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/Support/CommandLine.h"
78 #include "llvm/Support/ConstantRange.h"
79 #include "llvm/Support/Debug.h"
80 #include "llvm/Support/ErrorHandling.h"
81 #include "llvm/Support/GetElementPtrTypeIterator.h"
82 #include "llvm/Support/InstIterator.h"
83 #include "llvm/Support/MathExtras.h"
84 #include "llvm/Support/raw_ostream.h"
85 #include "llvm/ADT/Statistic.h"
86 #include "llvm/ADT/STLExtras.h"
87 #include "llvm/ADT/SmallPtrSet.h"
91 STATISTIC(NumArrayLenItCounts,
92 "Number of trip counts computed with array length");
93 STATISTIC(NumTripCountsComputed,
94 "Number of loops with predictable loop counts");
95 STATISTIC(NumTripCountsNotComputed,
96 "Number of loops without predictable loop counts");
97 STATISTIC(NumBruteForceTripCountsComputed,
98 "Number of loops with trip counts computed by force");
100 static cl::opt<unsigned>
101 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
102 cl::desc("Maximum number of iterations SCEV will "
103 "symbolically execute a constant "
107 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution",
108 "Scalar Evolution Analysis", false, true)
109 INITIALIZE_PASS_DEPENDENCY(LoopInfo)
110 INITIALIZE_PASS_DEPENDENCY(DominatorTree)
111 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution",
112 "Scalar Evolution Analysis", false, true)
113 char ScalarEvolution::ID = 0;
115 //===----------------------------------------------------------------------===//
116 // SCEV class definitions
117 //===----------------------------------------------------------------------===//
119 //===----------------------------------------------------------------------===//
120 // Implementation of the SCEV class.
123 void SCEV::dump() const {
128 void SCEV::print(raw_ostream &OS) const {
129 switch (getSCEVType()) {
131 WriteAsOperand(OS, cast<SCEVConstant>(this)->getValue(), false);
134 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
135 const SCEV *Op = Trunc->getOperand();
136 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
137 << *Trunc->getType() << ")";
141 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
142 const SCEV *Op = ZExt->getOperand();
143 OS << "(zext " << *Op->getType() << " " << *Op << " to "
144 << *ZExt->getType() << ")";
148 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
149 const SCEV *Op = SExt->getOperand();
150 OS << "(sext " << *Op->getType() << " " << *Op << " to "
151 << *SExt->getType() << ")";
155 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
156 OS << "{" << *AR->getOperand(0);
157 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
158 OS << ",+," << *AR->getOperand(i);
160 if (AR->getNoWrapFlags(FlagNUW))
162 if (AR->getNoWrapFlags(FlagNSW))
164 if (AR->getNoWrapFlags(FlagNW) &&
165 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
167 WriteAsOperand(OS, AR->getLoop()->getHeader(), /*PrintType=*/false);
175 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
176 const char *OpStr = 0;
177 switch (NAry->getSCEVType()) {
178 case scAddExpr: OpStr = " + "; break;
179 case scMulExpr: OpStr = " * "; break;
180 case scUMaxExpr: OpStr = " umax "; break;
181 case scSMaxExpr: OpStr = " smax "; break;
184 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
187 if (llvm::next(I) != E)
194 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
195 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
199 const SCEVUnknown *U = cast<SCEVUnknown>(this);
201 if (U->isSizeOf(AllocTy)) {
202 OS << "sizeof(" << *AllocTy << ")";
205 if (U->isAlignOf(AllocTy)) {
206 OS << "alignof(" << *AllocTy << ")";
212 if (U->isOffsetOf(CTy, FieldNo)) {
213 OS << "offsetof(" << *CTy << ", ";
214 WriteAsOperand(OS, FieldNo, false);
219 // Otherwise just print it normally.
220 WriteAsOperand(OS, U->getValue(), false);
223 case scCouldNotCompute:
224 OS << "***COULDNOTCOMPUTE***";
228 llvm_unreachable("Unknown SCEV kind!");
231 Type *SCEV::getType() const {
232 switch (getSCEVType()) {
234 return cast<SCEVConstant>(this)->getType();
238 return cast<SCEVCastExpr>(this)->getType();
243 return cast<SCEVNAryExpr>(this)->getType();
245 return cast<SCEVAddExpr>(this)->getType();
247 return cast<SCEVUDivExpr>(this)->getType();
249 return cast<SCEVUnknown>(this)->getType();
250 case scCouldNotCompute:
251 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
255 llvm_unreachable("Unknown SCEV kind!");
259 bool SCEV::isZero() const {
260 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
261 return SC->getValue()->isZero();
265 bool SCEV::isOne() const {
266 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
267 return SC->getValue()->isOne();
271 bool SCEV::isAllOnesValue() const {
272 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
273 return SC->getValue()->isAllOnesValue();
277 SCEVCouldNotCompute::SCEVCouldNotCompute() :
278 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
280 bool SCEVCouldNotCompute::classof(const SCEV *S) {
281 return S->getSCEVType() == scCouldNotCompute;
284 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
286 ID.AddInteger(scConstant);
289 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
290 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
291 UniqueSCEVs.InsertNode(S, IP);
295 const SCEV *ScalarEvolution::getConstant(const APInt& Val) {
296 return getConstant(ConstantInt::get(getContext(), Val));
300 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
301 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
302 return getConstant(ConstantInt::get(ITy, V, isSigned));
305 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
306 unsigned SCEVTy, const SCEV *op, Type *ty)
307 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
309 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
310 const SCEV *op, Type *ty)
311 : SCEVCastExpr(ID, scTruncate, op, ty) {
312 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
313 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
314 "Cannot truncate non-integer value!");
317 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
318 const SCEV *op, Type *ty)
319 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
320 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
321 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
322 "Cannot zero extend non-integer value!");
325 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
326 const SCEV *op, Type *ty)
327 : SCEVCastExpr(ID, scSignExtend, op, ty) {
328 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
329 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
330 "Cannot sign extend non-integer value!");
333 void SCEVUnknown::deleted() {
334 // Clear this SCEVUnknown from various maps.
335 SE->forgetMemoizedResults(this);
337 // Remove this SCEVUnknown from the uniquing map.
338 SE->UniqueSCEVs.RemoveNode(this);
340 // Release the value.
344 void SCEVUnknown::allUsesReplacedWith(Value *New) {
345 // Clear this SCEVUnknown from various maps.
346 SE->forgetMemoizedResults(this);
348 // Remove this SCEVUnknown from the uniquing map.
349 SE->UniqueSCEVs.RemoveNode(this);
351 // Update this SCEVUnknown to point to the new value. This is needed
352 // because there may still be outstanding SCEVs which still point to
357 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
358 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
359 if (VCE->getOpcode() == Instruction::PtrToInt)
360 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
361 if (CE->getOpcode() == Instruction::GetElementPtr &&
362 CE->getOperand(0)->isNullValue() &&
363 CE->getNumOperands() == 2)
364 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
366 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
374 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
375 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
376 if (VCE->getOpcode() == Instruction::PtrToInt)
377 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
378 if (CE->getOpcode() == Instruction::GetElementPtr &&
379 CE->getOperand(0)->isNullValue()) {
381 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
382 if (StructType *STy = dyn_cast<StructType>(Ty))
383 if (!STy->isPacked() &&
384 CE->getNumOperands() == 3 &&
385 CE->getOperand(1)->isNullValue()) {
386 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
388 STy->getNumElements() == 2 &&
389 STy->getElementType(0)->isIntegerTy(1)) {
390 AllocTy = STy->getElementType(1);
399 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
400 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
401 if (VCE->getOpcode() == Instruction::PtrToInt)
402 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
403 if (CE->getOpcode() == Instruction::GetElementPtr &&
404 CE->getNumOperands() == 3 &&
405 CE->getOperand(0)->isNullValue() &&
406 CE->getOperand(1)->isNullValue()) {
408 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
409 // Ignore vector types here so that ScalarEvolutionExpander doesn't
410 // emit getelementptrs that index into vectors.
411 if (Ty->isStructTy() || Ty->isArrayTy()) {
413 FieldNo = CE->getOperand(2);
421 //===----------------------------------------------------------------------===//
423 //===----------------------------------------------------------------------===//
426 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
427 /// than the complexity of the RHS. This comparator is used to canonicalize
429 class SCEVComplexityCompare {
430 const LoopInfo *const LI;
432 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
434 // Return true or false if LHS is less than, or at least RHS, respectively.
435 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
436 return compare(LHS, RHS) < 0;
439 // Return negative, zero, or positive, if LHS is less than, equal to, or
440 // greater than RHS, respectively. A three-way result allows recursive
441 // comparisons to be more efficient.
442 int compare(const SCEV *LHS, const SCEV *RHS) const {
443 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
447 // Primarily, sort the SCEVs by their getSCEVType().
448 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
450 return (int)LType - (int)RType;
452 // Aside from the getSCEVType() ordering, the particular ordering
453 // isn't very important except that it's beneficial to be consistent,
454 // so that (a + b) and (b + a) don't end up as different expressions.
457 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
458 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
460 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
461 // not as complete as it could be.
462 const Value *LV = LU->getValue(), *RV = RU->getValue();
464 // Order pointer values after integer values. This helps SCEVExpander
466 bool LIsPointer = LV->getType()->isPointerTy(),
467 RIsPointer = RV->getType()->isPointerTy();
468 if (LIsPointer != RIsPointer)
469 return (int)LIsPointer - (int)RIsPointer;
471 // Compare getValueID values.
472 unsigned LID = LV->getValueID(),
473 RID = RV->getValueID();
475 return (int)LID - (int)RID;
477 // Sort arguments by their position.
478 if (const Argument *LA = dyn_cast<Argument>(LV)) {
479 const Argument *RA = cast<Argument>(RV);
480 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
481 return (int)LArgNo - (int)RArgNo;
484 // For instructions, compare their loop depth, and their operand
485 // count. This is pretty loose.
486 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
487 const Instruction *RInst = cast<Instruction>(RV);
489 // Compare loop depths.
490 const BasicBlock *LParent = LInst->getParent(),
491 *RParent = RInst->getParent();
492 if (LParent != RParent) {
493 unsigned LDepth = LI->getLoopDepth(LParent),
494 RDepth = LI->getLoopDepth(RParent);
495 if (LDepth != RDepth)
496 return (int)LDepth - (int)RDepth;
499 // Compare the number of operands.
500 unsigned LNumOps = LInst->getNumOperands(),
501 RNumOps = RInst->getNumOperands();
502 return (int)LNumOps - (int)RNumOps;
509 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
510 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
512 // Compare constant values.
513 const APInt &LA = LC->getValue()->getValue();
514 const APInt &RA = RC->getValue()->getValue();
515 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
516 if (LBitWidth != RBitWidth)
517 return (int)LBitWidth - (int)RBitWidth;
518 return LA.ult(RA) ? -1 : 1;
522 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
523 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
525 // Compare addrec loop depths.
526 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
527 if (LLoop != RLoop) {
528 unsigned LDepth = LLoop->getLoopDepth(),
529 RDepth = RLoop->getLoopDepth();
530 if (LDepth != RDepth)
531 return (int)LDepth - (int)RDepth;
534 // Addrec complexity grows with operand count.
535 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
536 if (LNumOps != RNumOps)
537 return (int)LNumOps - (int)RNumOps;
539 // Lexicographically compare.
540 for (unsigned i = 0; i != LNumOps; ++i) {
541 long X = compare(LA->getOperand(i), RA->getOperand(i));
553 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
554 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
556 // Lexicographically compare n-ary expressions.
557 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
558 for (unsigned i = 0; i != LNumOps; ++i) {
561 long X = compare(LC->getOperand(i), RC->getOperand(i));
565 return (int)LNumOps - (int)RNumOps;
569 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
570 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
572 // Lexicographically compare udiv expressions.
573 long X = compare(LC->getLHS(), RC->getLHS());
576 return compare(LC->getRHS(), RC->getRHS());
582 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
583 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
585 // Compare cast expressions by operand.
586 return compare(LC->getOperand(), RC->getOperand());
593 llvm_unreachable("Unknown SCEV kind!");
599 /// GroupByComplexity - Given a list of SCEV objects, order them by their
600 /// complexity, and group objects of the same complexity together by value.
601 /// When this routine is finished, we know that any duplicates in the vector are
602 /// consecutive and that complexity is monotonically increasing.
604 /// Note that we go take special precautions to ensure that we get deterministic
605 /// results from this routine. In other words, we don't want the results of
606 /// this to depend on where the addresses of various SCEV objects happened to
609 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
611 if (Ops.size() < 2) return; // Noop
612 if (Ops.size() == 2) {
613 // This is the common case, which also happens to be trivially simple.
615 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
616 if (SCEVComplexityCompare(LI)(RHS, LHS))
621 // Do the rough sort by complexity.
622 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
624 // Now that we are sorted by complexity, group elements of the same
625 // complexity. Note that this is, at worst, N^2, but the vector is likely to
626 // be extremely short in practice. Note that we take this approach because we
627 // do not want to depend on the addresses of the objects we are grouping.
628 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
629 const SCEV *S = Ops[i];
630 unsigned Complexity = S->getSCEVType();
632 // If there are any objects of the same complexity and same value as this
634 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
635 if (Ops[j] == S) { // Found a duplicate.
636 // Move it to immediately after i'th element.
637 std::swap(Ops[i+1], Ops[j]);
638 ++i; // no need to rescan it.
639 if (i == e-2) return; // Done!
647 //===----------------------------------------------------------------------===//
648 // Simple SCEV method implementations
649 //===----------------------------------------------------------------------===//
651 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
653 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
656 // Handle the simplest case efficiently.
658 return SE.getTruncateOrZeroExtend(It, ResultTy);
660 // We are using the following formula for BC(It, K):
662 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
664 // Suppose, W is the bitwidth of the return value. We must be prepared for
665 // overflow. Hence, we must assure that the result of our computation is
666 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
667 // safe in modular arithmetic.
669 // However, this code doesn't use exactly that formula; the formula it uses
670 // is something like the following, where T is the number of factors of 2 in
671 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
674 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
676 // This formula is trivially equivalent to the previous formula. However,
677 // this formula can be implemented much more efficiently. The trick is that
678 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
679 // arithmetic. To do exact division in modular arithmetic, all we have
680 // to do is multiply by the inverse. Therefore, this step can be done at
683 // The next issue is how to safely do the division by 2^T. The way this
684 // is done is by doing the multiplication step at a width of at least W + T
685 // bits. This way, the bottom W+T bits of the product are accurate. Then,
686 // when we perform the division by 2^T (which is equivalent to a right shift
687 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
688 // truncated out after the division by 2^T.
690 // In comparison to just directly using the first formula, this technique
691 // is much more efficient; using the first formula requires W * K bits,
692 // but this formula less than W + K bits. Also, the first formula requires
693 // a division step, whereas this formula only requires multiplies and shifts.
695 // It doesn't matter whether the subtraction step is done in the calculation
696 // width or the input iteration count's width; if the subtraction overflows,
697 // the result must be zero anyway. We prefer here to do it in the width of
698 // the induction variable because it helps a lot for certain cases; CodeGen
699 // isn't smart enough to ignore the overflow, which leads to much less
700 // efficient code if the width of the subtraction is wider than the native
703 // (It's possible to not widen at all by pulling out factors of 2 before
704 // the multiplication; for example, K=2 can be calculated as
705 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
706 // extra arithmetic, so it's not an obvious win, and it gets
707 // much more complicated for K > 3.)
709 // Protection from insane SCEVs; this bound is conservative,
710 // but it probably doesn't matter.
712 return SE.getCouldNotCompute();
714 unsigned W = SE.getTypeSizeInBits(ResultTy);
716 // Calculate K! / 2^T and T; we divide out the factors of two before
717 // multiplying for calculating K! / 2^T to avoid overflow.
718 // Other overflow doesn't matter because we only care about the bottom
719 // W bits of the result.
720 APInt OddFactorial(W, 1);
722 for (unsigned i = 3; i <= K; ++i) {
724 unsigned TwoFactors = Mult.countTrailingZeros();
726 Mult = Mult.lshr(TwoFactors);
727 OddFactorial *= Mult;
730 // We need at least W + T bits for the multiplication step
731 unsigned CalculationBits = W + T;
733 // Calculate 2^T, at width T+W.
734 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
736 // Calculate the multiplicative inverse of K! / 2^T;
737 // this multiplication factor will perform the exact division by
739 APInt Mod = APInt::getSignedMinValue(W+1);
740 APInt MultiplyFactor = OddFactorial.zext(W+1);
741 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
742 MultiplyFactor = MultiplyFactor.trunc(W);
744 // Calculate the product, at width T+W
745 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
747 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
748 for (unsigned i = 1; i != K; ++i) {
749 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
750 Dividend = SE.getMulExpr(Dividend,
751 SE.getTruncateOrZeroExtend(S, CalculationTy));
755 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
757 // Truncate the result, and divide by K! / 2^T.
759 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
760 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
763 /// evaluateAtIteration - Return the value of this chain of recurrences at
764 /// the specified iteration number. We can evaluate this recurrence by
765 /// multiplying each element in the chain by the binomial coefficient
766 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
768 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
770 /// where BC(It, k) stands for binomial coefficient.
772 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
773 ScalarEvolution &SE) const {
774 const SCEV *Result = getStart();
775 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
776 // The computation is correct in the face of overflow provided that the
777 // multiplication is performed _after_ the evaluation of the binomial
779 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
780 if (isa<SCEVCouldNotCompute>(Coeff))
783 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
788 //===----------------------------------------------------------------------===//
789 // SCEV Expression folder implementations
790 //===----------------------------------------------------------------------===//
792 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
794 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
795 "This is not a truncating conversion!");
796 assert(isSCEVable(Ty) &&
797 "This is not a conversion to a SCEVable type!");
798 Ty = getEffectiveSCEVType(Ty);
801 ID.AddInteger(scTruncate);
805 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
807 // Fold if the operand is constant.
808 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
810 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(),
811 getEffectiveSCEVType(Ty))));
813 // trunc(trunc(x)) --> trunc(x)
814 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
815 return getTruncateExpr(ST->getOperand(), Ty);
817 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
818 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
819 return getTruncateOrSignExtend(SS->getOperand(), Ty);
821 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
822 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
823 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
825 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
826 // eliminate all the truncates.
827 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
828 SmallVector<const SCEV *, 4> Operands;
829 bool hasTrunc = false;
830 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
831 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
832 hasTrunc = isa<SCEVTruncateExpr>(S);
833 Operands.push_back(S);
836 return getAddExpr(Operands);
837 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
840 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
841 // eliminate all the truncates.
842 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
843 SmallVector<const SCEV *, 4> Operands;
844 bool hasTrunc = false;
845 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
846 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
847 hasTrunc = isa<SCEVTruncateExpr>(S);
848 Operands.push_back(S);
851 return getMulExpr(Operands);
852 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
855 // If the input value is a chrec scev, truncate the chrec's operands.
856 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
857 SmallVector<const SCEV *, 4> Operands;
858 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
859 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
860 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
863 // As a special case, fold trunc(undef) to undef. We don't want to
864 // know too much about SCEVUnknowns, but this special case is handy
866 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
867 if (isa<UndefValue>(U->getValue()))
868 return getSCEV(UndefValue::get(Ty));
870 // The cast wasn't folded; create an explicit cast node. We can reuse
871 // the existing insert position since if we get here, we won't have
872 // made any changes which would invalidate it.
873 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
875 UniqueSCEVs.InsertNode(S, IP);
879 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
881 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
882 "This is not an extending conversion!");
883 assert(isSCEVable(Ty) &&
884 "This is not a conversion to a SCEVable type!");
885 Ty = getEffectiveSCEVType(Ty);
887 // Fold if the operand is constant.
888 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
890 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(),
891 getEffectiveSCEVType(Ty))));
893 // zext(zext(x)) --> zext(x)
894 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
895 return getZeroExtendExpr(SZ->getOperand(), Ty);
897 // Before doing any expensive analysis, check to see if we've already
898 // computed a SCEV for this Op and Ty.
900 ID.AddInteger(scZeroExtend);
904 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
906 // zext(trunc(x)) --> zext(x) or x or trunc(x)
907 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
908 // It's possible the bits taken off by the truncate were all zero bits. If
909 // so, we should be able to simplify this further.
910 const SCEV *X = ST->getOperand();
911 ConstantRange CR = getUnsignedRange(X);
912 unsigned TruncBits = getTypeSizeInBits(ST->getType());
913 unsigned NewBits = getTypeSizeInBits(Ty);
914 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
915 CR.zextOrTrunc(NewBits)))
916 return getTruncateOrZeroExtend(X, Ty);
919 // If the input value is a chrec scev, and we can prove that the value
920 // did not overflow the old, smaller, value, we can zero extend all of the
921 // operands (often constants). This allows analysis of something like
922 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
923 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
924 if (AR->isAffine()) {
925 const SCEV *Start = AR->getStart();
926 const SCEV *Step = AR->getStepRecurrence(*this);
927 unsigned BitWidth = getTypeSizeInBits(AR->getType());
928 const Loop *L = AR->getLoop();
930 // If we have special knowledge that this addrec won't overflow,
931 // we don't need to do any further analysis.
932 if (AR->getNoWrapFlags(SCEV::FlagNUW))
933 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
934 getZeroExtendExpr(Step, Ty),
935 L, AR->getNoWrapFlags());
937 // Check whether the backedge-taken count is SCEVCouldNotCompute.
938 // Note that this serves two purposes: It filters out loops that are
939 // simply not analyzable, and it covers the case where this code is
940 // being called from within backedge-taken count analysis, such that
941 // attempting to ask for the backedge-taken count would likely result
942 // in infinite recursion. In the later case, the analysis code will
943 // cope with a conservative value, and it will take care to purge
944 // that value once it has finished.
945 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
946 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
947 // Manually compute the final value for AR, checking for
950 // Check whether the backedge-taken count can be losslessly casted to
951 // the addrec's type. The count is always unsigned.
952 const SCEV *CastedMaxBECount =
953 getTruncateOrZeroExtend(MaxBECount, Start->getType());
954 const SCEV *RecastedMaxBECount =
955 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
956 if (MaxBECount == RecastedMaxBECount) {
957 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
958 // Check whether Start+Step*MaxBECount has no unsigned overflow.
