1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression. These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
38 //===----------------------------------------------------------------------===//
40 // There are several good references for the techniques used in this analysis.
42 // Chains of recurrences -- a method to expedite the evaluation
43 // of closed-form functions
44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46 // On computational properties of chains of recurrences
49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 // Robert A. van Engelen
52 // Efficient Symbolic Analysis for Optimizing Compilers
53 // Robert A. van Engelen
55 // Using the chains of recurrences algebra for data dependence testing and
56 // induction variable substitution
57 // MS Thesis, Johnie Birch
59 //===----------------------------------------------------------------------===//
61 #define DEBUG_TYPE "scalar-evolution"
62 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
63 #include "llvm/Constants.h"
64 #include "llvm/DerivedTypes.h"
65 #include "llvm/GlobalVariable.h"
66 #include "llvm/GlobalAlias.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/LLVMContext.h"
69 #include "llvm/Operator.h"
70 #include "llvm/Analysis/ConstantFolding.h"
71 #include "llvm/Analysis/Dominators.h"
72 #include "llvm/Analysis/InstructionSimplify.h"
73 #include "llvm/Analysis/LoopInfo.h"
74 #include "llvm/Analysis/ValueTracking.h"
75 #include "llvm/Assembly/Writer.h"
76 #include "llvm/Target/TargetData.h"
77 #include "llvm/Target/TargetLibraryInfo.h"
78 #include "llvm/Support/CommandLine.h"
79 #include "llvm/Support/ConstantRange.h"
80 #include "llvm/Support/Debug.h"
81 #include "llvm/Support/ErrorHandling.h"
82 #include "llvm/Support/GetElementPtrTypeIterator.h"
83 #include "llvm/Support/InstIterator.h"
84 #include "llvm/Support/MathExtras.h"
85 #include "llvm/Support/raw_ostream.h"
86 #include "llvm/ADT/Statistic.h"
87 #include "llvm/ADT/STLExtras.h"
88 #include "llvm/ADT/SmallPtrSet.h"
92 STATISTIC(NumArrayLenItCounts,
93 "Number of trip counts computed with array length");
94 STATISTIC(NumTripCountsComputed,
95 "Number of loops with predictable loop counts");
96 STATISTIC(NumTripCountsNotComputed,
97 "Number of loops without predictable loop counts");
98 STATISTIC(NumBruteForceTripCountsComputed,
99 "Number of loops with trip counts computed by force");
101 static cl::opt<unsigned>
102 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
103 cl::desc("Maximum number of iterations SCEV will "
104 "symbolically execute a constant "
108 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution",
109 "Scalar Evolution Analysis", false, true)
110 INITIALIZE_PASS_DEPENDENCY(LoopInfo)
111 INITIALIZE_PASS_DEPENDENCY(DominatorTree)
112 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfo)
113 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution",
114 "Scalar Evolution Analysis", false, true)
115 char ScalarEvolution::ID = 0;
117 //===----------------------------------------------------------------------===//
118 // SCEV class definitions
119 //===----------------------------------------------------------------------===//
121 //===----------------------------------------------------------------------===//
122 // Implementation of the SCEV class.
125 void SCEV::dump() const {
130 void SCEV::print(raw_ostream &OS) const {
131 switch (getSCEVType()) {
133 WriteAsOperand(OS, cast<SCEVConstant>(this)->getValue(), false);
136 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
137 const SCEV *Op = Trunc->getOperand();
138 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
139 << *Trunc->getType() << ")";
143 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
144 const SCEV *Op = ZExt->getOperand();
145 OS << "(zext " << *Op->getType() << " " << *Op << " to "
146 << *ZExt->getType() << ")";
150 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
151 const SCEV *Op = SExt->getOperand();
152 OS << "(sext " << *Op->getType() << " " << *Op << " to "
153 << *SExt->getType() << ")";
157 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
158 OS << "{" << *AR->getOperand(0);
159 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
160 OS << ",+," << *AR->getOperand(i);
162 if (AR->getNoWrapFlags(FlagNUW))
164 if (AR->getNoWrapFlags(FlagNSW))
166 if (AR->getNoWrapFlags(FlagNW) &&
167 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
169 WriteAsOperand(OS, AR->getLoop()->getHeader(), /*PrintType=*/false);
177 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
178 const char *OpStr = 0;
179 switch (NAry->getSCEVType()) {
180 case scAddExpr: OpStr = " + "; break;
181 case scMulExpr: OpStr = " * "; break;
182 case scUMaxExpr: OpStr = " umax "; break;
183 case scSMaxExpr: OpStr = " smax "; break;
186 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
189 if (llvm::next(I) != E)
193 switch (NAry->getSCEVType()) {
196 if (NAry->getNoWrapFlags(FlagNUW))
198 if (NAry->getNoWrapFlags(FlagNSW))
204 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
205 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
209 const SCEVUnknown *U = cast<SCEVUnknown>(this);
211 if (U->isSizeOf(AllocTy)) {
212 OS << "sizeof(" << *AllocTy << ")";
215 if (U->isAlignOf(AllocTy)) {
216 OS << "alignof(" << *AllocTy << ")";
222 if (U->isOffsetOf(CTy, FieldNo)) {
223 OS << "offsetof(" << *CTy << ", ";
224 WriteAsOperand(OS, FieldNo, false);
229 // Otherwise just print it normally.
230 WriteAsOperand(OS, U->getValue(), false);
233 case scCouldNotCompute:
234 OS << "***COULDNOTCOMPUTE***";
238 llvm_unreachable("Unknown SCEV kind!");
241 Type *SCEV::getType() const {
242 switch (getSCEVType()) {
244 return cast<SCEVConstant>(this)->getType();
248 return cast<SCEVCastExpr>(this)->getType();
253 return cast<SCEVNAryExpr>(this)->getType();
255 return cast<SCEVAddExpr>(this)->getType();
257 return cast<SCEVUDivExpr>(this)->getType();
259 return cast<SCEVUnknown>(this)->getType();
260 case scCouldNotCompute:
261 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
265 llvm_unreachable("Unknown SCEV kind!");
269 bool SCEV::isZero() const {
270 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
271 return SC->getValue()->isZero();
275 bool SCEV::isOne() const {
276 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
277 return SC->getValue()->isOne();
281 bool SCEV::isAllOnesValue() const {
282 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
283 return SC->getValue()->isAllOnesValue();
287 /// isNonConstantNegative - Return true if the specified scev is negated, but
289 bool SCEV::isNonConstantNegative() const {
290 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
291 if (!Mul) return false;
293 // If there is a constant factor, it will be first.
294 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
295 if (!SC) return false;
297 // Return true if the value is negative, this matches things like (-42 * V).
298 return SC->getValue()->getValue().isNegative();
301 SCEVCouldNotCompute::SCEVCouldNotCompute() :
302 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
304 bool SCEVCouldNotCompute::classof(const SCEV *S) {
305 return S->getSCEVType() == scCouldNotCompute;
308 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
310 ID.AddInteger(scConstant);
313 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
314 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
315 UniqueSCEVs.InsertNode(S, IP);
319 const SCEV *ScalarEvolution::getConstant(const APInt& Val) {
320 return getConstant(ConstantInt::get(getContext(), Val));
324 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
325 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
326 return getConstant(ConstantInt::get(ITy, V, isSigned));
329 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
330 unsigned SCEVTy, const SCEV *op, Type *ty)
331 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
333 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
334 const SCEV *op, Type *ty)
335 : SCEVCastExpr(ID, scTruncate, op, ty) {
336 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
337 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
338 "Cannot truncate non-integer value!");
341 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
342 const SCEV *op, Type *ty)
343 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
344 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
345 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
346 "Cannot zero extend non-integer value!");
349 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
350 const SCEV *op, Type *ty)
351 : SCEVCastExpr(ID, scSignExtend, op, ty) {
352 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
353 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
354 "Cannot sign extend non-integer value!");
357 void SCEVUnknown::deleted() {
358 // Clear this SCEVUnknown from various maps.
359 SE->forgetMemoizedResults(this);
361 // Remove this SCEVUnknown from the uniquing map.
362 SE->UniqueSCEVs.RemoveNode(this);
364 // Release the value.
368 void SCEVUnknown::allUsesReplacedWith(Value *New) {
369 // Clear this SCEVUnknown from various maps.
370 SE->forgetMemoizedResults(this);
372 // Remove this SCEVUnknown from the uniquing map.
373 SE->UniqueSCEVs.RemoveNode(this);
375 // Update this SCEVUnknown to point to the new value. This is needed
376 // because there may still be outstanding SCEVs which still point to
381 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
382 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
383 if (VCE->getOpcode() == Instruction::PtrToInt)
384 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
385 if (CE->getOpcode() == Instruction::GetElementPtr &&
386 CE->getOperand(0)->isNullValue() &&
387 CE->getNumOperands() == 2)
388 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
390 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
398 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
399 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
400 if (VCE->getOpcode() == Instruction::PtrToInt)
401 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
402 if (CE->getOpcode() == Instruction::GetElementPtr &&
403 CE->getOperand(0)->isNullValue()) {
405 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
406 if (StructType *STy = dyn_cast<StructType>(Ty))
407 if (!STy->isPacked() &&
408 CE->getNumOperands() == 3 &&
409 CE->getOperand(1)->isNullValue()) {
410 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
412 STy->getNumElements() == 2 &&
413 STy->getElementType(0)->isIntegerTy(1)) {
414 AllocTy = STy->getElementType(1);
423 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
424 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
425 if (VCE->getOpcode() == Instruction::PtrToInt)
426 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
427 if (CE->getOpcode() == Instruction::GetElementPtr &&
428 CE->getNumOperands() == 3 &&
429 CE->getOperand(0)->isNullValue() &&
430 CE->getOperand(1)->isNullValue()) {
432 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
433 // Ignore vector types here so that ScalarEvolutionExpander doesn't
434 // emit getelementptrs that index into vectors.
435 if (Ty->isStructTy() || Ty->isArrayTy()) {
437 FieldNo = CE->getOperand(2);
445 //===----------------------------------------------------------------------===//
447 //===----------------------------------------------------------------------===//
450 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
451 /// than the complexity of the RHS. This comparator is used to canonicalize
453 class SCEVComplexityCompare {
454 const LoopInfo *const LI;
456 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
458 // Return true or false if LHS is less than, or at least RHS, respectively.
459 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
460 return compare(LHS, RHS) < 0;
463 // Return negative, zero, or positive, if LHS is less than, equal to, or
464 // greater than RHS, respectively. A three-way result allows recursive
465 // comparisons to be more efficient.
466 int compare(const SCEV *LHS, const SCEV *RHS) const {
467 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
471 // Primarily, sort the SCEVs by their getSCEVType().
472 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
474 return (int)LType - (int)RType;
476 // Aside from the getSCEVType() ordering, the particular ordering
477 // isn't very important except that it's beneficial to be consistent,
478 // so that (a + b) and (b + a) don't end up as different expressions.
481 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
482 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
484 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
485 // not as complete as it could be.
486 const Value *LV = LU->getValue(), *RV = RU->getValue();
488 // Order pointer values after integer values. This helps SCEVExpander
490 bool LIsPointer = LV->getType()->isPointerTy(),
491 RIsPointer = RV->getType()->isPointerTy();
492 if (LIsPointer != RIsPointer)
493 return (int)LIsPointer - (int)RIsPointer;
495 // Compare getValueID values.
496 unsigned LID = LV->getValueID(),
497 RID = RV->getValueID();
499 return (int)LID - (int)RID;
501 // Sort arguments by their position.
502 if (const Argument *LA = dyn_cast<Argument>(LV)) {
503 const Argument *RA = cast<Argument>(RV);
504 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
505 return (int)LArgNo - (int)RArgNo;
508 // For instructions, compare their loop depth, and their operand
509 // count. This is pretty loose.
510 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
511 const Instruction *RInst = cast<Instruction>(RV);
513 // Compare loop depths.
514 const BasicBlock *LParent = LInst->getParent(),
515 *RParent = RInst->getParent();
516 if (LParent != RParent) {
517 unsigned LDepth = LI->getLoopDepth(LParent),
518 RDepth = LI->getLoopDepth(RParent);
519 if (LDepth != RDepth)
520 return (int)LDepth - (int)RDepth;
523 // Compare the number of operands.
524 unsigned LNumOps = LInst->getNumOperands(),
525 RNumOps = RInst->getNumOperands();
526 return (int)LNumOps - (int)RNumOps;
533 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
534 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
536 // Compare constant values.
537 const APInt &LA = LC->getValue()->getValue();
538 const APInt &RA = RC->getValue()->getValue();
539 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
540 if (LBitWidth != RBitWidth)
541 return (int)LBitWidth - (int)RBitWidth;
542 return LA.ult(RA) ? -1 : 1;
546 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
547 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
549 // Compare addrec loop depths.
550 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
551 if (LLoop != RLoop) {
552 unsigned LDepth = LLoop->getLoopDepth(),
553 RDepth = RLoop->getLoopDepth();
554 if (LDepth != RDepth)
555 return (int)LDepth - (int)RDepth;
558 // Addrec complexity grows with operand count.
559 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
560 if (LNumOps != RNumOps)
561 return (int)LNumOps - (int)RNumOps;
563 // Lexicographically compare.
564 for (unsigned i = 0; i != LNumOps; ++i) {
565 long X = compare(LA->getOperand(i), RA->getOperand(i));
577 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
578 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
580 // Lexicographically compare n-ary expressions.
581 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
582 for (unsigned i = 0; i != LNumOps; ++i) {
585 long X = compare(LC->getOperand(i), RC->getOperand(i));
589 return (int)LNumOps - (int)RNumOps;
593 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
594 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
596 // Lexicographically compare udiv expressions.
597 long X = compare(LC->getLHS(), RC->getLHS());
600 return compare(LC->getRHS(), RC->getRHS());
606 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
607 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
609 // Compare cast expressions by operand.
610 return compare(LC->getOperand(), RC->getOperand());
617 llvm_unreachable("Unknown SCEV kind!");
623 /// GroupByComplexity - Given a list of SCEV objects, order them by their
624 /// complexity, and group objects of the same complexity together by value.
625 /// When this routine is finished, we know that any duplicates in the vector are
626 /// consecutive and that complexity is monotonically increasing.
628 /// Note that we go take special precautions to ensure that we get deterministic
629 /// results from this routine. In other words, we don't want the results of
630 /// this to depend on where the addresses of various SCEV objects happened to
633 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
635 if (Ops.size() < 2) return; // Noop
636 if (Ops.size() == 2) {
637 // This is the common case, which also happens to be trivially simple.
639 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
640 if (SCEVComplexityCompare(LI)(RHS, LHS))
645 // Do the rough sort by complexity.
646 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
648 // Now that we are sorted by complexity, group elements of the same
649 // complexity. Note that this is, at worst, N^2, but the vector is likely to
650 // be extremely short in practice. Note that we take this approach because we
651 // do not want to depend on the addresses of the objects we are grouping.
652 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
653 const SCEV *S = Ops[i];
654 unsigned Complexity = S->getSCEVType();
656 // If there are any objects of the same complexity and same value as this
658 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
659 if (Ops[j] == S) { // Found a duplicate.
660 // Move it to immediately after i'th element.
661 std::swap(Ops[i+1], Ops[j]);
662 ++i; // no need to rescan it.
663 if (i == e-2) return; // Done!
671 //===----------------------------------------------------------------------===//
672 // Simple SCEV method implementations
673 //===----------------------------------------------------------------------===//
675 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
677 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
680 // Handle the simplest case efficiently.
682 return SE.getTruncateOrZeroExtend(It, ResultTy);
684 // We are using the following formula for BC(It, K):
686 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
688 // Suppose, W is the bitwidth of the return value. We must be prepared for
689 // overflow. Hence, we must assure that the result of our computation is
690 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
691 // safe in modular arithmetic.
693 // However, this code doesn't use exactly that formula; the formula it uses
694 // is something like the following, where T is the number of factors of 2 in
695 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
698 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
700 // This formula is trivially equivalent to the previous formula. However,
701 // this formula can be implemented much more efficiently. The trick is that
702 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
703 // arithmetic. To do exact division in modular arithmetic, all we have
704 // to do is multiply by the inverse. Therefore, this step can be done at
707 // The next issue is how to safely do the division by 2^T. The way this
708 // is done is by doing the multiplication step at a width of at least W + T
709 // bits. This way, the bottom W+T bits of the product are accurate. Then,
710 // when we perform the division by 2^T (which is equivalent to a right shift
711 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
712 // truncated out after the division by 2^T.
714 // In comparison to just directly using the first formula, this technique
715 // is much more efficient; using the first formula requires W * K bits,
716 // but this formula less than W + K bits. Also, the first formula requires
717 // a division step, whereas this formula only requires multiplies and shifts.
719 // It doesn't matter whether the subtraction step is done in the calculation
720 // width or the input iteration count's width; if the subtraction overflows,
721 // the result must be zero anyway. We prefer here to do it in the width of
722 // the induction variable because it helps a lot for certain cases; CodeGen
723 // isn't smart enough to ignore the overflow, which leads to much less
724 // efficient code if the width of the subtraction is wider than the native
727 // (It's possible to not widen at all by pulling out factors of 2 before
728 // the multiplication; for example, K=2 can be calculated as
729 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
730 // extra arithmetic, so it's not an obvious win, and it gets
731 // much more complicated for K > 3.)
733 // Protection from insane SCEVs; this bound is conservative,
734 // but it probably doesn't matter.
736 return SE.getCouldNotCompute();
738 unsigned W = SE.getTypeSizeInBits(ResultTy);
740 // Calculate K! / 2^T and T; we divide out the factors of two before
741 // multiplying for calculating K! / 2^T to avoid overflow.
742 // Other overflow doesn't matter because we only care about the bottom
743 // W bits of the result.
744 APInt OddFactorial(W, 1);
746 for (unsigned i = 3; i <= K; ++i) {
748 unsigned TwoFactors = Mult.countTrailingZeros();
750 Mult = Mult.lshr(TwoFactors);
751 OddFactorial *= Mult;
754 // We need at least W + T bits for the multiplication step
755 unsigned CalculationBits = W + T;
757 // Calculate 2^T, at width T+W.
758 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
760 // Calculate the multiplicative inverse of K! / 2^T;
761 // this multiplication factor will perform the exact division by
763 APInt Mod = APInt::getSignedMinValue(W+1);
764 APInt MultiplyFactor = OddFactorial.zext(W+1);
765 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
766 MultiplyFactor = MultiplyFactor.trunc(W);
768 // Calculate the product, at width T+W
769 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
771 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
772 for (unsigned i = 1; i != K; ++i) {
773 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
774 Dividend = SE.getMulExpr(Dividend,
775 SE.getTruncateOrZeroExtend(S, CalculationTy));
779 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
781 // Truncate the result, and divide by K! / 2^T.
783 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
784 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
787 /// evaluateAtIteration - Return the value of this chain of recurrences at
788 /// the specified iteration number. We can evaluate this recurrence by
789 /// multiplying each element in the chain by the binomial coefficient
790 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
792 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
794 /// where BC(It, k) stands for binomial coefficient.
796 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
797 ScalarEvolution &SE) const {
798 const SCEV *Result = getStart();
799 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
800 // The computation is correct in the face of overflow provided that the
801 // multiplication is performed _after_ the evaluation of the binomial
803 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
804 if (isa<SCEVCouldNotCompute>(Coeff))
807 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
812 //===----------------------------------------------------------------------===//
813 // SCEV Expression folder implementations
814 //===----------------------------------------------------------------------===//
816 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
818 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
819 "This is not a truncating conversion!");
820 assert(isSCEVable(Ty) &&
821 "This is not a conversion to a SCEVable type!");
822 Ty = getEffectiveSCEVType(Ty);
825 ID.AddInteger(scTruncate);
829 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
831 // Fold if the operand is constant.
832 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
834 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(),
835 getEffectiveSCEVType(Ty))));
837 // trunc(trunc(x)) --> trunc(x)
838 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
839 return getTruncateExpr(ST->getOperand(), Ty);
841 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
842 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
843 return getTruncateOrSignExtend(SS->getOperand(), Ty);
845 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
846 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
847 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
849 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
850 // eliminate all the truncates.
851 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
852 SmallVector<const SCEV *, 4> Operands;
853 bool hasTrunc = false;
854 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
855 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
856 hasTrunc = isa<SCEVTruncateExpr>(S);
857 Operands.push_back(S);
860 return getAddExpr(Operands);
861 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
864 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
865 // eliminate all the truncates.
866 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
867 SmallVector<const SCEV *, 4> Operands;
868 bool hasTrunc = false;
869 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
870 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
871 hasTrunc = isa<SCEVTruncateExpr>(S);
872 Operands.push_back(S);
875 return getMulExpr(Operands);
876 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
879 // If the input value is a chrec scev, truncate the chrec's operands.
880 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
881 SmallVector<const SCEV *, 4> Operands;
882 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
883 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
884 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
887 // As a special case, fold trunc(undef) to undef. We don't want to
888 // know too much about SCEVUnknowns, but this special case is handy
890 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
891 if (isa<UndefValue>(U->getValue()))
892 return getSCEV(UndefValue::get(Ty));
894 // The cast wasn't folded; create an explicit cast node. We can reuse
895 // the existing insert position since if we get here, we won't have
896 // made any changes which would invalidate it.
897 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
899 UniqueSCEVs.InsertNode(S, IP);
903 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
905 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
906 "This is not an extending conversion!");
907 assert(isSCEVable(Ty) &&
908 "This is not a conversion to a SCEVable type!");
909 Ty = getEffectiveSCEVType(Ty);
911 // Fold if the operand is constant.
912 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
914 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(),
915 getEffectiveSCEVType(Ty))));
917 // zext(zext(x)) --> zext(x)
918 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
919 return getZeroExtendExpr(SZ->getOperand(), Ty);
921 // Before doing any expensive analysis, check to see if we've already
922 // computed a SCEV for this Op and Ty.
924 ID.AddInteger(scZeroExtend);
928 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
930 // zext(trunc(x)) --> zext(x) or x or trunc(x)
931 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
932 // It's possible the bits taken off by the truncate were all zero bits. If
933 // so, we should be able to simplify this further.
934 const SCEV *X = ST->getOperand();
935 ConstantRange CR = getUnsignedRange(X);
936 unsigned TruncBits = getTypeSizeInBits(ST->getType());
937 unsigned NewBits = getTypeSizeInBits(Ty);
938 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
939 CR.zextOrTrunc(NewBits)))
940 return getTruncateOrZeroExtend(X, Ty);
943 // If the input value is a chrec scev, and we can prove that the value
944 // did not overflow the old, smaller, value, we can zero extend all of the
945 // operands (often constants). This allows analysis of something like
946 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
947 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
948 if (AR->isAffine()) {
949 const SCEV *Start = AR->getStart();
950 const SCEV *Step = AR->getStepRecurrence(*this);
951 unsigned BitWidth = getTypeSizeInBits(AR->getType());
952 const Loop *L = AR->getLoop();
954 // If we have special knowledge that this addrec won't overflow,
955 // we don't need to do any further analysis.
956 if (AR->getNoWrapFlags(SCEV::FlagNUW))
957 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
958 getZeroExtendExpr(Step, Ty),
959 L, AR->getNoWrapFlags());
961 // Check whether the backedge-taken count is SCEVCouldNotCompute.
