ScalarEvolution.cpp revision 832254e1c2387c0cbeb0a820b8315fbe85cb003a
1//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
2//
3//                     The LLVM Compiler Infrastructure
4//
5// This file was developed by the LLVM research group and is distributed under
6// the University of Illinois Open Source License. See LICENSE.TXT for details.
7//
8//===----------------------------------------------------------------------===//
9//
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.
13//
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.  These classes are reference counted, managed by the SCEVHandle
18// class.  We only create one SCEV of a particular shape, so pointer-comparisons
19// for equality are legal.
20//
21// One important aspect of the SCEV objects is that they are never cyclic, even
22// if there is a cycle in the dataflow for an expression (ie, a PHI node).  If
23// the PHI node is one of the idioms that we can represent (e.g., a polynomial
24// recurrence) then we represent it directly as a recurrence node, otherwise we
25// represent it as a SCEVUnknown node.
26//
27// In addition to being able to represent expressions of various types, we also
28// have folders that are used to build the *canonical* representation for a
29// particular expression.  These folders are capable of using a variety of
30// rewrite rules to simplify the expressions.
31//
32// Once the folders are defined, we can implement the more interesting
33// higher-level code, such as the code that recognizes PHI nodes of various
34// types, computes the execution count of a loop, etc.
35//
36// TODO: We should use these routines and value representations to implement
37// dependence analysis!
38//
39//===----------------------------------------------------------------------===//
40//
41// There are several good references for the techniques used in this analysis.
42//
43//  Chains of recurrences -- a method to expedite the evaluation
44//  of closed-form functions
45//  Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46//
47//  On computational properties of chains of recurrences
48//  Eugene V. Zima
49//
50//  Symbolic Evaluation of Chains of Recurrences for Loop Optimization
51//  Robert A. van Engelen
52//
53//  Efficient Symbolic Analysis for Optimizing Compilers
54//  Robert A. van Engelen
55//
56//  Using the chains of recurrences algebra for data dependence testing and
57//  induction variable substitution
58//  MS Thesis, Johnie Birch
59//
60//===----------------------------------------------------------------------===//
61
62#define DEBUG_TYPE "scalar-evolution"
63#include "llvm/Analysis/ScalarEvolutionExpressions.h"
64#include "llvm/Constants.h"
65#include "llvm/DerivedTypes.h"
66#include "llvm/GlobalVariable.h"
67#include "llvm/Instructions.h"
68#include "llvm/Analysis/ConstantFolding.h"
69#include "llvm/Analysis/LoopInfo.h"
70#include "llvm/Assembly/Writer.h"
71#include "llvm/Transforms/Scalar.h"
72#include "llvm/Support/CFG.h"
73#include "llvm/Support/CommandLine.h"
74#include "llvm/Support/Compiler.h"
75#include "llvm/Support/ConstantRange.h"
76#include "llvm/Support/InstIterator.h"
77#include "llvm/Support/ManagedStatic.h"
78#include "llvm/Support/MathExtras.h"
79#include "llvm/Support/Streams.h"
80#include "llvm/ADT/Statistic.h"
81#include <ostream>
82#include <algorithm>
83#include <cmath>
84using namespace llvm;
85
86STATISTIC(NumBruteForceEvaluations,
87          "Number of brute force evaluations needed to "
88          "calculate high-order polynomial exit values");
89STATISTIC(NumArrayLenItCounts,
90          "Number of trip counts computed with array length");
91STATISTIC(NumTripCountsComputed,
92          "Number of loops with predictable loop counts");
93STATISTIC(NumTripCountsNotComputed,
94          "Number of loops without predictable loop counts");
95STATISTIC(NumBruteForceTripCountsComputed,
96          "Number of loops with trip counts computed by force");
97
98cl::opt<unsigned>
99MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
100                        cl::desc("Maximum number of iterations SCEV will "
101                                 "symbolically execute a constant derived loop"),
102                        cl::init(100));
103
104namespace {
105  RegisterPass<ScalarEvolution>
106  R("scalar-evolution", "Scalar Evolution Analysis");
107}
108
109//===----------------------------------------------------------------------===//
110//                           SCEV class definitions
111//===----------------------------------------------------------------------===//
112
113//===----------------------------------------------------------------------===//
114// Implementation of the SCEV class.