959 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
960 const SCEV *Add = getAddExpr(Start, ZMul);
961 const SCEV *OperandExtendedAdd =
962 getAddExpr(getZeroExtendExpr(Start, WideTy),
963 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
964 getZeroExtendExpr(Step, WideTy)));
965 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) {
966 // Cache knowledge of AR NUW, which is propagated to this AddRec.
967 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
968 // Return the expression with the addrec on the outside.
969 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
970 getZeroExtendExpr(Step, Ty),
971 L, AR->getNoWrapFlags());
973 // Similar to above, only this time treat the step value as signed.
974 // This covers loops that count down.
975 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
976 Add = getAddExpr(Start, SMul);
978 getAddExpr(getZeroExtendExpr(Start, WideTy),
979 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
980 getSignExtendExpr(Step, WideTy)));
981 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) {
982 // Cache knowledge of AR NW, which is propagated to this AddRec.
983 // Negative step causes unsigned wrap, but it still can't self-wrap.
984 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
985 // Return the expression with the addrec on the outside.
986 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
987 getSignExtendExpr(Step, Ty),
988 L, AR->getNoWrapFlags());
992 // If the backedge is guarded by a comparison with the pre-inc value
993 // the addrec is safe. Also, if the entry is guarded by a comparison
994 // with the start value and the backedge is guarded by a comparison
995 // with the post-inc value, the addrec is safe.
996 if (isKnownPositive(Step)) {
997 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
998 getUnsignedRange(Step).getUnsignedMax());
999 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1000 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1001 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1002 AR->getPostIncExpr(*this), N))) {
1003 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1004 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1005 // Return the expression with the addrec on the outside.
1006 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1007 getZeroExtendExpr(Step, Ty),
1008 L, AR->getNoWrapFlags());
1010 } else if (isKnownNegative(Step)) {
1011 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1012 getSignedRange(Step).getSignedMin());
1013 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1014 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1015 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1016 AR->getPostIncExpr(*this), N))) {
1017 // Cache knowledge of AR NW, which is propagated to this AddRec.
1018 // Negative step causes unsigned wrap, but it still can't self-wrap.
1019 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1020 // Return the expression with the addrec on the outside.
1021 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1022 getSignExtendExpr(Step, Ty),
1023 L, AR->getNoWrapFlags());
1029 // The cast wasn't folded; create an explicit cast node.
1030 // Recompute the insert position, as it may have been invalidated.
1031 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1032 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1034 UniqueSCEVs.InsertNode(S, IP);
1038 // Get the limit of a recurrence such that incrementing by Step cannot cause
1039 // signed overflow as long as the value of the recurrence within the loop does
1040 // not exceed this limit before incrementing.
1041 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1042 ICmpInst::Predicate *Pred,
1043 ScalarEvolution *SE) {
1044 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1045 if (SE->isKnownPositive(Step)) {
1046 *Pred = ICmpInst::ICMP_SLT;
1047 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1048 SE->getSignedRange(Step).getSignedMax());
1050 if (SE->isKnownNegative(Step)) {
1051 *Pred = ICmpInst::ICMP_SGT;
1052 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1053 SE->getSignedRange(Step).getSignedMin());
1058 // The recurrence AR has been shown to have no signed wrap. Typically, if we can
1059 // prove NSW for AR, then we can just as easily prove NSW for its preincrement
1060 // or postincrement sibling. This allows normalizing a sign extended AddRec as
1061 // such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a
1062 // result, the expression "Step + sext(PreIncAR)" is congruent with
1063 // "sext(PostIncAR)"
1064 static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR,
1066 ScalarEvolution *SE) {
1067 const Loop *L = AR->getLoop();
1068 const SCEV *Start = AR->getStart();
1069 const SCEV *Step = AR->getStepRecurrence(*SE);
1071 // Check for a simple looking step prior to loop entry.
1072 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1073 if (!SA || SA->getNumOperands() != 2 || SA->getOperand(0) != Step)
1076 // This is a postinc AR. Check for overflow on the preinc recurrence using the
1077 // same three conditions that getSignExtendedExpr checks.
1079 // 1. NSW flags on the step increment.
1080 const SCEV *PreStart = SA->getOperand(1);
1081 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1082 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1084 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW))
1087 // 2. Direct overflow check on the step operation's expression.
1088 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1089 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1090 const SCEV *OperandExtendedStart =
1091 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy),
1092 SE->getSignExtendExpr(Step, WideTy));
1093 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) {
1094 // Cache knowledge of PreAR NSW.
1096 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW);
1097 // FIXME: this optimization needs a unit test
1098 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n");
1102 // 3. Loop precondition.
1103 ICmpInst::Predicate Pred;
1104 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE);
1106 if (OverflowLimit &&
1107 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1113 // Get the normalized sign-extended expression for this AddRec's Start.
1114 static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR,
1116 ScalarEvolution *SE) {
1117 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE);
1119 return SE->getSignExtendExpr(AR->getStart(), Ty);
1121 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty),
1122 SE->getSignExtendExpr(PreStart, Ty));
1125 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1127 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1128 "This is not an extending conversion!");
1129 assert(isSCEVable(Ty) &&
1130 "This is not a conversion to a SCEVable type!");
1131 Ty = getEffectiveSCEVType(Ty);
1133 // Fold if the operand is constant.
1134 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1136 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(),
1137 getEffectiveSCEVType(Ty))));
1139 // sext(sext(x)) --> sext(x)
1140 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1141 return getSignExtendExpr(SS->getOperand(), Ty);
1143 // sext(zext(x)) --> zext(x)
1144 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1145 return getZeroExtendExpr(SZ->getOperand(), Ty);
1147 // Before doing any expensive analysis, check to see if we've already
1148 // computed a SCEV for this Op and Ty.
1149 FoldingSetNodeID ID;
1150 ID.AddInteger(scSignExtend);
1154 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1156 // If the input value is provably positive, build a zext instead.
1157 if (isKnownNonNegative(Op))
1158 return getZeroExtendExpr(Op, Ty);
1160 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1161 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1162 // It's possible the bits taken off by the truncate were all sign bits. If
1163 // so, we should be able to simplify this further.
1164 const SCEV *X = ST->getOperand();
1165 ConstantRange CR = getSignedRange(X);
1166 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1167 unsigned NewBits = getTypeSizeInBits(Ty);
1168 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1169 CR.sextOrTrunc(NewBits)))
1170 return getTruncateOrSignExtend(X, Ty);
1173 // If the input value is a chrec scev, and we can prove that the value
1174 // did not overflow the old, smaller, value, we can sign extend all of the
1175 // operands (often constants). This allows analysis of something like
1176 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1177 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1178 if (AR->isAffine()) {
1179 const SCEV *Start = AR->getStart();
1180 const SCEV *Step = AR->getStepRecurrence(*this);
1181 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1182 const Loop *L = AR->getLoop();
1184 // If we have special knowledge that this addrec won't overflow,
1185 // we don't need to do any further analysis.
1186 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1187 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1188 getSignExtendExpr(Step, Ty),
1191 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1192 // Note that this serves two purposes: It filters out loops that are
1193 // simply not analyzable, and it covers the case where this code is
1194 // being called from within backedge-taken count analysis, such that
1195 // attempting to ask for the backedge-taken count would likely result
1196 // in infinite recursion. In the later case, the analysis code will
1197 // cope with a conservative value, and it will take care to purge
1198 // that value once it has finished.
1199 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1200 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1201 // Manually compute the final value for AR, checking for
1204 // Check whether the backedge-taken count can be losslessly casted to
1205 // the addrec's type. The count is always unsigned.
1206 const SCEV *CastedMaxBECount =
1207 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1208 const SCEV *RecastedMaxBECount =
1209 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1210 if (MaxBECount == RecastedMaxBECount) {
1211 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1212 // Check whether Start+Step*MaxBECount has no signed overflow.
1213 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1214 const SCEV *Add = getAddExpr(Start, SMul);
1215 const SCEV *OperandExtendedAdd =
1216 getAddExpr(getSignExtendExpr(Start, WideTy),
1217 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1218 getSignExtendExpr(Step, WideTy)));
1219 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) {
1220 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1221 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1222 // Return the expression with the addrec on the outside.
1223 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1224 getSignExtendExpr(Step, Ty),
1225 L, AR->getNoWrapFlags());
1227 // Similar to above, only this time treat the step value as unsigned.
1228 // This covers loops that count up with an unsigned step.
1229 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step);
1230 Add = getAddExpr(Start, UMul);
1231 OperandExtendedAdd =
1232 getAddExpr(getSignExtendExpr(Start, WideTy),
1233 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1234 getZeroExtendExpr(Step, WideTy)));
1235 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) {
1236 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1237 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1238 // Return the expression with the addrec on the outside.
1239 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1240 getZeroExtendExpr(Step, Ty),
1241 L, AR->getNoWrapFlags());
1245 // If the backedge is guarded by a comparison with the pre-inc value
1246 // the addrec is safe. Also, if the entry is guarded by a comparison
1247 // with the start value and the backedge is guarded by a comparison
1248 // with the post-inc value, the addrec is safe.
1249 ICmpInst::Predicate Pred;
1250 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
1251 if (OverflowLimit &&
1252 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1253 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1254 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1256 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1257 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1258 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1259 getSignExtendExpr(Step, Ty),
1260 L, AR->getNoWrapFlags());
1265 // The cast wasn't folded; create an explicit cast node.
1266 // Recompute the insert position, as it may have been invalidated.
1267 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1268 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1270 UniqueSCEVs.InsertNode(S, IP);
1274 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1275 /// unspecified bits out to the given type.
1277 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1279 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1280 "This is not an extending conversion!");
1281 assert(isSCEVable(Ty) &&
1282 "This is not a conversion to a SCEVable type!");
1283 Ty = getEffectiveSCEVType(Ty);
1285 // Sign-extend negative constants.
1286 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1287 if (SC->getValue()->getValue().isNegative())
1288 return getSignExtendExpr(Op, Ty);
1290 // Peel off a truncate cast.
1291 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1292 const SCEV *NewOp = T->getOperand();
1293 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1294 return getAnyExtendExpr(NewOp, Ty);
1295 return getTruncateOrNoop(NewOp, Ty);
1298 // Next try a zext cast. If the cast is folded, use it.
1299 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1300 if (!isa<SCEVZeroExtendExpr>(ZExt))
1303 // Next try a sext cast. If the cast is folded, use it.
1304 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1305 if (!isa<SCEVSignExtendExpr>(SExt))
1308 // Force the cast to be folded into the operands of an addrec.
1309 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1310 SmallVector<const SCEV *, 4> Ops;
1311 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1313 Ops.push_back(getAnyExtendExpr(*I, Ty));
1314 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1317 // As a special case, fold anyext(undef) to undef. We don't want to
1318 // know too much about SCEVUnknowns, but this special case is handy
1320 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
1321 if (isa<UndefValue>(U->getValue()))
1322 return getSCEV(UndefValue::get(Ty));
1324 // If the expression is obviously signed, use the sext cast value.
1325 if (isa<SCEVSMaxExpr>(Op))
1328 // Absent any other information, use the zext cast value.
1332 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1333 /// a list of operands to be added under the given scale, update the given
1334 /// map. This is a helper function for getAddRecExpr. As an example of
1335 /// what it does, given a sequence of operands that would form an add
1336 /// expression like this:
1338 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1340 /// where A and B are constants, update the map with these values:
1342 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1344 /// and add 13 + A*B*29 to AccumulatedConstant.
1345 /// This will allow getAddRecExpr to produce this:
1347 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1349 /// This form often exposes folding opportunities that are hidden in
1350 /// the original operand list.
1352 /// Return true iff it appears that any interesting folding opportunities
1353 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1354 /// the common case where no interesting opportunities are present, and
1355 /// is also used as a check to avoid infinite recursion.
1358 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1359 SmallVector<const SCEV *, 8> &NewOps,
1360 APInt &AccumulatedConstant,
1361 const SCEV *const *Ops, size_t NumOperands,
1363 ScalarEvolution &SE) {
1364 bool Interesting = false;
1366 // Iterate over the add operands. They are sorted, with constants first.
1368 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1370 // Pull a buried constant out to the outside.
1371 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1373 AccumulatedConstant += Scale * C->getValue()->getValue();
1376 // Next comes everything else. We're especially interested in multiplies
1377 // here, but they're in the middle, so just visit the rest with one loop.
1378 for (; i != NumOperands; ++i) {
1379 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1380 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1382 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1383 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1384 // A multiplication of a constant with another add; recurse.
1385 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1387 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1388 Add->op_begin(), Add->getNumOperands(),
1391 // A multiplication of a constant with some other value. Update
1393 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1394 const SCEV *Key = SE.getMulExpr(MulOps);
1395 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1396 M.insert(std::make_pair(Key, NewScale));
1398 NewOps.push_back(Pair.first->first);
1400 Pair.first->second += NewScale;
1401 // The map already had an entry for this value, which may indicate
1402 // a folding opportunity.
1407 // An ordinary operand. Update the map.
1408 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1409 M.insert(std::make_pair(Ops[i], Scale));
1411 NewOps.push_back(Pair.first->first);
1413 Pair.first->second += Scale;
1414 // The map already had an entry for this value, which may indicate
1415 // a folding opportunity.
1425 struct APIntCompare {
1426 bool operator()(const APInt &LHS, const APInt &RHS) const {
1427 return LHS.ult(RHS);
1432 /// getAddExpr - Get a canonical add expression, or something simpler if
1434 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1435 SCEV::NoWrapFlags Flags) {
1436 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1437 "only nuw or nsw allowed");
1438 assert(!Ops.empty() && "Cannot get empty add!");
1439 if (Ops.size() == 1) return Ops[0];
1441 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1442 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1443 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1444 "SCEVAddExpr operand types don't match!");
1447 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1449 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1450 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1451 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1453 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1454 E = Ops.end(); I != E; ++I)
1455 if (!isKnownNonNegative(*I)) {
1459 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1462 // Sort by complexity, this groups all similar expression types together.
1463 GroupByComplexity(Ops, LI);
1465 // If there are any constants, fold them together.
1467 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1469 assert(Idx < Ops.size());
1470 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1471 // We found two constants, fold them together!
1472 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1473 RHSC->getValue()->getValue());
1474 if (Ops.size() == 2) return Ops[0];
1475 Ops.erase(Ops.begin()+1); // Erase the folded element
1476 LHSC = cast<SCEVConstant>(Ops[0]);
1479 // If we are left with a constant zero being added, strip it off.
1480 if (LHSC->getValue()->isZero()) {
1481 Ops.erase(Ops.begin());
1485 if (Ops.size() == 1) return Ops[0];
1488 // Okay, check to see if the same value occurs in the operand list more than
1489 // once. If so, merge them together into an multiply expression. Since we
1490 // sorted the list, these values are required to be adjacent.
1491 Type *Ty = Ops[0]->getType();
1492 bool FoundMatch = false;
1493 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1494 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1495 // Scan ahead to count how many equal operands there are.
1497 while (i+Count != e && Ops[i+Count] == Ops[i])
1499 // Merge the values into a multiply.
1500 const SCEV *Scale = getConstant(Ty, Count);
1501 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1502 if (Ops.size() == Count)
1505 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1506 --i; e -= Count - 1;
1510 return getAddExpr(Ops, Flags);
1512 // Check for truncates. If all the operands are truncated from the same
1513 // type, see if factoring out the truncate would permit the result to be
1514 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1515 // if the contents of the resulting outer trunc fold to something simple.
1516 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1517 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1518 Type *DstType = Trunc->getType();
1519 Type *SrcType = Trunc->getOperand()->getType();
1520 SmallVector<const SCEV *, 8> LargeOps;
1522 // Check all the operands to see if they can be represented in the
1523 // source type of the truncate.
1524 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1525 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1526 if (T->getOperand()->getType() != SrcType) {
1530 LargeOps.push_back(T->getOperand());
1531 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1532 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1533 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1534 SmallVector<const SCEV *, 8> LargeMulOps;
1535 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1536 if (const SCEVTruncateExpr *T =
1537 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1538 if (T->getOperand()->getType() != SrcType) {
1542 LargeMulOps.push_back(T->getOperand());
1543 } else if (const SCEVConstant *C =
1544 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1545 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1552 LargeOps.push_back(getMulExpr(LargeMulOps));
1559 // Evaluate the expression in the larger type.
1560 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1561 // If it folds to something simple, use it. Otherwise, don't.
1562 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1563 return getTruncateExpr(Fold, DstType);
1567 // Skip past any other cast SCEVs.
1568 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1571 // If there are add operands they would be next.
1572 if (Idx < Ops.size()) {
1573 bool DeletedAdd = false;
1574 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1575 // If we have an add, expand the add operands onto the end of the operands
1577 Ops.erase(Ops.begin()+Idx);
1578 Ops.append(Add->op_begin(), Add->op_end());
1582 // If we deleted at least one add, we added operands to the end of the list,
1583 // and they are not necessarily sorted. Recurse to resort and resimplify
1584 // any operands we just acquired.
1586 return getAddExpr(Ops);
1589 // Skip over the add expression until we get to a multiply.
1590 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1593 // Check to see if there are any folding opportunities present with
1594 // operands multiplied by constant values.
1595 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1596 uint64_t BitWidth = getTypeSizeInBits(Ty);
1597 DenseMap<const SCEV *, APInt> M;
1598 SmallVector<const SCEV *, 8> NewOps;
1599 APInt AccumulatedConstant(BitWidth, 0);
1600 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1601 Ops.data(), Ops.size(),
1602 APInt(BitWidth, 1), *this)) {
1603 // Some interesting folding opportunity is present, so its worthwhile to
1604 // re-generate the operands list. Group the operands by constant scale,
1605 // to avoid multiplying by the same constant scale multiple times.
1606 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1607 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(),
1608 E = NewOps.end(); I != E; ++I)
1609 MulOpLists[M.find(*I)->second].push_back(*I);
1610 // Re-generate the operands list.
1612 if (AccumulatedConstant != 0)
1613 Ops.push_back(getConstant(AccumulatedConstant));
1614 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1615 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1617 Ops.push_back(getMulExpr(getConstant(I->first),
1618 getAddExpr(I->second)));
1620 return getConstant(Ty, 0);
1621 if (Ops.size() == 1)
1623 return getAddExpr(Ops);
1627 // If we are adding something to a multiply expression, make sure the
1628 // something is not already an operand of the multiply. If so, merge it into
1630 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1631 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1632 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1633 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1634 if (isa<SCEVConstant>(MulOpSCEV))
1636 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1637 if (MulOpSCEV == Ops[AddOp]) {
1638 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1639 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1640 if (Mul->getNumOperands() != 2) {
1641 // If the multiply has more than two operands, we must get the
1643 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1644 Mul->op_begin()+MulOp);
1645 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1646 InnerMul = getMulExpr(MulOps);
1648 const SCEV *One = getConstant(Ty, 1);
1649 const SCEV *AddOne = getAddExpr(One, InnerMul);
1650 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1651 if (Ops.size() == 2) return OuterMul;
1653 Ops.erase(Ops.begin()+AddOp);
1654 Ops.erase(Ops.begin()+Idx-1);
1656 Ops.erase(Ops.begin()+Idx);
1657 Ops.erase(Ops.begin()+AddOp-1);
1659 Ops.push_back(OuterMul);
1660 return getAddExpr(Ops);
1663 // Check this multiply against other multiplies being added together.
1664 for (unsigned OtherMulIdx = Idx+1;
1665 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1667 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1668 // If MulOp occurs in OtherMul, we can fold the two multiplies
1670 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1671 OMulOp != e; ++OMulOp)
1672 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1673 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1674 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1675 if (Mul->getNumOperands() != 2) {
1676 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1677 Mul->op_begin()+MulOp);
1678 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1679 InnerMul1 = getMulExpr(MulOps);
1681 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1682 if (OtherMul->getNumOperands() != 2) {
1683 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1684 OtherMul->op_begin()+OMulOp);
1685 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1686 InnerMul2 = getMulExpr(MulOps);
1688 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1689 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1690 if (Ops.size() == 2) return OuterMul;
1691 Ops.erase(Ops.begin()+Idx);
1692 Ops.erase(Ops.begin()+OtherMulIdx-1);
1693 Ops.push_back(OuterMul);
1694 return getAddExpr(Ops);
1700 // If there are any add recurrences in the operands list, see if any other
1701 // added values are loop invariant. If so, we can fold them into the
1703 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1706 // Scan over all recurrences, trying to fold loop invariants into them.
1707 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1708 // Scan all of the other operands to this add and add them to the vector if
1709 // they are loop invariant w.r.t. the recurrence.
1710 SmallVector<const SCEV *, 8> LIOps;
1711 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1712 const Loop *AddRecLoop = AddRec->getLoop();
1713 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1714 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1715 LIOps.push_back(Ops[i]);
1716 Ops.erase(Ops.begin()+i);
1720 // If we found some loop invariants, fold them into the recurrence.
1721 if (!LIOps.empty()) {
1722 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1723 LIOps.push_back(AddRec->getStart());
1725 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1727 AddRecOps[0] = getAddExpr(LIOps);
1729 // Build the new addrec. Propagate the NUW and NSW flags if both the
1730 // outer add and the inner addrec are guaranteed to have no overflow.
1731 // Always propagate NW.
1732 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
1733 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
1735 // If all of the other operands were loop invariant, we are done.
1736 if (Ops.size() == 1) return NewRec;
1738 // Otherwise, add the folded AddRec by the non-invariant parts.
1739 for (unsigned i = 0;; ++i)
1740 if (Ops[i] == AddRec) {
1744 return getAddExpr(Ops);
1747 // Okay, if there weren't any loop invariants to be folded, check to see if
1748 // there are multiple AddRec's with the same loop induction variable being
1749 // added together. If so, we can fold them.
1750 for (unsigned OtherIdx = Idx+1;
1751 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1753 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1754 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
1755 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1757 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1759 if (const SCEVAddRecExpr *OtherAddRec =
1760 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1761 if (OtherAddRec->getLoop() == AddRecLoop) {
1762 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
1764 if (i >= AddRecOps.size()) {
1765 AddRecOps.append(OtherAddRec->op_begin()+i,
1766 OtherAddRec->op_end());
1769 AddRecOps[i] = getAddExpr(AddRecOps[i],
1770 OtherAddRec->getOperand(i));
1772 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1774 // Step size has changed, so we cannot guarantee no self-wraparound.