962 // Note that this serves two purposes: It filters out loops that are
963 // simply not analyzable, and it covers the case where this code is
964 // being called from within backedge-taken count analysis, such that
965 // attempting to ask for the backedge-taken count would likely result
966 // in infinite recursion. In the later case, the analysis code will
967 // cope with a conservative value, and it will take care to purge
968 // that value once it has finished.
969 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
970 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
971 // Manually compute the final value for AR, checking for
974 // Check whether the backedge-taken count can be losslessly casted to
975 // the addrec's type. The count is always unsigned.
976 const SCEV *CastedMaxBECount =
977 getTruncateOrZeroExtend(MaxBECount, Start->getType());
978 const SCEV *RecastedMaxBECount =
979 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
980 if (MaxBECount == RecastedMaxBECount) {
981 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
982 // Check whether Start+Step*MaxBECount has no unsigned overflow.
983 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
984 const SCEV *Add = getAddExpr(Start, ZMul);
985 const SCEV *OperandExtendedAdd =
986 getAddExpr(getZeroExtendExpr(Start, WideTy),
987 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
988 getZeroExtendExpr(Step, WideTy)));
989 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) {
990 // Cache knowledge of AR NUW, which is propagated to this AddRec.
991 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
992 // Return the expression with the addrec on the outside.
993 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
994 getZeroExtendExpr(Step, Ty),
995 L, AR->getNoWrapFlags());
997 // Similar to above, only this time treat the step value as signed.
998 // This covers loops that count down.
999 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1000 Add = getAddExpr(Start, SMul);
1001 OperandExtendedAdd =
1002 getAddExpr(getZeroExtendExpr(Start, WideTy),
1003 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1004 getSignExtendExpr(Step, WideTy)));
1005 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) {
1006 // Cache knowledge of AR NW, which is propagated to this AddRec.
1007 // Negative step causes unsigned wrap, but it still can't self-wrap.
1008 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1009 // Return the expression with the addrec on the outside.
1010 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1011 getSignExtendExpr(Step, Ty),
1012 L, AR->getNoWrapFlags());
1016 // If the backedge is guarded by a comparison with the pre-inc value
1017 // the addrec is safe. Also, if the entry is guarded by a comparison
1018 // with the start value and the backedge is guarded by a comparison
1019 // with the post-inc value, the addrec is safe.
1020 if (isKnownPositive(Step)) {
1021 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1022 getUnsignedRange(Step).getUnsignedMax());
1023 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1024 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1025 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1026 AR->getPostIncExpr(*this), N))) {
1027 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1028 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1029 // Return the expression with the addrec on the outside.
1030 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1031 getZeroExtendExpr(Step, Ty),
1032 L, AR->getNoWrapFlags());
1034 } else if (isKnownNegative(Step)) {
1035 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1036 getSignedRange(Step).getSignedMin());
1037 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1038 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1039 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1040 AR->getPostIncExpr(*this), N))) {
1041 // Cache knowledge of AR NW, which is propagated to this AddRec.
1042 // Negative step causes unsigned wrap, but it still can't self-wrap.
1043 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1044 // Return the expression with the addrec on the outside.
1045 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1046 getSignExtendExpr(Step, Ty),
1047 L, AR->getNoWrapFlags());
1053 // The cast wasn't folded; create an explicit cast node.
1054 // Recompute the insert position, as it may have been invalidated.
1055 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1056 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1058 UniqueSCEVs.InsertNode(S, IP);
1062 // Get the limit of a recurrence such that incrementing by Step cannot cause
1063 // signed overflow as long as the value of the recurrence within the loop does
1064 // not exceed this limit before incrementing.
1065 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1066 ICmpInst::Predicate *Pred,
1067 ScalarEvolution *SE) {
1068 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1069 if (SE->isKnownPositive(Step)) {
1070 *Pred = ICmpInst::ICMP_SLT;
1071 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1072 SE->getSignedRange(Step).getSignedMax());
1074 if (SE->isKnownNegative(Step)) {
1075 *Pred = ICmpInst::ICMP_SGT;
1076 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1077 SE->getSignedRange(Step).getSignedMin());
1082 // The recurrence AR has been shown to have no signed wrap. Typically, if we can
1083 // prove NSW for AR, then we can just as easily prove NSW for its preincrement
1084 // or postincrement sibling. This allows normalizing a sign extended AddRec as
1085 // such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a
1086 // result, the expression "Step + sext(PreIncAR)" is congruent with
1087 // "sext(PostIncAR)"
1088 static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR,
1090 ScalarEvolution *SE) {
1091 const Loop *L = AR->getLoop();
1092 const SCEV *Start = AR->getStart();
1093 const SCEV *Step = AR->getStepRecurrence(*SE);
1095 // Check for a simple looking step prior to loop entry.
1096 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1100 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1101 // subtraction is expensive. For this purpose, perform a quick and dirty
1102 // difference, by checking for Step in the operand list.
1103 SmallVector<const SCEV *, 4> DiffOps;
1104 for (SCEVAddExpr::op_iterator I = SA->op_begin(), E = SA->op_end();
1107 DiffOps.push_back(*I);
1109 if (DiffOps.size() == SA->getNumOperands())
1112 // This is a postinc AR. Check for overflow on the preinc recurrence using the
1113 // same three conditions that getSignExtendedExpr checks.
1115 // 1. NSW flags on the step increment.
1116 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1117 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1118 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1120 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW))
1123 // 2. Direct overflow check on the step operation's expression.
1124 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1125 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1126 const SCEV *OperandExtendedStart =
1127 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy),
1128 SE->getSignExtendExpr(Step, WideTy));
1129 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) {
1130 // Cache knowledge of PreAR NSW.
1132 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW);
1133 // FIXME: this optimization needs a unit test
1134 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n");
1138 // 3. Loop precondition.
1139 ICmpInst::Predicate Pred;
1140 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE);
1142 if (OverflowLimit &&
1143 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1149 // Get the normalized sign-extended expression for this AddRec's Start.
1150 static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR,
1152 ScalarEvolution *SE) {
1153 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE);
1155 return SE->getSignExtendExpr(AR->getStart(), Ty);
1157 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty),
1158 SE->getSignExtendExpr(PreStart, Ty));
1161 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1163 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1164 "This is not an extending conversion!");
1165 assert(isSCEVable(Ty) &&
1166 "This is not a conversion to a SCEVable type!");
1167 Ty = getEffectiveSCEVType(Ty);
1169 // Fold if the operand is constant.
1170 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1172 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(),
1173 getEffectiveSCEVType(Ty))));
1175 // sext(sext(x)) --> sext(x)
1176 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1177 return getSignExtendExpr(SS->getOperand(), Ty);
1179 // sext(zext(x)) --> zext(x)
1180 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1181 return getZeroExtendExpr(SZ->getOperand(), Ty);
1183 // Before doing any expensive analysis, check to see if we've already
1184 // computed a SCEV for this Op and Ty.
1185 FoldingSetNodeID ID;
1186 ID.AddInteger(scSignExtend);
1190 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1192 // If the input value is provably positive, build a zext instead.
1193 if (isKnownNonNegative(Op))
1194 return getZeroExtendExpr(Op, Ty);
1196 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1197 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1198 // It's possible the bits taken off by the truncate were all sign bits. If
1199 // so, we should be able to simplify this further.
1200 const SCEV *X = ST->getOperand();
1201 ConstantRange CR = getSignedRange(X);
1202 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1203 unsigned NewBits = getTypeSizeInBits(Ty);
1204 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1205 CR.sextOrTrunc(NewBits)))
1206 return getTruncateOrSignExtend(X, Ty);
1209 // If the input value is a chrec scev, and we can prove that the value
1210 // did not overflow the old, smaller, value, we can sign extend all of the
1211 // operands (often constants). This allows analysis of something like
1212 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1213 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1214 if (AR->isAffine()) {
1215 const SCEV *Start = AR->getStart();
1216 const SCEV *Step = AR->getStepRecurrence(*this);
1217 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1218 const Loop *L = AR->getLoop();
1220 // If we have special knowledge that this addrec won't overflow,
1221 // we don't need to do any further analysis.
1222 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1223 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1224 getSignExtendExpr(Step, Ty),
1227 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1228 // Note that this serves two purposes: It filters out loops that are
1229 // simply not analyzable, and it covers the case where this code is
1230 // being called from within backedge-taken count analysis, such that
1231 // attempting to ask for the backedge-taken count would likely result
1232 // in infinite recursion. In the later case, the analysis code will
1233 // cope with a conservative value, and it will take care to purge
1234 // that value once it has finished.
1235 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1236 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1237 // Manually compute the final value for AR, checking for
1240 // Check whether the backedge-taken count can be losslessly casted to
1241 // the addrec's type. The count is always unsigned.
1242 const SCEV *CastedMaxBECount =
1243 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1244 const SCEV *RecastedMaxBECount =
1245 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1246 if (MaxBECount == RecastedMaxBECount) {
1247 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1248 // Check whether Start+Step*MaxBECount has no signed overflow.
1249 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1250 const SCEV *Add = getAddExpr(Start, SMul);
1251 const SCEV *OperandExtendedAdd =
1252 getAddExpr(getSignExtendExpr(Start, WideTy),
1253 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1254 getSignExtendExpr(Step, WideTy)));
1255 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) {
1256 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1257 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1258 // Return the expression with the addrec on the outside.
1259 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1260 getSignExtendExpr(Step, Ty),
1261 L, AR->getNoWrapFlags());
1263 // Similar to above, only this time treat the step value as unsigned.
1264 // This covers loops that count up with an unsigned step.
1265 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step);
1266 Add = getAddExpr(Start, UMul);
1267 OperandExtendedAdd =
1268 getAddExpr(getSignExtendExpr(Start, WideTy),
1269 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1270 getZeroExtendExpr(Step, WideTy)));
1271 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) {
1272 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1273 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1274 // Return the expression with the addrec on the outside.
1275 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1276 getZeroExtendExpr(Step, Ty),
1277 L, AR->getNoWrapFlags());
1281 // If the backedge is guarded by a comparison with the pre-inc value
1282 // the addrec is safe. Also, if the entry is guarded by a comparison
1283 // with the start value and the backedge is guarded by a comparison
1284 // with the post-inc value, the addrec is safe.
1285 ICmpInst::Predicate Pred;
1286 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
1287 if (OverflowLimit &&
1288 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1289 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1290 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1292 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1293 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1294 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1295 getSignExtendExpr(Step, Ty),
1296 L, AR->getNoWrapFlags());
1301 // The cast wasn't folded; create an explicit cast node.
1302 // Recompute the insert position, as it may have been invalidated.
1303 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1304 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1306 UniqueSCEVs.InsertNode(S, IP);
1310 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1311 /// unspecified bits out to the given type.
1313 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1315 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1316 "This is not an extending conversion!");
1317 assert(isSCEVable(Ty) &&
1318 "This is not a conversion to a SCEVable type!");
1319 Ty = getEffectiveSCEVType(Ty);
1321 // Sign-extend negative constants.
1322 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1323 if (SC->getValue()->getValue().isNegative())
1324 return getSignExtendExpr(Op, Ty);
1326 // Peel off a truncate cast.
1327 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1328 const SCEV *NewOp = T->getOperand();
1329 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1330 return getAnyExtendExpr(NewOp, Ty);
1331 return getTruncateOrNoop(NewOp, Ty);
1334 // Next try a zext cast. If the cast is folded, use it.
1335 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1336 if (!isa<SCEVZeroExtendExpr>(ZExt))
1339 // Next try a sext cast. If the cast is folded, use it.
1340 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1341 if (!isa<SCEVSignExtendExpr>(SExt))
1344 // Force the cast to be folded into the operands of an addrec.
1345 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1346 SmallVector<const SCEV *, 4> Ops;
1347 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1349 Ops.push_back(getAnyExtendExpr(*I, Ty));
1350 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1353 // As a special case, fold anyext(undef) to undef. We don't want to
1354 // know too much about SCEVUnknowns, but this special case is handy
1356 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
1357 if (isa<UndefValue>(U->getValue()))
1358 return getSCEV(UndefValue::get(Ty));
1360 // If the expression is obviously signed, use the sext cast value.
1361 if (isa<SCEVSMaxExpr>(Op))
1364 // Absent any other information, use the zext cast value.
1368 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1369 /// a list of operands to be added under the given scale, update the given
1370 /// map. This is a helper function for getAddRecExpr. As an example of
1371 /// what it does, given a sequence of operands that would form an add
1372 /// expression like this:
1374 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1376 /// where A and B are constants, update the map with these values:
1378 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1380 /// and add 13 + A*B*29 to AccumulatedConstant.
1381 /// This will allow getAddRecExpr to produce this:
1383 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1385 /// This form often exposes folding opportunities that are hidden in
1386 /// the original operand list.
1388 /// Return true iff it appears that any interesting folding opportunities
1389 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1390 /// the common case where no interesting opportunities are present, and
1391 /// is also used as a check to avoid infinite recursion.
1394 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1395 SmallVector<const SCEV *, 8> &NewOps,
1396 APInt &AccumulatedConstant,
1397 const SCEV *const *Ops, size_t NumOperands,
1399 ScalarEvolution &SE) {
1400 bool Interesting = false;
1402 // Iterate over the add operands. They are sorted, with constants first.
1404 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1406 // Pull a buried constant out to the outside.
1407 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1409 AccumulatedConstant += Scale * C->getValue()->getValue();
1412 // Next comes everything else. We're especially interested in multiplies
1413 // here, but they're in the middle, so just visit the rest with one loop.
1414 for (; i != NumOperands; ++i) {
1415 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1416 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1418 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1419 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1420 // A multiplication of a constant with another add; recurse.
1421 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1423 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1424 Add->op_begin(), Add->getNumOperands(),
1427 // A multiplication of a constant with some other value. Update
1429 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1430 const SCEV *Key = SE.getMulExpr(MulOps);
1431 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1432 M.insert(std::make_pair(Key, NewScale));
1434 NewOps.push_back(Pair.first->first);
1436 Pair.first->second += NewScale;
1437 // The map already had an entry for this value, which may indicate
1438 // a folding opportunity.
1443 // An ordinary operand. Update the map.
1444 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1445 M.insert(std::make_pair(Ops[i], Scale));
1447 NewOps.push_back(Pair.first->first);
1449 Pair.first->second += Scale;
1450 // The map already had an entry for this value, which may indicate
1451 // a folding opportunity.
1461 struct APIntCompare {
1462 bool operator()(const APInt &LHS, const APInt &RHS) const {
1463 return LHS.ult(RHS);
1468 /// getAddExpr - Get a canonical add expression, or something simpler if
1470 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1471 SCEV::NoWrapFlags Flags) {
1472 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1473 "only nuw or nsw allowed");
1474 assert(!Ops.empty() && "Cannot get empty add!");
1475 if (Ops.size() == 1) return Ops[0];
1477 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1478 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1479 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1480 "SCEVAddExpr operand types don't match!");
1483 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1485 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1486 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1487 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1489 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1490 E = Ops.end(); I != E; ++I)
1491 if (!isKnownNonNegative(*I)) {
1495 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1498 // Sort by complexity, this groups all similar expression types together.
1499 GroupByComplexity(Ops, LI);
1501 // If there are any constants, fold them together.
1503 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1505 assert(Idx < Ops.size());
1506 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1507 // We found two constants, fold them together!
1508 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1509 RHSC->getValue()->getValue());
1510 if (Ops.size() == 2) return Ops[0];
1511 Ops.erase(Ops.begin()+1); // Erase the folded element
1512 LHSC = cast<SCEVConstant>(Ops[0]);
1515 // If we are left with a constant zero being added, strip it off.
1516 if (LHSC->getValue()->isZero()) {
1517 Ops.erase(Ops.begin());
1521 if (Ops.size() == 1) return Ops[0];
1524 // Okay, check to see if the same value occurs in the operand list more than
1525 // once. If so, merge them together into an multiply expression. Since we
1526 // sorted the list, these values are required to be adjacent.
1527 Type *Ty = Ops[0]->getType();
1528 bool FoundMatch = false;
1529 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1530 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1531 // Scan ahead to count how many equal operands there are.
1533 while (i+Count != e && Ops[i+Count] == Ops[i])
1535 // Merge the values into a multiply.
1536 const SCEV *Scale = getConstant(Ty, Count);
1537 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1538 if (Ops.size() == Count)
1541 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1542 --i; e -= Count - 1;
1546 return getAddExpr(Ops, Flags);
1548 // Check for truncates. If all the operands are truncated from the same
1549 // type, see if factoring out the truncate would permit the result to be
1550 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1551 // if the contents of the resulting outer trunc fold to something simple.
1552 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1553 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1554 Type *DstType = Trunc->getType();
1555 Type *SrcType = Trunc->getOperand()->getType();
1556 SmallVector<const SCEV *, 8> LargeOps;
1558 // Check all the operands to see if they can be represented in the
1559 // source type of the truncate.
1560 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1561 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1562 if (T->getOperand()->getType() != SrcType) {
1566 LargeOps.push_back(T->getOperand());
1567 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1568 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1569 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1570 SmallVector<const SCEV *, 8> LargeMulOps;
1571 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1572 if (const SCEVTruncateExpr *T =
1573 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1574 if (T->getOperand()->getType() != SrcType) {
1578 LargeMulOps.push_back(T->getOperand());
1579 } else if (const SCEVConstant *C =
1580 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1581 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1588 LargeOps.push_back(getMulExpr(LargeMulOps));
1595 // Evaluate the expression in the larger type.
1596 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1597 // If it folds to something simple, use it. Otherwise, don't.
1598 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1599 return getTruncateExpr(Fold, DstType);
1603 // Skip past any other cast SCEVs.
1604 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1607 // If there are add operands they would be next.
1608 if (Idx < Ops.size()) {
1609 bool DeletedAdd = false;
1610 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1611 // If we have an add, expand the add operands onto the end of the operands
1613 Ops.erase(Ops.begin()+Idx);
1614 Ops.append(Add->op_begin(), Add->op_end());
1618 // If we deleted at least one add, we added operands to the end of the list,
1619 // and they are not necessarily sorted. Recurse to resort and resimplify
1620 // any operands we just acquired.
1622 return getAddExpr(Ops);
1625 // Skip over the add expression until we get to a multiply.
1626 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1629 // Check to see if there are any folding opportunities present with
1630 // operands multiplied by constant values.
1631 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1632 uint64_t BitWidth = getTypeSizeInBits(Ty);
1633 DenseMap<const SCEV *, APInt> M;
1634 SmallVector<const SCEV *, 8> NewOps;
1635 APInt AccumulatedConstant(BitWidth, 0);
1636 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1637 Ops.data(), Ops.size(),
1638 APInt(BitWidth, 1), *this)) {
1639 // Some interesting folding opportunity is present, so its worthwhile to
1640 // re-generate the operands list. Group the operands by constant scale,
1641 // to avoid multiplying by the same constant scale multiple times.
1642 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1643 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(),
1644 E = NewOps.end(); I != E; ++I)
1645 MulOpLists[M.find(*I)->second].push_back(*I);
1646 // Re-generate the operands list.
1648 if (AccumulatedConstant != 0)
1649 Ops.push_back(getConstant(AccumulatedConstant));
1650 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1651 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1653 Ops.push_back(getMulExpr(getConstant(I->first),
1654 getAddExpr(I->second)));
1656 return getConstant(Ty, 0);
1657 if (Ops.size() == 1)
1659 return getAddExpr(Ops);
1663 // If we are adding something to a multiply expression, make sure the
1664 // something is not already an operand of the multiply. If so, merge it into
1666 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1667 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1668 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1669 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1670 if (isa<SCEVConstant>(MulOpSCEV))
1672 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1673 if (MulOpSCEV == Ops[AddOp]) {
1674 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1675 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1676 if (Mul->getNumOperands() != 2) {
1677 // If the multiply has more than two operands, we must get the
1679 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1680 Mul->op_begin()+MulOp);
1681 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1682 InnerMul = getMulExpr(MulOps);
1684 const SCEV *One = getConstant(Ty, 1);
1685 const SCEV *AddOne = getAddExpr(One, InnerMul);
1686 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1687 if (Ops.size() == 2) return OuterMul;
1689 Ops.erase(Ops.begin()+AddOp);
1690 Ops.erase(Ops.begin()+Idx-1);
1692 Ops.erase(Ops.begin()+Idx);
1693 Ops.erase(Ops.begin()+AddOp-1);
1695 Ops.push_back(OuterMul);
1696 return getAddExpr(Ops);
1699 // Check this multiply against other multiplies being added together.
1700 for (unsigned OtherMulIdx = Idx+1;
1701 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1703 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1704 // If MulOp occurs in OtherMul, we can fold the two multiplies
1706 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1707 OMulOp != e; ++OMulOp)
1708 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1709 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1710 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1711 if (Mul->getNumOperands() != 2) {
1712 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1713 Mul->op_begin()+MulOp);
1714 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1715 InnerMul1 = getMulExpr(MulOps);
1717 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1718 if (OtherMul->getNumOperands() != 2) {
1719 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1720 OtherMul->op_begin()+OMulOp);
1721 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1722 InnerMul2 = getMulExpr(MulOps);
1724 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1725 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1726 if (Ops.size() == 2) return OuterMul;
1727 Ops.erase(Ops.begin()+Idx);
1728 Ops.erase(Ops.begin()+OtherMulIdx-1);
1729 Ops.push_back(OuterMul);
1730 return getAddExpr(Ops);
1736 // If there are any add recurrences in the operands list, see if any other
1737 // added values are loop invariant. If so, we can fold them into the
1739 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1742 // Scan over all recurrences, trying to fold loop invariants into them.
1743 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1744 // Scan all of the other operands to this add and add them to the vector if
1745 // they are loop invariant w.r.t. the recurrence.
1746 SmallVector<const SCEV *, 8> LIOps;
1747 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1748 const Loop *AddRecLoop = AddRec->getLoop();
1749 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1750 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1751 LIOps.push_back(Ops[i]);
1752 Ops.erase(Ops.begin()+i);
1756 // If we found some loop invariants, fold them into the recurrence.
1757 if (!LIOps.empty()) {
1758 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1759 LIOps.push_back(AddRec->getStart());
1761 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1763 AddRecOps[0] = getAddExpr(LIOps);
1765 // Build the new addrec. Propagate the NUW and NSW flags if both the
1766 // outer add and the inner addrec are guaranteed to have no overflow.
1767 // Always propagate NW.
1768 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
1769 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
1771 // If all of the other operands were loop invariant, we are done.
1772 if (Ops.size() == 1) return NewRec;
1774 // Otherwise, add the folded AddRec by the non-invariant parts.
1775 for (unsigned i = 0;; ++i)
1776 if (Ops[i] == AddRec) {
1780 return getAddExpr(Ops);
1783 // Okay, if there weren't any loop invariants to be folded, check to see if
1784 // there are multiple AddRec's with the same loop induction variable being
1785 // added together. If so, we can fold them.
1786 for (unsigned OtherIdx = Idx+1;
1787 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1789 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1790 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
1791 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1793 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1795 if (const SCEVAddRecExpr *OtherAddRec =
1796 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1797 if (OtherAddRec->getLoop() == AddRecLoop) {
1798 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
1800 if (i >= AddRecOps.size()) {
1801 AddRecOps.append(OtherAddRec->op_begin()+i,
1802 OtherAddRec->op_end());
1805 AddRecOps[i] = getAddExpr(AddRecOps[i],
1806 OtherAddRec->getOperand(i));
1808 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1810 // Step size has changed, so we cannot guarantee no self-wraparound.