115//
116SCEV::~SCEV() {}
117void SCEV::dump() const {
118  print(cerr);
119}
120
121/// getValueRange - Return the tightest constant bounds that this value is
122/// known to have.  This method is only valid on integer SCEV objects.
123ConstantRange SCEV::getValueRange() const {
124  const Type *Ty = getType();
125  assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!");
126  // Default to a full range if no better information is available.
127  return ConstantRange(getType());
128}
129
130
131SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
132
133bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
134  assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
135  return false;
136}
137
138const Type *SCEVCouldNotCompute::getType() const {
139  assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
140  return 0;
141}
142
143bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
144  assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
145  return false;
146}
147
148SCEVHandle SCEVCouldNotCompute::
149replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
150                                  const SCEVHandle &Conc) const {
151  return this;
152}
153
154void SCEVCouldNotCompute::print(std::ostream &OS) const {
155  OS << "***COULDNOTCOMPUTE***";
156}
157
158bool SCEVCouldNotCompute::classof(const SCEV *S) {
159  return S->getSCEVType() == scCouldNotCompute;
160}
161
162
163// SCEVConstants - Only allow the creation of one SCEVConstant for any
164// particular value.  Don't use a SCEVHandle here, or else the object will
165// never be deleted!
166static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
167
168
169SCEVConstant::~SCEVConstant() {
170  SCEVConstants->erase(V);
171}
172
173SCEVHandle SCEVConstant::get(ConstantInt *V) {
174  SCEVConstant *&R = (*SCEVConstants)[V];
175  if (R == 0) R = new SCEVConstant(V);
176  return R;
177}
178
179ConstantRange SCEVConstant::getValueRange() const {
180  return ConstantRange(V);
181}
182
183const Type *SCEVConstant::getType() const { return V->getType(); }
184
185void SCEVConstant::print(std::ostream &OS) const {
186  WriteAsOperand(OS, V, false);
187}
188
189// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
190// particular input.  Don't use a SCEVHandle here, or else the object will
191// never be deleted!
192static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
193                     SCEVTruncateExpr*> > SCEVTruncates;
194
195SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
196  : SCEV(scTruncate), Op(op), Ty(ty) {
197  assert(Op->getType()->isInteger() && Ty->isInteger() &&
198         "Cannot truncate non-integer value!");
199  assert(Op->getType()->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()
200         && "This is not a truncating conversion!");
201}
202
203SCEVTruncateExpr::~SCEVTruncateExpr() {
204  SCEVTruncates->erase(std::make_pair(Op, Ty));
205}
206
207ConstantRange SCEVTruncateExpr::getValueRange() const {
208  return getOperand()->getValueRange().truncate(getType());
209}
210
211void SCEVTruncateExpr::print(std::ostream &OS) const {
212  OS << "(truncate " << *Op << " to " << *Ty << ")";
213}
214
215// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
216// particular input.  Don't use a SCEVHandle here, or else the object will never
217// be deleted!
218static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
219                     SCEVZeroExtendExpr*> > SCEVZeroExtends;
220
221SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
222  : SCEV(scZeroExtend), Op(op), Ty(ty) {
223  assert(Op->getType()->isInteger() && Ty->isInteger() &&
224         "Cannot zero extend non-integer value!");
225  assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits()
226         && "This is not an extending conversion!");
227}
228
229SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
230  SCEVZeroExtends->erase(std::make_pair(Op, Ty));
231}
232
233ConstantRange SCEVZeroExtendExpr::getValueRange() const {
234  return getOperand()->getValueRange().zeroExtend(getType());
235}
236
237void SCEVZeroExtendExpr::print(std::ostream &OS) const {
238  OS << "(zeroextend " << *Op << " to " << *Ty << ")";
239}
240
241// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
242// particular input.  Don't use a SCEVHandle here, or else the object will never
243// be deleted!