1775 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
1776 return getAddExpr(Ops);
1779 // Otherwise couldn't fold anything into this recurrence. Move onto the
1783 // Okay, it looks like we really DO need an add expr. Check to see if we
1784 // already have one, otherwise create a new one.
1785 FoldingSetNodeID ID;
1786 ID.AddInteger(scAddExpr);
1787 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1788 ID.AddPointer(Ops[i]);
1791 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1793 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1794 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1795 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1797 UniqueSCEVs.InsertNode(S, IP);
1799 S->setNoWrapFlags(Flags);
1803 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1805 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1806 SCEV::NoWrapFlags Flags) {
1807 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
1808 "only nuw or nsw allowed");
1809 assert(!Ops.empty() && "Cannot get empty mul!");
1810 if (Ops.size() == 1) return Ops[0];
1812 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1813 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1814 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1815 "SCEVMulExpr operand types don't match!");
1818 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1820 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1821 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1822 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1824 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1825 E = Ops.end(); I != E; ++I)
1826 if (!isKnownNonNegative(*I)) {
1830 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1833 // Sort by complexity, this groups all similar expression types together.
1834 GroupByComplexity(Ops, LI);
1836 // If there are any constants, fold them together.
1838 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1840 // C1*(C2+V) -> C1*C2 + C1*V
1841 if (Ops.size() == 2)
1842 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1843 if (Add->getNumOperands() == 2 &&
1844 isa<SCEVConstant>(Add->getOperand(0)))
1845 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1846 getMulExpr(LHSC, Add->getOperand(1)));
1849 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1850 // We found two constants, fold them together!
1851 ConstantInt *Fold = ConstantInt::get(getContext(),
1852 LHSC->getValue()->getValue() *
1853 RHSC->getValue()->getValue());
1854 Ops[0] = getConstant(Fold);
1855 Ops.erase(Ops.begin()+1); // Erase the folded element
1856 if (Ops.size() == 1) return Ops[0];
1857 LHSC = cast<SCEVConstant>(Ops[0]);
1860 // If we are left with a constant one being multiplied, strip it off.
1861 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1862 Ops.erase(Ops.begin());
1864 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1865 // If we have a multiply of zero, it will always be zero.
1867 } else if (Ops[0]->isAllOnesValue()) {
1868 // If we have a mul by -1 of an add, try distributing the -1 among the
1870 if (Ops.size() == 2) {
1871 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1872 SmallVector<const SCEV *, 4> NewOps;
1873 bool AnyFolded = false;
1874 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
1875 E = Add->op_end(); I != E; ++I) {
1876 const SCEV *Mul = getMulExpr(Ops[0], *I);
1877 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1878 NewOps.push_back(Mul);
1881 return getAddExpr(NewOps);
1883 else if (const SCEVAddRecExpr *
1884 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
1885 // Negation preserves a recurrence's no self-wrap property.
1886 SmallVector<const SCEV *, 4> Operands;
1887 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
1888 E = AddRec->op_end(); I != E; ++I) {
1889 Operands.push_back(getMulExpr(Ops[0], *I));
1891 return getAddRecExpr(Operands, AddRec->getLoop(),
1892 AddRec->getNoWrapFlags(SCEV::FlagNW));
1897 if (Ops.size() == 1)
1901 // Skip over the add expression until we get to a multiply.
1902 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1905 // If there are mul operands inline them all into this expression.
1906 if (Idx < Ops.size()) {
1907 bool DeletedMul = false;
1908 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1909 // If we have an mul, expand the mul operands onto the end of the operands
1911 Ops.erase(Ops.begin()+Idx);
1912 Ops.append(Mul->op_begin(), Mul->op_end());
1916 // If we deleted at least one mul, we added operands to the end of the list,
1917 // and they are not necessarily sorted. Recurse to resort and resimplify
1918 // any operands we just acquired.
1920 return getMulExpr(Ops);
1923 // If there are any add recurrences in the operands list, see if any other
1924 // added values are loop invariant. If so, we can fold them into the
1926 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1929 // Scan over all recurrences, trying to fold loop invariants into them.
1930 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1931 // Scan all of the other operands to this mul and add them to the vector if
1932 // they are loop invariant w.r.t. the recurrence.
1933 SmallVector<const SCEV *, 8> LIOps;
1934 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1935 const Loop *AddRecLoop = AddRec->getLoop();
1936 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1937 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1938 LIOps.push_back(Ops[i]);
1939 Ops.erase(Ops.begin()+i);
1943 // If we found some loop invariants, fold them into the recurrence.
1944 if (!LIOps.empty()) {
1945 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1946 SmallVector<const SCEV *, 4> NewOps;
1947 NewOps.reserve(AddRec->getNumOperands());
1948 const SCEV *Scale = getMulExpr(LIOps);
1949 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1950 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1952 // Build the new addrec. Propagate the NUW and NSW flags if both the
1953 // outer mul and the inner addrec are guaranteed to have no overflow.
1955 // No self-wrap cannot be guaranteed after changing the step size, but
1956 // will be inferred if either NUW or NSW is true.
1957 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
1958 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
1960 // If all of the other operands were loop invariant, we are done.
1961 if (Ops.size() == 1) return NewRec;
1963 // Otherwise, multiply the folded AddRec by the non-invariant parts.
1964 for (unsigned i = 0;; ++i)
1965 if (Ops[i] == AddRec) {
1969 return getMulExpr(Ops);
1972 // Okay, if there weren't any loop invariants to be folded, check to see if
1973 // there are multiple AddRec's with the same loop induction variable being
1974 // multiplied together. If so, we can fold them.
1975 for (unsigned OtherIdx = Idx+1;
1976 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1979 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1980 // {A,+,B}<L> * {C,+,D}<L> --> {A*C,+,A*D + B*C + B*D,+,2*B*D}<L>
1982 // {A,+,B} * {C,+,D} = A+It*B * C+It*D = A*C + (A*D + B*C)*It + B*D*It^2
1983 // Given an equation of the form x + y*It + z*It^2 (above), we want to
1984 // express it in terms of {X,+,Y,+,Z}.
1985 // {X,+,Y,+,Z} = X + Y*It + Z*(It^2 - It)/2.
1986 // Rearranging, X = x, Y = y+z, Z = 2z.
1988 // x = A*C, y = (A*D + B*C), z = B*D.
1989 // Therefore X = A*C, Y = A*D + B*C + B*D and Z = 2*B*D.
1990 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1992 if (const SCEVAddRecExpr *OtherAddRec =
1993 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1994 if (OtherAddRec->getLoop() == AddRecLoop) {
1995 const SCEV *A = AddRec->getStart();
1996 const SCEV *B = AddRec->getStepRecurrence(*this);
1997 const SCEV *C = OtherAddRec->getStart();
1998 const SCEV *D = OtherAddRec->getStepRecurrence(*this);
1999 const SCEV *NewStart = getMulExpr(A, C);
2000 const SCEV *BD = getMulExpr(B, D);
2001 const SCEV *NewStep = getAddExpr(getMulExpr(A, D),
2002 getMulExpr(B, C), BD);
2003 const SCEV *NewSecondOrderStep =
2004 getMulExpr(BD, getConstant(BD->getType(), 2));
2006 // This can happen when AddRec or OtherAddRec have >3 operands.
2007 // TODO: support these add-recs.
2008 if (isLoopInvariant(NewStart, AddRecLoop) &&
2009 isLoopInvariant(NewStep, AddRecLoop) &&
2010 isLoopInvariant(NewSecondOrderStep, AddRecLoop)) {
2011 SmallVector<const SCEV *, 3> AddRecOps;
2012 AddRecOps.push_back(NewStart);
2013 AddRecOps.push_back(NewStep);
2014 AddRecOps.push_back(NewSecondOrderStep);
2015 const SCEV *NewAddRec = getAddRecExpr(AddRecOps,
2018 if (Ops.size() == 2) return NewAddRec;
2019 Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec);
2020 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2025 return getMulExpr(Ops);
2029 // Otherwise couldn't fold anything into this recurrence. Move onto the
2033 // Okay, it looks like we really DO need an mul expr. Check to see if we
2034 // already have one, otherwise create a new one.
2035 FoldingSetNodeID ID;
2036 ID.AddInteger(scMulExpr);
2037 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2038 ID.AddPointer(Ops[i]);
2041 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2043 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2044 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2045 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2047 UniqueSCEVs.InsertNode(S, IP);
2049 S->setNoWrapFlags(Flags);
2053 /// getUDivExpr - Get a canonical unsigned division expression, or something
2054 /// simpler if possible.
2055 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2057 assert(getEffectiveSCEVType(LHS->getType()) ==
2058 getEffectiveSCEVType(RHS->getType()) &&
2059 "SCEVUDivExpr operand types don't match!");
2061 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2062 if (RHSC->getValue()->equalsInt(1))
2063 return LHS; // X udiv 1 --> x
2064 // If the denominator is zero, the result of the udiv is undefined. Don't
2065 // try to analyze it, because the resolution chosen here may differ from
2066 // the resolution chosen in other parts of the compiler.
2067 if (!RHSC->getValue()->isZero()) {
2068 // Determine if the division can be folded into the operands of
2070 // TODO: Generalize this to non-constants by using known-bits information.
2071 Type *Ty = LHS->getType();
2072 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2073 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2074 // For non-power-of-two values, effectively round the value up to the
2075 // nearest power of two.
2076 if (!RHSC->getValue()->getValue().isPowerOf2())
2078 IntegerType *ExtTy =
2079 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2080 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2081 if (const SCEVConstant *Step =
2082 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2083 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2084 const APInt &StepInt = Step->getValue()->getValue();
2085 const APInt &DivInt = RHSC->getValue()->getValue();
2086 if (!StepInt.urem(DivInt) &&
2087 getZeroExtendExpr(AR, ExtTy) ==
2088 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2089 getZeroExtendExpr(Step, ExtTy),
2090 AR->getLoop(), SCEV::FlagAnyWrap)) {
2091 SmallVector<const SCEV *, 4> Operands;
2092 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2093 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2094 return getAddRecExpr(Operands, AR->getLoop(),
2097 /// Get a canonical UDivExpr for a recurrence.
2098 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2099 // We can currently only fold X%N if X is constant.
2100 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2101 if (StartC && !DivInt.urem(StepInt) &&
2102 getZeroExtendExpr(AR, ExtTy) ==
2103 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2104 getZeroExtendExpr(Step, ExtTy),
2105 AR->getLoop(), SCEV::FlagAnyWrap)) {
2106 const APInt &StartInt = StartC->getValue()->getValue();
2107 const APInt &StartRem = StartInt.urem(StepInt);
2109 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2110 AR->getLoop(), SCEV::FlagNW);
2113 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2114 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2115 SmallVector<const SCEV *, 4> Operands;
2116 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2117 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2118 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2119 // Find an operand that's safely divisible.
2120 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2121 const SCEV *Op = M->getOperand(i);
2122 const SCEV *Div = getUDivExpr(Op, RHSC);
2123 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2124 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2127 return getMulExpr(Operands);
2131 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2132 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2133 SmallVector<const SCEV *, 4> Operands;
2134 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2135 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2136 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2138 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2139 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2140 if (isa<SCEVUDivExpr>(Op) ||
2141 getMulExpr(Op, RHS) != A->getOperand(i))
2143 Operands.push_back(Op);
2145 if (Operands.size() == A->getNumOperands())
2146 return getAddExpr(Operands);
2150 // Fold if both operands are constant.
2151 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2152 Constant *LHSCV = LHSC->getValue();
2153 Constant *RHSCV = RHSC->getValue();
2154 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2160 FoldingSetNodeID ID;
2161 ID.AddInteger(scUDivExpr);
2165 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2166 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2168 UniqueSCEVs.InsertNode(S, IP);
2173 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2174 /// Simplify the expression as much as possible.
2175 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2177 SCEV::NoWrapFlags Flags) {
2178 SmallVector<const SCEV *, 4> Operands;
2179 Operands.push_back(Start);
2180 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2181 if (StepChrec->getLoop() == L) {
2182 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2183 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2186 Operands.push_back(Step);
2187 return getAddRecExpr(Operands, L, Flags);
2190 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2191 /// Simplify the expression as much as possible.
2193 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2194 const Loop *L, SCEV::NoWrapFlags Flags) {
2195 if (Operands.size() == 1) return Operands[0];
2197 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2198 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2199 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2200 "SCEVAddRecExpr operand types don't match!");
2201 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2202 assert(isLoopInvariant(Operands[i], L) &&
2203 "SCEVAddRecExpr operand is not loop-invariant!");
2206 if (Operands.back()->isZero()) {
2207 Operands.pop_back();
2208 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2211 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2212 // use that information to infer NUW and NSW flags. However, computing a
2213 // BE count requires calling getAddRecExpr, so we may not yet have a
2214 // meaningful BE count at this point (and if we don't, we'd be stuck
2215 // with a SCEVCouldNotCompute as the cached BE count).
2217 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2219 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2220 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
2221 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
2223 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2224 E = Operands.end(); I != E; ++I)
2225 if (!isKnownNonNegative(*I)) {
2229 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2232 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2233 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2234 const Loop *NestedLoop = NestedAR->getLoop();
2235 if (L->contains(NestedLoop) ?
2236 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2237 (!NestedLoop->contains(L) &&
2238 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2239 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2240 NestedAR->op_end());
2241 Operands[0] = NestedAR->getStart();
2242 // AddRecs require their operands be loop-invariant with respect to their
2243 // loops. Don't perform this transformation if it would break this
2245 bool AllInvariant = true;
2246 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2247 if (!isLoopInvariant(Operands[i], L)) {
2248 AllInvariant = false;
2252 // Create a recurrence for the outer loop with the same step size.
2254 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2255 // inner recurrence has the same property.
2256 SCEV::NoWrapFlags OuterFlags =
2257 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2259 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2260 AllInvariant = true;
2261 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2262 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2263 AllInvariant = false;
2267 // Ok, both add recurrences are valid after the transformation.
2269 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2270 // the outer recurrence has the same property.
2271 SCEV::NoWrapFlags InnerFlags =
2272 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2273 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2276 // Reset Operands to its original state.
2277 Operands[0] = NestedAR;
2281 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2282 // already have one, otherwise create a new one.
2283 FoldingSetNodeID ID;
2284 ID.AddInteger(scAddRecExpr);
2285 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2286 ID.AddPointer(Operands[i]);
2290 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2292 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2293 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2294 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2295 O, Operands.size(), L);
2296 UniqueSCEVs.InsertNode(S, IP);
2298 S->setNoWrapFlags(Flags);
2302 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2304 SmallVector<const SCEV *, 2> Ops;
2307 return getSMaxExpr(Ops);
2311 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2312 assert(!Ops.empty() && "Cannot get empty smax!");
2313 if (Ops.size() == 1) return Ops[0];
2315 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2316 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2317 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2318 "SCEVSMaxExpr operand types don't match!");
2321 // Sort by complexity, this groups all similar expression types together.
2322 GroupByComplexity(Ops, LI);
2324 // If there are any constants, fold them together.
2326 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2328 assert(Idx < Ops.size());
2329 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2330 // We found two constants, fold them together!
2331 ConstantInt *Fold = ConstantInt::get(getContext(),
2332 APIntOps::smax(LHSC->getValue()->getValue(),
2333 RHSC->getValue()->getValue()));
2334 Ops[0] = getConstant(Fold);
2335 Ops.erase(Ops.begin()+1); // Erase the folded element
2336 if (Ops.size() == 1) return Ops[0];
2337 LHSC = cast<SCEVConstant>(Ops[0]);
2340 // If we are left with a constant minimum-int, strip it off.
2341 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2342 Ops.erase(Ops.begin());
2344 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2345 // If we have an smax with a constant maximum-int, it will always be
2350 if (Ops.size() == 1) return Ops[0];
2353 // Find the first SMax
2354 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2357 // Check to see if one of the operands is an SMax. If so, expand its operands
2358 // onto our operand list, and recurse to simplify.
2359 if (Idx < Ops.size()) {
2360 bool DeletedSMax = false;
2361 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2362 Ops.erase(Ops.begin()+Idx);
2363 Ops.append(SMax->op_begin(), SMax->op_end());
2368 return getSMaxExpr(Ops);
2371 // Okay, check to see if the same value occurs in the operand list twice. If
2372 // so, delete one. Since we sorted the list, these values are required to
2374 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2375 // X smax Y smax Y --> X smax Y
2376 // X smax Y --> X, if X is always greater than Y
2377 if (Ops[i] == Ops[i+1] ||
2378 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2379 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2381 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2382 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2386 if (Ops.size() == 1) return Ops[0];
2388 assert(!Ops.empty() && "Reduced smax down to nothing!");
2390 // Okay, it looks like we really DO need an smax expr. Check to see if we
2391 // already have one, otherwise create a new one.
2392 FoldingSetNodeID ID;
2393 ID.AddInteger(scSMaxExpr);
2394 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2395 ID.AddPointer(Ops[i]);
2397 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2398 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2399 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2400 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2402 UniqueSCEVs.InsertNode(S, IP);
2406 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2408 SmallVector<const SCEV *, 2> Ops;
2411 return getUMaxExpr(Ops);
2415 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2416 assert(!Ops.empty() && "Cannot get empty umax!");
2417 if (Ops.size() == 1) return Ops[0];
2419 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2420 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2421 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2422 "SCEVUMaxExpr operand types don't match!");
2425 // Sort by complexity, this groups all similar expression types together.
2426 GroupByComplexity(Ops, LI);
2428 // If there are any constants, fold them together.
2430 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2432 assert(Idx < Ops.size());
2433 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2434 // We found two constants, fold them together!
2435 ConstantInt *Fold = ConstantInt::get(getContext(),
2436 APIntOps::umax(LHSC->getValue()->getValue(),
2437 RHSC->getValue()->getValue()));
2438 Ops[0] = getConstant(Fold);
2439 Ops.erase(Ops.begin()+1); // Erase the folded element
2440 if (Ops.size() == 1) return Ops[0];
2441 LHSC = cast<SCEVConstant>(Ops[0]);
2444 // If we are left with a constant minimum-int, strip it off.
2445 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2446 Ops.erase(Ops.begin());
2448 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2449 // If we have an umax with a constant maximum-int, it will always be
2454 if (Ops.size() == 1) return Ops[0];
2457 // Find the first UMax
2458 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2461 // Check to see if one of the operands is a UMax. If so, expand its operands
2462 // onto our operand list, and recurse to simplify.
2463 if (Idx < Ops.size()) {
2464 bool DeletedUMax = false;
2465 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2466 Ops.erase(Ops.begin()+Idx);
2467 Ops.append(UMax->op_begin(), UMax->op_end());
2472 return getUMaxExpr(Ops);
2475 // Okay, check to see if the same value occurs in the operand list twice. If
2476 // so, delete one. Since we sorted the list, these values are required to
2478 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2479 // X umax Y umax Y --> X umax Y
2480 // X umax Y --> X, if X is always greater than Y
2481 if (Ops[i] == Ops[i+1] ||
2482 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2483 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2485 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2486 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2490 if (Ops.size() == 1) return Ops[0];
2492 assert(!Ops.empty() && "Reduced umax down to nothing!");
2494 // Okay, it looks like we really DO need a umax expr. Check to see if we
2495 // already have one, otherwise create a new one.
2496 FoldingSetNodeID ID;
2497 ID.AddInteger(scUMaxExpr);
2498 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2499 ID.AddPointer(Ops[i]);
2501 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2502 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2503 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2504 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2506 UniqueSCEVs.InsertNode(S, IP);
2510 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2512 // ~smax(~x, ~y) == smin(x, y).
2513 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2516 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2518 // ~umax(~x, ~y) == umin(x, y)
2519 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2522 const SCEV *ScalarEvolution::getSizeOfExpr(Type *AllocTy) {
2523 // If we have TargetData, we can bypass creating a target-independent
2524 // constant expression and then folding it back into a ConstantInt.
2525 // This is just a compile-time optimization.
2527 return getConstant(TD->getIntPtrType(getContext()),
2528 TD->getTypeAllocSize(AllocTy));
2530 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2531 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2532 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2534 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2535 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2538 const SCEV *ScalarEvolution::getAlignOfExpr(Type *AllocTy) {
2539 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2540 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2541 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2543 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2544 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2547 const SCEV *ScalarEvolution::getOffsetOfExpr(StructType *STy,
2549 // If we have TargetData, we can bypass creating a target-independent
2550 // constant expression and then folding it back into a ConstantInt.
2551 // This is just a compile-time optimization.
2553 return getConstant(TD->getIntPtrType(getContext()),
2554 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2556 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2557 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2558 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2560 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2561 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2564 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *CTy,
2565 Constant *FieldNo) {
2566 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2567 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2568 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2570 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2571 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2574 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2575 // Don't attempt to do anything other than create a SCEVUnknown object
2576 // here. createSCEV only calls getUnknown after checking for all other
2577 // interesting possibilities, and any other code that calls getUnknown
2578 // is doing so in order to hide a value from SCEV canonicalization.
2580 FoldingSetNodeID ID;
2581 ID.AddInteger(scUnknown);
2584 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2585 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2586 "Stale SCEVUnknown in uniquing map!");
2589 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2591 FirstUnknown = cast<SCEVUnknown>(S);
2592 UniqueSCEVs.InsertNode(S, IP);
2596 //===----------------------------------------------------------------------===//
2597 // Basic SCEV Analysis and PHI Idiom Recognition Code
2600 /// isSCEVable - Test if values of the given type are analyzable within
2601 /// the SCEV framework. This primarily includes integer types, and it
2602 /// can optionally include pointer types if the ScalarEvolution class
2603 /// has access to target-specific information.
2604 bool ScalarEvolution::isSCEVable(Type *Ty) const {
2605 // Integers and pointers are always SCEVable.
2606 return Ty->isIntegerTy() || Ty->isPointerTy();
2609 /// getTypeSizeInBits - Return the size in bits of the specified type,
2610 /// for which isSCEVable must return true.
2611 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
2612 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2614 // If we have a TargetData, use it!