1811 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
1812 return getAddExpr(Ops);
1815 // Otherwise couldn't fold anything into this recurrence. Move onto the
1819 // Okay, it looks like we really DO need an add expr. Check to see if we
1820 // already have one, otherwise create a new one.
1821 FoldingSetNodeID ID;
1822 ID.AddInteger(scAddExpr);
1823 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1824 ID.AddPointer(Ops[i]);
1827 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1829 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1830 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1831 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1833 UniqueSCEVs.InsertNode(S, IP);
1835 S->setNoWrapFlags(Flags);
1839 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
1841 if (j > 1 && k / j != i) Overflow = true;
1845 /// Compute the result of "n choose k", the binomial coefficient. If an
1846 /// intermediate computation overflows, Overflow will be set and the return will
1847 /// be garbage. Overflow is not cleared on absense of overflow.
1848 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
1849 // We use the multiplicative formula:
1850 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
1851 // At each iteration, we take the n-th term of the numeral and divide by the
1852 // (k-n)th term of the denominator. This division will always produce an
1853 // integral result, and helps reduce the chance of overflow in the
1854 // intermediate computations. However, we can still overflow even when the
1855 // final result would fit.
1857 if (n == 0 || n == k) return 1;
1858 if (k > n) return 0;
1864 for (uint64_t i = 1; i <= k; ++i) {
1865 r = umul_ov(r, n-(i-1), Overflow);
1871 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1873 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1874 SCEV::NoWrapFlags Flags) {
1875 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
1876 "only nuw or nsw allowed");
1877 assert(!Ops.empty() && "Cannot get empty mul!");
1878 if (Ops.size() == 1) return Ops[0];
1880 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1881 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1882 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1883 "SCEVMulExpr operand types don't match!");
1886 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1888 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1889 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1890 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1892 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1893 E = Ops.end(); I != E; ++I)
1894 if (!isKnownNonNegative(*I)) {
1898 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1901 // Sort by complexity, this groups all similar expression types together.
1902 GroupByComplexity(Ops, LI);
1904 // If there are any constants, fold them together.
1906 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1908 // C1*(C2+V) -> C1*C2 + C1*V
1909 if (Ops.size() == 2)
1910 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1911 if (Add->getNumOperands() == 2 &&
1912 isa<SCEVConstant>(Add->getOperand(0)))
1913 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1914 getMulExpr(LHSC, Add->getOperand(1)));
1917 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1918 // We found two constants, fold them together!
1919 ConstantInt *Fold = ConstantInt::get(getContext(),
1920 LHSC->getValue()->getValue() *
1921 RHSC->getValue()->getValue());
1922 Ops[0] = getConstant(Fold);
1923 Ops.erase(Ops.begin()+1); // Erase the folded element
1924 if (Ops.size() == 1) return Ops[0];
1925 LHSC = cast<SCEVConstant>(Ops[0]);
1928 // If we are left with a constant one being multiplied, strip it off.
1929 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1930 Ops.erase(Ops.begin());
1932 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1933 // If we have a multiply of zero, it will always be zero.
1935 } else if (Ops[0]->isAllOnesValue()) {
1936 // If we have a mul by -1 of an add, try distributing the -1 among the
1938 if (Ops.size() == 2) {
1939 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1940 SmallVector<const SCEV *, 4> NewOps;
1941 bool AnyFolded = false;
1942 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
1943 E = Add->op_end(); I != E; ++I) {
1944 const SCEV *Mul = getMulExpr(Ops[0], *I);
1945 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1946 NewOps.push_back(Mul);
1949 return getAddExpr(NewOps);
1951 else if (const SCEVAddRecExpr *
1952 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
1953 // Negation preserves a recurrence's no self-wrap property.
1954 SmallVector<const SCEV *, 4> Operands;
1955 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
1956 E = AddRec->op_end(); I != E; ++I) {
1957 Operands.push_back(getMulExpr(Ops[0], *I));
1959 return getAddRecExpr(Operands, AddRec->getLoop(),
1960 AddRec->getNoWrapFlags(SCEV::FlagNW));
1965 if (Ops.size() == 1)
1969 // Skip over the add expression until we get to a multiply.
1970 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1973 // If there are mul operands inline them all into this expression.
1974 if (Idx < Ops.size()) {
1975 bool DeletedMul = false;
1976 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1977 // If we have an mul, expand the mul operands onto the end of the operands
1979 Ops.erase(Ops.begin()+Idx);
1980 Ops.append(Mul->op_begin(), Mul->op_end());
1984 // If we deleted at least one mul, we added operands to the end of the list,
1985 // and they are not necessarily sorted. Recurse to resort and resimplify
1986 // any operands we just acquired.
1988 return getMulExpr(Ops);
1991 // If there are any add recurrences in the operands list, see if any other
1992 // added values are loop invariant. If so, we can fold them into the
1994 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1997 // Scan over all recurrences, trying to fold loop invariants into them.
1998 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1999 // Scan all of the other operands to this mul and add them to the vector if
2000 // they are loop invariant w.r.t. the recurrence.
2001 SmallVector<const SCEV *, 8> LIOps;
2002 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2003 const Loop *AddRecLoop = AddRec->getLoop();
2004 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2005 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2006 LIOps.push_back(Ops[i]);
2007 Ops.erase(Ops.begin()+i);
2011 // If we found some loop invariants, fold them into the recurrence.
2012 if (!LIOps.empty()) {
2013 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2014 SmallVector<const SCEV *, 4> NewOps;
2015 NewOps.reserve(AddRec->getNumOperands());
2016 const SCEV *Scale = getMulExpr(LIOps);
2017 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2018 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2020 // Build the new addrec. Propagate the NUW and NSW flags if both the
2021 // outer mul and the inner addrec are guaranteed to have no overflow.
2023 // No self-wrap cannot be guaranteed after changing the step size, but
2024 // will be inferred if either NUW or NSW is true.
2025 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2026 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2028 // If all of the other operands were loop invariant, we are done.
2029 if (Ops.size() == 1) return NewRec;
2031 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2032 for (unsigned i = 0;; ++i)
2033 if (Ops[i] == AddRec) {
2037 return getMulExpr(Ops);
2040 // Okay, if there weren't any loop invariants to be folded, check to see if
2041 // there are multiple AddRec's with the same loop induction variable being
2042 // multiplied together. If so, we can fold them.
2043 for (unsigned OtherIdx = Idx+1;
2044 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2046 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2047 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2048 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2049 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2050 // ]]],+,...up to x=2n}.
2051 // Note that the arguments to choose() are always integers with values
2052 // known at compile time, never SCEV objects.
2054 // The implementation avoids pointless extra computations when the two
2055 // addrec's are of different length (mathematically, it's equivalent to
2056 // an infinite stream of zeros on the right).
2057 bool OpsModified = false;
2058 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2060 if (const SCEVAddRecExpr *OtherAddRec =
2061 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2062 if (OtherAddRec->getLoop() == AddRecLoop) {
2063 bool Overflow = false;
2064 Type *Ty = AddRec->getType();
2065 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2066 SmallVector<const SCEV*, 7> AddRecOps;
2067 for (int x = 0, xe = AddRec->getNumOperands() +
2068 OtherAddRec->getNumOperands() - 1;
2069 x != xe && !Overflow; ++x) {
2070 const SCEV *Term = getConstant(Ty, 0);
2071 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2072 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2073 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2074 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2075 z < ze && !Overflow; ++z) {
2076 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2078 if (LargerThan64Bits)
2079 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2081 Coeff = Coeff1*Coeff2;
2082 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2083 const SCEV *Term1 = AddRec->getOperand(y-z);
2084 const SCEV *Term2 = OtherAddRec->getOperand(z);
2085 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2088 AddRecOps.push_back(Term);
2091 const SCEV *NewAddRec = getAddRecExpr(AddRecOps,
2094 if (Ops.size() == 2) return NewAddRec;
2095 Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec);
2096 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2101 return getMulExpr(Ops);
2105 // Otherwise couldn't fold anything into this recurrence. Move onto the
2109 // Okay, it looks like we really DO need an mul expr. Check to see if we
2110 // already have one, otherwise create a new one.
2111 FoldingSetNodeID ID;
2112 ID.AddInteger(scMulExpr);
2113 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2114 ID.AddPointer(Ops[i]);
2117 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2119 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2120 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2121 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2123 UniqueSCEVs.InsertNode(S, IP);
2125 S->setNoWrapFlags(Flags);
2129 /// getUDivExpr - Get a canonical unsigned division expression, or something
2130 /// simpler if possible.
2131 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2133 assert(getEffectiveSCEVType(LHS->getType()) ==
2134 getEffectiveSCEVType(RHS->getType()) &&
2135 "SCEVUDivExpr operand types don't match!");
2137 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2138 if (RHSC->getValue()->equalsInt(1))
2139 return LHS; // X udiv 1 --> x
2140 // If the denominator is zero, the result of the udiv is undefined. Don't
2141 // try to analyze it, because the resolution chosen here may differ from
2142 // the resolution chosen in other parts of the compiler.
2143 if (!RHSC->getValue()->isZero()) {
2144 // Determine if the division can be folded into the operands of
2146 // TODO: Generalize this to non-constants by using known-bits information.
2147 Type *Ty = LHS->getType();
2148 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2149 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2150 // For non-power-of-two values, effectively round the value up to the
2151 // nearest power of two.
2152 if (!RHSC->getValue()->getValue().isPowerOf2())
2154 IntegerType *ExtTy =
2155 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2156 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2157 if (const SCEVConstant *Step =
2158 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2159 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2160 const APInt &StepInt = Step->getValue()->getValue();
2161 const APInt &DivInt = RHSC->getValue()->getValue();
2162 if (!StepInt.urem(DivInt) &&
2163 getZeroExtendExpr(AR, ExtTy) ==
2164 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2165 getZeroExtendExpr(Step, ExtTy),
2166 AR->getLoop(), SCEV::FlagAnyWrap)) {
2167 SmallVector<const SCEV *, 4> Operands;
2168 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2169 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2170 return getAddRecExpr(Operands, AR->getLoop(),
2173 /// Get a canonical UDivExpr for a recurrence.
2174 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2175 // We can currently only fold X%N if X is constant.
2176 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2177 if (StartC && !DivInt.urem(StepInt) &&
2178 getZeroExtendExpr(AR, ExtTy) ==
2179 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2180 getZeroExtendExpr(Step, ExtTy),
2181 AR->getLoop(), SCEV::FlagAnyWrap)) {
2182 const APInt &StartInt = StartC->getValue()->getValue();
2183 const APInt &StartRem = StartInt.urem(StepInt);
2185 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2186 AR->getLoop(), SCEV::FlagNW);
2189 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2190 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2191 SmallVector<const SCEV *, 4> Operands;
2192 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2193 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2194 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2195 // Find an operand that's safely divisible.
2196 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2197 const SCEV *Op = M->getOperand(i);
2198 const SCEV *Div = getUDivExpr(Op, RHSC);
2199 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2200 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2203 return getMulExpr(Operands);
2207 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2208 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2209 SmallVector<const SCEV *, 4> Operands;
2210 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2211 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2212 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2214 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2215 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2216 if (isa<SCEVUDivExpr>(Op) ||
2217 getMulExpr(Op, RHS) != A->getOperand(i))
2219 Operands.push_back(Op);
2221 if (Operands.size() == A->getNumOperands())
2222 return getAddExpr(Operands);
2226 // Fold if both operands are constant.
2227 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2228 Constant *LHSCV = LHSC->getValue();
2229 Constant *RHSCV = RHSC->getValue();
2230 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2236 FoldingSetNodeID ID;
2237 ID.AddInteger(scUDivExpr);
2241 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2242 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2244 UniqueSCEVs.InsertNode(S, IP);
2249 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2250 /// Simplify the expression as much as possible.
2251 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2253 SCEV::NoWrapFlags Flags) {
2254 SmallVector<const SCEV *, 4> Operands;
2255 Operands.push_back(Start);
2256 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2257 if (StepChrec->getLoop() == L) {
2258 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2259 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2262 Operands.push_back(Step);
2263 return getAddRecExpr(Operands, L, Flags);
2266 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2267 /// Simplify the expression as much as possible.
2269 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2270 const Loop *L, SCEV::NoWrapFlags Flags) {
2271 if (Operands.size() == 1) return Operands[0];
2273 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2274 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2275 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2276 "SCEVAddRecExpr operand types don't match!");
2277 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2278 assert(isLoopInvariant(Operands[i], L) &&
2279 "SCEVAddRecExpr operand is not loop-invariant!");
2282 if (Operands.back()->isZero()) {
2283 Operands.pop_back();
2284 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2287 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2288 // use that information to infer NUW and NSW flags. However, computing a
2289 // BE count requires calling getAddRecExpr, so we may not yet have a
2290 // meaningful BE count at this point (and if we don't, we'd be stuck
2291 // with a SCEVCouldNotCompute as the cached BE count).
2293 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2295 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2296 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
2297 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
2299 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2300 E = Operands.end(); I != E; ++I)
2301 if (!isKnownNonNegative(*I)) {
2305 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2308 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2309 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2310 const Loop *NestedLoop = NestedAR->getLoop();
2311 if (L->contains(NestedLoop) ?
2312 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2313 (!NestedLoop->contains(L) &&
2314 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2315 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2316 NestedAR->op_end());
2317 Operands[0] = NestedAR->getStart();
2318 // AddRecs require their operands be loop-invariant with respect to their
2319 // loops. Don't perform this transformation if it would break this
2321 bool AllInvariant = true;
2322 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2323 if (!isLoopInvariant(Operands[i], L)) {
2324 AllInvariant = false;
2328 // Create a recurrence for the outer loop with the same step size.
2330 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2331 // inner recurrence has the same property.
2332 SCEV::NoWrapFlags OuterFlags =
2333 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2335 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2336 AllInvariant = true;
2337 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2338 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2339 AllInvariant = false;
2343 // Ok, both add recurrences are valid after the transformation.
2345 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2346 // the outer recurrence has the same property.
2347 SCEV::NoWrapFlags InnerFlags =
2348 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2349 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2352 // Reset Operands to its original state.
2353 Operands[0] = NestedAR;
2357 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2358 // already have one, otherwise create a new one.
2359 FoldingSetNodeID ID;
2360 ID.AddInteger(scAddRecExpr);
2361 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2362 ID.AddPointer(Operands[i]);
2366 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2368 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2369 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2370 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2371 O, Operands.size(), L);
2372 UniqueSCEVs.InsertNode(S, IP);
2374 S->setNoWrapFlags(Flags);
2378 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2380 SmallVector<const SCEV *, 2> Ops;
2383 return getSMaxExpr(Ops);
2387 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2388 assert(!Ops.empty() && "Cannot get empty smax!");
2389 if (Ops.size() == 1) return Ops[0];
2391 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2392 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2393 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2394 "SCEVSMaxExpr operand types don't match!");
2397 // Sort by complexity, this groups all similar expression types together.
2398 GroupByComplexity(Ops, LI);
2400 // If there are any constants, fold them together.
2402 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2404 assert(Idx < Ops.size());
2405 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2406 // We found two constants, fold them together!
2407 ConstantInt *Fold = ConstantInt::get(getContext(),
2408 APIntOps::smax(LHSC->getValue()->getValue(),
2409 RHSC->getValue()->getValue()));
2410 Ops[0] = getConstant(Fold);
2411 Ops.erase(Ops.begin()+1); // Erase the folded element
2412 if (Ops.size() == 1) return Ops[0];
2413 LHSC = cast<SCEVConstant>(Ops[0]);
2416 // If we are left with a constant minimum-int, strip it off.
2417 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2418 Ops.erase(Ops.begin());
2420 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2421 // If we have an smax with a constant maximum-int, it will always be
2426 if (Ops.size() == 1) return Ops[0];
2429 // Find the first SMax
2430 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2433 // Check to see if one of the operands is an SMax. If so, expand its operands
2434 // onto our operand list, and recurse to simplify.
2435 if (Idx < Ops.size()) {
2436 bool DeletedSMax = false;
2437 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2438 Ops.erase(Ops.begin()+Idx);
2439 Ops.append(SMax->op_begin(), SMax->op_end());
2444 return getSMaxExpr(Ops);
2447 // Okay, check to see if the same value occurs in the operand list twice. If
2448 // so, delete one. Since we sorted the list, these values are required to
2450 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2451 // X smax Y smax Y --> X smax Y
2452 // X smax Y --> X, if X is always greater than Y
2453 if (Ops[i] == Ops[i+1] ||
2454 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2455 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2457 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2458 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2462 if (Ops.size() == 1) return Ops[0];
2464 assert(!Ops.empty() && "Reduced smax down to nothing!");
2466 // Okay, it looks like we really DO need an smax expr. Check to see if we
2467 // already have one, otherwise create a new one.
2468 FoldingSetNodeID ID;
2469 ID.AddInteger(scSMaxExpr);
2470 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2471 ID.AddPointer(Ops[i]);
2473 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2474 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2475 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2476 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2478 UniqueSCEVs.InsertNode(S, IP);
2482 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2484 SmallVector<const SCEV *, 2> Ops;
2487 return getUMaxExpr(Ops);
2491 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2492 assert(!Ops.empty() && "Cannot get empty umax!");
2493 if (Ops.size() == 1) return Ops[0];
2495 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2496 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2497 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2498 "SCEVUMaxExpr operand types don't match!");
2501 // Sort by complexity, this groups all similar expression types together.
2502 GroupByComplexity(Ops, LI);
2504 // If there are any constants, fold them together.
2506 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2508 assert(Idx < Ops.size());
2509 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2510 // We found two constants, fold them together!
2511 ConstantInt *Fold = ConstantInt::get(getContext(),
2512 APIntOps::umax(LHSC->getValue()->getValue(),
2513 RHSC->getValue()->getValue()));
2514 Ops[0] = getConstant(Fold);
2515 Ops.erase(Ops.begin()+1); // Erase the folded element
2516 if (Ops.size() == 1) return Ops[0];
2517 LHSC = cast<SCEVConstant>(Ops[0]);
2520 // If we are left with a constant minimum-int, strip it off.
2521 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2522 Ops.erase(Ops.begin());
2524 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2525 // If we have an umax with a constant maximum-int, it will always be
2530 if (Ops.size() == 1) return Ops[0];
2533 // Find the first UMax
2534 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2537 // Check to see if one of the operands is a UMax. If so, expand its operands
2538 // onto our operand list, and recurse to simplify.
2539 if (Idx < Ops.size()) {
2540 bool DeletedUMax = false;
2541 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2542 Ops.erase(Ops.begin()+Idx);
2543 Ops.append(UMax->op_begin(), UMax->op_end());
2548 return getUMaxExpr(Ops);
2551 // Okay, check to see if the same value occurs in the operand list twice. If
2552 // so, delete one. Since we sorted the list, these values are required to
2554 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2555 // X umax Y umax Y --> X umax Y
2556 // X umax Y --> X, if X is always greater than Y
2557 if (Ops[i] == Ops[i+1] ||
2558 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2559 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2561 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2562 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2566 if (Ops.size() == 1) return Ops[0];
2568 assert(!Ops.empty() && "Reduced umax down to nothing!");
2570 // Okay, it looks like we really DO need a umax expr. Check to see if we
2571 // already have one, otherwise create a new one.
2572 FoldingSetNodeID ID;
2573 ID.AddInteger(scUMaxExpr);
2574 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2575 ID.AddPointer(Ops[i]);
2577 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2578 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2579 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2580 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2582 UniqueSCEVs.InsertNode(S, IP);
2586 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2588 // ~smax(~x, ~y) == smin(x, y).
2589 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2592 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2594 // ~umax(~x, ~y) == umin(x, y)
2595 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2598 const SCEV *ScalarEvolution::getSizeOfExpr(Type *AllocTy) {
2599 // If we have TargetData, we can bypass creating a target-independent
2600 // constant expression and then folding it back into a ConstantInt.
2601 // This is just a compile-time optimization.
2603 return getConstant(TD->getIntPtrType(getContext()),
2604 TD->getTypeAllocSize(AllocTy));
2606 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2607 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2608 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2610 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2611 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2614 const SCEV *ScalarEvolution::getAlignOfExpr(Type *AllocTy) {
2615 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2616 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2617 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2619 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2620 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2623 const SCEV *ScalarEvolution::getOffsetOfExpr(StructType *STy,
2625 // If we have TargetData, we can bypass creating a target-independent
2626 // constant expression and then folding it back into a ConstantInt.
2627 // This is just a compile-time optimization.
2629 return getConstant(TD->getIntPtrType(getContext()),
2630 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2632 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2633 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2634 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2636 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2637 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2640 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *CTy,
2641 Constant *FieldNo) {
2642 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2643 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2644 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2646 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2647 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2650 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2651 // Don't attempt to do anything other than create a SCEVUnknown object
2652 // here. createSCEV only calls getUnknown after checking for all other
2653 // interesting possibilities, and any other code that calls getUnknown
2654 // is doing so in order to hide a value from SCEV canonicalization.
2656 FoldingSetNodeID ID;
2657 ID.AddInteger(scUnknown);
2660 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2661 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2662 "Stale SCEVUnknown in uniquing map!");
2665 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2667 FirstUnknown = cast<SCEVUnknown>(S);
2668 UniqueSCEVs.InsertNode(S, IP);
2672 //===----------------------------------------------------------------------===//
2673 // Basic SCEV Analysis and PHI Idiom Recognition Code
2676 /// isSCEVable - Test if values of the given type are analyzable within
2677 /// the SCEV framework. This primarily includes integer types, and it
2678 /// can optionally include pointer types if the ScalarEvolution class
2679 /// has access to target-specific information.
2680 bool ScalarEvolution::isSCEVable(Type *Ty) const {
2681 // Integers and pointers are always SCEVable.
2682 return Ty->isIntegerTy() || Ty->isPointerTy();
2685 /// getTypeSizeInBits - Return the size in bits of the specified type,
2686 /// for which isSCEVable must return true.
2687 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
2688 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2690 // If we have a TargetData, use it!
2692 return TD->getTypeSizeInBits(Ty);
2694 // Integer types have fixed sizes.
2695 if (Ty->isIntegerTy())
2696 return Ty->getPrimitiveSizeInBits();
2698 // The only other support type is pointer. Without TargetData, conservatively
2699 // assume pointers are 64-bit.
2700 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2704 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2705 /// the given type and which represents how SCEV will treat the given
2706 /// type, for which isSCEVable must return true. For pointer types,
2707 /// this is the pointer-sized integer type.
2708 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
2709 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2711 if (Ty->isIntegerTy())
2714 // The only other support type is pointer.
2715 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2716 if (TD) return TD->getIntPtrType(getContext());
2718 // Without TargetData, conservatively assume pointers are 64-bit.
2719 return Type::getInt64Ty(getContext());
2722 const SCEV *ScalarEvolution::getCouldNotCompute() {
2723 return &CouldNotCompute;
2726 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2727 /// expression and create a new one.
2728 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2729 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2731 ValueExprMapType::const_iterator I = ValueExprMap.find(V);
2732 if (I != ValueExprMap.end()) return I->second;
2733 const SCEV *S = createSCEV(V);
2735 // The process of creating a SCEV for V may have caused other SCEVs
2736 // to have been created, so it's necessary to insert the new entry
2737 // from scratch, rather than trying to remember the insert position
2739 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2743 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2745 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2746 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2748 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2750 Type *Ty = V->getType();
2751 Ty = getEffectiveSCEVType(Ty);
2752 return getMulExpr(V,
2753 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2756 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2757 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2758 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2760 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2762 Type *Ty = V->getType();
2763 Ty = getEffectiveSCEVType(Ty);
2764 const SCEV *AllOnes =
2765 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2766 return getMinusSCEV(AllOnes, V);
2769 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
2770 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2771 SCEV::NoWrapFlags Flags) {
2772 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
2774 // Fast path: X - X --> 0.
