(OldI->first == NewI->first && "Loop order changed!");
|
|
|
|
// Compare the stringified SCEVs. We don't care if undef backedgetaken count
|
|
// changes.
|
|
// FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
|
|
// means that a pass is buggy or SCEV has to learn a new pattern but is
|
|
// usually not harmful.
|
|
if (OldI->second != NewI->second &&
|
|
OldI->second.find("undef") == std::string::npos &&
|
|
NewI->second.find("undef") == std::string::npos &&
|
|
OldI->second != "***COULDNOTCOMPUTE***" &&
|
|
NewI->second != "***COULDNOTCOMPUTE***") {
|
|
dbgs() << "SCEVValidator: SCEV for loop '"
|
|
<< OldI->first->getHeader()->getName()
|
|
<< "' changed from '" << OldI->second
|
|
<< "' to '" << NewI->second << "'!\n";
|
|
std::abort();
|
|
}
|
|
}
|
|
|
|
// TODO: Verify more things.
|
|
}
|