2616 return TD->getTypeSizeInBits(Ty);
2618 // Integer types have fixed sizes.
2619 if (Ty->isIntegerTy())
2620 return Ty->getPrimitiveSizeInBits();
2622 // The only other support type is pointer. Without TargetData, conservatively
2623 // assume pointers are 64-bit.
2624 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2628 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2629 /// the given type and which represents how SCEV will treat the given
2630 /// type, for which isSCEVable must return true. For pointer types,
2631 /// this is the pointer-sized integer type.
2632 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
2633 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2635 if (Ty->isIntegerTy())
2638 // The only other support type is pointer.
2639 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2640 if (TD) return TD->getIntPtrType(getContext());
2642 // Without TargetData, conservatively assume pointers are 64-bit.
2643 return Type::getInt64Ty(getContext());
2646 const SCEV *ScalarEvolution::getCouldNotCompute() {
2647 return &CouldNotCompute;
2650 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2651 /// expression and create a new one.
2652 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2653 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2655 ValueExprMapType::const_iterator I = ValueExprMap.find(V);
2656 if (I != ValueExprMap.end()) return I->second;
2657 const SCEV *S = createSCEV(V);
2659 // The process of creating a SCEV for V may have caused other SCEVs
2660 // to have been created, so it's necessary to insert the new entry
2661 // from scratch, rather than trying to remember the insert position
2663 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2667 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2669 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2670 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2672 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2674 Type *Ty = V->getType();
2675 Ty = getEffectiveSCEVType(Ty);
2676 return getMulExpr(V,
2677 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2680 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2681 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2682 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2684 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2686 Type *Ty = V->getType();
2687 Ty = getEffectiveSCEVType(Ty);
2688 const SCEV *AllOnes =
2689 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2690 return getMinusSCEV(AllOnes, V);
2693 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
2694 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2695 SCEV::NoWrapFlags Flags) {
2696 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
2698 // Fast path: X - X --> 0.
2700 return getConstant(LHS->getType(), 0);
2703 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
2706 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2707 /// input value to the specified type. If the type must be extended, it is zero
2710 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
2711 Type *SrcTy = V->getType();
2712 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2713 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2714 "Cannot truncate or zero extend with non-integer arguments!");
2715 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2716 return V; // No conversion
2717 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2718 return getTruncateExpr(V, Ty);
2719 return getZeroExtendExpr(V, Ty);
2722 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2723 /// input value to the specified type. If the type must be extended, it is sign
2726 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2728 Type *SrcTy = V->getType();
2729 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2730 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2731 "Cannot truncate or zero extend with non-integer arguments!");
2732 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2733 return V; // No conversion
2734 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2735 return getTruncateExpr(V, Ty);
2736 return getSignExtendExpr(V, Ty);
2739 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2740 /// input value to the specified type. If the type must be extended, it is zero
2741 /// extended. The conversion must not be narrowing.
2743 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
2744 Type *SrcTy = V->getType();
2745 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2746 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2747 "Cannot noop or zero extend with non-integer arguments!");
2748 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2749 "getNoopOrZeroExtend cannot truncate!");
2750 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2751 return V; // No conversion
2752 return getZeroExtendExpr(V, Ty);
2755 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2756 /// input value to the specified type. If the type must be extended, it is sign
2757 /// extended. The conversion must not be narrowing.
2759 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
2760 Type *SrcTy = V->getType();
2761 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2762 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2763 "Cannot noop or sign extend with non-integer arguments!");
2764 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2765 "getNoopOrSignExtend cannot truncate!");
2766 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2767 return V; // No conversion
2768 return getSignExtendExpr(V, Ty);
2771 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2772 /// the input value to the specified type. If the type must be extended,
2773 /// it is extended with unspecified bits. The conversion must not be
2776 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
2777 Type *SrcTy = V->getType();
2778 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2779 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2780 "Cannot noop or any extend with non-integer arguments!");
2781 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2782 "getNoopOrAnyExtend cannot truncate!");
2783 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2784 return V; // No conversion
2785 return getAnyExtendExpr(V, Ty);
2788 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2789 /// input value to the specified type. The conversion must not be widening.
2791 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
2792 Type *SrcTy = V->getType();
2793 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2794 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2795 "Cannot truncate or noop with non-integer arguments!");
2796 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2797 "getTruncateOrNoop cannot extend!");
2798 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2799 return V; // No conversion
2800 return getTruncateExpr(V, Ty);
2803 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2804 /// the types using zero-extension, and then perform a umax operation
2806 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2808 const SCEV *PromotedLHS = LHS;
2809 const SCEV *PromotedRHS = RHS;
2811 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2812 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2814 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2816 return getUMaxExpr(PromotedLHS, PromotedRHS);
2819 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2820 /// the types using zero-extension, and then perform a umin operation
2822 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2824 const SCEV *PromotedLHS = LHS;
2825 const SCEV *PromotedRHS = RHS;
2827 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2828 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2830 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2832 return getUMinExpr(PromotedLHS, PromotedRHS);
2835 /// getPointerBase - Transitively follow the chain of pointer-type operands
2836 /// until reaching a SCEV that does not have a single pointer operand. This
2837 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
2838 /// but corner cases do exist.
2839 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
2840 // A pointer operand may evaluate to a nonpointer expression, such as null.
2841 if (!V->getType()->isPointerTy())
2844 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
2845 return getPointerBase(Cast->getOperand());
2847 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
2848 const SCEV *PtrOp = 0;
2849 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
2851 if ((*I)->getType()->isPointerTy()) {
2852 // Cannot find the base of an expression with multiple pointer operands.
2860 return getPointerBase(PtrOp);
2865 /// PushDefUseChildren - Push users of the given Instruction
2866 /// onto the given Worklist.
2868 PushDefUseChildren(Instruction *I,
2869 SmallVectorImpl<Instruction *> &Worklist) {
2870 // Push the def-use children onto the Worklist stack.
2871 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2873 Worklist.push_back(cast<Instruction>(*UI));
2876 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2877 /// instructions that depend on the given instruction and removes them from
2878 /// the ValueExprMapType map if they reference SymName. This is used during PHI
2881 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2882 SmallVector<Instruction *, 16> Worklist;
2883 PushDefUseChildren(PN, Worklist);
2885 SmallPtrSet<Instruction *, 8> Visited;
2887 while (!Worklist.empty()) {
2888 Instruction *I = Worklist.pop_back_val();
2889 if (!Visited.insert(I)) continue;
2891 ValueExprMapType::iterator It =
2892 ValueExprMap.find(static_cast<Value *>(I));
2893 if (It != ValueExprMap.end()) {
2894 const SCEV *Old = It->second;
2896 // Short-circuit the def-use traversal if the symbolic name
2897 // ceases to appear in expressions.
2898 if (Old != SymName && !hasOperand(Old, SymName))
2901 // SCEVUnknown for a PHI either means that it has an unrecognized
2902 // structure, it's a PHI that's in the progress of being computed
2903 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2904 // additional loop trip count information isn't going to change anything.
2905 // In the second case, createNodeForPHI will perform the necessary
2906 // updates on its own when it gets to that point. In the third, we do
2907 // want to forget the SCEVUnknown.
2908 if (!isa<PHINode>(I) ||
2909 !isa<SCEVUnknown>(Old) ||
2910 (I != PN && Old == SymName)) {
2911 forgetMemoizedResults(Old);
2912 ValueExprMap.erase(It);
2916 PushDefUseChildren(I, Worklist);
2920 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2921 /// a loop header, making it a potential recurrence, or it doesn't.
2923 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2924 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2925 if (L->getHeader() == PN->getParent()) {
2926 // The loop may have multiple entrances or multiple exits; we can analyze
2927 // this phi as an addrec if it has a unique entry value and a unique
2929 Value *BEValueV = 0, *StartValueV = 0;
2930 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
2931 Value *V = PN->getIncomingValue(i);
2932 if (L->contains(PN->getIncomingBlock(i))) {
2935 } else if (BEValueV != V) {
2939 } else if (!StartValueV) {
2941 } else if (StartValueV != V) {
2946 if (BEValueV && StartValueV) {
2947 // While we are analyzing this PHI node, handle its value symbolically.
2948 const SCEV *SymbolicName = getUnknown(PN);
2949 assert(ValueExprMap.find(PN) == ValueExprMap.end() &&
2950 "PHI node already processed?");
2951 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2953 // Using this symbolic name for the PHI, analyze the value coming around
2955 const SCEV *BEValue = getSCEV(BEValueV);
2957 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2958 // has a special value for the first iteration of the loop.
2960 // If the value coming around the backedge is an add with the symbolic
2961 // value we just inserted, then we found a simple induction variable!
2962 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2963 // If there is a single occurrence of the symbolic value, replace it
2964 // with a recurrence.
2965 unsigned FoundIndex = Add->getNumOperands();
2966 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2967 if (Add->getOperand(i) == SymbolicName)
2968 if (FoundIndex == e) {
2973 if (FoundIndex != Add->getNumOperands()) {
2974 // Create an add with everything but the specified operand.
2975 SmallVector<const SCEV *, 8> Ops;
2976 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2977 if (i != FoundIndex)
2978 Ops.push_back(Add->getOperand(i));
2979 const SCEV *Accum = getAddExpr(Ops);
2981 // This is not a valid addrec if the step amount is varying each
2982 // loop iteration, but is not itself an addrec in this loop.
2983 if (isLoopInvariant(Accum, L) ||
2984 (isa<SCEVAddRecExpr>(Accum) &&
2985 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2986 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
2988 // If the increment doesn't overflow, then neither the addrec nor
2989 // the post-increment will overflow.
2990 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
2991 if (OBO->hasNoUnsignedWrap())
2992 Flags = setFlags(Flags, SCEV::FlagNUW);
2993 if (OBO->hasNoSignedWrap())
2994 Flags = setFlags(Flags, SCEV::FlagNSW);
2995 } else if (const GEPOperator *GEP =
2996 dyn_cast<GEPOperator>(BEValueV)) {
2997 // If the increment is an inbounds GEP, then we know the address
2998 // space cannot be wrapped around. We cannot make any guarantee
2999 // about signed or unsigned overflow because pointers are
3000 // unsigned but we may have a negative index from the base
3002 if (GEP->isInBounds())
3003 Flags = setFlags(Flags, SCEV::FlagNW);
3006 const SCEV *StartVal = getSCEV(StartValueV);
3007 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3009 // Since the no-wrap flags are on the increment, they apply to the
3010 // post-incremented value as well.
3011 if (isLoopInvariant(Accum, L))
3012 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3015 // Okay, for the entire analysis of this edge we assumed the PHI
3016 // to be symbolic. We now need to go back and purge all of the
3017 // entries for the scalars that use the symbolic expression.
3018 ForgetSymbolicName(PN, SymbolicName);
3019 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3023 } else if (const SCEVAddRecExpr *AddRec =
3024 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3025 // Otherwise, this could be a loop like this:
3026 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3027 // In this case, j = {1,+,1} and BEValue is j.
3028 // Because the other in-value of i (0) fits the evolution of BEValue
3029 // i really is an addrec evolution.
3030 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3031 const SCEV *StartVal = getSCEV(StartValueV);
3033 // If StartVal = j.start - j.stride, we can use StartVal as the
3034 // initial step of the addrec evolution.
3035 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3036 AddRec->getOperand(1))) {
3037 // FIXME: For constant StartVal, we should be able to infer
3039 const SCEV *PHISCEV =
3040 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3043 // Okay, for the entire analysis of this edge we assumed the PHI
3044 // to be symbolic. We now need to go back and purge all of the
3045 // entries for the scalars that use the symbolic expression.
3046 ForgetSymbolicName(PN, SymbolicName);
3047 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3055 // If the PHI has a single incoming value, follow that value, unless the
3056 // PHI's incoming blocks are in a different loop, in which case doing so
3057 // risks breaking LCSSA form. Instcombine would normally zap these, but
3058 // it doesn't have DominatorTree information, so it may miss cases.
3059 if (Value *V = SimplifyInstruction(PN, TD, DT))
3060 if (LI->replacementPreservesLCSSAForm(PN, V))
3063 // If it's not a loop phi, we can't handle it yet.
3064 return getUnknown(PN);
3067 /// createNodeForGEP - Expand GEP instructions into add and multiply
3068 /// operations. This allows them to be analyzed by regular SCEV code.
3070 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3072 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3073 // Add expression, because the Instruction may be guarded by control flow
3074 // and the no-overflow bits may not be valid for the expression in any
3076 bool isInBounds = GEP->isInBounds();
3078 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3079 Value *Base = GEP->getOperand(0);
3080 // Don't attempt to analyze GEPs over unsized objects.
3081 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
3082 return getUnknown(GEP);
3083 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3084 gep_type_iterator GTI = gep_type_begin(GEP);
3085 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()),
3089 // Compute the (potentially symbolic) offset in bytes for this index.
3090 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3091 // For a struct, add the member offset.
3092 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3093 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo);
3095 // Add the field offset to the running total offset.
3096 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3098 // For an array, add the element offset, explicitly scaled.
3099 const SCEV *ElementSize = getSizeOfExpr(*GTI);
3100 const SCEV *IndexS = getSCEV(Index);
3101 // Getelementptr indices are signed.
3102 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3104 // Multiply the index by the element size to compute the element offset.
3105 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize,
3106 isInBounds ? SCEV::FlagNSW :
3109 // Add the element offset to the running total offset.
3110 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3114 // Get the SCEV for the GEP base.
3115 const SCEV *BaseS = getSCEV(Base);
3117 // Add the total offset from all the GEP indices to the base.
3118 return getAddExpr(BaseS, TotalOffset,
3119 isInBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap);
3122 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3123 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3124 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3125 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3127 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3128 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3129 return C->getValue()->getValue().countTrailingZeros();
3131 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3132 return std::min(GetMinTrailingZeros(T->getOperand()),
3133 (uint32_t)getTypeSizeInBits(T->getType()));
3135 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3136 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3137 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3138 getTypeSizeInBits(E->getType()) : OpRes;
3141 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3142 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3143 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3144 getTypeSizeInBits(E->getType()) : OpRes;
3147 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3148 // The result is the min of all operands results.
3149 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3150 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3151 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3155 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3156 // The result is the sum of all operands results.
3157 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3158 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3159 for (unsigned i = 1, e = M->getNumOperands();
3160 SumOpRes != BitWidth && i != e; ++i)
3161 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3166 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3167 // The result is the min of all operands results.
3168 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3169 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3170 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3174 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3175 // The result is the min of all operands results.
3176 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3177 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3178 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3182 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3183 // The result is the min of all operands results.
3184 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3185 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3186 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3190 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3191 // For a SCEVUnknown, ask ValueTracking.
3192 unsigned BitWidth = getTypeSizeInBits(U->getType());
3193 APInt Mask = APInt::getAllOnesValue(BitWidth);
3194 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3195 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
3196 return Zeros.countTrailingOnes();
3203 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3206 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3207 // See if we've computed this range already.
3208 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3209 if (I != UnsignedRanges.end())
3212 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3213 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3215 unsigned BitWidth = getTypeSizeInBits(S->getType());
3216 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3218 // If the value has known zeros, the maximum unsigned value will have those
3219 // known zeros as well.
3220 uint32_t TZ = GetMinTrailingZeros(S);
3222 ConservativeResult =
3223 ConstantRange(APInt::getMinValue(BitWidth),
3224 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3226 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3227 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3228 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3229 X = X.add(getUnsignedRange(Add->getOperand(i)));
3230 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3233 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3234 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3235 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3236 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3237 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3240 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3241 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3242 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3243 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3244 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3247 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3248 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3249 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3250 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3251 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3254 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3255 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3256 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3257 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3260 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3261 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3262 return setUnsignedRange(ZExt,
3263 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3266 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3267 ConstantRange X = getUnsignedRange(SExt->getOperand());
3268 return setUnsignedRange(SExt,
3269 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3272 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3273 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3274 return setUnsignedRange(Trunc,
3275 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3278 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3279 // If there's no unsigned wrap, the value will never be less than its
3281 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3282 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3283 if (!C->getValue()->isZero())
3284 ConservativeResult =
3285 ConservativeResult.intersectWith(
3286 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3288 // TODO: non-affine addrec
3289 if (AddRec->isAffine()) {
3290 Type *Ty = AddRec->getType();
3291 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3292 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3293 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3294 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3296 const SCEV *Start = AddRec->getStart();
3297 const SCEV *Step = AddRec->getStepRecurrence(*this);
3299 ConstantRange StartRange = getUnsignedRange(Start);
3300 ConstantRange StepRange = getSignedRange(Step);
3301 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3302 ConstantRange EndRange =
3303 StartRange.add(MaxBECountRange.multiply(StepRange));
3305 // Check for overflow. This must be done with ConstantRange arithmetic
3306 // because we could be called from within the ScalarEvolution overflow
3308 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3309 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3310 ConstantRange ExtMaxBECountRange =
3311 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3312 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3313 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3315 return setUnsignedRange(AddRec, ConservativeResult);
3317 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3318 EndRange.getUnsignedMin());
3319 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3320 EndRange.getUnsignedMax());
3321 if (Min.isMinValue() && Max.isMaxValue())
3322 return setUnsignedRange(AddRec, ConservativeResult);
3323 return setUnsignedRange(AddRec,
3324 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3328 return setUnsignedRange(AddRec, ConservativeResult);
3331 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3332 // For a SCEVUnknown, ask ValueTracking.
3333 APInt Mask = APInt::getAllOnesValue(BitWidth);
3334 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3335 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
3336 if (Ones == ~Zeros + 1)
3337 return setUnsignedRange(U, ConservativeResult);
3338 return setUnsignedRange(U,
3339 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3342 return setUnsignedRange(S, ConservativeResult);
3345 /// getSignedRange - Determine the signed range for a particular SCEV.
3348 ScalarEvolution::getSignedRange(const SCEV *S) {
3349 // See if we've computed this range already.
3350 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3351 if (I != SignedRanges.end())
3354 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3355 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3357 unsigned BitWidth = getTypeSizeInBits(S->getType());
3358 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3360 // If the value has known zeros, the maximum signed value will have those
3361 // known zeros as well.
3362 uint32_t TZ = GetMinTrailingZeros(S);
3364 ConservativeResult =
3365 ConstantRange(APInt::getSignedMinValue(BitWidth),
3366 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3368 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3369 ConstantRange X = getSignedRange(Add->getOperand(0));
3370 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3371 X = X.add(getSignedRange(Add->getOperand(i)));
3372 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3375 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3376 ConstantRange X = getSignedRange(Mul->getOperand(0));
3377 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3378 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3379 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3382 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3383 ConstantRange X = getSignedRange(SMax->getOperand(0));
3384 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3385 X = X.smax(getSignedRange(SMax->getOperand(i)));
3386 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3389 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3390 ConstantRange X = getSignedRange(UMax->getOperand(0));
3391 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3392 X = X.umax(getSignedRange(UMax->getOperand(i)));
3393 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3396 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3397 ConstantRange X = getSignedRange(UDiv->getLHS());
3398 ConstantRange Y = getSignedRange(UDiv->getRHS());
3399 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3402 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3403 ConstantRange X = getSignedRange(ZExt->getOperand());
3404 return setSignedRange(ZExt,
3405 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3408 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3409 ConstantRange X = getSignedRange(SExt->getOperand());
3410 return setSignedRange(SExt,
3411 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3414 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3415 ConstantRange X = getSignedRange(Trunc->getOperand());
3416 return setSignedRange(Trunc,
3417 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3420 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3421 // If there's no signed wrap, and all the operands have the same sign or
3422 // zero, the value won't ever change sign.
3423 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3424 bool AllNonNeg = true;
3425 bool AllNonPos = true;
3426 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3427 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3428 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3431 ConservativeResult = ConservativeResult.intersectWith(
3432 ConstantRange(APInt(BitWidth, 0),
3433 APInt::getSignedMinValue(BitWidth)));
3435 ConservativeResult = ConservativeResult.intersectWith(
3436 ConstantRange(APInt::getSignedMinValue(BitWidth),
3437 APInt(BitWidth, 1)));
3440 // TODO: non-affine addrec
3441 if (AddRec->isAffine()) {
3442 Type *Ty = AddRec->getType();
3443 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3444 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3445 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3446 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3448 const SCEV *Start = AddRec->getStart();
3449 const SCEV *Step = AddRec->getStepRecurrence(*this);
3451 ConstantRange StartRange = getSignedRange(Start);
3452 ConstantRange StepRange = getSignedRange(Step);
3453 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3454 ConstantRange EndRange =
3455 StartRange.add(MaxBECountRange.multiply(StepRange));
3457 // Check for overflow. This must be done with ConstantRange arithmetic
3458 // because we could be called from within the ScalarEvolution overflow
3460 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3461 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3462 ConstantRange ExtMaxBECountRange =
3463 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3464 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3465 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3467 return setSignedRange(AddRec, ConservativeResult);
3469 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3470 EndRange.getSignedMin());
3471 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3472 EndRange.getSignedMax());
3473 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3474 return setSignedRange(AddRec, ConservativeResult);
3475 return setSignedRange(AddRec,
3476 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3480 return setSignedRange(AddRec, ConservativeResult);
3483 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3484 // For a SCEVUnknown, ask ValueTracking.
3485 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3486 return setSignedRange(U, ConservativeResult);
3487 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3489 return setSignedRange(U, ConservativeResult);
3490 return setSignedRange(U, ConservativeResult.intersectWith(
3491 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3492 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3495 return setSignedRange(S, ConservativeResult);
3498 /// createSCEV - We know that there is no SCEV for the specified value.
3499 /// Analyze the expression.
3501 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3502 if (!isSCEVable(V->getType()))
3503 return getUnknown(V);
3505 unsigned Opcode = Instruction::UserOp1;
3506 if (Instruction *I = dyn_cast<Instruction>(V)) {
3507 Opcode = I->getOpcode();
3509 // Don't attempt to analyze instructions in blocks that aren't
3510 // reachable. Such instructions don't matter, and they aren't required
3511 // to obey basic rules for definitions dominating uses which this
3512 // analysis depends on.