2776 return getConstant(LHS->getType(), 0);
2779 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
2782 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2783 /// input value to the specified type. If the type must be extended, it is zero
2786 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
2787 Type *SrcTy = V->getType();
2788 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2789 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2790 "Cannot truncate or zero extend with non-integer arguments!");
2791 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2792 return V; // No conversion
2793 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2794 return getTruncateExpr(V, Ty);
2795 return getZeroExtendExpr(V, Ty);
2798 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2799 /// input value to the specified type. If the type must be extended, it is sign
2802 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2804 Type *SrcTy = V->getType();
2805 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2806 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2807 "Cannot truncate or zero extend with non-integer arguments!");
2808 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2809 return V; // No conversion
2810 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2811 return getTruncateExpr(V, Ty);
2812 return getSignExtendExpr(V, Ty);
2815 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2816 /// input value to the specified type. If the type must be extended, it is zero
2817 /// extended. The conversion must not be narrowing.
2819 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
2820 Type *SrcTy = V->getType();
2821 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2822 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2823 "Cannot noop or zero extend with non-integer arguments!");
2824 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2825 "getNoopOrZeroExtend cannot truncate!");
2826 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2827 return V; // No conversion
2828 return getZeroExtendExpr(V, Ty);
2831 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2832 /// input value to the specified type. If the type must be extended, it is sign
2833 /// extended. The conversion must not be narrowing.
2835 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
2836 Type *SrcTy = V->getType();
2837 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2838 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2839 "Cannot noop or sign extend with non-integer arguments!");
2840 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2841 "getNoopOrSignExtend cannot truncate!");
2842 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2843 return V; // No conversion
2844 return getSignExtendExpr(V, Ty);
2847 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2848 /// the input value to the specified type. If the type must be extended,
2849 /// it is extended with unspecified bits. The conversion must not be
2852 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
2853 Type *SrcTy = V->getType();
2854 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2855 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2856 "Cannot noop or any extend with non-integer arguments!");
2857 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2858 "getNoopOrAnyExtend cannot truncate!");
2859 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2860 return V; // No conversion
2861 return getAnyExtendExpr(V, Ty);
2864 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2865 /// input value to the specified type. The conversion must not be widening.
2867 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
2868 Type *SrcTy = V->getType();
2869 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2870 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2871 "Cannot truncate or noop with non-integer arguments!");
2872 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2873 "getTruncateOrNoop cannot extend!");
2874 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2875 return V; // No conversion
2876 return getTruncateExpr(V, Ty);
2879 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2880 /// the types using zero-extension, and then perform a umax operation
2882 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2884 const SCEV *PromotedLHS = LHS;
2885 const SCEV *PromotedRHS = RHS;
2887 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2888 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2890 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2892 return getUMaxExpr(PromotedLHS, PromotedRHS);
2895 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2896 /// the types using zero-extension, and then perform a umin operation
2898 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2900 const SCEV *PromotedLHS = LHS;
2901 const SCEV *PromotedRHS = RHS;
2903 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2904 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2906 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2908 return getUMinExpr(PromotedLHS, PromotedRHS);
2911 /// getPointerBase - Transitively follow the chain of pointer-type operands
2912 /// until reaching a SCEV that does not have a single pointer operand. This
2913 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
2914 /// but corner cases do exist.
2915 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
2916 // A pointer operand may evaluate to a nonpointer expression, such as null.
2917 if (!V->getType()->isPointerTy())
2920 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
2921 return getPointerBase(Cast->getOperand());
2923 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
2924 const SCEV *PtrOp = 0;
2925 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
2927 if ((*I)->getType()->isPointerTy()) {
2928 // Cannot find the base of an expression with multiple pointer operands.
2936 return getPointerBase(PtrOp);
2941 /// PushDefUseChildren - Push users of the given Instruction
2942 /// onto the given Worklist.
2944 PushDefUseChildren(Instruction *I,
2945 SmallVectorImpl<Instruction *> &Worklist) {
2946 // Push the def-use children onto the Worklist stack.
2947 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2949 Worklist.push_back(cast<Instruction>(*UI));
2952 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2953 /// instructions that depend on the given instruction and removes them from
2954 /// the ValueExprMapType map if they reference SymName. This is used during PHI
2957 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2958 SmallVector<Instruction *, 16> Worklist;
2959 PushDefUseChildren(PN, Worklist);
2961 SmallPtrSet<Instruction *, 8> Visited;
2963 while (!Worklist.empty()) {
2964 Instruction *I = Worklist.pop_back_val();
2965 if (!Visited.insert(I)) continue;
2967 ValueExprMapType::iterator It =
2968 ValueExprMap.find(static_cast<Value *>(I));
2969 if (It != ValueExprMap.end()) {
2970 const SCEV *Old = It->second;
2972 // Short-circuit the def-use traversal if the symbolic name
2973 // ceases to appear in expressions.
2974 if (Old != SymName && !hasOperand(Old, SymName))
2977 // SCEVUnknown for a PHI either means that it has an unrecognized
2978 // structure, it's a PHI that's in the progress of being computed
2979 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2980 // additional loop trip count information isn't going to change anything.
2981 // In the second case, createNodeForPHI will perform the necessary
2982 // updates on its own when it gets to that point. In the third, we do
2983 // want to forget the SCEVUnknown.
2984 if (!isa<PHINode>(I) ||
2985 !isa<SCEVUnknown>(Old) ||
2986 (I != PN && Old == SymName)) {
2987 forgetMemoizedResults(Old);
2988 ValueExprMap.erase(It);
2992 PushDefUseChildren(I, Worklist);
2996 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2997 /// a loop header, making it a potential recurrence, or it doesn't.
2999 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3000 if (const Loop *L = LI->getLoopFor(PN->getParent()))
3001 if (L->getHeader() == PN->getParent()) {
3002 // The loop may have multiple entrances or multiple exits; we can analyze
3003 // this phi as an addrec if it has a unique entry value and a unique
3005 Value *BEValueV = 0, *StartValueV = 0;
3006 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3007 Value *V = PN->getIncomingValue(i);
3008 if (L->contains(PN->getIncomingBlock(i))) {
3011 } else if (BEValueV != V) {
3015 } else if (!StartValueV) {
3017 } else if (StartValueV != V) {
3022 if (BEValueV && StartValueV) {
3023 // While we are analyzing this PHI node, handle its value symbolically.
3024 const SCEV *SymbolicName = getUnknown(PN);
3025 assert(ValueExprMap.find(PN) == ValueExprMap.end() &&
3026 "PHI node already processed?");
3027 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3029 // Using this symbolic name for the PHI, analyze the value coming around
3031 const SCEV *BEValue = getSCEV(BEValueV);
3033 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3034 // has a special value for the first iteration of the loop.
3036 // If the value coming around the backedge is an add with the symbolic
3037 // value we just inserted, then we found a simple induction variable!
3038 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3039 // If there is a single occurrence of the symbolic value, replace it
3040 // with a recurrence.
3041 unsigned FoundIndex = Add->getNumOperands();
3042 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3043 if (Add->getOperand(i) == SymbolicName)
3044 if (FoundIndex == e) {
3049 if (FoundIndex != Add->getNumOperands()) {
3050 // Create an add with everything but the specified operand.
3051 SmallVector<const SCEV *, 8> Ops;
3052 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3053 if (i != FoundIndex)
3054 Ops.push_back(Add->getOperand(i));
3055 const SCEV *Accum = getAddExpr(Ops);
3057 // This is not a valid addrec if the step amount is varying each
3058 // loop iteration, but is not itself an addrec in this loop.
3059 if (isLoopInvariant(Accum, L) ||
3060 (isa<SCEVAddRecExpr>(Accum) &&
3061 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3062 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3064 // If the increment doesn't overflow, then neither the addrec nor
3065 // the post-increment will overflow.
3066 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3067 if (OBO->hasNoUnsignedWrap())
3068 Flags = setFlags(Flags, SCEV::FlagNUW);
3069 if (OBO->hasNoSignedWrap())
3070 Flags = setFlags(Flags, SCEV::FlagNSW);
3071 } else if (const GEPOperator *GEP =
3072 dyn_cast<GEPOperator>(BEValueV)) {
3073 // If the increment is an inbounds GEP, then we know the address
3074 // space cannot be wrapped around. We cannot make any guarantee
3075 // about signed or unsigned overflow because pointers are
3076 // unsigned but we may have a negative index from the base
3078 if (GEP->isInBounds())
3079 Flags = setFlags(Flags, SCEV::FlagNW);
3082 const SCEV *StartVal = getSCEV(StartValueV);
3083 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3085 // Since the no-wrap flags are on the increment, they apply to the
3086 // post-incremented value as well.
3087 if (isLoopInvariant(Accum, L))
3088 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3091 // Okay, for the entire analysis of this edge we assumed the PHI
3092 // to be symbolic. We now need to go back and purge all of the
3093 // entries for the scalars that use the symbolic expression.
3094 ForgetSymbolicName(PN, SymbolicName);
3095 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3099 } else if (const SCEVAddRecExpr *AddRec =
3100 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3101 // Otherwise, this could be a loop like this:
3102 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3103 // In this case, j = {1,+,1} and BEValue is j.
3104 // Because the other in-value of i (0) fits the evolution of BEValue
3105 // i really is an addrec evolution.
3106 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3107 const SCEV *StartVal = getSCEV(StartValueV);
3109 // If StartVal = j.start - j.stride, we can use StartVal as the
3110 // initial step of the addrec evolution.
3111 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3112 AddRec->getOperand(1))) {
3113 // FIXME: For constant StartVal, we should be able to infer
3115 const SCEV *PHISCEV =
3116 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3119 // Okay, for the entire analysis of this edge we assumed the PHI
3120 // to be symbolic. We now need to go back and purge all of the
3121 // entries for the scalars that use the symbolic expression.
3122 ForgetSymbolicName(PN, SymbolicName);
3123 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3131 // If the PHI has a single incoming value, follow that value, unless the
3132 // PHI's incoming blocks are in a different loop, in which case doing so
3133 // risks breaking LCSSA form. Instcombine would normally zap these, but
3134 // it doesn't have DominatorTree information, so it may miss cases.
3135 if (Value *V = SimplifyInstruction(PN, TD, TLI, DT))
3136 if (LI->replacementPreservesLCSSAForm(PN, V))
3139 // If it's not a loop phi, we can't handle it yet.
3140 return getUnknown(PN);
3143 /// createNodeForGEP - Expand GEP instructions into add and multiply
3144 /// operations. This allows them to be analyzed by regular SCEV code.
3146 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3148 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3149 // Add expression, because the Instruction may be guarded by control flow
3150 // and the no-overflow bits may not be valid for the expression in any
3152 bool isInBounds = GEP->isInBounds();
3154 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3155 Value *Base = GEP->getOperand(0);
3156 // Don't attempt to analyze GEPs over unsized objects.
3157 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
3158 return getUnknown(GEP);
3159 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3160 gep_type_iterator GTI = gep_type_begin(GEP);
3161 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()),
3165 // Compute the (potentially symbolic) offset in bytes for this index.
3166 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3167 // For a struct, add the member offset.
3168 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3169 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo);
3171 // Add the field offset to the running total offset.
3172 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3174 // For an array, add the element offset, explicitly scaled.
3175 const SCEV *ElementSize = getSizeOfExpr(*GTI);
3176 const SCEV *IndexS = getSCEV(Index);
3177 // Getelementptr indices are signed.
3178 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3180 // Multiply the index by the element size to compute the element offset.
3181 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize,
3182 isInBounds ? SCEV::FlagNSW :
3185 // Add the element offset to the running total offset.
3186 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3190 // Get the SCEV for the GEP base.
3191 const SCEV *BaseS = getSCEV(Base);
3193 // Add the total offset from all the GEP indices to the base.
3194 return getAddExpr(BaseS, TotalOffset,
3195 isInBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap);
3198 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3199 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3200 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3201 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3203 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3204 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3205 return C->getValue()->getValue().countTrailingZeros();
3207 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3208 return std::min(GetMinTrailingZeros(T->getOperand()),
3209 (uint32_t)getTypeSizeInBits(T->getType()));
3211 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3212 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3213 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3214 getTypeSizeInBits(E->getType()) : OpRes;
3217 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3218 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3219 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3220 getTypeSizeInBits(E->getType()) : OpRes;
3223 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3224 // The result is the min of all operands results.
3225 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3226 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3227 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3231 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3232 // The result is the sum of all operands results.
3233 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3234 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3235 for (unsigned i = 1, e = M->getNumOperands();
3236 SumOpRes != BitWidth && i != e; ++i)
3237 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3242 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3243 // The result is the min of all operands results.
3244 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3245 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3246 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3250 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3251 // The result is the min of all operands results.
3252 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3253 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3254 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3258 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3259 // The result is the min of all operands results.
3260 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3261 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3262 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3266 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3267 // For a SCEVUnknown, ask ValueTracking.
3268 unsigned BitWidth = getTypeSizeInBits(U->getType());
3269 APInt Mask = APInt::getAllOnesValue(BitWidth);
3270 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3271 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
3272 return Zeros.countTrailingOnes();
3279 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3282 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3283 // See if we've computed this range already.
3284 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3285 if (I != UnsignedRanges.end())
3288 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3289 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3291 unsigned BitWidth = getTypeSizeInBits(S->getType());
3292 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3294 // If the value has known zeros, the maximum unsigned value will have those
3295 // known zeros as well.
3296 uint32_t TZ = GetMinTrailingZeros(S);
3298 ConservativeResult =
3299 ConstantRange(APInt::getMinValue(BitWidth),
3300 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3302 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3303 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3304 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3305 X = X.add(getUnsignedRange(Add->getOperand(i)));
3306 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3309 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3310 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3311 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3312 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3313 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3316 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3317 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3318 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3319 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3320 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3323 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3324 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3325 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3326 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3327 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3330 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3331 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3332 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3333 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3336 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3337 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3338 return setUnsignedRange(ZExt,
3339 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3342 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3343 ConstantRange X = getUnsignedRange(SExt->getOperand());
3344 return setUnsignedRange(SExt,
3345 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3348 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3349 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3350 return setUnsignedRange(Trunc,
3351 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3354 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3355 // If there's no unsigned wrap, the value will never be less than its
3357 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3358 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3359 if (!C->getValue()->isZero())
3360 ConservativeResult =
3361 ConservativeResult.intersectWith(
3362 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3364 // TODO: non-affine addrec
3365 if (AddRec->isAffine()) {
3366 Type *Ty = AddRec->getType();
3367 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3368 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3369 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3370 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3372 const SCEV *Start = AddRec->getStart();
3373 const SCEV *Step = AddRec->getStepRecurrence(*this);
3375 ConstantRange StartRange = getUnsignedRange(Start);
3376 ConstantRange StepRange = getSignedRange(Step);
3377 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3378 ConstantRange EndRange =
3379 StartRange.add(MaxBECountRange.multiply(StepRange));
3381 // Check for overflow. This must be done with ConstantRange arithmetic
3382 // because we could be called from within the ScalarEvolution overflow
3384 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3385 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3386 ConstantRange ExtMaxBECountRange =
3387 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3388 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3389 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3391 return setUnsignedRange(AddRec, ConservativeResult);
3393 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3394 EndRange.getUnsignedMin());
3395 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3396 EndRange.getUnsignedMax());
3397 if (Min.isMinValue() && Max.isMaxValue())
3398 return setUnsignedRange(AddRec, ConservativeResult);
3399 return setUnsignedRange(AddRec,
3400 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3404 return setUnsignedRange(AddRec, ConservativeResult);
3407 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3408 // For a SCEVUnknown, ask ValueTracking.
3409 APInt Mask = APInt::getAllOnesValue(BitWidth);
3410 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3411 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
3412 if (Ones == ~Zeros + 1)
3413 return setUnsignedRange(U, ConservativeResult);
3414 return setUnsignedRange(U,
3415 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3418 return setUnsignedRange(S, ConservativeResult);
3421 /// getSignedRange - Determine the signed range for a particular SCEV.
3424 ScalarEvolution::getSignedRange(const SCEV *S) {
3425 // See if we've computed this range already.
3426 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3427 if (I != SignedRanges.end())
3430 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3431 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3433 unsigned BitWidth = getTypeSizeInBits(S->getType());
3434 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3436 // If the value has known zeros, the maximum signed value will have those
3437 // known zeros as well.
3438 uint32_t TZ = GetMinTrailingZeros(S);
3440 ConservativeResult =
3441 ConstantRange(APInt::getSignedMinValue(BitWidth),
3442 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3444 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3445 ConstantRange X = getSignedRange(Add->getOperand(0));
3446 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3447 X = X.add(getSignedRange(Add->getOperand(i)));
3448 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3451 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3452 ConstantRange X = getSignedRange(Mul->getOperand(0));
3453 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3454 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3455 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3458 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3459 ConstantRange X = getSignedRange(SMax->getOperand(0));
3460 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3461 X = X.smax(getSignedRange(SMax->getOperand(i)));
3462 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3465 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3466 ConstantRange X = getSignedRange(UMax->getOperand(0));
3467 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3468 X = X.umax(getSignedRange(UMax->getOperand(i)));
3469 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3472 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3473 ConstantRange X = getSignedRange(UDiv->getLHS());
3474 ConstantRange Y = getSignedRange(UDiv->getRHS());
3475 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3478 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3479 ConstantRange X = getSignedRange(ZExt->getOperand());
3480 return setSignedRange(ZExt,
3481 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3484 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3485 ConstantRange X = getSignedRange(SExt->getOperand());
3486 return setSignedRange(SExt,
3487 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3490 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3491 ConstantRange X = getSignedRange(Trunc->getOperand());
3492 return setSignedRange(Trunc,
3493 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3496 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3497 // If there's no signed wrap, and all the operands have the same sign or
3498 // zero, the value won't ever change sign.
3499 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3500 bool AllNonNeg = true;
3501 bool AllNonPos = true;
3502 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3503 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3504 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3507 ConservativeResult = ConservativeResult.intersectWith(
3508 ConstantRange(APInt(BitWidth, 0),
3509 APInt::getSignedMinValue(BitWidth)));
3511 ConservativeResult = ConservativeResult.intersectWith(
3512 ConstantRange(APInt::getSignedMinValue(BitWidth),
3513 APInt(BitWidth, 1)));
3516 // TODO: non-affine addrec
3517 if (AddRec->isAffine()) {
3518 Type *Ty = AddRec->getType();
3519 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3520 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3521 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3522 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3524 const SCEV *Start = AddRec->getStart();
3525 const SCEV *Step = AddRec->getStepRecurrence(*this);
3527 ConstantRange StartRange = getSignedRange(Start);
3528 ConstantRange StepRange = getSignedRange(Step);
3529 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3530 ConstantRange EndRange =
3531 StartRange.add(MaxBECountRange.multiply(StepRange));
3533 // Check for overflow. This must be done with ConstantRange arithmetic
3534 // because we could be called from within the ScalarEvolution overflow
3536 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3537 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3538 ConstantRange ExtMaxBECountRange =
3539 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3540 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3541 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3543 return setSignedRange(AddRec, ConservativeResult);
3545 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3546 EndRange.getSignedMin());
3547 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3548 EndRange.getSignedMax());
3549 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3550 return setSignedRange(AddRec, ConservativeResult);
3551 return setSignedRange(AddRec,
3552 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3556 return setSignedRange(AddRec, ConservativeResult);
3559 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3560 // For a SCEVUnknown, ask ValueTracking.
3561 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3562 return setSignedRange(U, ConservativeResult);
3563 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3565 return setSignedRange(U, ConservativeResult);
3566 return setSignedRange(U, ConservativeResult.intersectWith(
3567 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3568 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3571 return setSignedRange(S, ConservativeResult);
3574 /// createSCEV - We know that there is no SCEV for the specified value.
3575 /// Analyze the expression.
3577 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3578 if (!isSCEVable(V->getType()))
3579 return getUnknown(V);
3581 unsigned Opcode = Instruction::UserOp1;
3582 if (Instruction *I = dyn_cast<Instruction>(V)) {
3583 Opcode = I->getOpcode();
3585 // Don't attempt to analyze instructions in blocks that aren't
3586 // reachable. Such instructions don't matter, and they aren't required
3587 // to obey basic rules for definitions dominating uses which this
3588 // analysis depends on.
3589 if (!DT->isReachableFromEntry(I->getParent()))
3590 return getUnknown(V);
3591 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3592 Opcode = CE->getOpcode();
3593 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3594 return getConstant(CI);
3595 else if (isa<ConstantPointerNull>(V))
3596 return getConstant(V->getType(), 0);
3597 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3598 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3600 return getUnknown(V);
3602 Operator *U = cast<Operator>(V);
3604 case Instruction::Add: {
3605 // The simple thing to do would be to just call getSCEV on both operands
3606 // and call getAddExpr with the result. However if we're looking at a
3607 // bunch of things all added together, this can be quite inefficient,
3608 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3609 // Instead, gather up all the operands and make a single getAddExpr call.
3610 // LLVM IR canonical form means we need only traverse the left operands.
3612 // Don't apply this instruction's NSW or NUW flags to the new
3613 // expression. The instruction may be guarded by control flow that the
3614 // no-wrap behavior depends on. Non-control-equivalent instructions can be
3615 // mapped to the same SCEV expression, and it would be incorrect to transfer
3616 // NSW/NUW semantics to those operations.
3617 SmallVector<const SCEV *, 4> AddOps;
3618 AddOps.push_back(getSCEV(U->getOperand(1)));
3619 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3620 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3621 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3623 U = cast<Operator>(Op);
3624 const SCEV *Op1 = getSCEV(U->getOperand(1));
3625 if (Opcode == Instruction::Sub)
3626 AddOps.push_back(getNegativeSCEV(Op1));
3628 AddOps.push_back(Op1);
3630 AddOps.push_back(getSCEV(U->getOperand(0)));
3631 return getAddExpr(AddOps);
3633 case Instruction::Mul: {
3634 // Don't transfer NSW/NUW for the same reason as AddExpr.
3635 SmallVector<const SCEV *, 4> MulOps;
3636 MulOps.push_back(getSCEV(U->getOperand(1)));
3637 for (Value *Op = U->getOperand(0);
3638 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3639 Op = U->getOperand(0)) {
3640 U = cast<Operator>(Op);
3641 MulOps.push_back(getSCEV(U->getOperand(1)));
3643 MulOps.push_back(getSCEV(U->getOperand(0)));
3644 return getMulExpr(MulOps);
3646 case Instruction::UDiv:
3647 return getUDivExpr(getSCEV(U->getOperand(0)),
3648 getSCEV(U->getOperand(1)));
3649 case Instruction::Sub:
3650 return getMinusSCEV(getSCEV(U->getOperand(0)),
3651 getSCEV(U->getOperand(1)));
3652 case Instruction::And:
3653 // For an expression like x&255 that merely masks off the high bits,
3654 // use zext(trunc(x)) as the SCEV expression.