244static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >,
245                     SCEVCommutativeExpr*> > SCEVCommExprs;
246
247SCEVCommutativeExpr::~SCEVCommutativeExpr() {
248  SCEVCommExprs->erase(std::make_pair(getSCEVType(),
249                                      std::vector<SCEV*>(Operands.begin(),
250                                                         Operands.end())));
251}
252
253void SCEVCommutativeExpr::print(std::ostream &OS) const {
254  assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
255  const char *OpStr = getOperationStr();
256  OS << "(" << *Operands[0];
257  for (unsigned i = 1, e = Operands.size(); i != e; ++i)
258    OS << OpStr << *Operands[i];
259  OS << ")";
260}
261
262SCEVHandle SCEVCommutativeExpr::
263replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
264                                  const SCEVHandle &Conc) const {
265  for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
266    SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc);
267    if (H != getOperand(i)) {
268      std::vector<SCEVHandle> NewOps;
269      NewOps.reserve(getNumOperands());
270      for (unsigned j = 0; j != i; ++j)
271        NewOps.push_back(getOperand(j));
272      NewOps.push_back(H);
273      for (++i; i != e; ++i)
274        NewOps.push_back(getOperand(i)->
275                         replaceSymbolicValuesWithConcrete(Sym, Conc));
276
277      if (isa<SCEVAddExpr>(this))
278        return SCEVAddExpr::get(NewOps);
279      else if (isa<SCEVMulExpr>(this))
280        return SCEVMulExpr::get(NewOps);
281      else
282        assert(0 && "Unknown commutative expr!");
283    }
284  }
285  return this;
286}
287
288
289// SCEVSDivs - Only allow the creation of one SCEVSDivExpr for any particular
290// input.  Don't use a SCEVHandle here, or else the object will never be
291// deleted!
292static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>,
293                     SCEVSDivExpr*> > SCEVSDivs;
294
295SCEVSDivExpr::~SCEVSDivExpr() {
296  SCEVSDivs->erase(std::make_pair(LHS, RHS));
297}
298
299void SCEVSDivExpr::print(std::ostream &OS) const {
300  OS << "(" << *LHS << " /s " << *RHS << ")";
301}
302
303const Type *SCEVSDivExpr::getType() const {
304  return LHS->getType();
305}
306
307// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
308// particular input.  Don't use a SCEVHandle here, or else the object will never
309// be deleted!
310static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >,
311                     SCEVAddRecExpr*> > SCEVAddRecExprs;
312
313SCEVAddRecExpr::~SCEVAddRecExpr() {
314  SCEVAddRecExprs->erase(std::make_pair(L,
315                                        std::vector<SCEV*>(Operands.begin(),
316                                                           Operands.end())));
317}
318
319SCEVHandle SCEVAddRecExpr::
320replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
321                                  const SCEVHandle &Conc) const {
322  for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
323    SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc);
324    if (H != getOperand(i)) {
325      std::vector<SCEVHandle> NewOps;
326      NewOps.reserve(getNumOperands());
327      for (unsigned j = 0; j != i; ++j)
328        NewOps.push_back(getOperand(j));
329      NewOps.push_back(H);
330      for (++i; i != e; ++i)
331        NewOps.push_back(getOperand(i)->
332                         replaceSymbolicValuesWithConcrete(Sym, Conc));
333
334      return get(NewOps, L);
335    }
336  }
337  return this;
338}
339
340
341bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
342  // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
343  // contain L and if the start is invariant.