3513 if (!DT->isReachableFromEntry(I->getParent()))
3514 return getUnknown(V);
3515 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3516 Opcode = CE->getOpcode();
3517 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3518 return getConstant(CI);
3519 else if (isa<ConstantPointerNull>(V))
3520 return getConstant(V->getType(), 0);
3521 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3522 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3524 return getUnknown(V);
3526 Operator *U = cast<Operator>(V);
3528 case Instruction::Add: {
3529 // The simple thing to do would be to just call getSCEV on both operands
3530 // and call getAddExpr with the result. However if we're looking at a
3531 // bunch of things all added together, this can be quite inefficient,
3532 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3533 // Instead, gather up all the operands and make a single getAddExpr call.
3534 // LLVM IR canonical form means we need only traverse the left operands.
3535 SmallVector<const SCEV *, 4> AddOps;
3536 AddOps.push_back(getSCEV(U->getOperand(1)));
3537 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3538 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3539 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3541 U = cast<Operator>(Op);
3542 const SCEV *Op1 = getSCEV(U->getOperand(1));
3543 if (Opcode == Instruction::Sub)
3544 AddOps.push_back(getNegativeSCEV(Op1));
3546 AddOps.push_back(Op1);
3548 AddOps.push_back(getSCEV(U->getOperand(0)));
3549 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3550 OverflowingBinaryOperator *OBO = cast<OverflowingBinaryOperator>(V);
3551 if (OBO->hasNoSignedWrap())
3552 setFlags(Flags, SCEV::FlagNSW);
3553 if (OBO->hasNoUnsignedWrap())
3554 setFlags(Flags, SCEV::FlagNUW);
3555 return getAddExpr(AddOps, Flags);
3557 case Instruction::Mul: {
3558 // See the Add code above.
3559 SmallVector<const SCEV *, 4> MulOps;
3560 MulOps.push_back(getSCEV(U->getOperand(1)));
3561 for (Value *Op = U->getOperand(0);
3562 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3563 Op = U->getOperand(0)) {
3564 U = cast<Operator>(Op);
3565 MulOps.push_back(getSCEV(U->getOperand(1)));
3567 MulOps.push_back(getSCEV(U->getOperand(0)));
3568 return getMulExpr(MulOps);
3570 case Instruction::UDiv:
3571 return getUDivExpr(getSCEV(U->getOperand(0)),
3572 getSCEV(U->getOperand(1)));
3573 case Instruction::Sub:
3574 return getMinusSCEV(getSCEV(U->getOperand(0)),
3575 getSCEV(U->getOperand(1)));
3576 case Instruction::And:
3577 // For an expression like x&255 that merely masks off the high bits,
3578 // use zext(trunc(x)) as the SCEV expression.
3579 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3580 if (CI->isNullValue())
3581 return getSCEV(U->getOperand(1));
3582 if (CI->isAllOnesValue())
3583 return getSCEV(U->getOperand(0));
3584 const APInt &A = CI->getValue();
3586 // Instcombine's ShrinkDemandedConstant may strip bits out of
3587 // constants, obscuring what would otherwise be a low-bits mask.
3588 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3589 // knew about to reconstruct a low-bits mask value.
3590 unsigned LZ = A.countLeadingZeros();
3591 unsigned BitWidth = A.getBitWidth();
3592 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
3593 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3594 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
3596 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3598 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3600 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3601 IntegerType::get(getContext(), BitWidth - LZ)),
3606 case Instruction::Or:
3607 // If the RHS of the Or is a constant, we may have something like:
3608 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3609 // optimizations will transparently handle this case.
3611 // In order for this transformation to be safe, the LHS must be of the
3612 // form X*(2^n) and the Or constant must be less than 2^n.
3613 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3614 const SCEV *LHS = getSCEV(U->getOperand(0));
3615 const APInt &CIVal = CI->getValue();
3616 if (GetMinTrailingZeros(LHS) >=
3617 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3618 // Build a plain add SCEV.
3619 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3620 // If the LHS of the add was an addrec and it has no-wrap flags,
3621 // transfer the no-wrap flags, since an or won't introduce a wrap.
3622 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3623 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3624 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
3625 OldAR->getNoWrapFlags());
3631 case Instruction::Xor:
3632 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3633 // If the RHS of the xor is a signbit, then this is just an add.
3634 // Instcombine turns add of signbit into xor as a strength reduction step.
3635 if (CI->getValue().isSignBit())
3636 return getAddExpr(getSCEV(U->getOperand(0)),
3637 getSCEV(U->getOperand(1)));
3639 // If the RHS of xor is -1, then this is a not operation.
3640 if (CI->isAllOnesValue())
3641 return getNotSCEV(getSCEV(U->getOperand(0)));
3643 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3644 // This is a variant of the check for xor with -1, and it handles
3645 // the case where instcombine has trimmed non-demanded bits out
3646 // of an xor with -1.
3647 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3648 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3649 if (BO->getOpcode() == Instruction::And &&
3650 LCI->getValue() == CI->getValue())
3651 if (const SCEVZeroExtendExpr *Z =
3652 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3653 Type *UTy = U->getType();
3654 const SCEV *Z0 = Z->getOperand();
3655 Type *Z0Ty = Z0->getType();
3656 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3658 // If C is a low-bits mask, the zero extend is serving to
3659 // mask off the high bits. Complement the operand and
3660 // re-apply the zext.
3661 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3662 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3664 // If C is a single bit, it may be in the sign-bit position
3665 // before the zero-extend. In this case, represent the xor
3666 // using an add, which is equivalent, and re-apply the zext.
3667 APInt Trunc = CI->getValue().trunc(Z0TySize);
3668 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3670 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3676 case Instruction::Shl:
3677 // Turn shift left of a constant amount into a multiply.
3678 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3679 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3681 // If the shift count is not less than the bitwidth, the result of
3682 // the shift is undefined. Don't try to analyze it, because the
3683 // resolution chosen here may differ from the resolution chosen in
3684 // other parts of the compiler.
3685 if (SA->getValue().uge(BitWidth))
3688 Constant *X = ConstantInt::get(getContext(),
3689 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3690 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3694 case Instruction::LShr:
3695 // Turn logical shift right of a constant into a unsigned divide.
3696 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3697 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3699 // If the shift count is not less than the bitwidth, the result of
3700 // the shift is undefined. Don't try to analyze it, because the
3701 // resolution chosen here may differ from the resolution chosen in
3702 // other parts of the compiler.
3703 if (SA->getValue().uge(BitWidth))
3706 Constant *X = ConstantInt::get(getContext(),
3707 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3708 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3712 case Instruction::AShr:
3713 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3714 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3715 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3716 if (L->getOpcode() == Instruction::Shl &&
3717 L->getOperand(1) == U->getOperand(1)) {
3718 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3720 // If the shift count is not less than the bitwidth, the result of
3721 // the shift is undefined. Don't try to analyze it, because the
3722 // resolution chosen here may differ from the resolution chosen in
3723 // other parts of the compiler.
3724 if (CI->getValue().uge(BitWidth))
3727 uint64_t Amt = BitWidth - CI->getZExtValue();
3728 if (Amt == BitWidth)
3729 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3731 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3732 IntegerType::get(getContext(),
3738 case Instruction::Trunc:
3739 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3741 case Instruction::ZExt:
3742 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3744 case Instruction::SExt:
3745 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3747 case Instruction::BitCast:
3748 // BitCasts are no-op casts so we just eliminate the cast.
3749 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3750 return getSCEV(U->getOperand(0));
3753 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3754 // lead to pointer expressions which cannot safely be expanded to GEPs,
3755 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3756 // simplifying integer expressions.
3758 case Instruction::GetElementPtr:
3759 return createNodeForGEP(cast<GEPOperator>(U));
3761 case Instruction::PHI:
3762 return createNodeForPHI(cast<PHINode>(U));
3764 case Instruction::Select:
3765 // This could be a smax or umax that was lowered earlier.
3766 // Try to recover it.
3767 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3768 Value *LHS = ICI->getOperand(0);
3769 Value *RHS = ICI->getOperand(1);
3770 switch (ICI->getPredicate()) {
3771 case ICmpInst::ICMP_SLT:
3772 case ICmpInst::ICMP_SLE:
3773 std::swap(LHS, RHS);
3775 case ICmpInst::ICMP_SGT:
3776 case ICmpInst::ICMP_SGE:
3777 // a >s b ? a+x : b+x -> smax(a, b)+x
3778 // a >s b ? b+x : a+x -> smin(a, b)+x
3779 if (LHS->getType() == U->getType()) {
3780 const SCEV *LS = getSCEV(LHS);
3781 const SCEV *RS = getSCEV(RHS);
3782 const SCEV *LA = getSCEV(U->getOperand(1));
3783 const SCEV *RA = getSCEV(U->getOperand(2));
3784 const SCEV *LDiff = getMinusSCEV(LA, LS);
3785 const SCEV *RDiff = getMinusSCEV(RA, RS);
3787 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3788 LDiff = getMinusSCEV(LA, RS);
3789 RDiff = getMinusSCEV(RA, LS);
3791 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3794 case ICmpInst::ICMP_ULT:
3795 case ICmpInst::ICMP_ULE:
3796 std::swap(LHS, RHS);
3798 case ICmpInst::ICMP_UGT:
3799 case ICmpInst::ICMP_UGE:
3800 // a >u b ? a+x : b+x -> umax(a, b)+x
3801 // a >u b ? b+x : a+x -> umin(a, b)+x
3802 if (LHS->getType() == U->getType()) {
3803 const SCEV *LS = getSCEV(LHS);
3804 const SCEV *RS = getSCEV(RHS);
3805 const SCEV *LA = getSCEV(U->getOperand(1));
3806 const SCEV *RA = getSCEV(U->getOperand(2));
3807 const SCEV *LDiff = getMinusSCEV(LA, LS);
3808 const SCEV *RDiff = getMinusSCEV(RA, RS);
3810 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3811 LDiff = getMinusSCEV(LA, RS);
3812 RDiff = getMinusSCEV(RA, LS);
3814 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3817 case ICmpInst::ICMP_NE:
3818 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3819 if (LHS->getType() == U->getType() &&
3820 isa<ConstantInt>(RHS) &&
3821 cast<ConstantInt>(RHS)->isZero()) {
3822 const SCEV *One = getConstant(LHS->getType(), 1);
3823 const SCEV *LS = getSCEV(LHS);
3824 const SCEV *LA = getSCEV(U->getOperand(1));
3825 const SCEV *RA = getSCEV(U->getOperand(2));
3826 const SCEV *LDiff = getMinusSCEV(LA, LS);
3827 const SCEV *RDiff = getMinusSCEV(RA, One);
3829 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3832 case ICmpInst::ICMP_EQ:
3833 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3834 if (LHS->getType() == U->getType() &&
3835 isa<ConstantInt>(RHS) &&
3836 cast<ConstantInt>(RHS)->isZero()) {
3837 const SCEV *One = getConstant(LHS->getType(), 1);
3838 const SCEV *LS = getSCEV(LHS);
3839 const SCEV *LA = getSCEV(U->getOperand(1));
3840 const SCEV *RA = getSCEV(U->getOperand(2));
3841 const SCEV *LDiff = getMinusSCEV(LA, One);
3842 const SCEV *RDiff = getMinusSCEV(RA, LS);
3844 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3852 default: // We cannot analyze this expression.
3856 return getUnknown(V);
3861 //===----------------------------------------------------------------------===//
3862 // Iteration Count Computation Code
3865 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
3866 /// normal unsigned value, if possible. Returns 0 if the trip count is unknown
3867 /// or not constant. Will also return 0 if the maximum trip count is very large
3869 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
3870 BasicBlock *ExitBlock) {
3871 const SCEVConstant *ExitCount =
3872 dyn_cast<SCEVConstant>(getExitCount(L, ExitBlock));
3876 ConstantInt *ExitConst = ExitCount->getValue();
3878 // Guard against huge trip counts.
3879 if (ExitConst->getValue().getActiveBits() > 32)
3882 // In case of integer overflow, this returns 0, which is correct.
3883 return ((unsigned)ExitConst->getZExtValue()) + 1;
3886 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
3887 /// trip count of this loop as a normal unsigned value, if possible. This
3888 /// means that the actual trip count is always a multiple of the returned
3889 /// value (don't forget the trip count could very well be zero as well!).
3891 /// Returns 1 if the trip count is unknown or not guaranteed to be the
3892 /// multiple of a constant (which is also the case if the trip count is simply
3893 /// constant, use getSmallConstantTripCount for that case), Will also return 1
3894 /// if the trip count is very large (>= 2^32).
3895 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
3896 BasicBlock *ExitBlock) {
3897 const SCEV *ExitCount = getExitCount(L, ExitBlock);
3898 if (ExitCount == getCouldNotCompute())
3901 // Get the trip count from the BE count by adding 1.
3902 const SCEV *TCMul = getAddExpr(ExitCount,
3903 getConstant(ExitCount->getType(), 1));
3904 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
3905 // to factor simple cases.
3906 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
3907 TCMul = Mul->getOperand(0);
3909 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
3913 ConstantInt *Result = MulC->getValue();
3915 // Guard against huge trip counts.
3916 if (!Result || Result->getValue().getActiveBits() > 32)
3919 return (unsigned)Result->getZExtValue();
3922 // getExitCount - Get the expression for the number of loop iterations for which
3923 // this loop is guaranteed not to exit via ExitintBlock. Otherwise return
3924 // SCEVCouldNotCompute.
3925 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
3926 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
3929 /// getBackedgeTakenCount - If the specified loop has a predictable
3930 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3931 /// object. The backedge-taken count is the number of times the loop header
3932 /// will be branched to from within the loop. This is one less than the
3933 /// trip count of the loop, since it doesn't count the first iteration,
3934 /// when the header is branched to from outside the loop.
3936 /// Note that it is not valid to call this method on a loop without a
3937 /// loop-invariant backedge-taken count (see
3938 /// hasLoopInvariantBackedgeTakenCount).
3940 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3941 return getBackedgeTakenInfo(L).getExact(this);
3944 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3945 /// return the least SCEV value that is known never to be less than the
3946 /// actual backedge taken count.
3947 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3948 return getBackedgeTakenInfo(L).getMax(this);
3951 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
3952 /// onto the given Worklist.
3954 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3955 BasicBlock *Header = L->getHeader();
3957 // Push all Loop-header PHIs onto the Worklist stack.
3958 for (BasicBlock::iterator I = Header->begin();
3959 PHINode *PN = dyn_cast<PHINode>(I); ++I)
3960 Worklist.push_back(PN);
3963 const ScalarEvolution::BackedgeTakenInfo &
3964 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3965 // Initially insert an invalid entry for this loop. If the insertion
3966 // succeeds, proceed to actually compute a backedge-taken count and
3967 // update the value. The temporary CouldNotCompute value tells SCEV
3968 // code elsewhere that it shouldn't attempt to request a new
3969 // backedge-taken count, which could result in infinite recursion.
3970 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
3971 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
3973 return Pair.first->second;
3975 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
3976 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
3977 // must be cleared in this scope.
3978 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
3980 if (Result.getExact(this) != getCouldNotCompute()) {
3981 assert(isLoopInvariant(Result.getExact(this), L) &&
3982 isLoopInvariant(Result.getMax(this), L) &&
3983 "Computed backedge-taken count isn't loop invariant for loop!");
3984 ++NumTripCountsComputed;
3986 else if (Result.getMax(this) == getCouldNotCompute() &&
3987 isa<PHINode>(L->getHeader()->begin())) {
3988 // Only count loops that have phi nodes as not being computable.
3989 ++NumTripCountsNotComputed;
3992 // Now that we know more about the trip count for this loop, forget any
3993 // existing SCEV values for PHI nodes in this loop since they are only
3994 // conservative estimates made without the benefit of trip count
3995 // information. This is similar to the code in forgetLoop, except that
3996 // it handles SCEVUnknown PHI nodes specially.
3997 if (Result.hasAnyInfo()) {
3998 SmallVector<Instruction *, 16> Worklist;
3999 PushLoopPHIs(L, Worklist);
4001 SmallPtrSet<Instruction *, 8> Visited;
4002 while (!Worklist.empty()) {
4003 Instruction *I = Worklist.pop_back_val();
4004 if (!Visited.insert(I)) continue;
4006 ValueExprMapType::iterator It =
4007 ValueExprMap.find(static_cast<Value *>(I));
4008 if (It != ValueExprMap.end()) {
4009 const SCEV *Old = It->second;
4011 // SCEVUnknown for a PHI either means that it has an unrecognized
4012 // structure, or it's a PHI that's in the progress of being computed
4013 // by createNodeForPHI. In the former case, additional loop trip
4014 // count information isn't going to change anything. In the later
4015 // case, createNodeForPHI will perform the necessary updates on its
4016 // own when it gets to that point.
4017 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4018 forgetMemoizedResults(Old);
4019 ValueExprMap.erase(It);
4021 if (PHINode *PN = dyn_cast<PHINode>(I))
4022 ConstantEvolutionLoopExitValue.erase(PN);
4025 PushDefUseChildren(I, Worklist);
4029 // Re-lookup the insert position, since the call to
4030 // ComputeBackedgeTakenCount above could result in a
4031 // recusive call to getBackedgeTakenInfo (on a different
4032 // loop), which would invalidate the iterator computed
4034 return BackedgeTakenCounts.find(L)->second = Result;
4037 /// forgetLoop - This method should be called by the client when it has
4038 /// changed a loop in a way that may effect ScalarEvolution's ability to
4039 /// compute a trip count, or if the loop is deleted.
4040 void ScalarEvolution::forgetLoop(const Loop *L) {
4041 // Drop any stored trip count value.
4042 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4043 BackedgeTakenCounts.find(L);
4044 if (BTCPos != BackedgeTakenCounts.end()) {
4045 BTCPos->second.clear();
4046 BackedgeTakenCounts.erase(BTCPos);
4049 // Drop information about expressions based on loop-header PHIs.
4050 SmallVector<Instruction *, 16> Worklist;
4051 PushLoopPHIs(L, Worklist);
4053 SmallPtrSet<Instruction *, 8> Visited;
4054 while (!Worklist.empty()) {
4055 Instruction *I = Worklist.pop_back_val();
4056 if (!Visited.insert(I)) continue;
4058 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
4059 if (It != ValueExprMap.end()) {
4060 forgetMemoizedResults(It->second);
4061 ValueExprMap.erase(It);
4062 if (PHINode *PN = dyn_cast<PHINode>(I))
4063 ConstantEvolutionLoopExitValue.erase(PN);
4066 PushDefUseChildren(I, Worklist);
4069 // Forget all contained loops too, to avoid dangling entries in the
4070 // ValuesAtScopes map.
4071 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4075 /// forgetValue - This method should be called by the client when it has
4076 /// changed a value in a way that may effect its value, or which may
4077 /// disconnect it from a def-use chain linking it to a loop.
4078 void ScalarEvolution::forgetValue(Value *V) {
4079 Instruction *I = dyn_cast<Instruction>(V);
4082 // Drop information about expressions based on loop-header PHIs.
4083 SmallVector<Instruction *, 16> Worklist;
4084 Worklist.push_back(I);
4086 SmallPtrSet<Instruction *, 8> Visited;
4087 while (!Worklist.empty()) {
4088 I = Worklist.pop_back_val();
4089 if (!Visited.insert(I)) continue;
4091 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
4092 if (It != ValueExprMap.end()) {
4093 forgetMemoizedResults(It->second);
4094 ValueExprMap.erase(It);
4095 if (PHINode *PN = dyn_cast<PHINode>(I))
4096 ConstantEvolutionLoopExitValue.erase(PN);
4099 PushDefUseChildren(I, Worklist);
4103 /// getExact - Get the exact loop backedge taken count considering all loop
4104 /// exits. If all exits are computable, this is the minimum computed count.
4106 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4107 // If any exits were not computable, the loop is not computable.
4108 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4110 // We need at least one computable exit.
4111 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4112 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4114 const SCEV *BECount = 0;
4115 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4116 ENT != 0; ENT = ENT->getNextExit()) {
4118 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4121 BECount = ENT->ExactNotTaken;
4123 BECount = SE->getUMinFromMismatchedTypes(BECount, ENT->ExactNotTaken);
4125 assert(BECount && "Invalid not taken count for loop exit");
4129 /// getExact - Get the exact not taken count for this loop exit.
4131 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4132 ScalarEvolution *SE) const {
4133 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4134 ENT != 0; ENT = ENT->getNextExit()) {
4136 if (ENT->ExitingBlock == ExitingBlock)
4137 return ENT->ExactNotTaken;
4139 return SE->getCouldNotCompute();
4142 /// getMax - Get the max backedge taken count for the loop.
4144 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4145 return Max ? Max : SE->getCouldNotCompute();
4148 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4149 /// computable exit into a persistent ExitNotTakenInfo array.
4150 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4151 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4152 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4155 ExitNotTaken.setIncomplete();
4157 unsigned NumExits = ExitCounts.size();
4158 if (NumExits == 0) return;
4160 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4161 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4162 if (NumExits == 1) return;
4164 // Handle the rare case of multiple computable exits.
4165 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4167 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4168 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4169 PrevENT->setNextExit(ENT);
4170 ENT->ExitingBlock = ExitCounts[i].first;
4171 ENT->ExactNotTaken = ExitCounts[i].second;
4175 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4176 void ScalarEvolution::BackedgeTakenInfo::clear() {
4177 ExitNotTaken.ExitingBlock = 0;
4178 ExitNotTaken.ExactNotTaken = 0;
4179 delete[] ExitNotTaken.getNextExit();
4182 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4183 /// of the specified loop will execute.
4184 ScalarEvolution::BackedgeTakenInfo
4185 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4186 SmallVector<BasicBlock *, 8> ExitingBlocks;
4187 L->getExitingBlocks(ExitingBlocks);
4189 // Examine all exits and pick the most conservative values.
4190 const SCEV *MaxBECount = getCouldNotCompute();
4191 bool CouldComputeBECount = true;
4192 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4193 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4194 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]);
4195 if (EL.Exact == getCouldNotCompute())
4196 // We couldn't compute an exact value for this exit, so
4197 // we won't be able to compute an exact value for the loop.
4198 CouldComputeBECount = false;
4200 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact));
4202 if (MaxBECount == getCouldNotCompute())
4203 MaxBECount = EL.Max;
4204 else if (EL.Max != getCouldNotCompute())
4205 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, EL.Max);
4208 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4211 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4212 /// loop will execute if it exits via the specified block.