3655 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3656 if (CI->isNullValue())
3657 return getSCEV(U->getOperand(1));
3658 if (CI->isAllOnesValue())
3659 return getSCEV(U->getOperand(0));
3660 const APInt &A = CI->getValue();
3662 // Instcombine's ShrinkDemandedConstant may strip bits out of
3663 // constants, obscuring what would otherwise be a low-bits mask.
3664 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3665 // knew about to reconstruct a low-bits mask value.
3666 unsigned LZ = A.countLeadingZeros();
3667 unsigned BitWidth = A.getBitWidth();
3668 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
3669 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3670 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
3672 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3674 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3676 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3677 IntegerType::get(getContext(), BitWidth - LZ)),
3682 case Instruction::Or:
3683 // If the RHS of the Or is a constant, we may have something like:
3684 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3685 // optimizations will transparently handle this case.
3687 // In order for this transformation to be safe, the LHS must be of the
3688 // form X*(2^n) and the Or constant must be less than 2^n.
3689 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3690 const SCEV *LHS = getSCEV(U->getOperand(0));
3691 const APInt &CIVal = CI->getValue();
3692 if (GetMinTrailingZeros(LHS) >=
3693 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3694 // Build a plain add SCEV.
3695 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3696 // If the LHS of the add was an addrec and it has no-wrap flags,
3697 // transfer the no-wrap flags, since an or won't introduce a wrap.
3698 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3699 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3700 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
3701 OldAR->getNoWrapFlags());
3707 case Instruction::Xor:
3708 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3709 // If the RHS of the xor is a signbit, then this is just an add.
3710 // Instcombine turns add of signbit into xor as a strength reduction step.
3711 if (CI->getValue().isSignBit())
3712 return getAddExpr(getSCEV(U->getOperand(0)),
3713 getSCEV(U->getOperand(1)));
3715 // If the RHS of xor is -1, then this is a not operation.
3716 if (CI->isAllOnesValue())
3717 return getNotSCEV(getSCEV(U->getOperand(0)));
3719 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3720 // This is a variant of the check for xor with -1, and it handles
3721 // the case where instcombine has trimmed non-demanded bits out
3722 // of an xor with -1.
3723 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3724 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3725 if (BO->getOpcode() == Instruction::And &&
3726 LCI->getValue() == CI->getValue())
3727 if (const SCEVZeroExtendExpr *Z =
3728 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3729 Type *UTy = U->getType();
3730 const SCEV *Z0 = Z->getOperand();
3731 Type *Z0Ty = Z0->getType();
3732 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3734 // If C is a low-bits mask, the zero extend is serving to
3735 // mask off the high bits. Complement the operand and
3736 // re-apply the zext.
3737 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3738 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3740 // If C is a single bit, it may be in the sign-bit position
3741 // before the zero-extend. In this case, represent the xor
3742 // using an add, which is equivalent, and re-apply the zext.
3743 APInt Trunc = CI->getValue().trunc(Z0TySize);
3744 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3746 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3752 case Instruction::Shl:
3753 // Turn shift left of a constant amount into a multiply.
3754 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3755 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3757 // If the shift count is not less than the bitwidth, the result of
3758 // the shift is undefined. Don't try to analyze it, because the
3759 // resolution chosen here may differ from the resolution chosen in
3760 // other parts of the compiler.
3761 if (SA->getValue().uge(BitWidth))
3764 Constant *X = ConstantInt::get(getContext(),
3765 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3766 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3770 case Instruction::LShr:
3771 // Turn logical shift right of a constant into a unsigned divide.
3772 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3773 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3775 // If the shift count is not less than the bitwidth, the result of
3776 // the shift is undefined. Don't try to analyze it, because the
3777 // resolution chosen here may differ from the resolution chosen in
3778 // other parts of the compiler.
3779 if (SA->getValue().uge(BitWidth))
3782 Constant *X = ConstantInt::get(getContext(),
3783 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3784 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3788 case Instruction::AShr:
3789 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3790 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3791 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3792 if (L->getOpcode() == Instruction::Shl &&
3793 L->getOperand(1) == U->getOperand(1)) {
3794 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3796 // If the shift count is not less than the bitwidth, the result of
3797 // the shift is undefined. Don't try to analyze it, because the
3798 // resolution chosen here may differ from the resolution chosen in
3799 // other parts of the compiler.
3800 if (CI->getValue().uge(BitWidth))
3803 uint64_t Amt = BitWidth - CI->getZExtValue();
3804 if (Amt == BitWidth)
3805 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3807 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3808 IntegerType::get(getContext(),
3814 case Instruction::Trunc:
3815 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3817 case Instruction::ZExt:
3818 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3820 case Instruction::SExt:
3821 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3823 case Instruction::BitCast:
3824 // BitCasts are no-op casts so we just eliminate the cast.
3825 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3826 return getSCEV(U->getOperand(0));
3829 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3830 // lead to pointer expressions which cannot safely be expanded to GEPs,
3831 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3832 // simplifying integer expressions.
3834 case Instruction::GetElementPtr:
3835 return createNodeForGEP(cast<GEPOperator>(U));
3837 case Instruction::PHI:
3838 return createNodeForPHI(cast<PHINode>(U));
3840 case Instruction::Select:
3841 // This could be a smax or umax that was lowered earlier.
3842 // Try to recover it.
3843 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3844 Value *LHS = ICI->getOperand(0);
3845 Value *RHS = ICI->getOperand(1);
3846 switch (ICI->getPredicate()) {
3847 case ICmpInst::ICMP_SLT:
3848 case ICmpInst::ICMP_SLE:
3849 std::swap(LHS, RHS);
3851 case ICmpInst::ICMP_SGT:
3852 case ICmpInst::ICMP_SGE:
3853 // a >s b ? a+x : b+x -> smax(a, b)+x
3854 // a >s b ? b+x : a+x -> smin(a, b)+x
3855 if (LHS->getType() == U->getType()) {
3856 const SCEV *LS = getSCEV(LHS);
3857 const SCEV *RS = getSCEV(RHS);
3858 const SCEV *LA = getSCEV(U->getOperand(1));
3859 const SCEV *RA = getSCEV(U->getOperand(2));
3860 const SCEV *LDiff = getMinusSCEV(LA, LS);
3861 const SCEV *RDiff = getMinusSCEV(RA, RS);
3863 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3864 LDiff = getMinusSCEV(LA, RS);
3865 RDiff = getMinusSCEV(RA, LS);
3867 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3870 case ICmpInst::ICMP_ULT:
3871 case ICmpInst::ICMP_ULE:
3872 std::swap(LHS, RHS);
3874 case ICmpInst::ICMP_UGT:
3875 case ICmpInst::ICMP_UGE:
3876 // a >u b ? a+x : b+x -> umax(a, b)+x
3877 // a >u b ? b+x : a+x -> umin(a, b)+x
3878 if (LHS->getType() == U->getType()) {
3879 const SCEV *LS = getSCEV(LHS);
3880 const SCEV *RS = getSCEV(RHS);
3881 const SCEV *LA = getSCEV(U->getOperand(1));
3882 const SCEV *RA = getSCEV(U->getOperand(2));
3883 const SCEV *LDiff = getMinusSCEV(LA, LS);
3884 const SCEV *RDiff = getMinusSCEV(RA, RS);
3886 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3887 LDiff = getMinusSCEV(LA, RS);
3888 RDiff = getMinusSCEV(RA, LS);
3890 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3893 case ICmpInst::ICMP_NE:
3894 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3895 if (LHS->getType() == U->getType() &&
3896 isa<ConstantInt>(RHS) &&
3897 cast<ConstantInt>(RHS)->isZero()) {
3898 const SCEV *One = getConstant(LHS->getType(), 1);
3899 const SCEV *LS = getSCEV(LHS);
3900 const SCEV *LA = getSCEV(U->getOperand(1));
3901 const SCEV *RA = getSCEV(U->getOperand(2));
3902 const SCEV *LDiff = getMinusSCEV(LA, LS);
3903 const SCEV *RDiff = getMinusSCEV(RA, One);
3905 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3908 case ICmpInst::ICMP_EQ:
3909 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3910 if (LHS->getType() == U->getType() &&
3911 isa<ConstantInt>(RHS) &&
3912 cast<ConstantInt>(RHS)->isZero()) {
3913 const SCEV *One = getConstant(LHS->getType(), 1);
3914 const SCEV *LS = getSCEV(LHS);
3915 const SCEV *LA = getSCEV(U->getOperand(1));
3916 const SCEV *RA = getSCEV(U->getOperand(2));
3917 const SCEV *LDiff = getMinusSCEV(LA, One);
3918 const SCEV *RDiff = getMinusSCEV(RA, LS);
3920 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3928 default: // We cannot analyze this expression.
3932 return getUnknown(V);
3937 //===----------------------------------------------------------------------===//
3938 // Iteration Count Computation Code
3941 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
3942 /// normal unsigned value. Returns 0 if the trip count is unknown or not
3943 /// constant. Will also return 0 if the maximum trip count is very large (>=
3946 /// This "trip count" assumes that control exits via ExitingBlock. More
3947 /// precisely, it is the number of times that control may reach ExitingBlock
3948 /// before taking the branch. For loops with multiple exits, it may not be the
3949 /// number times that the loop header executes because the loop may exit
3950 /// prematurely via another branch.
3951 unsigned ScalarEvolution::
3952 getSmallConstantTripCount(Loop *L, BasicBlock *ExitingBlock) {
3953 const SCEVConstant *ExitCount =
3954 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
3958 ConstantInt *ExitConst = ExitCount->getValue();
3960 // Guard against huge trip counts.
3961 if (ExitConst->getValue().getActiveBits() > 32)
3964 // In case of integer overflow, this returns 0, which is correct.
3965 return ((unsigned)ExitConst->getZExtValue()) + 1;
3968 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
3969 /// trip count of this loop as a normal unsigned value, if possible. This
3970 /// means that the actual trip count is always a multiple of the returned
3971 /// value (don't forget the trip count could very well be zero as well!).
3973 /// Returns 1 if the trip count is unknown or not guaranteed to be the
3974 /// multiple of a constant (which is also the case if the trip count is simply
3975 /// constant, use getSmallConstantTripCount for that case), Will also return 1
3976 /// if the trip count is very large (>= 2^32).
3978 /// As explained in the comments for getSmallConstantTripCount, this assumes
3979 /// that control exits the loop via ExitingBlock.
3980 unsigned ScalarEvolution::
3981 getSmallConstantTripMultiple(Loop *L, BasicBlock *ExitingBlock) {
3982 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
3983 if (ExitCount == getCouldNotCompute())
3986 // Get the trip count from the BE count by adding 1.
3987 const SCEV *TCMul = getAddExpr(ExitCount,
3988 getConstant(ExitCount->getType(), 1));
3989 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
3990 // to factor simple cases.
3991 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
3992 TCMul = Mul->getOperand(0);
3994 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
3998 ConstantInt *Result = MulC->getValue();
4000 // Guard against huge trip counts.
4001 if (!Result || Result->getValue().getActiveBits() > 32)
4004 return (unsigned)Result->getZExtValue();
4007 // getExitCount - Get the expression for the number of loop iterations for which
4008 // this loop is guaranteed not to exit via ExitintBlock. Otherwise return
4009 // SCEVCouldNotCompute.
4010 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4011 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4014 /// getBackedgeTakenCount - If the specified loop has a predictable
4015 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4016 /// object. The backedge-taken count is the number of times the loop header
4017 /// will be branched to from within the loop. This is one less than the
4018 /// trip count of the loop, since it doesn't count the first iteration,
4019 /// when the header is branched to from outside the loop.
4021 /// Note that it is not valid to call this method on a loop without a
4022 /// loop-invariant backedge-taken count (see
4023 /// hasLoopInvariantBackedgeTakenCount).
4025 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4026 return getBackedgeTakenInfo(L).getExact(this);
4029 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4030 /// return the least SCEV value that is known never to be less than the
4031 /// actual backedge taken count.
4032 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4033 return getBackedgeTakenInfo(L).getMax(this);
4036 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4037 /// onto the given Worklist.
4039 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4040 BasicBlock *Header = L->getHeader();
4042 // Push all Loop-header PHIs onto the Worklist stack.
4043 for (BasicBlock::iterator I = Header->begin();
4044 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4045 Worklist.push_back(PN);
4048 const ScalarEvolution::BackedgeTakenInfo &
4049 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4050 // Initially insert an invalid entry for this loop. If the insertion
4051 // succeeds, proceed to actually compute a backedge-taken count and
4052 // update the value. The temporary CouldNotCompute value tells SCEV
4053 // code elsewhere that it shouldn't attempt to request a new
4054 // backedge-taken count, which could result in infinite recursion.
4055 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4056 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4058 return Pair.first->second;
4060 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4061 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4062 // must be cleared in this scope.
4063 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4065 if (Result.getExact(this) != getCouldNotCompute()) {
4066 assert(isLoopInvariant(Result.getExact(this), L) &&
4067 isLoopInvariant(Result.getMax(this), L) &&
4068 "Computed backedge-taken count isn't loop invariant for loop!");
4069 ++NumTripCountsComputed;
4071 else if (Result.getMax(this) == getCouldNotCompute() &&
4072 isa<PHINode>(L->getHeader()->begin())) {
4073 // Only count loops that have phi nodes as not being computable.
4074 ++NumTripCountsNotComputed;
4077 // Now that we know more about the trip count for this loop, forget any
4078 // existing SCEV values for PHI nodes in this loop since they are only
4079 // conservative estimates made without the benefit of trip count
4080 // information. This is similar to the code in forgetLoop, except that
4081 // it handles SCEVUnknown PHI nodes specially.
4082 if (Result.hasAnyInfo()) {
4083 SmallVector<Instruction *, 16> Worklist;
4084 PushLoopPHIs(L, Worklist);
4086 SmallPtrSet<Instruction *, 8> Visited;
4087 while (!Worklist.empty()) {
4088 Instruction *I = Worklist.pop_back_val();
4089 if (!Visited.insert(I)) continue;
4091 ValueExprMapType::iterator It =
4092 ValueExprMap.find(static_cast<Value *>(I));
4093 if (It != ValueExprMap.end()) {
4094 const SCEV *Old = It->second;
4096 // SCEVUnknown for a PHI either means that it has an unrecognized
4097 // structure, or it's a PHI that's in the progress of being computed
4098 // by createNodeForPHI. In the former case, additional loop trip
4099 // count information isn't going to change anything. In the later
4100 // case, createNodeForPHI will perform the necessary updates on its
4101 // own when it gets to that point.
4102 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4103 forgetMemoizedResults(Old);
4104 ValueExprMap.erase(It);
4106 if (PHINode *PN = dyn_cast<PHINode>(I))
4107 ConstantEvolutionLoopExitValue.erase(PN);
4110 PushDefUseChildren(I, Worklist);
4114 // Re-lookup the insert position, since the call to
4115 // ComputeBackedgeTakenCount above could result in a
4116 // recusive call to getBackedgeTakenInfo (on a different
4117 // loop), which would invalidate the iterator computed
4119 return BackedgeTakenCounts.find(L)->second = Result;
4122 /// forgetLoop - This method should be called by the client when it has
4123 /// changed a loop in a way that may effect ScalarEvolution's ability to
4124 /// compute a trip count, or if the loop is deleted.
4125 void ScalarEvolution::forgetLoop(const Loop *L) {
4126 // Drop any stored trip count value.
4127 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4128 BackedgeTakenCounts.find(L);
4129 if (BTCPos != BackedgeTakenCounts.end()) {
4130 BTCPos->second.clear();
4131 BackedgeTakenCounts.erase(BTCPos);
4134 // Drop information about expressions based on loop-header PHIs.
4135 SmallVector<Instruction *, 16> Worklist;
4136 PushLoopPHIs(L, Worklist);
4138 SmallPtrSet<Instruction *, 8> Visited;
4139 while (!Worklist.empty()) {
4140 Instruction *I = Worklist.pop_back_val();
4141 if (!Visited.insert(I)) continue;
4143 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
4144 if (It != ValueExprMap.end()) {
4145 forgetMemoizedResults(It->second);
4146 ValueExprMap.erase(It);
4147 if (PHINode *PN = dyn_cast<PHINode>(I))
4148 ConstantEvolutionLoopExitValue.erase(PN);
4151 PushDefUseChildren(I, Worklist);
4154 // Forget all contained loops too, to avoid dangling entries in the
4155 // ValuesAtScopes map.
4156 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4160 /// forgetValue - This method should be called by the client when it has
4161 /// changed a value in a way that may effect its value, or which may
4162 /// disconnect it from a def-use chain linking it to a loop.
4163 void ScalarEvolution::forgetValue(Value *V) {
4164 Instruction *I = dyn_cast<Instruction>(V);
4167 // Drop information about expressions based on loop-header PHIs.
4168 SmallVector<Instruction *, 16> Worklist;
4169 Worklist.push_back(I);
4171 SmallPtrSet<Instruction *, 8> Visited;
4172 while (!Worklist.empty()) {
4173 I = Worklist.pop_back_val();
4174 if (!Visited.insert(I)) continue;
4176 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
4177 if (It != ValueExprMap.end()) {
4178 forgetMemoizedResults(It->second);
4179 ValueExprMap.erase(It);
4180 if (PHINode *PN = dyn_cast<PHINode>(I))
4181 ConstantEvolutionLoopExitValue.erase(PN);
4184 PushDefUseChildren(I, Worklist);
4188 /// getExact - Get the exact loop backedge taken count considering all loop
4189 /// exits. A computable result can only be return for loops with a single exit.
4190 /// Returning the minimum taken count among all exits is incorrect because one
4191 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4192 /// the limit of each loop test is never skipped. This is a valid assumption as
4193 /// long as the loop exits via that test. For precise results, it is the
4194 /// caller's responsibility to specify the relevant loop exit using
4195 /// getExact(ExitingBlock, SE).
4197 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4198 // If any exits were not computable, the loop is not computable.
4199 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4201 // We need exactly one computable exit.
4202 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4203 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4205 const SCEV *BECount = 0;
4206 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4207 ENT != 0; ENT = ENT->getNextExit()) {
4209 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4212 BECount = ENT->ExactNotTaken;
4213 else if (BECount != ENT->ExactNotTaken)
4214 return SE->getCouldNotCompute();
4216 assert(BECount && "Invalid not taken count for loop exit");
4220 /// getExact - Get the exact not taken count for this loop exit.
4222 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4223 ScalarEvolution *SE) const {
4224 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4225 ENT != 0; ENT = ENT->getNextExit()) {
4227 if (ENT->ExitingBlock == ExitingBlock)
4228 return ENT->ExactNotTaken;
4230 return SE->getCouldNotCompute();
4233 /// getMax - Get the max backedge taken count for the loop.
4235 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4236 return Max ? Max : SE->getCouldNotCompute();
4239 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4240 /// computable exit into a persistent ExitNotTakenInfo array.
4241 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4242 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4243 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4246 ExitNotTaken.setIncomplete();
4248 unsigned NumExits = ExitCounts.size();
4249 if (NumExits == 0) return;
4251 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4252 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4253 if (NumExits == 1) return;
4255 // Handle the rare case of multiple computable exits.
4256 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4258 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4259 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4260 PrevENT->setNextExit(ENT);
4261 ENT->ExitingBlock = ExitCounts[i].first;
4262 ENT->ExactNotTaken = ExitCounts[i].second;
4266 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4267 void ScalarEvolution::BackedgeTakenInfo::clear() {
4268 ExitNotTaken.ExitingBlock = 0;
4269 ExitNotTaken.ExactNotTaken = 0;
4270 delete[] ExitNotTaken.getNextExit();
4273 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4274 /// of the specified loop will execute.
4275 ScalarEvolution::BackedgeTakenInfo
4276 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4277 SmallVector<BasicBlock *, 8> ExitingBlocks;
4278 L->getExitingBlocks(ExitingBlocks);
4280 // Examine all exits and pick the most conservative values.
4281 const SCEV *MaxBECount = getCouldNotCompute();
4282 bool CouldComputeBECount = true;
4283 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4284 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4285 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]);
4286 if (EL.Exact == getCouldNotCompute())
4287 // We couldn't compute an exact value for this exit, so
4288 // we won't be able to compute an exact value for the loop.
4289 CouldComputeBECount = false;
4291 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact));
4293 if (MaxBECount == getCouldNotCompute())
4294 MaxBECount = EL.Max;
4295 else if (EL.Max != getCouldNotCompute()) {
4296 // We cannot take the "min" MaxBECount, because non-unit stride loops may
4297 // skip some loop tests. Taking the max over the exits is sufficiently
4298 // conservative. TODO: We could do better taking into consideration
4299 // that (1) the loop has unit stride (2) the last loop test is
4300 // less-than/greater-than (3) any loop test is less-than/greater-than AND
4301 // falls-through some constant times less then the other tests.
4302 MaxBECount = getUMaxFromMismatchedTypes(MaxBECount, EL.Max);
4306 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4309 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4310 /// loop will execute if it exits via the specified block.
4311 ScalarEvolution::ExitLimit
4312 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4314 // Okay, we've chosen an exiting block. See what condition causes us to
4315 // exit at this block.
4317 // FIXME: we should be able to handle switch instructions (with a single exit)
4318 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
4319 if (ExitBr == 0) return getCouldNotCompute();
4320 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
4322 // At this point, we know we have a conditional branch that determines whether
4323 // the loop is exited. However, we don't know if the branch is executed each
4324 // time through the loop. If not, then the execution count of the branch will
4325 // not be equal to the trip count of the loop.
4327 // Currently we check for this by checking to see if the Exit branch goes to
4328 // the loop header. If so, we know it will always execute the same number of
4329 // times as the loop. We also handle the case where the exit block *is* the
4330 // loop header. This is common for un-rotated loops.
4332 // If both of those tests fail, walk up the unique predecessor chain to the
4333 // header, stopping if there is an edge that doesn't exit the loop. If the
4334 // header is reached, the execution count of the branch will be equal to the
4335 // trip count of the loop.
4337 // More extensive analysis could be done to handle more cases here.
4339 if (ExitBr->getSuccessor(0) != L->getHeader() &&
4340 ExitBr->getSuccessor(1) != L->getHeader() &&
4341 ExitBr->getParent() != L->getHeader()) {
4342 // The simple checks failed, try climbing the unique predecessor chain
4343 // up to the header.
4345 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
4346 BasicBlock *Pred = BB->getUniquePredecessor();
4348 return getCouldNotCompute();
4349 TerminatorInst *PredTerm = Pred->getTerminator();
4350 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4351 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4354 // If the predecessor has a successor that isn't BB and isn't
4355 // outside the loop, assume the worst.
4356 if (L->contains(PredSucc))
4357 return getCouldNotCompute();
4359 if (Pred == L->getHeader()) {
4366 return getCouldNotCompute();
4369 // Proceed to the next level to examine the exit condition expression.
4370 return ComputeExitLimitFromCond(L, ExitBr->getCondition(),
4371 ExitBr->getSuccessor(0),
4372 ExitBr->getSuccessor(1));
4375 /// ComputeExitLimitFromCond - Compute the number of times the
4376 /// backedge of the specified loop will execute if its exit condition
4377 /// were a conditional branch of ExitCond, TBB, and FBB.
4378 ScalarEvolution::ExitLimit
4379 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4383 // Check if the controlling expression for this loop is an And or Or.
4384 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4385 if (BO->getOpcode() == Instruction::And) {
4386 // Recurse on the operands of the and.