344  return !QueryLoop->contains(L->getHeader()) &&
345         getOperand(0)->isLoopInvariant(QueryLoop);
346}
347
348
349void SCEVAddRecExpr::print(std::ostream &OS) const {
350  OS << "{" << *Operands[0];
351  for (unsigned i = 1, e = Operands.size(); i != e; ++i)
352    OS << ",+," << *Operands[i];
353  OS << "}<" << L->getHeader()->getName() + ">";
354}
355
356// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
357// value.  Don't use a SCEVHandle here, or else the object will never be
358// deleted!
359static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
360
361SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
362
363bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
364  // All non-instruction values are loop invariant.  All instructions are loop
365  // invariant if they are not contained in the specified loop.
366  if (Instruction *I = dyn_cast<Instruction>(V))
367    return !L->contains(I->getParent());
368  return true;
369}
370
371const Type *SCEVUnknown::getType() const {
372  return V->getType();
373}
374
375void SCEVUnknown::print(std::ostream &OS) const {
376  WriteAsOperand(OS, V, false);
377}
378
379//===----------------------------------------------------------------------===//
380//                               SCEV Utilities
381//===----------------------------------------------------------------------===//
382
383namespace {
384  /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
385  /// than the complexity of the RHS.  This comparator is used to canonicalize
386  /// expressions.
387  struct VISIBILITY_HIDDEN SCEVComplexityCompare {
388    bool operator()(SCEV *LHS, SCEV *RHS) {
389      return LHS->getSCEVType() < RHS->getSCEVType();
390    }
391  };
392}
393
394/// GroupByComplexity - Given a list of SCEV objects, order them by their
395/// complexity, and group objects of the same complexity together by value.
396/// When this routine is finished, we know that any duplicates in the vector are
397/// consecutive and that complexity is monotonically increasing.
398///
399/// Note that we go take special precautions to ensure that we get determinstic
400/// results from this routine.  In other words, we don't want the results of
401/// this to depend on where the addresses of various SCEV objects happened to
402/// land in memory.
403///
404static void GroupByComplexity(std::vector<SCEVHandle> &Ops) {
405  if (Ops.size() < 2) return;  // Noop
406  if (Ops.size() == 2) {
407    // This is the common case, which also happens to be trivially simple.
408    // Special case it.
409    if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType())
410      std::swap(Ops[0], Ops[1]);
411    return;
412  }
413
414  // Do the rough sort by complexity.
415  std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
416
417  // Now that we are sorted by complexity, group elements of the same
418  // complexity.  Note that this is, at worst, N^2, but the vector is likely to
419  // be extremely short in practice.  Note that we take this approach because we
420  // do not want to depend on the addresses of the objects we are grouping.
421  for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
422    SCEV *S = Ops[i];
423    unsigned Complexity = S->getSCEVType();
424
425    // If there are any objects of the same complexity and same value as this
426    // one, group them.
427    for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
428      if (Ops[j] == S) { // Found a duplicate.
429        // Move it to immediately after i'th element.
430        std::swap(Ops[i+1], Ops[j]);
431        ++i;   // no need to rescan it.
432        if (i == e-2) return;  // Done!
433      }
434    }
435  }
436}
437
438
439
440//===----------------------------------------------------------------------===//
441//                      Simple SCEV method implementations
442//===----------------------------------------------------------------------===//
443
444/// getIntegerSCEV - Given an integer or FP type, create a constant for the
445/// specified signed integer value and return a SCEV for the constant.
446SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) {
447  Constant *C;
448  if (Val == 0)
449    C = Constant::getNullValue(Ty);
450  else if (Ty->isFloatingPoint())
451    C = ConstantFP::get(Ty, Val);
452  else
453    C = ConstantInt::get(Ty, Val);
454  return SCEVUnknown::get(C);
455}
456
457/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
458/// input value to the specified type.  If the type must be extended, it is zero
459/// extended.