4213 ScalarEvolution::ExitLimit
4214 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4216 // Okay, we've chosen an exiting block. See what condition causes us to
4217 // exit at this block.
4219 // FIXME: we should be able to handle switch instructions (with a single exit)
4220 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
4221 if (ExitBr == 0) return getCouldNotCompute();
4222 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
4224 // At this point, we know we have a conditional branch that determines whether
4225 // the loop is exited. However, we don't know if the branch is executed each
4226 // time through the loop. If not, then the execution count of the branch will
4227 // not be equal to the trip count of the loop.
4229 // Currently we check for this by checking to see if the Exit branch goes to
4230 // the loop header. If so, we know it will always execute the same number of
4231 // times as the loop. We also handle the case where the exit block *is* the
4232 // loop header. This is common for un-rotated loops.
4234 // If both of those tests fail, walk up the unique predecessor chain to the
4235 // header, stopping if there is an edge that doesn't exit the loop. If the
4236 // header is reached, the execution count of the branch will be equal to the
4237 // trip count of the loop.
4239 // More extensive analysis could be done to handle more cases here.
4241 if (ExitBr->getSuccessor(0) != L->getHeader() &&
4242 ExitBr->getSuccessor(1) != L->getHeader() &&
4243 ExitBr->getParent() != L->getHeader()) {
4244 // The simple checks failed, try climbing the unique predecessor chain
4245 // up to the header.
4247 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
4248 BasicBlock *Pred = BB->getUniquePredecessor();
4250 return getCouldNotCompute();
4251 TerminatorInst *PredTerm = Pred->getTerminator();
4252 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4253 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4256 // If the predecessor has a successor that isn't BB and isn't
4257 // outside the loop, assume the worst.
4258 if (L->contains(PredSucc))
4259 return getCouldNotCompute();
4261 if (Pred == L->getHeader()) {
4268 return getCouldNotCompute();
4271 // Proceed to the next level to examine the exit condition expression.
4272 return ComputeExitLimitFromCond(L, ExitBr->getCondition(),
4273 ExitBr->getSuccessor(0),
4274 ExitBr->getSuccessor(1));
4277 /// ComputeExitLimitFromCond - Compute the number of times the
4278 /// backedge of the specified loop will execute if its exit condition
4279 /// were a conditional branch of ExitCond, TBB, and FBB.
4280 ScalarEvolution::ExitLimit
4281 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4285 // Check if the controlling expression for this loop is an And or Or.
4286 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4287 if (BO->getOpcode() == Instruction::And) {
4288 // Recurse on the operands of the and.
4289 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB);
4290 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB);
4291 const SCEV *BECount = getCouldNotCompute();
4292 const SCEV *MaxBECount = getCouldNotCompute();
4293 if (L->contains(TBB)) {
4294 // Both conditions must be true for the loop to continue executing.
4295 // Choose the less conservative count.
4296 if (EL0.Exact == getCouldNotCompute() ||
4297 EL1.Exact == getCouldNotCompute())
4298 BECount = getCouldNotCompute();
4300 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4301 if (EL0.Max == getCouldNotCompute())
4302 MaxBECount = EL1.Max;
4303 else if (EL1.Max == getCouldNotCompute())
4304 MaxBECount = EL0.Max;
4306 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4308 // Both conditions must be true at the same time for the loop to exit.
4309 // For now, be conservative.
4310 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4311 if (EL0.Max == EL1.Max)
4312 MaxBECount = EL0.Max;
4313 if (EL0.Exact == EL1.Exact)
4314 BECount = EL0.Exact;
4317 return ExitLimit(BECount, MaxBECount);
4319 if (BO->getOpcode() == Instruction::Or) {
4320 // Recurse on the operands of the or.
4321 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB);
4322 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB);
4323 const SCEV *BECount = getCouldNotCompute();
4324 const SCEV *MaxBECount = getCouldNotCompute();
4325 if (L->contains(FBB)) {
4326 // Both conditions must be false for the loop to continue executing.
4327 // Choose the less conservative count.
4328 if (EL0.Exact == getCouldNotCompute() ||
4329 EL1.Exact == getCouldNotCompute())
4330 BECount = getCouldNotCompute();
4332 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4333 if (EL0.Max == getCouldNotCompute())
4334 MaxBECount = EL1.Max;
4335 else if (EL1.Max == getCouldNotCompute())
4336 MaxBECount = EL0.Max;
4338 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4340 // Both conditions must be false at the same time for the loop to exit.
4341 // For now, be conservative.
4342 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4343 if (EL0.Max == EL1.Max)
4344 MaxBECount = EL0.Max;
4345 if (EL0.Exact == EL1.Exact)
4346 BECount = EL0.Exact;
4349 return ExitLimit(BECount, MaxBECount);
4353 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4354 // Proceed to the next level to examine the icmp.
4355 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4356 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB);
4358 // Check for a constant condition. These are normally stripped out by
4359 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4360 // preserve the CFG and is temporarily leaving constant conditions
4362 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4363 if (L->contains(FBB) == !CI->getZExtValue())
4364 // The backedge is always taken.
4365 return getCouldNotCompute();
4367 // The backedge is never taken.
4368 return getConstant(CI->getType(), 0);
4371 // If it's not an integer or pointer comparison then compute it the hard way.
4372 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4375 /// ComputeExitLimitFromICmp - Compute the number of times the
4376 /// backedge of the specified loop will execute if its exit condition
4377 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4378 ScalarEvolution::ExitLimit
4379 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
4384 // If the condition was exit on true, convert the condition to exit on false
4385 ICmpInst::Predicate Cond;
4386 if (!L->contains(FBB))
4387 Cond = ExitCond->getPredicate();
4389 Cond = ExitCond->getInversePredicate();
4391 // Handle common loops like: for (X = "string"; *X; ++X)
4392 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4393 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4395 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
4396 if (ItCnt.hasAnyInfo())
4400 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4401 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4403 // Try to evaluate any dependencies out of the loop.
4404 LHS = getSCEVAtScope(LHS, L);
4405 RHS = getSCEVAtScope(RHS, L);
4407 // At this point, we would like to compute how many iterations of the
4408 // loop the predicate will return true for these inputs.
4409 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4410 // If there is a loop-invariant, force it into the RHS.
4411 std::swap(LHS, RHS);
4412 Cond = ICmpInst::getSwappedPredicate(Cond);
4415 // Simplify the operands before analyzing them.
4416 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4418 // If we have a comparison of a chrec against a constant, try to use value
4419 // ranges to answer this query.
4420 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4421 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4422 if (AddRec->getLoop() == L) {
4423 // Form the constant range.
4424 ConstantRange CompRange(
4425 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4427 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4428 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4432 case ICmpInst::ICMP_NE: { // while (X != Y)
4433 // Convert to: while (X-Y != 0)
4434 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L);
4435 if (EL.hasAnyInfo()) return EL;
4438 case ICmpInst::ICMP_EQ: { // while (X == Y)
4439 // Convert to: while (X-Y == 0)
4440 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4441 if (EL.hasAnyInfo()) return EL;
4444 case ICmpInst::ICMP_SLT: {
4445 ExitLimit EL = HowManyLessThans(LHS, RHS, L, true);
4446 if (EL.hasAnyInfo()) return EL;
4449 case ICmpInst::ICMP_SGT: {
4450 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4451 getNotSCEV(RHS), L, true);
4452 if (EL.hasAnyInfo()) return EL;
4455 case ICmpInst::ICMP_ULT: {
4456 ExitLimit EL = HowManyLessThans(LHS, RHS, L, false);
4457 if (EL.hasAnyInfo()) return EL;
4460 case ICmpInst::ICMP_UGT: {
4461 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4462 getNotSCEV(RHS), L, false);
4463 if (EL.hasAnyInfo()) return EL;
4468 dbgs() << "ComputeBackedgeTakenCount ";
4469 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4470 dbgs() << "[unsigned] ";
4471 dbgs() << *LHS << " "
4472 << Instruction::getOpcodeName(Instruction::ICmp)
4473 << " " << *RHS << "\n";
4477 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4480 static ConstantInt *
4481 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4482 ScalarEvolution &SE) {
4483 const SCEV *InVal = SE.getConstant(C);
4484 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4485 assert(isa<SCEVConstant>(Val) &&
4486 "Evaluation of SCEV at constant didn't fold correctly?");
4487 return cast<SCEVConstant>(Val)->getValue();
4490 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
4491 /// and a GEP expression (missing the pointer index) indexing into it, return
4492 /// the addressed element of the initializer or null if the index expression is
4495 GetAddressedElementFromGlobal(GlobalVariable *GV,
4496 const std::vector<ConstantInt*> &Indices) {
4497 Constant *Init = GV->getInitializer();
4498 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
4499 uint64_t Idx = Indices[i]->getZExtValue();
4500 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
4501 assert(Idx < CS->getNumOperands() && "Bad struct index!");
4502 Init = cast<Constant>(CS->getOperand(Idx));
4503 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
4504 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
4505 Init = cast<Constant>(CA->getOperand(Idx));
4506 } else if (isa<ConstantAggregateZero>(Init)) {
4507 if (StructType *STy = dyn_cast<StructType>(Init->getType())) {
4508 assert(Idx < STy->getNumElements() && "Bad struct index!");
4509 Init = Constant::getNullValue(STy->getElementType(Idx));
4510 } else if (ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
4511 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
4512 Init = Constant::getNullValue(ATy->getElementType());
4514 llvm_unreachable("Unknown constant aggregate type!");
4518 return 0; // Unknown initializer type
4524 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
4525 /// 'icmp op load X, cst', try to see if we can compute the backedge
4526 /// execution count.
4527 ScalarEvolution::ExitLimit
4528 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
4532 ICmpInst::Predicate predicate) {
4534 if (LI->isVolatile()) return getCouldNotCompute();
4536 // Check to see if the loaded pointer is a getelementptr of a global.
4537 // TODO: Use SCEV instead of manually grubbing with GEPs.
4538 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4539 if (!GEP) return getCouldNotCompute();
4541 // Make sure that it is really a constant global we are gepping, with an
4542 // initializer, and make sure the first IDX is really 0.
4543 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4544 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4545 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4546 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4547 return getCouldNotCompute();
4549 // Okay, we allow one non-constant index into the GEP instruction.
4551 std::vector<ConstantInt*> Indexes;
4552 unsigned VarIdxNum = 0;
4553 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4554 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4555 Indexes.push_back(CI);
4556 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4557 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4558 VarIdx = GEP->getOperand(i);
4560 Indexes.push_back(0);
4563 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4564 // Check to see if X is a loop variant variable value now.
4565 const SCEV *Idx = getSCEV(VarIdx);
4566 Idx = getSCEVAtScope(Idx, L);
4568 // We can only recognize very limited forms of loop index expressions, in
4569 // particular, only affine AddRec's like {C1,+,C2}.
4570 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4571 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4572 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4573 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4574 return getCouldNotCompute();
4576 unsigned MaxSteps = MaxBruteForceIterations;
4577 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4578 ConstantInt *ItCst = ConstantInt::get(
4579 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4580 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4582 // Form the GEP offset.
4583 Indexes[VarIdxNum] = Val;
4585 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
4586 if (Result == 0) break; // Cannot compute!
4588 // Evaluate the condition for this iteration.
4589 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4590 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4591 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4593 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4594 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4597 ++NumArrayLenItCounts;
4598 return getConstant(ItCst); // Found terminating iteration!
4601 return getCouldNotCompute();
4605 /// CanConstantFold - Return true if we can constant fold an instruction of the
4606 /// specified type, assuming that all operands were constants.
4607 static bool CanConstantFold(const Instruction *I) {
4608 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4609 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
4612 if (const CallInst *CI = dyn_cast<CallInst>(I))
4613 if (const Function *F = CI->getCalledFunction())
4614 return canConstantFoldCallTo(F);
4618 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4619 /// in the loop that V is derived from. We allow arbitrary operations along the
4620 /// way, but the operands of an operation must either be constants or a value
4621 /// derived from a constant PHI. If this expression does not fit with these
4622 /// constraints, return null.
4623 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4624 // If this is not an instruction, or if this is an instruction outside of the
4625 // loop, it can't be derived from a loop PHI.
4626 Instruction *I = dyn_cast<Instruction>(V);
4627 if (I == 0 || !L->contains(I)) return 0;
4629 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4630 if (L->getHeader() == I->getParent())
4633 // We don't currently keep track of the control flow needed to evaluate
4634 // PHIs, so we cannot handle PHIs inside of loops.
4638 // If we won't be able to constant fold this expression even if the operands
4639 // are constants, return early.
4640 if (!CanConstantFold(I)) return 0;
4642 // Otherwise, we can evaluate this instruction if all of its operands are
4643 // constant or derived from a PHI node themselves.
4645 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
4646 if (!isa<Constant>(I->getOperand(Op))) {
4647 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
4648 if (P == 0) return 0; // Not evolving from PHI
4652 return 0; // Evolving from multiple different PHIs.
4655 // This is a expression evolving from a constant PHI!
4659 /// EvaluateExpression - Given an expression that passes the
4660 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4661 /// in the loop has the value PHIVal. If we can't fold this expression for some
4662 /// reason, return null.
4663 static Constant *EvaluateExpression(Value *V, Constant *PHIVal,
4664 const TargetData *TD) {
4665 if (isa<PHINode>(V)) return PHIVal;
4666 if (Constant *C = dyn_cast<Constant>(V)) return C;
4667 Instruction *I = cast<Instruction>(V);
4669 std::vector<Constant*> Operands(I->getNumOperands());
4671 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4672 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD);
4673 if (Operands[i] == 0) return 0;
4676 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4677 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4679 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, TD);
4682 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4683 /// in the header of its containing loop, we know the loop executes a
4684 /// constant number of times, and the PHI node is just a recurrence
4685 /// involving constants, fold it.
4687 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4690 DenseMap<PHINode*, Constant*>::const_iterator I =
4691 ConstantEvolutionLoopExitValue.find(PN);
4692 if (I != ConstantEvolutionLoopExitValue.end())
4695 if (BEs.ugt(MaxBruteForceIterations))
4696 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4698 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4700 // Since the loop is canonicalized, the PHI node must have two entries. One
4701 // entry must be a constant (coming in from outside of the loop), and the
4702 // second must be derived from the same PHI.
4703 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4704 Constant *StartCST =
4705 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4707 return RetVal = 0; // Must be a constant.
4709 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4710 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4711 !isa<Constant>(BEValue))
4712 return RetVal = 0; // Not derived from same PHI.
4714 // Execute the loop symbolically to determine the exit value.
4715 if (BEs.getActiveBits() >= 32)
4716 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4718 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4719 unsigned IterationNum = 0;
4720 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
4721 if (IterationNum == NumIterations)
4722 return RetVal = PHIVal; // Got exit value!
4724 // Compute the value of the PHI node for the next iteration.
4725 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4726 if (NextPHI == PHIVal)
4727 return RetVal = NextPHI; // Stopped evolving!
4729 return 0; // Couldn't evaluate!
4734 /// ComputeExitCountExhaustively - If the loop is known to execute a
4735 /// constant number of times (the condition evolves only from constants),
4736 /// try to evaluate a few iterations of the loop until we get the exit
4737 /// condition gets a value of ExitWhen (true or false). If we cannot
4738 /// evaluate the trip count of the loop, return getCouldNotCompute().
4739 const SCEV * ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
4742 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4743 if (PN == 0) return getCouldNotCompute();
4745 // If the loop is canonicalized, the PHI will have exactly two entries.
4746 // That's the only form we support here.
4747 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4749 // One entry must be a constant (coming in from outside of the loop), and the
4750 // second must be derived from the same PHI.
4751 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4752 Constant *StartCST =
4753 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4754 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
4756 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4757 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4758 !isa<Constant>(BEValue))
4759 return getCouldNotCompute(); // Not derived from same PHI.
4761 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4762 // the loop symbolically to determine when the condition gets a value of
4764 unsigned IterationNum = 0;
4765 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4766 for (Constant *PHIVal = StartCST;
4767 IterationNum != MaxIterations; ++IterationNum) {
4768 ConstantInt *CondVal =
4769 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD));
4771 // Couldn't symbolically evaluate.
4772 if (!CondVal) return getCouldNotCompute();
4774 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4775 ++NumBruteForceTripCountsComputed;
4776 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4779 // Compute the value of the PHI node for the next iteration.
4780 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4781 if (NextPHI == 0 || NextPHI == PHIVal)
4782 return getCouldNotCompute();// Couldn't evaluate or not making progress...
4786 // Too many iterations were needed to evaluate.
4787 return getCouldNotCompute();
4790 /// getSCEVAtScope - Return a SCEV expression for the specified value
4791 /// at the specified scope in the program. The L value specifies a loop
4792 /// nest to evaluate the expression at, where null is the top-level or a
4793 /// specified loop is immediately inside of the loop.
4795 /// This method can be used to compute the exit value for a variable defined
4796 /// in a loop by querying what the value will hold in the parent loop.
4798 /// In the case that a relevant loop exit value cannot be computed, the
4799 /// original value V is returned.
4800 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4801 // Check to see if we've folded this expression at this loop before.
4802 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4803 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4804 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4806 return Pair.first->second ? Pair.first->second : V;
4808 // Otherwise compute it.
4809 const SCEV *C = computeSCEVAtScope(V, L);
4810 ValuesAtScopes[V][L] = C;
4814 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
4815 if (isa<SCEVConstant>(V)) return V;
4817 // If this instruction is evolved from a constant-evolving PHI, compute the
4818 // exit value from the loop without using SCEVs.
4819 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
4820 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
4821 const Loop *LI = (*this->LI)[I->getParent()];
4822 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
4823 if (PHINode *PN = dyn_cast<PHINode>(I))
4824 if (PN->getParent() == LI->getHeader()) {
4825 // Okay, there is no closed form solution for the PHI node. Check
4826 // to see if the loop that contains it has a known backedge-taken
4827 // count. If so, we may be able to force computation of the exit
4829 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
4830 if (const SCEVConstant *BTCC =
4831 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
4832 // Okay, we know how many times the containing loop executes. If
4833 // this is a constant evolving PHI node, get the final value at
4834 // the specified iteration number.
4835 Constant *RV = getConstantEvolutionLoopExitValue(PN,
4836 BTCC->getValue()->getValue(),
4838 if (RV) return getSCEV(RV);
4842 // Okay, this is an expression that we cannot symbolically evaluate
4843 // into a SCEV. Check to see if it's possible to symbolically evaluate
4844 // the arguments into constants, and if so, try to constant propagate the
4845 // result. This is particularly useful for computing loop exit values.
4846 if (CanConstantFold(I)) {
4847 SmallVector<Constant *, 4> Operands;
4848 bool MadeImprovement = false;
4849 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4850 Value *Op = I->getOperand(i);
4851 if (Constant *C = dyn_cast<Constant>(Op)) {
4852 Operands.push_back(C);
4856 // If any of the operands is non-constant and if they are
4857 // non-integer and non-pointer, don't even try to analyze them
4858 // with scev techniques.
4859 if (!isSCEVable(Op->getType()))
4862 const SCEV *OrigV = getSCEV(Op);
4863 const SCEV *OpV = getSCEVAtScope(OrigV, L);
4864 MadeImprovement |= OrigV != OpV;
4867 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
4869 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV))
4870 C = dyn_cast<Constant>(SU->getValue());
4872 if (C->getType() != Op->getType())
4873 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4877 Operands.push_back(C);
4880 // Check to see if getSCEVAtScope actually made an improvement.
4881 if (MadeImprovement) {
4883 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4884 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
4885 Operands[0], Operands[1], TD);
4887 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4895 // This is some other type of SCEVUnknown, just return it.
4899 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
4900 // Avoid performing the look-up in the common case where the specified
4901 // expression has no loop-variant portions.
4902 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
4903 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4904 if (OpAtScope != Comm->getOperand(i)) {
4905 // Okay, at least one of these operands is loop variant but might be
4906 // foldable. Build a new instance of the folded commutative expression.
4907 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
4908 Comm->op_begin()+i);
4909 NewOps.push_back(OpAtScope);
4911 for (++i; i != e; ++i) {
4912 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4913 NewOps.push_back(OpAtScope);
4915 if (isa<SCEVAddExpr>(Comm))
4916 return getAddExpr(NewOps);
4917 if (isa<SCEVMulExpr>(Comm))
4918 return getMulExpr(NewOps);
4919 if (isa<SCEVSMaxExpr>(Comm))
4920 return getSMaxExpr(NewOps);
4921 if (isa<SCEVUMaxExpr>(Comm))
4922 return getUMaxExpr(NewOps);
4923 llvm_unreachable("Unknown commutative SCEV type!");
4926 // If we got here, all operands are loop invariant.
4930 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
4931 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
4932 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
4933 if (LHS == Div->getLHS() && RHS == Div->getRHS())
4934 return Div; // must be loop invariant
4935 return getUDivExpr(LHS, RHS);
4938 // If this is a loop recurrence for a loop that does not contain L, then we
4939 // are dealing with the final value computed by the loop.
4940 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
4941 // First, attempt to evaluate each operand.
4942 // Avoid performing the look-up in the common case where the specified
4943 // expression has no loop-variant portions.
4944 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4945 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
4946 if (OpAtScope == AddRec->getOperand(i))
4949 // Okay, at least one of these operands is loop variant but might be
4950 // foldable. Build a new instance of the folded commutative expression.
4951 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
4952 AddRec->op_begin()+i);
4953 NewOps.push_back(OpAtScope);
4954 for (++i; i != e; ++i)
4955 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
4957 const SCEV *FoldedRec =
4958 getAddRecExpr(NewOps, AddRec->getLoop(),
4959 AddRec->getNoWrapFlags(SCEV::FlagNW));
4960 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
4961 // The addrec may be folded to a nonrecurrence, for example, if the
4962 // induction variable is multiplied by zero after constant folding. Go
4963 // ahead and return the folded value.
4969 // If the scope is outside the addrec's loop, evaluate it by using the
4970 // loop exit value of the addrec.
4971 if (!AddRec->getLoop()->contains(L)) {
4972 // To evaluate this recurrence, we need to know how many times the AddRec
4973 // loop iterates. Compute this now.