4387 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB);
4388 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB);
4389 const SCEV *BECount = getCouldNotCompute();
4390 const SCEV *MaxBECount = getCouldNotCompute();
4391 if (L->contains(TBB)) {
4392 // Both conditions must be true for the loop to continue executing.
4393 // Choose the less conservative count.
4394 if (EL0.Exact == getCouldNotCompute() ||
4395 EL1.Exact == getCouldNotCompute())
4396 BECount = getCouldNotCompute();
4398 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4399 if (EL0.Max == getCouldNotCompute())
4400 MaxBECount = EL1.Max;
4401 else if (EL1.Max == getCouldNotCompute())
4402 MaxBECount = EL0.Max;
4404 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4406 // Both conditions must be true at the same time for the loop to exit.
4407 // For now, be conservative.
4408 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4409 if (EL0.Max == EL1.Max)
4410 MaxBECount = EL0.Max;
4411 if (EL0.Exact == EL1.Exact)
4412 BECount = EL0.Exact;
4415 return ExitLimit(BECount, MaxBECount);
4417 if (BO->getOpcode() == Instruction::Or) {
4418 // Recurse on the operands of the or.
4419 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB);
4420 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB);
4421 const SCEV *BECount = getCouldNotCompute();
4422 const SCEV *MaxBECount = getCouldNotCompute();
4423 if (L->contains(FBB)) {
4424 // Both conditions must be false for the loop to continue executing.
4425 // Choose the less conservative count.
4426 if (EL0.Exact == getCouldNotCompute() ||
4427 EL1.Exact == getCouldNotCompute())
4428 BECount = getCouldNotCompute();
4430 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4431 if (EL0.Max == getCouldNotCompute())
4432 MaxBECount = EL1.Max;
4433 else if (EL1.Max == getCouldNotCompute())
4434 MaxBECount = EL0.Max;
4436 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4438 // Both conditions must be false at the same time for the loop to exit.
4439 // For now, be conservative.
4440 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4441 if (EL0.Max == EL1.Max)
4442 MaxBECount = EL0.Max;
4443 if (EL0.Exact == EL1.Exact)
4444 BECount = EL0.Exact;
4447 return ExitLimit(BECount, MaxBECount);
4451 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4452 // Proceed to the next level to examine the icmp.
4453 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4454 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB);
4456 // Check for a constant condition. These are normally stripped out by
4457 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4458 // preserve the CFG and is temporarily leaving constant conditions
4460 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4461 if (L->contains(FBB) == !CI->getZExtValue())
4462 // The backedge is always taken.
4463 return getCouldNotCompute();
4465 // The backedge is never taken.
4466 return getConstant(CI->getType(), 0);
4469 // If it's not an integer or pointer comparison then compute it the hard way.
4470 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4473 /// ComputeExitLimitFromICmp - Compute the number of times the
4474 /// backedge of the specified loop will execute if its exit condition
4475 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4476 ScalarEvolution::ExitLimit
4477 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
4482 // If the condition was exit on true, convert the condition to exit on false
4483 ICmpInst::Predicate Cond;
4484 if (!L->contains(FBB))
4485 Cond = ExitCond->getPredicate();
4487 Cond = ExitCond->getInversePredicate();
4489 // Handle common loops like: for (X = "string"; *X; ++X)
4490 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4491 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4493 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
4494 if (ItCnt.hasAnyInfo())
4498 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4499 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4501 // Try to evaluate any dependencies out of the loop.
4502 LHS = getSCEVAtScope(LHS, L);
4503 RHS = getSCEVAtScope(RHS, L);
4505 // At this point, we would like to compute how many iterations of the
4506 // loop the predicate will return true for these inputs.
4507 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4508 // If there is a loop-invariant, force it into the RHS.
4509 std::swap(LHS, RHS);
4510 Cond = ICmpInst::getSwappedPredicate(Cond);
4513 // Simplify the operands before analyzing them.
4514 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4516 // If we have a comparison of a chrec against a constant, try to use value
4517 // ranges to answer this query.
4518 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4519 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4520 if (AddRec->getLoop() == L) {
4521 // Form the constant range.
4522 ConstantRange CompRange(
4523 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4525 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4526 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4530 case ICmpInst::ICMP_NE: { // while (X != Y)
4531 // Convert to: while (X-Y != 0)
4532 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L);
4533 if (EL.hasAnyInfo()) return EL;
4536 case ICmpInst::ICMP_EQ: { // while (X == Y)
4537 // Convert to: while (X-Y == 0)
4538 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4539 if (EL.hasAnyInfo()) return EL;
4542 case ICmpInst::ICMP_SLT: {
4543 ExitLimit EL = HowManyLessThans(LHS, RHS, L, true);
4544 if (EL.hasAnyInfo()) return EL;
4547 case ICmpInst::ICMP_SGT: {
4548 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4549 getNotSCEV(RHS), L, true);
4550 if (EL.hasAnyInfo()) return EL;
4553 case ICmpInst::ICMP_ULT: {
4554 ExitLimit EL = HowManyLessThans(LHS, RHS, L, false);
4555 if (EL.hasAnyInfo()) return EL;
4558 case ICmpInst::ICMP_UGT: {
4559 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4560 getNotSCEV(RHS), L, false);
4561 if (EL.hasAnyInfo()) return EL;
4566 dbgs() << "ComputeBackedgeTakenCount ";
4567 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4568 dbgs() << "[unsigned] ";
4569 dbgs() << *LHS << " "
4570 << Instruction::getOpcodeName(Instruction::ICmp)
4571 << " " << *RHS << "\n";
4575 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4578 static ConstantInt *
4579 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4580 ScalarEvolution &SE) {
4581 const SCEV *InVal = SE.getConstant(C);
4582 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4583 assert(isa<SCEVConstant>(Val) &&
4584 "Evaluation of SCEV at constant didn't fold correctly?");
4585 return cast<SCEVConstant>(Val)->getValue();
4588 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
4589 /// and a GEP expression (missing the pointer index) indexing into it, return
4590 /// the addressed element of the initializer or null if the index expression is
4593 GetAddressedElementFromGlobal(GlobalVariable *GV,
4594 const std::vector<ConstantInt*> &Indices) {
4595 Constant *Init = GV->getInitializer();
4596 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
4597 uint64_t Idx = Indices[i]->getZExtValue();
4598 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
4599 assert(Idx < CS->getNumOperands() && "Bad struct index!");
4600 Init = cast<Constant>(CS->getOperand(Idx));
4601 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
4602 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
4603 Init = cast<Constant>(CA->getOperand(Idx));
4604 } else if (isa<ConstantAggregateZero>(Init)) {
4605 if (StructType *STy = dyn_cast<StructType>(Init->getType())) {
4606 assert(Idx < STy->getNumElements() && "Bad struct index!");
4607 Init = Constant::getNullValue(STy->getElementType(Idx));
4608 } else if (ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
4609 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
4610 Init = Constant::getNullValue(ATy->getElementType());
4612 llvm_unreachable("Unknown constant aggregate type!");
4615 return 0; // Unknown initializer type
4621 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
4622 /// 'icmp op load X, cst', try to see if we can compute the backedge
4623 /// execution count.
4624 ScalarEvolution::ExitLimit
4625 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
4629 ICmpInst::Predicate predicate) {
4631 if (LI->isVolatile()) return getCouldNotCompute();
4633 // Check to see if the loaded pointer is a getelementptr of a global.
4634 // TODO: Use SCEV instead of manually grubbing with GEPs.
4635 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4636 if (!GEP) return getCouldNotCompute();
4638 // Make sure that it is really a constant global we are gepping, with an
4639 // initializer, and make sure the first IDX is really 0.
4640 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4641 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4642 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4643 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4644 return getCouldNotCompute();
4646 // Okay, we allow one non-constant index into the GEP instruction.
4648 std::vector<ConstantInt*> Indexes;
4649 unsigned VarIdxNum = 0;
4650 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4651 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4652 Indexes.push_back(CI);
4653 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4654 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4655 VarIdx = GEP->getOperand(i);
4657 Indexes.push_back(0);
4660 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4661 // Check to see if X is a loop variant variable value now.
4662 const SCEV *Idx = getSCEV(VarIdx);
4663 Idx = getSCEVAtScope(Idx, L);
4665 // We can only recognize very limited forms of loop index expressions, in
4666 // particular, only affine AddRec's like {C1,+,C2}.
4667 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4668 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4669 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4670 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4671 return getCouldNotCompute();
4673 unsigned MaxSteps = MaxBruteForceIterations;
4674 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4675 ConstantInt *ItCst = ConstantInt::get(
4676 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4677 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4679 // Form the GEP offset.
4680 Indexes[VarIdxNum] = Val;
4682 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
4683 if (Result == 0) break; // Cannot compute!
4685 // Evaluate the condition for this iteration.
4686 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4687 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4688 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4690 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4691 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4694 ++NumArrayLenItCounts;
4695 return getConstant(ItCst); // Found terminating iteration!
4698 return getCouldNotCompute();
4702 /// CanConstantFold - Return true if we can constant fold an instruction of the
4703 /// specified type, assuming that all operands were constants.
4704 static bool CanConstantFold(const Instruction *I) {
4705 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4706 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
4710 if (const CallInst *CI = dyn_cast<CallInst>(I))
4711 if (const Function *F = CI->getCalledFunction())
4712 return canConstantFoldCallTo(F);
4716 /// Determine whether this instruction can constant evolve within this loop
4717 /// assuming its operands can all constant evolve.
4718 static bool canConstantEvolve(Instruction *I, const Loop *L) {
4719 // An instruction outside of the loop can't be derived from a loop PHI.
4720 if (!L->contains(I)) return false;
4722 if (isa<PHINode>(I)) {
4723 if (L->getHeader() == I->getParent())
4726 // We don't currently keep track of the control flow needed to evaluate
4727 // PHIs, so we cannot handle PHIs inside of loops.
4731 // If we won't be able to constant fold this expression even if the operands
4732 // are constants, bail early.
4733 return CanConstantFold(I);
4736 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
4737 /// recursing through each instruction operand until reaching a loop header phi.
4739 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
4740 DenseMap<Instruction *, PHINode *> &PHIMap) {
4742 // Otherwise, we can evaluate this instruction if all of its operands are
4743 // constant or derived from a PHI node themselves.
4745 for (Instruction::op_iterator OpI = UseInst->op_begin(),
4746 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
4748 if (isa<Constant>(*OpI)) continue;
4750 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
4751 if (!OpInst || !canConstantEvolve(OpInst, L)) return 0;
4753 PHINode *P = dyn_cast<PHINode>(OpInst);
4755 // If this operand is already visited, reuse the prior result.
4756 // We may have P != PHI if this is the deepest point at which the
4757 // inconsistent paths meet.
4758 P = PHIMap.lookup(OpInst);
4760 // Recurse and memoize the results, whether a phi is found or not.
4761 // This recursive call invalidates pointers into PHIMap.
4762 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
4765 if (P == 0) return 0; // Not evolving from PHI
4766 if (PHI && PHI != P) return 0; // Evolving from multiple different PHIs.
4769 // This is a expression evolving from a constant PHI!
4773 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4774 /// in the loop that V is derived from. We allow arbitrary operations along the
4775 /// way, but the operands of an operation must either be constants or a value
4776 /// derived from a constant PHI. If this expression does not fit with these
4777 /// constraints, return null.
4778 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4779 Instruction *I = dyn_cast<Instruction>(V);
4780 if (I == 0 || !canConstantEvolve(I, L)) return 0;
4782 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4786 // Record non-constant instructions contained by the loop.
4787 DenseMap<Instruction *, PHINode *> PHIMap;
4788 return getConstantEvolvingPHIOperands(I, L, PHIMap);
4791 /// EvaluateExpression - Given an expression that passes the
4792 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4793 /// in the loop has the value PHIVal. If we can't fold this expression for some
4794 /// reason, return null.
4795 static Constant *EvaluateExpression(Value *V, const Loop *L,
4796 DenseMap<Instruction *, Constant *> &Vals,
4797 const TargetData *TD,
4798 const TargetLibraryInfo *TLI) {
4799 // Convenient constant check, but redundant for recursive calls.
4800 if (Constant *C = dyn_cast<Constant>(V)) return C;
4801 Instruction *I = dyn_cast<Instruction>(V);
4804 if (Constant *C = Vals.lookup(I)) return C;
4806 // An instruction inside the loop depends on a value outside the loop that we
4807 // weren't given a mapping for, or a value such as a call inside the loop.
4808 if (!canConstantEvolve(I, L)) return 0;
4810 // An unmapped PHI can be due to a branch or another loop inside this loop,
4811 // or due to this not being the initial iteration through a loop where we
4812 // couldn't compute the evolution of this particular PHI last time.
4813 if (isa<PHINode>(I)) return 0;
4815 std::vector<Constant*> Operands(I->getNumOperands());
4817 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4818 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
4820 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
4821 if (!Operands[i]) return 0;
4824 Constant *C = EvaluateExpression(Operand, L, Vals, TD, TLI);
4830 if (CmpInst *CI = dyn_cast<CmpInst>(I))
4831 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4832 Operands[1], TD, TLI);
4833 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
4834 if (!LI->isVolatile())
4835 return ConstantFoldLoadFromConstPtr(Operands[0], TD);
4837 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, TD,
4841 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4842 /// in the header of its containing loop, we know the loop executes a
4843 /// constant number of times, and the PHI node is just a recurrence
4844 /// involving constants, fold it.
4846 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4849 DenseMap<PHINode*, Constant*>::const_iterator I =
4850 ConstantEvolutionLoopExitValue.find(PN);
4851 if (I != ConstantEvolutionLoopExitValue.end())
4854 if (BEs.ugt(MaxBruteForceIterations))
4855 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4857 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4859 DenseMap<Instruction *, Constant *> CurrentIterVals;
4860 BasicBlock *Header = L->getHeader();
4861 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
4863 // Since the loop is canonicalized, the PHI node must have two entries. One
4864 // entry must be a constant (coming in from outside of the loop), and the
4865 // second must be derived from the same PHI.
4866 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4868 for (BasicBlock::iterator I = Header->begin();
4869 (PHI = dyn_cast<PHINode>(I)); ++I) {
4870 Constant *StartCST =
4871 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
4872 if (StartCST == 0) continue;
4873 CurrentIterVals[PHI] = StartCST;
4875 if (!CurrentIterVals.count(PN))
4878 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4880 // Execute the loop symbolically to determine the exit value.
4881 if (BEs.getActiveBits() >= 32)
4882 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4884 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4885 unsigned IterationNum = 0;
4886 for (; ; ++IterationNum) {
4887 if (IterationNum == NumIterations)
4888 return RetVal = CurrentIterVals[PN]; // Got exit value!
4890 // Compute the value of the PHIs for the next iteration.
4891 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
4892 DenseMap<Instruction *, Constant *> NextIterVals;
4893 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD,
4896 return 0; // Couldn't evaluate!
4897 NextIterVals[PN] = NextPHI;
4899 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
4901 // Also evaluate the other PHI nodes. However, we don't get to stop if we
4902 // cease to be able to evaluate one of them or if they stop evolving,
4903 // because that doesn't necessarily prevent us from computing PN.
4904 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
4905 for (DenseMap<Instruction *, Constant *>::const_iterator
4906 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
4907 PHINode *PHI = dyn_cast<PHINode>(I->first);
4908 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
4909 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
4911 // We use two distinct loops because EvaluateExpression may invalidate any
4912 // iterators into CurrentIterVals.
4913 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
4914 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
4915 PHINode *PHI = I->first;
4916 Constant *&NextPHI = NextIterVals[PHI];
4917 if (!NextPHI) { // Not already computed.
4918 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
4919 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
4921 if (NextPHI != I->second)
4922 StoppedEvolving = false;
4925 // If all entries in CurrentIterVals == NextIterVals then we can stop
4926 // iterating, the loop can't continue to change.
4927 if (StoppedEvolving)
4928 return RetVal = CurrentIterVals[PN];
4930 CurrentIterVals.swap(NextIterVals);
4934 /// ComputeExitCountExhaustively - If the loop is known to execute a
4935 /// constant number of times (the condition evolves only from constants),
4936 /// try to evaluate a few iterations of the loop until we get the exit
4937 /// condition gets a value of ExitWhen (true or false). If we cannot
4938 /// evaluate the trip count of the loop, return getCouldNotCompute().
4939 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
4942 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4943 if (PN == 0) return getCouldNotCompute();
4945 // If the loop is canonicalized, the PHI will have exactly two entries.
4946 // That's the only form we support here.
4947 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4949 DenseMap<Instruction *, Constant *> CurrentIterVals;
4950 BasicBlock *Header = L->getHeader();
4951 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
4953 // One entry must be a constant (coming in from outside of the loop), and the
4954 // second must be derived from the same PHI.
4955 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4957 for (BasicBlock::iterator I = Header->begin();
4958 (PHI = dyn_cast<PHINode>(I)); ++I) {
4959 Constant *StartCST =
4960 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
4961 if (StartCST == 0) continue;
4962 CurrentIterVals[PHI] = StartCST;
4964 if (!CurrentIterVals.count(PN))
4965 return getCouldNotCompute();
4967 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4968 // the loop symbolically to determine when the condition gets a value of
4971 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4972 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
4973 ConstantInt *CondVal =
4974 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
4977 // Couldn't symbolically evaluate.
4978 if (!CondVal) return getCouldNotCompute();
4980 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4981 ++NumBruteForceTripCountsComputed;
4982 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4985 // Update all the PHI nodes for the next iteration.
4986 DenseMap<Instruction *, Constant *> NextIterVals;
4988 // Create a list of which PHIs we need to compute. We want to do this before
4989 // calling EvaluateExpression on them because that may invalidate iterators
4990 // into CurrentIterVals.
4991 SmallVector<PHINode *, 8> PHIsToCompute;
4992 for (DenseMap<Instruction *, Constant *>::const_iterator
4993 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
4994 PHINode *PHI = dyn_cast<PHINode>(I->first);
4995 if (!PHI || PHI->getParent() != Header) continue;
4996 PHIsToCompute.push_back(PHI);
4998 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
4999 E = PHIsToCompute.end(); I != E; ++I) {
5001 Constant *&NextPHI = NextIterVals[PHI];
5002 if (NextPHI) continue; // Already computed!
5004 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5005 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
5007 CurrentIterVals.swap(NextIterVals);
5010 // Too many iterations were needed to evaluate.
5011 return getCouldNotCompute();
5014 /// getSCEVAtScope - Return a SCEV expression for the specified value
5015 /// at the specified scope in the program. The L value specifies a loop
5016 /// nest to evaluate the expression at, where null is the top-level or a
5017 /// specified loop is immediately inside of the loop.
5019 /// This method can be used to compute the exit value for a variable defined
5020 /// in a loop by querying what the value will hold in the parent loop.
5022 /// In the case that a relevant loop exit value cannot be computed, the
5023 /// original value V is returned.
5024 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5025 // Check to see if we've folded this expression at this loop before.
5026 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
5027 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
5028 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
5030 return Pair.first->second ? Pair.first->second : V;
5032 // Otherwise compute it.
5033 const SCEV *C = computeSCEVAtScope(V, L);
5034 ValuesAtScopes[V][L] = C;
5038 /// This builds up a Constant using the ConstantExpr interface. That way, we
5039 /// will return Constants for objects which aren't represented by a
5040 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5041 /// Returns NULL if the SCEV isn't representable as a Constant.
5042 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5043 switch (V->getSCEVType()) {
5044 default: // TODO: smax, umax.
5045 case scCouldNotCompute:
5049 return cast<SCEVConstant>(V)->getValue();
5051 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5052 case scSignExtend: {
5053 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5054 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5055 return ConstantExpr::getSExt(CastOp, SS->getType());
5058 case scZeroExtend: {
5059 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5060 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5061 return ConstantExpr::getZExt(CastOp, SZ->getType());
5065 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5066 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5067 return ConstantExpr::getTrunc(CastOp, ST->getType());
5071 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5072 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5073 if (C->getType()->isPointerTy())
5074 C = ConstantExpr::getBitCast(C, Type::getInt8PtrTy(C->getContext()));
5075 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5076 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5080 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5082 // The offsets have been converted to bytes. We can add bytes to an
5083 // i8* by GEP with the byte count in the first index.
5084 C = ConstantExpr::getBitCast(C,Type::getInt8PtrTy(C->getContext()));
5087 // Don't bother trying to sum two pointers. We probably can't
5088 // statically compute a load that results from it anyway.
5089 if (C2->getType()->isPointerTy())
5092 if (C->getType()->isPointerTy()) {
5093 if (cast<PointerType>(C->getType())->getElementType()->isStructTy())
5094 C2 = ConstantExpr::getIntegerCast(
5095 C2, Type::getInt32Ty(C->getContext()), true);
5096 C = ConstantExpr::getGetElementPtr(C, C2);
5098 C = ConstantExpr::getAdd(C, C2);
5105 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5106 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5107 // Don't bother with pointers at all.
5108 if (C->getType()->isPointerTy()) return 0;
5109 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5110 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5111 if (!C2 || C2->getType()->isPointerTy()) return 0;
5112 C = ConstantExpr::getMul(C, C2);
5119 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5120 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5121 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5122 if (LHS->getType() == RHS->getType())
5123 return ConstantExpr::getUDiv(LHS, RHS);
5130 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5131 if (isa<SCEVConstant>(V)) return V;
5133 // If this instruction is evolved from a constant-evolving PHI, compute the
5134 // exit value from the loop without using SCEVs.
5135 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5136 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5137 const Loop *LI = (*this->LI)[I->getParent()];
5138 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5139 if (PHINode *PN = dyn_cast<PHINode>(I))
5140 if (PN->getParent() == LI->getHeader()) {
5141 // Okay, there is no closed form solution for the PHI node. Check
5142 // to see if the loop that contains it has a known backedge-taken
5143 // count. If so, we may be able to force computation of the exit
5145 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5146 if (const SCEVConstant *BTCC =
5147 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5148 // Okay, we know how many times the containing loop executes. If
5149 // this is a constant evolving PHI node, get the final value at
5150 // the specified iteration number.
5151 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5152 BTCC->getValue()->getValue(),
5154 if (RV) return getSCEV(RV);
5158 // Okay, this is an expression that we cannot symbolically evaluate
5159 // into a SCEV. Check to see if it's possible to symbolically evaluate
5160 // the arguments into constants, and if so, try to constant propagate the
5161 // result. This is particularly useful for computing loop exit values.
5162 if (CanConstantFold(I)) {
5163 SmallVector<Constant *, 4> Operands;
5164 bool MadeImprovement = false;
5165 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5166 Value *Op = I->getOperand(i);
5167 if (Constant *C = dyn_cast<Constant>(Op)) {
5168 Operands.push_back(C);
5172 // If any of the operands is non-constant and if they are
5173 // non-integer and non-pointer, don't even try to analyze them
5174 // with scev techniques.
5175 if (!isSCEVable(Op->getType()))
5178 const SCEV *OrigV = getSCEV(Op);
5179 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5180 MadeImprovement |= OrigV != OpV;
5182 Constant *C = BuildConstantFromSCEV(OpV);
5184 if (C->getType() != Op->getType())
5185 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5189 Operands.push_back(C);
5192 // Check to see if getSCEVAtScope actually made an improvement.
5193 if (MadeImprovement) {
5195 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5196 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5197 Operands[0], Operands[1], TD,
5199 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5200 if (!LI->isVolatile())
5201 C = ConstantFoldLoadFromConstPtr(Operands[0], TD);
5203 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5211 // This is some other type of SCEVUnknown, just return it.