4974 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
4975 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
4977 // Then, evaluate the AddRec.
4978 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
4984 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
4985 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4986 if (Op == Cast->getOperand())
4987 return Cast; // must be loop invariant
4988 return getZeroExtendExpr(Op, Cast->getType());
4991 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
4992 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4993 if (Op == Cast->getOperand())
4994 return Cast; // must be loop invariant
4995 return getSignExtendExpr(Op, Cast->getType());
4998 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
4999 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5000 if (Op == Cast->getOperand())
5001 return Cast; // must be loop invariant
5002 return getTruncateExpr(Op, Cast->getType());
5005 llvm_unreachable("Unknown SCEV type!");
5009 /// getSCEVAtScope - This is a convenience function which does
5010 /// getSCEVAtScope(getSCEV(V), L).
5011 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5012 return getSCEVAtScope(getSCEV(V), L);
5015 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5016 /// following equation:
5018 /// A * X = B (mod N)
5020 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5021 /// A and B isn't important.
5023 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5024 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5025 ScalarEvolution &SE) {
5026 uint32_t BW = A.getBitWidth();
5027 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5028 assert(A != 0 && "A must be non-zero.");
5032 // The gcd of A and N may have only one prime factor: 2. The number of
5033 // trailing zeros in A is its multiplicity
5034 uint32_t Mult2 = A.countTrailingZeros();
5037 // 2. Check if B is divisible by D.
5039 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5040 // is not less than multiplicity of this prime factor for D.
5041 if (B.countTrailingZeros() < Mult2)
5042 return SE.getCouldNotCompute();
5044 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5047 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5048 // bit width during computations.
5049 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5050 APInt Mod(BW + 1, 0);
5051 Mod.setBit(BW - Mult2); // Mod = N / D
5052 APInt I = AD.multiplicativeInverse(Mod);
5054 // 4. Compute the minimum unsigned root of the equation:
5055 // I * (B / D) mod (N / D)
5056 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5058 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5060 return SE.getConstant(Result.trunc(BW));
5063 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5064 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5065 /// might be the same) or two SCEVCouldNotCompute objects.
5067 static std::pair<const SCEV *,const SCEV *>
5068 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5069 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5070 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5071 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5072 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5074 // We currently can only solve this if the coefficients are constants.
5075 if (!LC || !MC || !NC) {
5076 const SCEV *CNC = SE.getCouldNotCompute();
5077 return std::make_pair(CNC, CNC);
5080 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5081 const APInt &L = LC->getValue()->getValue();
5082 const APInt &M = MC->getValue()->getValue();
5083 const APInt &N = NC->getValue()->getValue();
5084 APInt Two(BitWidth, 2);
5085 APInt Four(BitWidth, 4);
5088 using namespace APIntOps;
5090 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5091 // The B coefficient is M-N/2
5095 // The A coefficient is N/2
5096 APInt A(N.sdiv(Two));
5098 // Compute the B^2-4ac term.
5101 SqrtTerm -= Four * (A * C);
5103 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5104 // integer value or else APInt::sqrt() will assert.
5105 APInt SqrtVal(SqrtTerm.sqrt());
5107 // Compute the two solutions for the quadratic formula.
5108 // The divisions must be performed as signed divisions.
5110 APInt TwoA( A << 1 );
5111 if (TwoA.isMinValue()) {
5112 const SCEV *CNC = SE.getCouldNotCompute();
5113 return std::make_pair(CNC, CNC);
5116 LLVMContext &Context = SE.getContext();
5118 ConstantInt *Solution1 =
5119 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5120 ConstantInt *Solution2 =
5121 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5123 return std::make_pair(SE.getConstant(Solution1),
5124 SE.getConstant(Solution2));
5125 } // end APIntOps namespace
5128 /// HowFarToZero - Return the number of times a backedge comparing the specified
5129 /// value to zero will execute. If not computable, return CouldNotCompute.
5131 /// This is only used for loops with a "x != y" exit test. The exit condition is
5132 /// now expressed as a single expression, V = x-y. So the exit test is
5133 /// effectively V != 0. We know and take advantage of the fact that this
5134 /// expression only being used in a comparison by zero context.
5135 ScalarEvolution::ExitLimit
5136 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
5137 // If the value is a constant
5138 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5139 // If the value is already zero, the branch will execute zero times.
5140 if (C->getValue()->isZero()) return C;
5141 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5144 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
5145 if (!AddRec || AddRec->getLoop() != L)
5146 return getCouldNotCompute();
5148 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
5149 // the quadratic equation to solve it.
5150 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
5151 std::pair<const SCEV *,const SCEV *> Roots =
5152 SolveQuadraticEquation(AddRec, *this);
5153 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5154 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5157 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
5158 << " sol#2: " << *R2 << "\n";
5160 // Pick the smallest positive root value.
5161 if (ConstantInt *CB =
5162 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
5165 if (CB->getZExtValue() == false)
5166 std::swap(R1, R2); // R1 is the minimum root now.
5168 // We can only use this value if the chrec ends up with an exact zero
5169 // value at this index. When solving for "X*X != 5", for example, we
5170 // should not accept a root of 2.
5171 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
5173 return R1; // We found a quadratic root!
5176 return getCouldNotCompute();
5179 // Otherwise we can only handle this if it is affine.
5180 if (!AddRec->isAffine())
5181 return getCouldNotCompute();
5183 // If this is an affine expression, the execution count of this branch is
5184 // the minimum unsigned root of the following equation:
5186 // Start + Step*N = 0 (mod 2^BW)
5190 // Step*N = -Start (mod 2^BW)
5192 // where BW is the common bit width of Start and Step.
5194 // Get the initial value for the loop.
5195 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
5196 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
5198 // For now we handle only constant steps.
5200 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
5201 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
5202 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
5203 // We have not yet seen any such cases.
5204 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
5206 return getCouldNotCompute();
5208 // For positive steps (counting up until unsigned overflow):
5209 // N = -Start/Step (as unsigned)
5210 // For negative steps (counting down to zero):
5212 // First compute the unsigned distance from zero in the direction of Step.
5213 bool CountDown = StepC->getValue()->getValue().isNegative();
5214 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
5216 // Handle unitary steps, which cannot wraparound.
5217 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
5218 // N = Distance (as unsigned)
5219 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue())
5222 // If the recurrence is known not to wraparound, unsigned divide computes the
5223 // back edge count. We know that the value will either become zero (and thus
5224 // the loop terminates), that the loop will terminate through some other exit
5225 // condition first, or that the loop has undefined behavior. This means
5226 // we can't "miss" the exit value, even with nonunit stride.
5228 // FIXME: Prove that loops always exhibits *acceptable* undefined
5229 // behavior. Loops must exhibit defined behavior until a wrapped value is
5230 // actually used. So the trip count computed by udiv could be smaller than the
5231 // number of well-defined iterations.
5232 if (AddRec->getNoWrapFlags(SCEV::FlagNW))
5233 // FIXME: We really want an "isexact" bit for udiv.
5234 return getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5236 // Then, try to solve the above equation provided that Start is constant.
5237 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
5238 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
5239 -StartC->getValue()->getValue(),
5241 return getCouldNotCompute();
5244 /// HowFarToNonZero - Return the number of times a backedge checking the
5245 /// specified value for nonzero will execute. If not computable, return
5247 ScalarEvolution::ExitLimit
5248 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
5249 // Loops that look like: while (X == 0) are very strange indeed. We don't
5250 // handle them yet except for the trivial case. This could be expanded in the
5251 // future as needed.
5253 // If the value is a constant, check to see if it is known to be non-zero
5254 // already. If so, the backedge will execute zero times.
5255 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5256 if (!C->getValue()->isNullValue())
5257 return getConstant(C->getType(), 0);
5258 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5261 // We could implement others, but I really doubt anyone writes loops like
5262 // this, and if they did, they would already be constant folded.
5263 return getCouldNotCompute();
5266 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
5267 /// (which may not be an immediate predecessor) which has exactly one
5268 /// successor from which BB is reachable, or null if no such block is
5271 std::pair<BasicBlock *, BasicBlock *>
5272 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
5273 // If the block has a unique predecessor, then there is no path from the
5274 // predecessor to the block that does not go through the direct edge
5275 // from the predecessor to the block.
5276 if (BasicBlock *Pred = BB->getSinglePredecessor())
5277 return std::make_pair(Pred, BB);
5279 // A loop's header is defined to be a block that dominates the loop.
5280 // If the header has a unique predecessor outside the loop, it must be
5281 // a block that has exactly one successor that can reach the loop.
5282 if (Loop *L = LI->getLoopFor(BB))
5283 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5285 return std::pair<BasicBlock *, BasicBlock *>();
5288 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5289 /// testing whether two expressions are equal, however for the purposes of
5290 /// looking for a condition guarding a loop, it can be useful to be a little
5291 /// more general, since a front-end may have replicated the controlling
5294 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5295 // Quick check to see if they are the same SCEV.
5296 if (A == B) return true;
5298 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5299 // two different instructions with the same value. Check for this case.
5300 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5301 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5302 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5303 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5304 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5307 // Otherwise assume they may have a different value.
5311 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5312 /// predicate Pred. Return true iff any changes were made.
5314 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5315 const SCEV *&LHS, const SCEV *&RHS) {
5316 bool Changed = false;
5318 // Canonicalize a constant to the right side.
5319 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5320 // Check for both operands constant.
5321 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5322 if (ConstantExpr::getICmp(Pred,
5324 RHSC->getValue())->isNullValue())
5325 goto trivially_false;
5327 goto trivially_true;
5329 // Otherwise swap the operands to put the constant on the right.
5330 std::swap(LHS, RHS);
5331 Pred = ICmpInst::getSwappedPredicate(Pred);
5335 // If we're comparing an addrec with a value which is loop-invariant in the
5336 // addrec's loop, put the addrec on the left. Also make a dominance check,
5337 // as both operands could be addrecs loop-invariant in each other's loop.
5338 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5339 const Loop *L = AR->getLoop();
5340 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5341 std::swap(LHS, RHS);
5342 Pred = ICmpInst::getSwappedPredicate(Pred);
5347 // If there's a constant operand, canonicalize comparisons with boundary
5348 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5349 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5350 const APInt &RA = RC->getValue()->getValue();
5352 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5353 case ICmpInst::ICMP_EQ:
5354 case ICmpInst::ICMP_NE:
5356 case ICmpInst::ICMP_UGE:
5357 if ((RA - 1).isMinValue()) {
5358 Pred = ICmpInst::ICMP_NE;
5359 RHS = getConstant(RA - 1);
5363 if (RA.isMaxValue()) {
5364 Pred = ICmpInst::ICMP_EQ;
5368 if (RA.isMinValue()) goto trivially_true;
5370 Pred = ICmpInst::ICMP_UGT;
5371 RHS = getConstant(RA - 1);
5374 case ICmpInst::ICMP_ULE:
5375 if ((RA + 1).isMaxValue()) {
5376 Pred = ICmpInst::ICMP_NE;
5377 RHS = getConstant(RA + 1);
5381 if (RA.isMinValue()) {
5382 Pred = ICmpInst::ICMP_EQ;
5386 if (RA.isMaxValue()) goto trivially_true;
5388 Pred = ICmpInst::ICMP_ULT;
5389 RHS = getConstant(RA + 1);
5392 case ICmpInst::ICMP_SGE:
5393 if ((RA - 1).isMinSignedValue()) {
5394 Pred = ICmpInst::ICMP_NE;
5395 RHS = getConstant(RA - 1);
5399 if (RA.isMaxSignedValue()) {
5400 Pred = ICmpInst::ICMP_EQ;
5404 if (RA.isMinSignedValue()) goto trivially_true;
5406 Pred = ICmpInst::ICMP_SGT;
5407 RHS = getConstant(RA - 1);
5410 case ICmpInst::ICMP_SLE:
5411 if ((RA + 1).isMaxSignedValue()) {
5412 Pred = ICmpInst::ICMP_NE;
5413 RHS = getConstant(RA + 1);
5417 if (RA.isMinSignedValue()) {
5418 Pred = ICmpInst::ICMP_EQ;
5422 if (RA.isMaxSignedValue()) goto trivially_true;
5424 Pred = ICmpInst::ICMP_SLT;
5425 RHS = getConstant(RA + 1);
5428 case ICmpInst::ICMP_UGT:
5429 if (RA.isMinValue()) {
5430 Pred = ICmpInst::ICMP_NE;
5434 if ((RA + 1).isMaxValue()) {
5435 Pred = ICmpInst::ICMP_EQ;
5436 RHS = getConstant(RA + 1);
5440 if (RA.isMaxValue()) goto trivially_false;
5442 case ICmpInst::ICMP_ULT:
5443 if (RA.isMaxValue()) {
5444 Pred = ICmpInst::ICMP_NE;
5448 if ((RA - 1).isMinValue()) {
5449 Pred = ICmpInst::ICMP_EQ;
5450 RHS = getConstant(RA - 1);
5454 if (RA.isMinValue()) goto trivially_false;
5456 case ICmpInst::ICMP_SGT:
5457 if (RA.isMinSignedValue()) {
5458 Pred = ICmpInst::ICMP_NE;
5462 if ((RA + 1).isMaxSignedValue()) {
5463 Pred = ICmpInst::ICMP_EQ;
5464 RHS = getConstant(RA + 1);
5468 if (RA.isMaxSignedValue()) goto trivially_false;
5470 case ICmpInst::ICMP_SLT:
5471 if (RA.isMaxSignedValue()) {
5472 Pred = ICmpInst::ICMP_NE;
5476 if ((RA - 1).isMinSignedValue()) {
5477 Pred = ICmpInst::ICMP_EQ;
5478 RHS = getConstant(RA - 1);
5482 if (RA.isMinSignedValue()) goto trivially_false;
5487 // Check for obvious equality.
5488 if (HasSameValue(LHS, RHS)) {
5489 if (ICmpInst::isTrueWhenEqual(Pred))
5490 goto trivially_true;
5491 if (ICmpInst::isFalseWhenEqual(Pred))
5492 goto trivially_false;
5495 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
5496 // adding or subtracting 1 from one of the operands.
5498 case ICmpInst::ICMP_SLE:
5499 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
5500 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5502 Pred = ICmpInst::ICMP_SLT;
5504 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
5505 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5507 Pred = ICmpInst::ICMP_SLT;
5511 case ICmpInst::ICMP_SGE:
5512 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5513 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5515 Pred = ICmpInst::ICMP_SGT;
5517 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5518 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5520 Pred = ICmpInst::ICMP_SGT;
5524 case ICmpInst::ICMP_ULE:
5525 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5526 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5528 Pred = ICmpInst::ICMP_ULT;
5530 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5531 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5533 Pred = ICmpInst::ICMP_ULT;
5537 case ICmpInst::ICMP_UGE:
5538 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5539 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5541 Pred = ICmpInst::ICMP_UGT;
5543 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5544 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5546 Pred = ICmpInst::ICMP_UGT;
5554 // TODO: More simplifications are possible here.
5560 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5561 Pred = ICmpInst::ICMP_EQ;
5566 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5567 Pred = ICmpInst::ICMP_NE;
5571 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5572 return getSignedRange(S).getSignedMax().isNegative();
5575 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5576 return getSignedRange(S).getSignedMin().isStrictlyPositive();
5579 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5580 return !getSignedRange(S).getSignedMin().isNegative();
5583 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5584 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5587 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5588 return isKnownNegative(S) || isKnownPositive(S);
5591 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5592 const SCEV *LHS, const SCEV *RHS) {
5593 // Canonicalize the inputs first.
5594 (void)SimplifyICmpOperands(Pred, LHS, RHS);
5596 // If LHS or RHS is an addrec, check to see if the condition is true in
5597 // every iteration of the loop.
5598 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
5599 if (isLoopEntryGuardedByCond(
5600 AR->getLoop(), Pred, AR->getStart(), RHS) &&
5601 isLoopBackedgeGuardedByCond(
5602 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
5604 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
5605 if (isLoopEntryGuardedByCond(
5606 AR->getLoop(), Pred, LHS, AR->getStart()) &&
5607 isLoopBackedgeGuardedByCond(
5608 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
5611 // Otherwise see what can be done with known constant ranges.
5612 return isKnownPredicateWithRanges(Pred, LHS, RHS);
5616 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
5617 const SCEV *LHS, const SCEV *RHS) {
5618 if (HasSameValue(LHS, RHS))
5619 return ICmpInst::isTrueWhenEqual(Pred);
5621 // This code is split out from isKnownPredicate because it is called from
5622 // within isLoopEntryGuardedByCond.
5625 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5627 case ICmpInst::ICMP_SGT:
5628 Pred = ICmpInst::ICMP_SLT;
5629 std::swap(LHS, RHS);
5630 case ICmpInst::ICMP_SLT: {
5631 ConstantRange LHSRange = getSignedRange(LHS);
5632 ConstantRange RHSRange = getSignedRange(RHS);
5633 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
5635 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
5639 case ICmpInst::ICMP_SGE:
5640 Pred = ICmpInst::ICMP_SLE;
5641 std::swap(LHS, RHS);
5642 case ICmpInst::ICMP_SLE: {
5643 ConstantRange LHSRange = getSignedRange(LHS);
5644 ConstantRange RHSRange = getSignedRange(RHS);
5645 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
5647 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
5651 case ICmpInst::ICMP_UGT:
5652 Pred = ICmpInst::ICMP_ULT;
5653 std::swap(LHS, RHS);
5654 case ICmpInst::ICMP_ULT: {
5655 ConstantRange LHSRange = getUnsignedRange(LHS);
5656 ConstantRange RHSRange = getUnsignedRange(RHS);
5657 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
5659 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
5663 case ICmpInst::ICMP_UGE:
5664 Pred = ICmpInst::ICMP_ULE;
5665 std::swap(LHS, RHS);
5666 case ICmpInst::ICMP_ULE: {
5667 ConstantRange LHSRange = getUnsignedRange(LHS);
5668 ConstantRange RHSRange = getUnsignedRange(RHS);
5669 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
5671 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
5675 case ICmpInst::ICMP_NE: {
5676 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
5678 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
5681 const SCEV *Diff = getMinusSCEV(LHS, RHS);
5682 if (isKnownNonZero(Diff))
5686 case ICmpInst::ICMP_EQ:
5687 // The check at the top of the function catches the case where
5688 // the values are known to be equal.
5694 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
5695 /// protected by a conditional between LHS and RHS. This is used to
5696 /// to eliminate casts.
5698 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
5699 ICmpInst::Predicate Pred,
5700 const SCEV *LHS, const SCEV *RHS) {
5701 // Interpret a null as meaning no loop, where there is obviously no guard
5702 // (interprocedural conditions notwithstanding).
5703 if (!L) return true;
5705 BasicBlock *Latch = L->getLoopLatch();
5709 BranchInst *LoopContinuePredicate =
5710 dyn_cast<BranchInst>(Latch->getTerminator());
5711 if (!LoopContinuePredicate ||
5712 LoopContinuePredicate->isUnconditional())
5715 return isImpliedCond(Pred, LHS, RHS,
5716 LoopContinuePredicate->getCondition(),
5717 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
5720 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
5721 /// by a conditional between LHS and RHS. This is used to help avoid max
5722 /// expressions in loop trip counts, and to eliminate casts.
5724 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
5725 ICmpInst::Predicate Pred,
5726 const SCEV *LHS, const SCEV *RHS) {
5727 // Interpret a null as meaning no loop, where there is obviously no guard
5728 // (interprocedural conditions notwithstanding).
5729 if (!L) return false;
5731 // Starting at the loop predecessor, climb up the predecessor chain, as long
5732 // as there are predecessors that can be found that have unique successors
5733 // leading to the original header.
5734 for (std::pair<BasicBlock *, BasicBlock *>
5735 Pair(L->getLoopPredecessor(), L->getHeader());
5737 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
5739 BranchInst *LoopEntryPredicate =
5740 dyn_cast<BranchInst>(Pair.first->getTerminator());
5741 if (!LoopEntryPredicate ||
5742 LoopEntryPredicate->isUnconditional())
5745 if (isImpliedCond(Pred, LHS, RHS,
5746 LoopEntryPredicate->getCondition(),
5747 LoopEntryPredicate->getSuccessor(0) != Pair.second))
5754 /// isImpliedCond - Test whether the condition described by Pred, LHS,
5755 /// and RHS is true whenever the given Cond value evaluates to true.
5756 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
5757 const SCEV *LHS, const SCEV *RHS,
5758 Value *FoundCondValue,
5760 // Recursively handle And and Or conditions.
5761 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
5762 if (BO->getOpcode() == Instruction::And) {
5764 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
5765 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
5766 } else if (BO->getOpcode() == Instruction::Or) {
5768 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
5769 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
5773 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
5774 if (!ICI) return false;
5776 // Bail if the ICmp's operands' types are wider than the needed type
5777 // before attempting to call getSCEV on them. This avoids infinite
5778 // recursion, since the analysis of widening casts can require loop
5779 // exit condition information for overflow checking, which would
5781 if (getTypeSizeInBits(LHS->getType()) <
5782 getTypeSizeInBits(ICI->getOperand(0)->getType()))
5785 // Now that we found a conditional branch that dominates the loop, check to
5786 // see if it is the comparison we are looking for.
5787 ICmpInst::Predicate FoundPred;
5789 FoundPred = ICI->getInversePredicate();
5791 FoundPred = ICI->getPredicate();
5793 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
5794 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
5796 // Balance the types. The case where FoundLHS' type is wider than
5797 // LHS' type is checked for above.
5798 if (getTypeSizeInBits(LHS->getType()) >
5799 getTypeSizeInBits(FoundLHS->getType())) {
5800 if (CmpInst::isSigned(Pred)) {
5801 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
5802 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
5804 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
5805 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
5809 // Canonicalize the query to match the way instcombine will have
5810 // canonicalized the comparison.
5811 if (SimplifyICmpOperands(Pred, LHS, RHS))
5813 return CmpInst::isTrueWhenEqual(Pred);
5814 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
5815 if (FoundLHS == FoundRHS)
5816 return CmpInst::isFalseWhenEqual(Pred);
5818 // Check to see if we can make the LHS or RHS match.