5215 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5216 // Avoid performing the look-up in the common case where the specified
5217 // expression has no loop-variant portions.
5218 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5219 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5220 if (OpAtScope != Comm->getOperand(i)) {
5221 // Okay, at least one of these operands is loop variant but might be
5222 // foldable. Build a new instance of the folded commutative expression.
5223 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5224 Comm->op_begin()+i);
5225 NewOps.push_back(OpAtScope);
5227 for (++i; i != e; ++i) {
5228 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5229 NewOps.push_back(OpAtScope);
5231 if (isa<SCEVAddExpr>(Comm))
5232 return getAddExpr(NewOps);
5233 if (isa<SCEVMulExpr>(Comm))
5234 return getMulExpr(NewOps);
5235 if (isa<SCEVSMaxExpr>(Comm))
5236 return getSMaxExpr(NewOps);
5237 if (isa<SCEVUMaxExpr>(Comm))
5238 return getUMaxExpr(NewOps);
5239 llvm_unreachable("Unknown commutative SCEV type!");
5242 // If we got here, all operands are loop invariant.
5246 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5247 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5248 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5249 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5250 return Div; // must be loop invariant
5251 return getUDivExpr(LHS, RHS);
5254 // If this is a loop recurrence for a loop that does not contain L, then we
5255 // are dealing with the final value computed by the loop.
5256 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5257 // First, attempt to evaluate each operand.
5258 // Avoid performing the look-up in the common case where the specified
5259 // expression has no loop-variant portions.
5260 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5261 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5262 if (OpAtScope == AddRec->getOperand(i))
5265 // Okay, at least one of these operands is loop variant but might be
5266 // foldable. Build a new instance of the folded commutative expression.
5267 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5268 AddRec->op_begin()+i);
5269 NewOps.push_back(OpAtScope);
5270 for (++i; i != e; ++i)
5271 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5273 const SCEV *FoldedRec =
5274 getAddRecExpr(NewOps, AddRec->getLoop(),
5275 AddRec->getNoWrapFlags(SCEV::FlagNW));
5276 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5277 // The addrec may be folded to a nonrecurrence, for example, if the
5278 // induction variable is multiplied by zero after constant folding. Go
5279 // ahead and return the folded value.
5285 // If the scope is outside the addrec's loop, evaluate it by using the
5286 // loop exit value of the addrec.
5287 if (!AddRec->getLoop()->contains(L)) {
5288 // To evaluate this recurrence, we need to know how many times the AddRec
5289 // loop iterates. Compute this now.
5290 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5291 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5293 // Then, evaluate the AddRec.
5294 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5300 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5301 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5302 if (Op == Cast->getOperand())
5303 return Cast; // must be loop invariant
5304 return getZeroExtendExpr(Op, Cast->getType());
5307 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5308 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5309 if (Op == Cast->getOperand())
5310 return Cast; // must be loop invariant
5311 return getSignExtendExpr(Op, Cast->getType());
5314 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5315 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5316 if (Op == Cast->getOperand())
5317 return Cast; // must be loop invariant
5318 return getTruncateExpr(Op, Cast->getType());
5321 llvm_unreachable("Unknown SCEV type!");
5325 /// getSCEVAtScope - This is a convenience function which does
5326 /// getSCEVAtScope(getSCEV(V), L).
5327 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5328 return getSCEVAtScope(getSCEV(V), L);
5331 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5332 /// following equation:
5334 /// A * X = B (mod N)
5336 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5337 /// A and B isn't important.
5339 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5340 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5341 ScalarEvolution &SE) {
5342 uint32_t BW = A.getBitWidth();
5343 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5344 assert(A != 0 && "A must be non-zero.");
5348 // The gcd of A and N may have only one prime factor: 2. The number of
5349 // trailing zeros in A is its multiplicity
5350 uint32_t Mult2 = A.countTrailingZeros();
5353 // 2. Check if B is divisible by D.
5355 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5356 // is not less than multiplicity of this prime factor for D.
5357 if (B.countTrailingZeros() < Mult2)
5358 return SE.getCouldNotCompute();
5360 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5363 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5364 // bit width during computations.
5365 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5366 APInt Mod(BW + 1, 0);
5367 Mod.setBit(BW - Mult2); // Mod = N / D
5368 APInt I = AD.multiplicativeInverse(Mod);
5370 // 4. Compute the minimum unsigned root of the equation:
5371 // I * (B / D) mod (N / D)
5372 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5374 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5376 return SE.getConstant(Result.trunc(BW));
5379 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5380 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5381 /// might be the same) or two SCEVCouldNotCompute objects.
5383 static std::pair<const SCEV *,const SCEV *>
5384 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5385 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5386 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5387 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5388 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5390 // We currently can only solve this if the coefficients are constants.
5391 if (!LC || !MC || !NC) {
5392 const SCEV *CNC = SE.getCouldNotCompute();
5393 return std::make_pair(CNC, CNC);
5396 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5397 const APInt &L = LC->getValue()->getValue();
5398 const APInt &M = MC->getValue()->getValue();
5399 const APInt &N = NC->getValue()->getValue();
5400 APInt Two(BitWidth, 2);
5401 APInt Four(BitWidth, 4);
5404 using namespace APIntOps;
5406 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5407 // The B coefficient is M-N/2
5411 // The A coefficient is N/2
5412 APInt A(N.sdiv(Two));
5414 // Compute the B^2-4ac term.
5417 SqrtTerm -= Four * (A * C);
5419 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5420 // integer value or else APInt::sqrt() will assert.
5421 APInt SqrtVal(SqrtTerm.sqrt());
5423 // Compute the two solutions for the quadratic formula.
5424 // The divisions must be performed as signed divisions.
5427 if (TwoA.isMinValue()) {
5428 const SCEV *CNC = SE.getCouldNotCompute();
5429 return std::make_pair(CNC, CNC);
5432 LLVMContext &Context = SE.getContext();
5434 ConstantInt *Solution1 =
5435 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5436 ConstantInt *Solution2 =
5437 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5439 return std::make_pair(SE.getConstant(Solution1),
5440 SE.getConstant(Solution2));
5441 } // end APIntOps namespace
5444 /// HowFarToZero - Return the number of times a backedge comparing the specified
5445 /// value to zero will execute. If not computable, return CouldNotCompute.
5447 /// This is only used for loops with a "x != y" exit test. The exit condition is
5448 /// now expressed as a single expression, V = x-y. So the exit test is
5449 /// effectively V != 0. We know and take advantage of the fact that this
5450 /// expression only being used in a comparison by zero context.
5451 ScalarEvolution::ExitLimit
5452 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
5453 // If the value is a constant
5454 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5455 // If the value is already zero, the branch will execute zero times.
5456 if (C->getValue()->isZero()) return C;
5457 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5460 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
5461 if (!AddRec || AddRec->getLoop() != L)
5462 return getCouldNotCompute();
5464 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
5465 // the quadratic equation to solve it.
5466 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
5467 std::pair<const SCEV *,const SCEV *> Roots =
5468 SolveQuadraticEquation(AddRec, *this);
5469 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5470 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5473 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
5474 << " sol#2: " << *R2 << "\n";
5476 // Pick the smallest positive root value.
5477 if (ConstantInt *CB =
5478 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
5481 if (CB->getZExtValue() == false)
5482 std::swap(R1, R2); // R1 is the minimum root now.
5484 // We can only use this value if the chrec ends up with an exact zero
5485 // value at this index. When solving for "X*X != 5", for example, we
5486 // should not accept a root of 2.
5487 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
5489 return R1; // We found a quadratic root!
5492 return getCouldNotCompute();
5495 // Otherwise we can only handle this if it is affine.
5496 if (!AddRec->isAffine())
5497 return getCouldNotCompute();
5499 // If this is an affine expression, the execution count of this branch is
5500 // the minimum unsigned root of the following equation:
5502 // Start + Step*N = 0 (mod 2^BW)
5506 // Step*N = -Start (mod 2^BW)
5508 // where BW is the common bit width of Start and Step.
5510 // Get the initial value for the loop.
5511 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
5512 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
5514 // For now we handle only constant steps.
5516 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
5517 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
5518 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
5519 // We have not yet seen any such cases.
5520 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
5522 return getCouldNotCompute();
5524 // For positive steps (counting up until unsigned overflow):
5525 // N = -Start/Step (as unsigned)
5526 // For negative steps (counting down to zero):
5528 // First compute the unsigned distance from zero in the direction of Step.
5529 bool CountDown = StepC->getValue()->getValue().isNegative();
5530 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
5532 // Handle unitary steps, which cannot wraparound.
5533 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
5534 // N = Distance (as unsigned)
5535 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
5536 ConstantRange CR = getUnsignedRange(Start);
5537 const SCEV *MaxBECount;
5538 if (!CountDown && CR.getUnsignedMin().isMinValue())
5539 // When counting up, the worst starting value is 1, not 0.
5540 MaxBECount = CR.getUnsignedMax().isMinValue()
5541 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
5542 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
5544 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
5545 : -CR.getUnsignedMin());
5546 return ExitLimit(Distance, MaxBECount);
5549 // If the recurrence is known not to wraparound, unsigned divide computes the
5550 // back edge count. We know that the value will either become zero (and thus
5551 // the loop terminates), that the loop will terminate through some other exit
5552 // condition first, or that the loop has undefined behavior. This means
5553 // we can't "miss" the exit value, even with nonunit stride.
5555 // FIXME: Prove that loops always exhibits *acceptable* undefined
5556 // behavior. Loops must exhibit defined behavior until a wrapped value is
5557 // actually used. So the trip count computed by udiv could be smaller than the
5558 // number of well-defined iterations.
5559 if (AddRec->getNoWrapFlags(SCEV::FlagNW)) {
5560 // FIXME: We really want an "isexact" bit for udiv.
5561 return getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5563 // Then, try to solve the above equation provided that Start is constant.
5564 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
5565 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
5566 -StartC->getValue()->getValue(),
5568 return getCouldNotCompute();
5571 /// HowFarToNonZero - Return the number of times a backedge checking the
5572 /// specified value for nonzero will execute. If not computable, return
5574 ScalarEvolution::ExitLimit
5575 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
5576 // Loops that look like: while (X == 0) are very strange indeed. We don't
5577 // handle them yet except for the trivial case. This could be expanded in the
5578 // future as needed.
5580 // If the value is a constant, check to see if it is known to be non-zero
5581 // already. If so, the backedge will execute zero times.
5582 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5583 if (!C->getValue()->isNullValue())
5584 return getConstant(C->getType(), 0);
5585 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5588 // We could implement others, but I really doubt anyone writes loops like
5589 // this, and if they did, they would already be constant folded.
5590 return getCouldNotCompute();
5593 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
5594 /// (which may not be an immediate predecessor) which has exactly one
5595 /// successor from which BB is reachable, or null if no such block is
5598 std::pair<BasicBlock *, BasicBlock *>
5599 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
5600 // If the block has a unique predecessor, then there is no path from the
5601 // predecessor to the block that does not go through the direct edge
5602 // from the predecessor to the block.
5603 if (BasicBlock *Pred = BB->getSinglePredecessor())
5604 return std::make_pair(Pred, BB);
5606 // A loop's header is defined to be a block that dominates the loop.
5607 // If the header has a unique predecessor outside the loop, it must be
5608 // a block that has exactly one successor that can reach the loop.
5609 if (Loop *L = LI->getLoopFor(BB))
5610 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5612 return std::pair<BasicBlock *, BasicBlock *>();
5615 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5616 /// testing whether two expressions are equal, however for the purposes of
5617 /// looking for a condition guarding a loop, it can be useful to be a little
5618 /// more general, since a front-end may have replicated the controlling
5621 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5622 // Quick check to see if they are the same SCEV.
5623 if (A == B) return true;
5625 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5626 // two different instructions with the same value. Check for this case.
5627 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5628 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5629 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5630 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5631 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5634 // Otherwise assume they may have a different value.
5638 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5639 /// predicate Pred. Return true iff any changes were made.
5641 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5642 const SCEV *&LHS, const SCEV *&RHS) {
5643 bool Changed = false;
5645 // Canonicalize a constant to the right side.
5646 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5647 // Check for both operands constant.
5648 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5649 if (ConstantExpr::getICmp(Pred,
5651 RHSC->getValue())->isNullValue())
5652 goto trivially_false;
5654 goto trivially_true;
5656 // Otherwise swap the operands to put the constant on the right.
5657 std::swap(LHS, RHS);
5658 Pred = ICmpInst::getSwappedPredicate(Pred);
5662 // If we're comparing an addrec with a value which is loop-invariant in the
5663 // addrec's loop, put the addrec on the left. Also make a dominance check,
5664 // as both operands could be addrecs loop-invariant in each other's loop.
5665 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5666 const Loop *L = AR->getLoop();
5667 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5668 std::swap(LHS, RHS);
5669 Pred = ICmpInst::getSwappedPredicate(Pred);
5674 // If there's a constant operand, canonicalize comparisons with boundary
5675 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5676 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5677 const APInt &RA = RC->getValue()->getValue();
5679 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5680 case ICmpInst::ICMP_EQ:
5681 case ICmpInst::ICMP_NE:
5683 case ICmpInst::ICMP_UGE:
5684 if ((RA - 1).isMinValue()) {
5685 Pred = ICmpInst::ICMP_NE;
5686 RHS = getConstant(RA - 1);
5690 if (RA.isMaxValue()) {
5691 Pred = ICmpInst::ICMP_EQ;
5695 if (RA.isMinValue()) goto trivially_true;
5697 Pred = ICmpInst::ICMP_UGT;
5698 RHS = getConstant(RA - 1);
5701 case ICmpInst::ICMP_ULE:
5702 if ((RA + 1).isMaxValue()) {
5703 Pred = ICmpInst::ICMP_NE;
5704 RHS = getConstant(RA + 1);
5708 if (RA.isMinValue()) {
5709 Pred = ICmpInst::ICMP_EQ;
5713 if (RA.isMaxValue()) goto trivially_true;
5715 Pred = ICmpInst::ICMP_ULT;
5716 RHS = getConstant(RA + 1);
5719 case ICmpInst::ICMP_SGE:
5720 if ((RA - 1).isMinSignedValue()) {
5721 Pred = ICmpInst::ICMP_NE;
5722 RHS = getConstant(RA - 1);
5726 if (RA.isMaxSignedValue()) {
5727 Pred = ICmpInst::ICMP_EQ;
5731 if (RA.isMinSignedValue()) goto trivially_true;
5733 Pred = ICmpInst::ICMP_SGT;
5734 RHS = getConstant(RA - 1);
5737 case ICmpInst::ICMP_SLE:
5738 if ((RA + 1).isMaxSignedValue()) {
5739 Pred = ICmpInst::ICMP_NE;
5740 RHS = getConstant(RA + 1);
5744 if (RA.isMinSignedValue()) {
5745 Pred = ICmpInst::ICMP_EQ;
5749 if (RA.isMaxSignedValue()) goto trivially_true;
5751 Pred = ICmpInst::ICMP_SLT;
5752 RHS = getConstant(RA + 1);
5755 case ICmpInst::ICMP_UGT:
5756 if (RA.isMinValue()) {
5757 Pred = ICmpInst::ICMP_NE;
5761 if ((RA + 1).isMaxValue()) {
5762 Pred = ICmpInst::ICMP_EQ;
5763 RHS = getConstant(RA + 1);
5767 if (RA.isMaxValue()) goto trivially_false;
5769 case ICmpInst::ICMP_ULT:
5770 if (RA.isMaxValue()) {
5771 Pred = ICmpInst::ICMP_NE;
5775 if ((RA - 1).isMinValue()) {
5776 Pred = ICmpInst::ICMP_EQ;
5777 RHS = getConstant(RA - 1);
5781 if (RA.isMinValue()) goto trivially_false;
5783 case ICmpInst::ICMP_SGT:
5784 if (RA.isMinSignedValue()) {
5785 Pred = ICmpInst::ICMP_NE;
5789 if ((RA + 1).isMaxSignedValue()) {
5790 Pred = ICmpInst::ICMP_EQ;
5791 RHS = getConstant(RA + 1);
5795 if (RA.isMaxSignedValue()) goto trivially_false;
5797 case ICmpInst::ICMP_SLT:
5798 if (RA.isMaxSignedValue()) {
5799 Pred = ICmpInst::ICMP_NE;
5803 if ((RA - 1).isMinSignedValue()) {
5804 Pred = ICmpInst::ICMP_EQ;
5805 RHS = getConstant(RA - 1);
5809 if (RA.isMinSignedValue()) goto trivially_false;
5814 // Check for obvious equality.
5815 if (HasSameValue(LHS, RHS)) {
5816 if (ICmpInst::isTrueWhenEqual(Pred))
5817 goto trivially_true;
5818 if (ICmpInst::isFalseWhenEqual(Pred))
5819 goto trivially_false;
5822 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
5823 // adding or subtracting 1 from one of the operands.
5825 case ICmpInst::ICMP_SLE:
5826 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
5827 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5829 Pred = ICmpInst::ICMP_SLT;
5831 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
5832 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5834 Pred = ICmpInst::ICMP_SLT;
5838 case ICmpInst::ICMP_SGE:
5839 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5840 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5842 Pred = ICmpInst::ICMP_SGT;
5844 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5845 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5847 Pred = ICmpInst::ICMP_SGT;
5851 case ICmpInst::ICMP_ULE:
5852 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5853 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5855 Pred = ICmpInst::ICMP_ULT;
5857 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5858 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5860 Pred = ICmpInst::ICMP_ULT;
5864 case ICmpInst::ICMP_UGE:
5865 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5866 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5868 Pred = ICmpInst::ICMP_UGT;
5870 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5871 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5873 Pred = ICmpInst::ICMP_UGT;
5881 // TODO: More simplifications are possible here.
5887 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5888 Pred = ICmpInst::ICMP_EQ;
5893 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5894 Pred = ICmpInst::ICMP_NE;
5898 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5899 return getSignedRange(S).getSignedMax().isNegative();
5902 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5903 return getSignedRange(S).getSignedMin().isStrictlyPositive();
5906 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5907 return !getSignedRange(S).getSignedMin().isNegative();
5910 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5911 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5914 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5915 return isKnownNegative(S) || isKnownPositive(S);
5918 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5919 const SCEV *LHS, const SCEV *RHS) {
5920 // Canonicalize the inputs first.
5921 (void)SimplifyICmpOperands(Pred, LHS, RHS);
5923 // If LHS or RHS is an addrec, check to see if the condition is true in
5924 // every iteration of the loop.
5925 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
5926 if (isLoopEntryGuardedByCond(
5927 AR->getLoop(), Pred, AR->getStart(), RHS) &&
5928 isLoopBackedgeGuardedByCond(
5929 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
5931 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
5932 if (isLoopEntryGuardedByCond(
5933 AR->getLoop(), Pred, LHS, AR->getStart()) &&
5934 isLoopBackedgeGuardedByCond(
5935 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
5938 // Otherwise see what can be done with known constant ranges.
5939 return isKnownPredicateWithRanges(Pred, LHS, RHS);
5943 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
5944 const SCEV *LHS, const SCEV *RHS) {
5945 if (HasSameValue(LHS, RHS))
5946 return ICmpInst::isTrueWhenEqual(Pred);
5948 // This code is split out from isKnownPredicate because it is called from
5949 // within isLoopEntryGuardedByCond.
5952 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5954 case ICmpInst::ICMP_SGT:
5955 Pred = ICmpInst::ICMP_SLT;
5956 std::swap(LHS, RHS);
5957 case ICmpInst::ICMP_SLT: {
5958 ConstantRange LHSRange = getSignedRange(LHS);
5959 ConstantRange RHSRange = getSignedRange(RHS);
5960 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
5962 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
5966 case ICmpInst::ICMP_SGE:
5967 Pred = ICmpInst::ICMP_SLE;
5968 std::swap(LHS, RHS);
5969 case ICmpInst::ICMP_SLE: {
5970 ConstantRange LHSRange = getSignedRange(LHS);
5971 ConstantRange RHSRange = getSignedRange(RHS);
5972 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
5974 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
5978 case ICmpInst::ICMP_UGT:
5979 Pred = ICmpInst::ICMP_ULT;
5980 std::swap(LHS, RHS);
5981 case ICmpInst::ICMP_ULT: {
5982 ConstantRange LHSRange = getUnsignedRange(LHS);
5983 ConstantRange RHSRange = getUnsignedRange(RHS);
5984 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
5986 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
5990 case ICmpInst::ICMP_UGE:
5991 Pred = ICmpInst::ICMP_ULE;
5992 std::swap(LHS, RHS);
5993 case ICmpInst::ICMP_ULE: {
5994 ConstantRange LHSRange = getUnsignedRange(LHS);
5995 ConstantRange RHSRange = getUnsignedRange(RHS);
5996 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
5998 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6002 case ICmpInst::ICMP_NE: {
6003 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6005 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6008 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6009 if (isKnownNonZero(Diff))
6013 case ICmpInst::ICMP_EQ:
6014 // The check at the top of the function catches the case where
6015 // the values are known to be equal.
6021 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6022 /// protected by a conditional between LHS and RHS. This is used to
6023 /// to eliminate casts.
6025 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6026 ICmpInst::Predicate Pred,
6027 const SCEV *LHS, const SCEV *RHS) {
6028 // Interpret a null as meaning no loop, where there is obviously no guard
6029 // (interprocedural conditions notwithstanding).
6030 if (!L) return true;
6032 BasicBlock *Latch = L->getLoopLatch();
6036 BranchInst *LoopContinuePredicate =
6037 dyn_cast<BranchInst>(Latch->getTerminator());
6038 if (!LoopContinuePredicate ||
6039 LoopContinuePredicate->isUnconditional())
6042 return isImpliedCond(Pred, LHS, RHS,
6043 LoopContinuePredicate->getCondition(),
6044 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
6047 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6048 /// by a conditional between LHS and RHS. This is used to help avoid max
6049 /// expressions in loop trip counts, and to eliminate casts.
6051 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6052 ICmpInst::Predicate Pred,
6053 const SCEV *LHS, const SCEV *RHS) {
6054 // Interpret a null as meaning no loop, where there is obviously no guard
6055 // (interprocedural conditions notwithstanding).
6056 if (!L) return false;
6058 // Starting at the loop predecessor, climb up the predecessor chain, as long
6059 // as there are predecessors that can be found that have unique successors
6060 // leading to the original header.
6061 for (std::pair<BasicBlock *, BasicBlock *>
6062 Pair(L->getLoopPredecessor(), L->getHeader());
6064 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6066 BranchInst *LoopEntryPredicate =
6067 dyn_cast<BranchInst>(Pair.first->getTerminator());
6068 if (!LoopEntryPredicate ||
6069 LoopEntryPredicate->isUnconditional())
6072 if (isImpliedCond(Pred, LHS, RHS,
6073 LoopEntryPredicate->getCondition(),
6074 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6081 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6082 /// and RHS is true whenever the given Cond value evaluates to true.
6083 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6084 const SCEV *LHS, const SCEV *RHS,
6085 Value *FoundCondValue,
6087 // Recursively handle And and Or conditions.
6088 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6089 if (BO->getOpcode() == Instruction::And) {
6091 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6092 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6093 } else if (BO->getOpcode() == Instruction::Or) {
6095 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6096 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6100 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6101 if (!ICI) return false;
6103 // Bail if the ICmp's operands' types are wider than the needed type
6104 // before attempting to call getSCEV on them. This avoids infinite
6105 // recursion, since the analysis of widening casts can require loop
6106 // exit condition information for overflow checking, which would
6108 if (getTypeSizeInBits(LHS->getType()) <
6109 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6112 // Now that we found a conditional branch that dominates the loop, check to
6113 // see if it is the comparison we are looking for.