5819 if (LHS == FoundRHS || RHS == FoundLHS) {
5820 if (isa<SCEVConstant>(RHS)) {
5821 std::swap(FoundLHS, FoundRHS);
5822 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
5824 std::swap(LHS, RHS);
5825 Pred = ICmpInst::getSwappedPredicate(Pred);
5829 // Check whether the found predicate is the same as the desired predicate.
5830 if (FoundPred == Pred)
5831 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
5833 // Check whether swapping the found predicate makes it the same as the
5834 // desired predicate.
5835 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
5836 if (isa<SCEVConstant>(RHS))
5837 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
5839 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
5840 RHS, LHS, FoundLHS, FoundRHS);
5843 // Check whether the actual condition is beyond sufficient.
5844 if (FoundPred == ICmpInst::ICMP_EQ)
5845 if (ICmpInst::isTrueWhenEqual(Pred))
5846 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
5848 if (Pred == ICmpInst::ICMP_NE)
5849 if (!ICmpInst::isTrueWhenEqual(FoundPred))
5850 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
5853 // Otherwise assume the worst.
5857 /// isImpliedCondOperands - Test whether the condition described by Pred,
5858 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
5859 /// and FoundRHS is true.
5860 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
5861 const SCEV *LHS, const SCEV *RHS,
5862 const SCEV *FoundLHS,
5863 const SCEV *FoundRHS) {
5864 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
5865 FoundLHS, FoundRHS) ||
5866 // ~x < ~y --> x > y
5867 isImpliedCondOperandsHelper(Pred, LHS, RHS,
5868 getNotSCEV(FoundRHS),
5869 getNotSCEV(FoundLHS));
5872 /// isImpliedCondOperandsHelper - Test whether the condition described by
5873 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
5874 /// FoundLHS, and FoundRHS is true.
5876 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
5877 const SCEV *LHS, const SCEV *RHS,
5878 const SCEV *FoundLHS,
5879 const SCEV *FoundRHS) {
5881 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5882 case ICmpInst::ICMP_EQ:
5883 case ICmpInst::ICMP_NE:
5884 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
5887 case ICmpInst::ICMP_SLT:
5888 case ICmpInst::ICMP_SLE:
5889 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
5890 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
5893 case ICmpInst::ICMP_SGT:
5894 case ICmpInst::ICMP_SGE:
5895 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
5896 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
5899 case ICmpInst::ICMP_ULT:
5900 case ICmpInst::ICMP_ULE:
5901 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
5902 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
5905 case ICmpInst::ICMP_UGT:
5906 case ICmpInst::ICMP_UGE:
5907 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
5908 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
5916 /// getBECount - Subtract the end and start values and divide by the step,
5917 /// rounding up, to get the number of times the backedge is executed. Return
5918 /// CouldNotCompute if an intermediate computation overflows.
5919 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
5923 assert(!isKnownNegative(Step) &&
5924 "This code doesn't handle negative strides yet!");
5926 Type *Ty = Start->getType();
5928 // When Start == End, we have an exact BECount == 0. Short-circuit this case
5929 // here because SCEV may not be able to determine that the unsigned division
5930 // after rounding is zero.
5932 return getConstant(Ty, 0);
5934 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
5935 const SCEV *Diff = getMinusSCEV(End, Start);
5936 const SCEV *RoundUp = getAddExpr(Step, NegOne);
5938 // Add an adjustment to the difference between End and Start so that
5939 // the division will effectively round up.
5940 const SCEV *Add = getAddExpr(Diff, RoundUp);
5943 // Check Add for unsigned overflow.
5944 // TODO: More sophisticated things could be done here.
5945 Type *WideTy = IntegerType::get(getContext(),
5946 getTypeSizeInBits(Ty) + 1);
5947 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
5948 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
5949 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
5950 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
5951 return getCouldNotCompute();
5954 return getUDivExpr(Add, Step);
5957 /// HowManyLessThans - Return the number of times a backedge containing the
5958 /// specified less-than comparison will execute. If not computable, return
5959 /// CouldNotCompute.
5960 ScalarEvolution::ExitLimit
5961 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
5962 const Loop *L, bool isSigned) {
5963 // Only handle: "ADDREC < LoopInvariant".
5964 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute();
5966 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
5967 if (!AddRec || AddRec->getLoop() != L)
5968 return getCouldNotCompute();
5970 // Check to see if we have a flag which makes analysis easy.
5971 bool NoWrap = isSigned ? AddRec->getNoWrapFlags(SCEV::FlagNSW) :
5972 AddRec->getNoWrapFlags(SCEV::FlagNUW);
5974 if (AddRec->isAffine()) {
5975 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
5976 const SCEV *Step = AddRec->getStepRecurrence(*this);
5979 return getCouldNotCompute();
5980 if (Step->isOne()) {
5981 // With unit stride, the iteration never steps past the limit value.
5982 } else if (isKnownPositive(Step)) {
5983 // Test whether a positive iteration can step past the limit
5984 // value and past the maximum value for its type in a single step.
5985 // Note that it's not sufficient to check NoWrap here, because even
5986 // though the value after a wrap is undefined, it's not undefined
5987 // behavior, so if wrap does occur, the loop could either terminate or
5988 // loop infinitely, but in either case, the loop is guaranteed to
5989 // iterate at least until the iteration where the wrapping occurs.
5990 const SCEV *One = getConstant(Step->getType(), 1);
5992 APInt Max = APInt::getSignedMaxValue(BitWidth);
5993 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
5994 .slt(getSignedRange(RHS).getSignedMax()))
5995 return getCouldNotCompute();
5997 APInt Max = APInt::getMaxValue(BitWidth);
5998 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
5999 .ult(getUnsignedRange(RHS).getUnsignedMax()))
6000 return getCouldNotCompute();
6003 // TODO: Handle negative strides here and below.
6004 return getCouldNotCompute();
6006 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
6007 // m. So, we count the number of iterations in which {n,+,s} < m is true.
6008 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
6009 // treat m-n as signed nor unsigned due to overflow possibility.
6011 // First, we get the value of the LHS in the first iteration: n
6012 const SCEV *Start = AddRec->getOperand(0);
6014 // Determine the minimum constant start value.
6015 const SCEV *MinStart = getConstant(isSigned ?
6016 getSignedRange(Start).getSignedMin() :
6017 getUnsignedRange(Start).getUnsignedMin());
6019 // If we know that the condition is true in order to enter the loop,
6020 // then we know that it will run exactly (m-n)/s times. Otherwise, we
6021 // only know that it will execute (max(m,n)-n)/s times. In both cases,
6022 // the division must round up.
6023 const SCEV *End = RHS;
6024 if (!isLoopEntryGuardedByCond(L,
6025 isSigned ? ICmpInst::ICMP_SLT :
6027 getMinusSCEV(Start, Step), RHS))
6028 End = isSigned ? getSMaxExpr(RHS, Start)
6029 : getUMaxExpr(RHS, Start);
6031 // Determine the maximum constant end value.
6032 const SCEV *MaxEnd = getConstant(isSigned ?
6033 getSignedRange(End).getSignedMax() :
6034 getUnsignedRange(End).getUnsignedMax());
6036 // If MaxEnd is within a step of the maximum integer value in its type,
6037 // adjust it down to the minimum value which would produce the same effect.
6038 // This allows the subsequent ceiling division of (N+(step-1))/step to
6039 // compute the correct value.
6040 const SCEV *StepMinusOne = getMinusSCEV(Step,
6041 getConstant(Step->getType(), 1));
6044 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
6047 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
6050 // Finally, we subtract these two values and divide, rounding up, to get
6051 // the number of times the backedge is executed.
6052 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
6054 // The maximum backedge count is similar, except using the minimum start
6055 // value and the maximum end value.
6056 // If we already have an exact constant BECount, use it instead.
6057 const SCEV *MaxBECount = isa<SCEVConstant>(BECount) ? BECount
6058 : getBECount(MinStart, MaxEnd, Step, NoWrap);
6060 // If the stride is nonconstant, and NoWrap == true, then
6061 // getBECount(MinStart, MaxEnd) may not compute. This would result in an
6062 // exact BECount and invalid MaxBECount, which should be avoided to catch
6063 // more optimization opportunities.
6064 if (isa<SCEVCouldNotCompute>(MaxBECount))
6065 MaxBECount = BECount;
6067 return ExitLimit(BECount, MaxBECount);
6070 return getCouldNotCompute();
6073 /// getNumIterationsInRange - Return the number of iterations of this loop that
6074 /// produce values in the specified constant range. Another way of looking at
6075 /// this is that it returns the first iteration number where the value is not in
6076 /// the condition, thus computing the exit count. If the iteration count can't
6077 /// be computed, an instance of SCEVCouldNotCompute is returned.
6078 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
6079 ScalarEvolution &SE) const {
6080 if (Range.isFullSet()) // Infinite loop.
6081 return SE.getCouldNotCompute();
6083 // If the start is a non-zero constant, shift the range to simplify things.
6084 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
6085 if (!SC->getValue()->isZero()) {
6086 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
6087 Operands[0] = SE.getConstant(SC->getType(), 0);
6088 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
6089 getNoWrapFlags(FlagNW));
6090 if (const SCEVAddRecExpr *ShiftedAddRec =
6091 dyn_cast<SCEVAddRecExpr>(Shifted))
6092 return ShiftedAddRec->getNumIterationsInRange(
6093 Range.subtract(SC->getValue()->getValue()), SE);
6094 // This is strange and shouldn't happen.
6095 return SE.getCouldNotCompute();
6098 // The only time we can solve this is when we have all constant indices.
6099 // Otherwise, we cannot determine the overflow conditions.
6100 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
6101 if (!isa<SCEVConstant>(getOperand(i)))
6102 return SE.getCouldNotCompute();
6105 // Okay at this point we know that all elements of the chrec are constants and
6106 // that the start element is zero.
6108 // First check to see if the range contains zero. If not, the first
6110 unsigned BitWidth = SE.getTypeSizeInBits(getType());
6111 if (!Range.contains(APInt(BitWidth, 0)))
6112 return SE.getConstant(getType(), 0);
6115 // If this is an affine expression then we have this situation:
6116 // Solve {0,+,A} in Range === Ax in Range
6118 // We know that zero is in the range. If A is positive then we know that
6119 // the upper value of the range must be the first possible exit value.
6120 // If A is negative then the lower of the range is the last possible loop
6121 // value. Also note that we already checked for a full range.
6122 APInt One(BitWidth,1);
6123 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
6124 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
6126 // The exit value should be (End+A)/A.
6127 APInt ExitVal = (End + A).udiv(A);
6128 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
6130 // Evaluate at the exit value. If we really did fall out of the valid
6131 // range, then we computed our trip count, otherwise wrap around or other
6132 // things must have happened.
6133 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
6134 if (Range.contains(Val->getValue()))
6135 return SE.getCouldNotCompute(); // Something strange happened
6137 // Ensure that the previous value is in the range. This is a sanity check.
6138 assert(Range.contains(
6139 EvaluateConstantChrecAtConstant(this,
6140 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
6141 "Linear scev computation is off in a bad way!");
6142 return SE.getConstant(ExitValue);
6143 } else if (isQuadratic()) {
6144 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
6145 // quadratic equation to solve it. To do this, we must frame our problem in
6146 // terms of figuring out when zero is crossed, instead of when
6147 // Range.getUpper() is crossed.
6148 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
6149 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
6150 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
6151 // getNoWrapFlags(FlagNW)
6154 // Next, solve the constructed addrec
6155 std::pair<const SCEV *,const SCEV *> Roots =
6156 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
6157 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6158 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6160 // Pick the smallest positive root value.
6161 if (ConstantInt *CB =
6162 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
6163 R1->getValue(), R2->getValue()))) {
6164 if (CB->getZExtValue() == false)
6165 std::swap(R1, R2); // R1 is the minimum root now.
6167 // Make sure the root is not off by one. The returned iteration should
6168 // not be in the range, but the previous one should be. When solving
6169 // for "X*X < 5", for example, we should not return a root of 2.
6170 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
6173 if (Range.contains(R1Val->getValue())) {
6174 // The next iteration must be out of the range...
6175 ConstantInt *NextVal =
6176 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
6178 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6179 if (!Range.contains(R1Val->getValue()))
6180 return SE.getConstant(NextVal);
6181 return SE.getCouldNotCompute(); // Something strange happened
6184 // If R1 was not in the range, then it is a good return value. Make
6185 // sure that R1-1 WAS in the range though, just in case.
6186 ConstantInt *NextVal =
6187 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
6188 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6189 if (Range.contains(R1Val->getValue()))
6191 return SE.getCouldNotCompute(); // Something strange happened
6196 return SE.getCouldNotCompute();
6201 //===----------------------------------------------------------------------===//
6202 // SCEVCallbackVH Class Implementation
6203 //===----------------------------------------------------------------------===//
6205 void ScalarEvolution::SCEVCallbackVH::deleted() {
6206 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6207 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
6208 SE->ConstantEvolutionLoopExitValue.erase(PN);
6209 SE->ValueExprMap.erase(getValPtr());
6210 // this now dangles!
6213 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
6214 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6216 // Forget all the expressions associated with users of the old value,
6217 // so that future queries will recompute the expressions using the new
6219 Value *Old = getValPtr();
6220 SmallVector<User *, 16> Worklist;
6221 SmallPtrSet<User *, 8> Visited;
6222 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
6224 Worklist.push_back(*UI);
6225 while (!Worklist.empty()) {
6226 User *U = Worklist.pop_back_val();
6227 // Deleting the Old value will cause this to dangle. Postpone
6228 // that until everything else is done.
6231 if (!Visited.insert(U))
6233 if (PHINode *PN = dyn_cast<PHINode>(U))
6234 SE->ConstantEvolutionLoopExitValue.erase(PN);
6235 SE->ValueExprMap.erase(U);
6236 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
6238 Worklist.push_back(*UI);
6240 // Delete the Old value.
6241 if (PHINode *PN = dyn_cast<PHINode>(Old))
6242 SE->ConstantEvolutionLoopExitValue.erase(PN);
6243 SE->ValueExprMap.erase(Old);
6244 // this now dangles!
6247 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
6248 : CallbackVH(V), SE(se) {}
6250 //===----------------------------------------------------------------------===//
6251 // ScalarEvolution Class Implementation
6252 //===----------------------------------------------------------------------===//
6254 ScalarEvolution::ScalarEvolution()
6255 : FunctionPass(ID), FirstUnknown(0) {
6256 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
6259 bool ScalarEvolution::runOnFunction(Function &F) {
6261 LI = &getAnalysis<LoopInfo>();
6262 TD = getAnalysisIfAvailable<TargetData>();
6263 DT = &getAnalysis<DominatorTree>();
6267 void ScalarEvolution::releaseMemory() {
6268 // Iterate through all the SCEVUnknown instances and call their
6269 // destructors, so that they release their references to their values.
6270 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
6274 ValueExprMap.clear();
6276 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
6277 // that a loop had multiple computable exits.
6278 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
6279 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
6284 BackedgeTakenCounts.clear();
6285 ConstantEvolutionLoopExitValue.clear();
6286 ValuesAtScopes.clear();
6287 LoopDispositions.clear();
6288 BlockDispositions.clear();
6289 UnsignedRanges.clear();
6290 SignedRanges.clear();
6291 UniqueSCEVs.clear();
6292 SCEVAllocator.Reset();
6295 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
6296 AU.setPreservesAll();
6297 AU.addRequiredTransitive<LoopInfo>();
6298 AU.addRequiredTransitive<DominatorTree>();
6301 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
6302 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
6305 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
6307 // Print all inner loops first
6308 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
6309 PrintLoopInfo(OS, SE, *I);
6312 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6315 SmallVector<BasicBlock *, 8> ExitBlocks;
6316 L->getExitBlocks(ExitBlocks);
6317 if (ExitBlocks.size() != 1)
6318 OS << "<multiple exits> ";
6320 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
6321 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
6323 OS << "Unpredictable backedge-taken count. ";
6328 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6331 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
6332 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
6334 OS << "Unpredictable max backedge-taken count. ";
6340 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
6341 // ScalarEvolution's implementation of the print method is to print
6342 // out SCEV values of all instructions that are interesting. Doing
6343 // this potentially causes it to create new SCEV objects though,
6344 // which technically conflicts with the const qualifier. This isn't
6345 // observable from outside the class though, so casting away the
6346 // const isn't dangerous.
6347 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
6349 OS << "Classifying expressions for: ";
6350 WriteAsOperand(OS, F, /*PrintType=*/false);
6352 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
6353 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
6356 const SCEV *SV = SE.getSCEV(&*I);
6359 const Loop *L = LI->getLoopFor((*I).getParent());
6361 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
6368 OS << "\t\t" "Exits: ";
6369 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
6370 if (!SE.isLoopInvariant(ExitValue, L)) {
6371 OS << "<<Unknown>>";
6380 OS << "Determining loop execution counts for: ";
6381 WriteAsOperand(OS, F, /*PrintType=*/false);
6383 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
6384 PrintLoopInfo(OS, &SE, *I);
6387 ScalarEvolution::LoopDisposition
6388 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
6389 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S];
6390 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair =
6391 Values.insert(std::make_pair(L, LoopVariant));
6393 return Pair.first->second;
6395 LoopDisposition D = computeLoopDisposition(S, L);
6396 return LoopDispositions[S][L] = D;
6399 ScalarEvolution::LoopDisposition
6400 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
6401 switch (S->getSCEVType()) {
6403 return LoopInvariant;
6407 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
6408 case scAddRecExpr: {
6409 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6411 // If L is the addrec's loop, it's computable.
6412 if (AR->getLoop() == L)
6413 return LoopComputable;
6415 // Add recurrences are never invariant in the function-body (null loop).
6419 // This recurrence is variant w.r.t. L if L contains AR's loop.
6420 if (L->contains(AR->getLoop()))
6423 // This recurrence is invariant w.r.t. L if AR's loop contains L.
6424 if (AR->getLoop()->contains(L))
6425 return LoopInvariant;
6427 // This recurrence is variant w.r.t. L if any of its operands
6429 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
6431 if (!isLoopInvariant(*I, L))
6434 // Otherwise it's loop-invariant.
6435 return LoopInvariant;
6441 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6442 bool HasVarying = false;
6443 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6445 LoopDisposition D = getLoopDisposition(*I, L);
6446 if (D == LoopVariant)
6448 if (D == LoopComputable)
6451 return HasVarying ? LoopComputable : LoopInvariant;
6454 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6455 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
6456 if (LD == LoopVariant)
6458 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
6459 if (RD == LoopVariant)
6461 return (LD == LoopInvariant && RD == LoopInvariant) ?
6462 LoopInvariant : LoopComputable;
6465 // All non-instruction values are loop invariant. All instructions are loop
6466 // invariant if they are not contained in the specified loop.
6467 // Instructions are never considered invariant in the function body
6468 // (null loop) because they are defined within the "loop".
6469 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
6470 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
6471 return LoopInvariant;
6472 case scCouldNotCompute:
6473 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6477 llvm_unreachable("Unknown SCEV kind!");
6481 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
6482 return getLoopDisposition(S, L) == LoopInvariant;
6485 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
6486 return getLoopDisposition(S, L) == LoopComputable;
6489 ScalarEvolution::BlockDisposition
6490 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6491 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S];
6492 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool>
6493 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock));
6495 return Pair.first->second;
6497 BlockDisposition D = computeBlockDisposition(S, BB);
6498 return BlockDispositions[S][BB] = D;
6501 ScalarEvolution::BlockDisposition
6502 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6503 switch (S->getSCEVType()) {
6505 return ProperlyDominatesBlock;
6509 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
6510 case scAddRecExpr: {
6511 // This uses a "dominates" query instead of "properly dominates" query
6512 // to test for proper dominance too, because the instruction which
6513 // produces the addrec's value is a PHI, and a PHI effectively properly
6514 // dominates its entire containing block.
6515 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6516 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
6517 return DoesNotDominateBlock;
6519 // FALL THROUGH into SCEVNAryExpr handling.
6524 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6526 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6528 BlockDisposition D = getBlockDisposition(*I, BB);
6529 if (D == DoesNotDominateBlock)
6530 return DoesNotDominateBlock;
6531 if (D == DominatesBlock)
6534 return Proper ? ProperlyDominatesBlock : DominatesBlock;
6537 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6538 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6539 BlockDisposition LD = getBlockDisposition(LHS, BB);
6540 if (LD == DoesNotDominateBlock)
6541 return DoesNotDominateBlock;
6542 BlockDisposition RD = getBlockDisposition(RHS, BB);
6543 if (RD == DoesNotDominateBlock)
6544 return DoesNotDominateBlock;
6545 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
6546 ProperlyDominatesBlock : DominatesBlock;
6549 if (Instruction *I =
6550 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
6551 if (I->getParent() == BB)
6552 return DominatesBlock;
6553 if (DT->properlyDominates(I->getParent(), BB))
6554 return ProperlyDominatesBlock;
6555 return DoesNotDominateBlock;
6557 return ProperlyDominatesBlock;
6558 case scCouldNotCompute:
6559 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6560 return DoesNotDominateBlock;
6563 llvm_unreachable("Unknown SCEV kind!");
6564 return DoesNotDominateBlock;
6567 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
6568 return getBlockDisposition(S, BB) >= DominatesBlock;
6571 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
6572 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
6575 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
6576 switch (S->getSCEVType()) {
6581 case scSignExtend: {
6582 const SCEVCastExpr *Cast = cast<SCEVCastExpr>(S);
6583 const SCEV *CastOp = Cast->getOperand();
6584 return Op == CastOp || hasOperand(CastOp, Op);
6591 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6592 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6594 const SCEV *NAryOp = *I;
6595 if (NAryOp == Op || hasOperand(NAryOp, Op))
6601 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6602 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6603 return LHS == Op || hasOperand(LHS, Op) ||
6604 RHS == Op || hasOperand(RHS, Op);
6608 case scCouldNotCompute:
6609 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6613 llvm_unreachable("Unknown SCEV kind!");
6617 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
6618 ValuesAtScopes.erase(S);
6619 LoopDispositions.erase(S);
6620 BlockDispositions.erase(S);
6621 UnsignedRanges.erase(S);
6622 SignedRanges.erase(S);