6114 ICmpInst::Predicate FoundPred;
6116 FoundPred = ICI->getInversePredicate();
6118 FoundPred = ICI->getPredicate();
6120 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6121 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6123 // Balance the types. The case where FoundLHS' type is wider than
6124 // LHS' type is checked for above.
6125 if (getTypeSizeInBits(LHS->getType()) >
6126 getTypeSizeInBits(FoundLHS->getType())) {
6127 if (CmpInst::isSigned(Pred)) {
6128 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6129 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6131 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6132 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6136 // Canonicalize the query to match the way instcombine will have
6137 // canonicalized the comparison.
6138 if (SimplifyICmpOperands(Pred, LHS, RHS))
6140 return CmpInst::isTrueWhenEqual(Pred);
6141 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6142 if (FoundLHS == FoundRHS)
6143 return CmpInst::isFalseWhenEqual(Pred);
6145 // Check to see if we can make the LHS or RHS match.
6146 if (LHS == FoundRHS || RHS == FoundLHS) {
6147 if (isa<SCEVConstant>(RHS)) {
6148 std::swap(FoundLHS, FoundRHS);
6149 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6151 std::swap(LHS, RHS);
6152 Pred = ICmpInst::getSwappedPredicate(Pred);
6156 // Check whether the found predicate is the same as the desired predicate.
6157 if (FoundPred == Pred)
6158 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6160 // Check whether swapping the found predicate makes it the same as the
6161 // desired predicate.
6162 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6163 if (isa<SCEVConstant>(RHS))
6164 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6166 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6167 RHS, LHS, FoundLHS, FoundRHS);
6170 // Check whether the actual condition is beyond sufficient.
6171 if (FoundPred == ICmpInst::ICMP_EQ)
6172 if (ICmpInst::isTrueWhenEqual(Pred))
6173 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6175 if (Pred == ICmpInst::ICMP_NE)
6176 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6177 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6180 // Otherwise assume the worst.
6184 /// isImpliedCondOperands - Test whether the condition described by Pred,
6185 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6186 /// and FoundRHS is true.
6187 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6188 const SCEV *LHS, const SCEV *RHS,
6189 const SCEV *FoundLHS,
6190 const SCEV *FoundRHS) {
6191 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6192 FoundLHS, FoundRHS) ||
6193 // ~x < ~y --> x > y
6194 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6195 getNotSCEV(FoundRHS),
6196 getNotSCEV(FoundLHS));
6199 /// isImpliedCondOperandsHelper - Test whether the condition described by
6200 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6201 /// FoundLHS, and FoundRHS is true.
6203 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6204 const SCEV *LHS, const SCEV *RHS,
6205 const SCEV *FoundLHS,
6206 const SCEV *FoundRHS) {
6208 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6209 case ICmpInst::ICMP_EQ:
6210 case ICmpInst::ICMP_NE:
6211 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
6214 case ICmpInst::ICMP_SLT:
6215 case ICmpInst::ICMP_SLE:
6216 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
6217 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
6220 case ICmpInst::ICMP_SGT:
6221 case ICmpInst::ICMP_SGE:
6222 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
6223 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
6226 case ICmpInst::ICMP_ULT:
6227 case ICmpInst::ICMP_ULE:
6228 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
6229 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
6232 case ICmpInst::ICMP_UGT:
6233 case ICmpInst::ICMP_UGE:
6234 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
6235 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
6243 /// getBECount - Subtract the end and start values and divide by the step,
6244 /// rounding up, to get the number of times the backedge is executed. Return
6245 /// CouldNotCompute if an intermediate computation overflows.
6246 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
6250 assert(!isKnownNegative(Step) &&
6251 "This code doesn't handle negative strides yet!");
6253 Type *Ty = Start->getType();
6255 // When Start == End, we have an exact BECount == 0. Short-circuit this case
6256 // here because SCEV may not be able to determine that the unsigned division
6257 // after rounding is zero.
6259 return getConstant(Ty, 0);
6261 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
6262 const SCEV *Diff = getMinusSCEV(End, Start);
6263 const SCEV *RoundUp = getAddExpr(Step, NegOne);
6265 // Add an adjustment to the difference between End and Start so that
6266 // the division will effectively round up.
6267 const SCEV *Add = getAddExpr(Diff, RoundUp);
6270 // Check Add for unsigned overflow.
6271 // TODO: More sophisticated things could be done here.
6272 Type *WideTy = IntegerType::get(getContext(),
6273 getTypeSizeInBits(Ty) + 1);
6274 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
6275 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
6276 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
6277 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
6278 return getCouldNotCompute();
6281 return getUDivExpr(Add, Step);
6284 /// HowManyLessThans - Return the number of times a backedge containing the
6285 /// specified less-than comparison will execute. If not computable, return
6286 /// CouldNotCompute.
6287 ScalarEvolution::ExitLimit
6288 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
6289 const Loop *L, bool isSigned) {
6290 // Only handle: "ADDREC < LoopInvariant".
6291 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute();
6293 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
6294 if (!AddRec || AddRec->getLoop() != L)
6295 return getCouldNotCompute();
6297 // Check to see if we have a flag which makes analysis easy.
6298 bool NoWrap = isSigned ?
6299 AddRec->getNoWrapFlags((SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNW)) :
6300 AddRec->getNoWrapFlags((SCEV::NoWrapFlags)(SCEV::FlagNUW | SCEV::FlagNW));
6302 if (AddRec->isAffine()) {
6303 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
6304 const SCEV *Step = AddRec->getStepRecurrence(*this);
6307 return getCouldNotCompute();
6308 if (Step->isOne()) {
6309 // With unit stride, the iteration never steps past the limit value.
6310 } else if (isKnownPositive(Step)) {
6311 // Test whether a positive iteration can step past the limit
6312 // value and past the maximum value for its type in a single step.
6313 // Note that it's not sufficient to check NoWrap here, because even
6314 // though the value after a wrap is undefined, it's not undefined
6315 // behavior, so if wrap does occur, the loop could either terminate or
6316 // loop infinitely, but in either case, the loop is guaranteed to
6317 // iterate at least until the iteration where the wrapping occurs.
6318 const SCEV *One = getConstant(Step->getType(), 1);
6320 APInt Max = APInt::getSignedMaxValue(BitWidth);
6321 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
6322 .slt(getSignedRange(RHS).getSignedMax()))
6323 return getCouldNotCompute();
6325 APInt Max = APInt::getMaxValue(BitWidth);
6326 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
6327 .ult(getUnsignedRange(RHS).getUnsignedMax()))
6328 return getCouldNotCompute();
6331 // TODO: Handle negative strides here and below.
6332 return getCouldNotCompute();
6334 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
6335 // m. So, we count the number of iterations in which {n,+,s} < m is true.
6336 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
6337 // treat m-n as signed nor unsigned due to overflow possibility.
6339 // First, we get the value of the LHS in the first iteration: n
6340 const SCEV *Start = AddRec->getOperand(0);
6342 // Determine the minimum constant start value.
6343 const SCEV *MinStart = getConstant(isSigned ?
6344 getSignedRange(Start).getSignedMin() :
6345 getUnsignedRange(Start).getUnsignedMin());
6347 // If we know that the condition is true in order to enter the loop,
6348 // then we know that it will run exactly (m-n)/s times. Otherwise, we
6349 // only know that it will execute (max(m,n)-n)/s times. In both cases,
6350 // the division must round up.
6351 const SCEV *End = RHS;
6352 if (!isLoopEntryGuardedByCond(L,
6353 isSigned ? ICmpInst::ICMP_SLT :
6355 getMinusSCEV(Start, Step), RHS))
6356 End = isSigned ? getSMaxExpr(RHS, Start)
6357 : getUMaxExpr(RHS, Start);
6359 // Determine the maximum constant end value.
6360 const SCEV *MaxEnd = getConstant(isSigned ?
6361 getSignedRange(End).getSignedMax() :
6362 getUnsignedRange(End).getUnsignedMax());
6364 // If MaxEnd is within a step of the maximum integer value in its type,
6365 // adjust it down to the minimum value which would produce the same effect.
6366 // This allows the subsequent ceiling division of (N+(step-1))/step to
6367 // compute the correct value.
6368 const SCEV *StepMinusOne = getMinusSCEV(Step,
6369 getConstant(Step->getType(), 1));
6372 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
6375 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
6378 // Finally, we subtract these two values and divide, rounding up, to get
6379 // the number of times the backedge is executed.
6380 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
6382 // The maximum backedge count is similar, except using the minimum start
6383 // value and the maximum end value.
6384 // If we already have an exact constant BECount, use it instead.
6385 const SCEV *MaxBECount = isa<SCEVConstant>(BECount) ? BECount
6386 : getBECount(MinStart, MaxEnd, Step, NoWrap);
6388 // If the stride is nonconstant, and NoWrap == true, then
6389 // getBECount(MinStart, MaxEnd) may not compute. This would result in an
6390 // exact BECount and invalid MaxBECount, which should be avoided to catch
6391 // more optimization opportunities.
6392 if (isa<SCEVCouldNotCompute>(MaxBECount))
6393 MaxBECount = BECount;
6395 return ExitLimit(BECount, MaxBECount);
6398 return getCouldNotCompute();
6401 /// getNumIterationsInRange - Return the number of iterations of this loop that
6402 /// produce values in the specified constant range. Another way of looking at
6403 /// this is that it returns the first iteration number where the value is not in
6404 /// the condition, thus computing the exit count. If the iteration count can't
6405 /// be computed, an instance of SCEVCouldNotCompute is returned.
6406 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
6407 ScalarEvolution &SE) const {
6408 if (Range.isFullSet()) // Infinite loop.
6409 return SE.getCouldNotCompute();
6411 // If the start is a non-zero constant, shift the range to simplify things.
6412 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
6413 if (!SC->getValue()->isZero()) {
6414 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
6415 Operands[0] = SE.getConstant(SC->getType(), 0);
6416 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
6417 getNoWrapFlags(FlagNW));
6418 if (const SCEVAddRecExpr *ShiftedAddRec =
6419 dyn_cast<SCEVAddRecExpr>(Shifted))
6420 return ShiftedAddRec->getNumIterationsInRange(
6421 Range.subtract(SC->getValue()->getValue()), SE);
6422 // This is strange and shouldn't happen.
6423 return SE.getCouldNotCompute();
6426 // The only time we can solve this is when we have all constant indices.
6427 // Otherwise, we cannot determine the overflow conditions.
6428 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
6429 if (!isa<SCEVConstant>(getOperand(i)))
6430 return SE.getCouldNotCompute();
6433 // Okay at this point we know that all elements of the chrec are constants and
6434 // that the start element is zero.
6436 // First check to see if the range contains zero. If not, the first
6438 unsigned BitWidth = SE.getTypeSizeInBits(getType());
6439 if (!Range.contains(APInt(BitWidth, 0)))
6440 return SE.getConstant(getType(), 0);
6443 // If this is an affine expression then we have this situation:
6444 // Solve {0,+,A} in Range === Ax in Range
6446 // We know that zero is in the range. If A is positive then we know that
6447 // the upper value of the range must be the first possible exit value.
6448 // If A is negative then the lower of the range is the last possible loop
6449 // value. Also note that we already checked for a full range.
6450 APInt One(BitWidth,1);
6451 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
6452 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
6454 // The exit value should be (End+A)/A.
6455 APInt ExitVal = (End + A).udiv(A);
6456 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
6458 // Evaluate at the exit value. If we really did fall out of the valid
6459 // range, then we computed our trip count, otherwise wrap around or other
6460 // things must have happened.
6461 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
6462 if (Range.contains(Val->getValue()))
6463 return SE.getCouldNotCompute(); // Something strange happened
6465 // Ensure that the previous value is in the range. This is a sanity check.
6466 assert(Range.contains(
6467 EvaluateConstantChrecAtConstant(this,
6468 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
6469 "Linear scev computation is off in a bad way!");
6470 return SE.getConstant(ExitValue);
6471 } else if (isQuadratic()) {
6472 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
6473 // quadratic equation to solve it. To do this, we must frame our problem in
6474 // terms of figuring out when zero is crossed, instead of when
6475 // Range.getUpper() is crossed.
6476 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
6477 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
6478 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
6479 // getNoWrapFlags(FlagNW)
6482 // Next, solve the constructed addrec
6483 std::pair<const SCEV *,const SCEV *> Roots =
6484 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
6485 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6486 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6488 // Pick the smallest positive root value.
6489 if (ConstantInt *CB =
6490 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
6491 R1->getValue(), R2->getValue()))) {
6492 if (CB->getZExtValue() == false)
6493 std::swap(R1, R2); // R1 is the minimum root now.
6495 // Make sure the root is not off by one. The returned iteration should
6496 // not be in the range, but the previous one should be. When solving
6497 // for "X*X < 5", for example, we should not return a root of 2.
6498 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
6501 if (Range.contains(R1Val->getValue())) {
6502 // The next iteration must be out of the range...
6503 ConstantInt *NextVal =
6504 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
6506 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6507 if (!Range.contains(R1Val->getValue()))
6508 return SE.getConstant(NextVal);
6509 return SE.getCouldNotCompute(); // Something strange happened
6512 // If R1 was not in the range, then it is a good return value. Make
6513 // sure that R1-1 WAS in the range though, just in case.
6514 ConstantInt *NextVal =
6515 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
6516 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6517 if (Range.contains(R1Val->getValue()))
6519 return SE.getCouldNotCompute(); // Something strange happened
6524 return SE.getCouldNotCompute();
6529 //===----------------------------------------------------------------------===//
6530 // SCEVCallbackVH Class Implementation
6531 //===----------------------------------------------------------------------===//
6533 void ScalarEvolution::SCEVCallbackVH::deleted() {
6534 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6535 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
6536 SE->ConstantEvolutionLoopExitValue.erase(PN);
6537 SE->ValueExprMap.erase(getValPtr());
6538 // this now dangles!
6541 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
6542 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6544 // Forget all the expressions associated with users of the old value,
6545 // so that future queries will recompute the expressions using the new
6547 Value *Old = getValPtr();
6548 SmallVector<User *, 16> Worklist;
6549 SmallPtrSet<User *, 8> Visited;
6550 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
6552 Worklist.push_back(*UI);
6553 while (!Worklist.empty()) {
6554 User *U = Worklist.pop_back_val();
6555 // Deleting the Old value will cause this to dangle. Postpone
6556 // that until everything else is done.
6559 if (!Visited.insert(U))
6561 if (PHINode *PN = dyn_cast<PHINode>(U))
6562 SE->ConstantEvolutionLoopExitValue.erase(PN);
6563 SE->ValueExprMap.erase(U);
6564 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
6566 Worklist.push_back(*UI);
6568 // Delete the Old value.
6569 if (PHINode *PN = dyn_cast<PHINode>(Old))
6570 SE->ConstantEvolutionLoopExitValue.erase(PN);
6571 SE->ValueExprMap.erase(Old);
6572 // this now dangles!
6575 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
6576 : CallbackVH(V), SE(se) {}
6578 //===----------------------------------------------------------------------===//
6579 // ScalarEvolution Class Implementation
6580 //===----------------------------------------------------------------------===//
6582 ScalarEvolution::ScalarEvolution()
6583 : FunctionPass(ID), FirstUnknown(0) {
6584 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
6587 bool ScalarEvolution::runOnFunction(Function &F) {
6589 LI = &getAnalysis<LoopInfo>();
6590 TD = getAnalysisIfAvailable<TargetData>();
6591 TLI = &getAnalysis<TargetLibraryInfo>();
6592 DT = &getAnalysis<DominatorTree>();
6596 void ScalarEvolution::releaseMemory() {
6597 // Iterate through all the SCEVUnknown instances and call their
6598 // destructors, so that they release their references to their values.
6599 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
6603 ValueExprMap.clear();
6605 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
6606 // that a loop had multiple computable exits.
6607 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
6608 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
6613 BackedgeTakenCounts.clear();
6614 ConstantEvolutionLoopExitValue.clear();
6615 ValuesAtScopes.clear();
6616 LoopDispositions.clear();
6617 BlockDispositions.clear();
6618 UnsignedRanges.clear();
6619 SignedRanges.clear();
6620 UniqueSCEVs.clear();
6621 SCEVAllocator.Reset();
6624 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
6625 AU.setPreservesAll();
6626 AU.addRequiredTransitive<LoopInfo>();
6627 AU.addRequiredTransitive<DominatorTree>();
6628 AU.addRequired<TargetLibraryInfo>();
6631 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
6632 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
6635 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
6637 // Print all inner loops first
6638 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
6639 PrintLoopInfo(OS, SE, *I);
6642 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6645 SmallVector<BasicBlock *, 8> ExitBlocks;
6646 L->getExitBlocks(ExitBlocks);
6647 if (ExitBlocks.size() != 1)
6648 OS << "<multiple exits> ";
6650 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
6651 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
6653 OS << "Unpredictable backedge-taken count. ";
6658 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6661 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
6662 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
6664 OS << "Unpredictable max backedge-taken count. ";
6670 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
6671 // ScalarEvolution's implementation of the print method is to print
6672 // out SCEV values of all instructions that are interesting. Doing
6673 // this potentially causes it to create new SCEV objects though,
6674 // which technically conflicts with the const qualifier. This isn't
6675 // observable from outside the class though, so casting away the
6676 // const isn't dangerous.
6677 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
6679 OS << "Classifying expressions for: ";
6680 WriteAsOperand(OS, F, /*PrintType=*/false);
6682 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
6683 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
6686 const SCEV *SV = SE.getSCEV(&*I);
6689 const Loop *L = LI->getLoopFor((*I).getParent());
6691 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
6698 OS << "\t\t" "Exits: ";
6699 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
6700 if (!SE.isLoopInvariant(ExitValue, L)) {
6701 OS << "<<Unknown>>";
6710 OS << "Determining loop execution counts for: ";
6711 WriteAsOperand(OS, F, /*PrintType=*/false);
6713 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
6714 PrintLoopInfo(OS, &SE, *I);
6717 ScalarEvolution::LoopDisposition
6718 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
6719 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S];
6720 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair =
6721 Values.insert(std::make_pair(L, LoopVariant));
6723 return Pair.first->second;
6725 LoopDisposition D = computeLoopDisposition(S, L);
6726 return LoopDispositions[S][L] = D;
6729 ScalarEvolution::LoopDisposition
6730 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
6731 switch (S->getSCEVType()) {
6733 return LoopInvariant;
6737 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
6738 case scAddRecExpr: {
6739 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6741 // If L is the addrec's loop, it's computable.
6742 if (AR->getLoop() == L)
6743 return LoopComputable;
6745 // Add recurrences are never invariant in the function-body (null loop).
6749 // This recurrence is variant w.r.t. L if L contains AR's loop.
6750 if (L->contains(AR->getLoop()))
6753 // This recurrence is invariant w.r.t. L if AR's loop contains L.
6754 if (AR->getLoop()->contains(L))
6755 return LoopInvariant;
6757 // This recurrence is variant w.r.t. L if any of its operands
6759 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
6761 if (!isLoopInvariant(*I, L))
6764 // Otherwise it's loop-invariant.
6765 return LoopInvariant;
6771 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6772 bool HasVarying = false;
6773 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6775 LoopDisposition D = getLoopDisposition(*I, L);
6776 if (D == LoopVariant)
6778 if (D == LoopComputable)
6781 return HasVarying ? LoopComputable : LoopInvariant;
6784 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6785 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
6786 if (LD == LoopVariant)
6788 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
6789 if (RD == LoopVariant)
6791 return (LD == LoopInvariant && RD == LoopInvariant) ?
6792 LoopInvariant : LoopComputable;
6795 // All non-instruction values are loop invariant. All instructions are loop
6796 // invariant if they are not contained in the specified loop.
6797 // Instructions are never considered invariant in the function body
6798 // (null loop) because they are defined within the "loop".
6799 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
6800 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
6801 return LoopInvariant;
6802 case scCouldNotCompute:
6803 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6807 llvm_unreachable("Unknown SCEV kind!");
6811 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
6812 return getLoopDisposition(S, L) == LoopInvariant;
6815 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
6816 return getLoopDisposition(S, L) == LoopComputable;
6819 ScalarEvolution::BlockDisposition
6820 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6821 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S];
6822 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool>
6823 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock));
6825 return Pair.first->second;
6827 BlockDisposition D = computeBlockDisposition(S, BB);
6828 return BlockDispositions[S][BB] = D;
6831 ScalarEvolution::BlockDisposition
6832 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6833 switch (S->getSCEVType()) {
6835 return ProperlyDominatesBlock;
6839 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
6840 case scAddRecExpr: {
6841 // This uses a "dominates" query instead of "properly dominates" query
6842 // to test for proper dominance too, because the instruction which
6843 // produces the addrec's value is a PHI, and a PHI effectively properly
6844 // dominates its entire containing block.
6845 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6846 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
6847 return DoesNotDominateBlock;
6849 // FALL THROUGH into SCEVNAryExpr handling.
6854 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6856 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6858 BlockDisposition D = getBlockDisposition(*I, BB);
6859 if (D == DoesNotDominateBlock)
6860 return DoesNotDominateBlock;
6861 if (D == DominatesBlock)
6864 return Proper ? ProperlyDominatesBlock : DominatesBlock;
6867 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6868 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6869 BlockDisposition LD = getBlockDisposition(LHS, BB);
6870 if (LD == DoesNotDominateBlock)
6871 return DoesNotDominateBlock;
6872 BlockDisposition RD = getBlockDisposition(RHS, BB);
6873 if (RD == DoesNotDominateBlock)
6874 return DoesNotDominateBlock;
6875 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
6876 ProperlyDominatesBlock : DominatesBlock;
6879 if (Instruction *I =
6880 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
6881 if (I->getParent() == BB)
6882 return DominatesBlock;
6883 if (DT->properlyDominates(I->getParent(), BB))
6884 return ProperlyDominatesBlock;
6885 return DoesNotDominateBlock;
6887 return ProperlyDominatesBlock;
6888 case scCouldNotCompute:
6889 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6890 return DoesNotDominateBlock;
6893 llvm_unreachable("Unknown SCEV kind!");
6894 return DoesNotDominateBlock;
6897 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
6898 return getBlockDisposition(S, BB) >= DominatesBlock;
6901 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
6902 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
6905 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
6906 switch (S->getSCEVType()) {
6911 case scSignExtend: {
6912 const SCEVCastExpr *Cast = cast<SCEVCastExpr>(S);
6913 const SCEV *CastOp = Cast->getOperand();
6914 return Op == CastOp || hasOperand(CastOp, Op);
6921 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6922 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6924 const SCEV *NAryOp = *I;
6925 if (NAryOp == Op || hasOperand(NAryOp, Op))
6931 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6932 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6933 return LHS == Op || hasOperand(LHS, Op) ||
6934 RHS == Op || hasOperand(RHS, Op);
6938 case scCouldNotCompute:
6939 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6943 llvm_unreachable("Unknown SCEV kind!");
6947 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
6948 ValuesAtScopes.erase(S);
6949 LoopDispositions.erase(S);
6950 BlockDispositions.erase(S);
6951 UnsignedRanges.erase(S);
6952 SignedRanges.erase(S);