460static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
461  const Type *SrcTy = V->getType();
462  assert(SrcTy->isInteger() && Ty->isInteger() &&
463         "Cannot truncate or zero extend with non-integer arguments!");
464  if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits())
465    return V;  // No conversion
466  if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits())
467    return SCEVTruncateExpr::get(V, Ty);
468  return SCEVZeroExtendExpr::get(V, Ty);
469}
470
471/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
472///
473SCEVHandle SCEV::getNegativeSCEV(const SCEVHandle &V) {
474  if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
475    return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue()));
476
477  return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType()));
478}
479
480/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
481///
482SCEVHandle SCEV::getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) {
483  // X - Y --> X + -Y
484  return SCEVAddExpr::get(LHS, SCEV::getNegativeSCEV(RHS));
485}
486
487
488/// PartialFact - Compute V!/(V-NumSteps)!
489static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) {
490  // Handle this case efficiently, it is common to have constant iteration
491  // counts while computing loop exit values.
492  if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) {
493    uint64_t Val = SC->getValue()->getZExtValue();
494    uint64_t Result = 1;
495    for (; NumSteps; --NumSteps)
496      Result *= Val-(NumSteps-1);
497    Constant *Res = ConstantInt::get(Type::Int64Ty, Result);
498    return SCEVUnknown::get(ConstantExpr::getTruncOrBitCast(Res, V->getType()));
499  }
500
501  const Type *Ty = V->getType();
502  if (NumSteps == 0)
503    return SCEVUnknown::getIntegerSCEV(1, Ty);
504
505  SCEVHandle Result = V;
506  for (unsigned i = 1; i != NumSteps; ++i)
507    Result = SCEVMulExpr::get(Result, SCEV::getMinusSCEV(V,
508                                          SCEVUnknown::getIntegerSCEV(i, Ty)));
509  return Result;
510}
511
512
513/// evaluateAtIteration - Return the value of this chain of recurrences at
514/// the specified iteration number.  We can evaluate this recurrence by
515/// multiplying each element in the chain by the binomial coefficient
516/// corresponding to it.  In other words, we can evaluate {A,+,B,+,C,+,D} as:
517///
518///   A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3)
519///
520/// FIXME/VERIFY: I don't trust that this is correct in the face of overflow.
521/// Is the binomial equation safe using modular arithmetic??
522///
523SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const {
524  SCEVHandle Result = getStart();
525  int Divisor = 1;
526  const Type *Ty = It->getType();
527  for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
528    SCEVHandle BC = PartialFact(It, i);
529    Divisor *= i;
530    SCEVHandle Val = SCEVSDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)),
531                                       SCEVUnknown::getIntegerSCEV(Divisor,Ty));
532    Result = SCEVAddExpr::get(Result, Val);
533  }
534  return Result;
535}
536
537
538//===----------------------------------------------------------------------===//
539//                    SCEV Expression folder implementations
540//===----------------------------------------------------------------------===//
541
542SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) {
543  if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
544    return SCEVUnknown::get(
545        ConstantExpr::getTrunc(SC->getValue(), Ty));
546
547  // If the input value is a chrec scev made out of constants, truncate
548  // all of the constants.
549  if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
550    std::vector<SCEVHandle> Operands;
551    for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
552      // FIXME: This should allow truncation of other expression types!
553      if (isa<SCEVConstant>(AddRec->getOperand(i)))
554        Operands.push_back(get(AddRec->getOperand(i), Ty));
555      else
556        break;
557    if (Operands.size() == AddRec->getNumOperands())
558      return SCEVAddRecExpr::get(Operands, AddRec->getLoop());
559  }
560
561  SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
562  if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
563  return Result;
564}
565
566SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) {
567  if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
568    return SCEVUnknown::get(
569        ConstantExpr::getZExt(SC->getValue(), Ty));
570
571  // FIXME: If the input value is a chrec scev, and we can prove that the value
572  // did not overflow the old, smaller, value, we can zero extend all of the
573  // operands (often constants).  This would allow analysis of something like
574  // this:  for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
575
576  SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
577  if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
578  return Result;
579}
580
581// get - Get a canonical add expression, or something simpler if possible.
582SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) {
583  assert(!Ops.empty() && "Cannot get empty add!");
584  if (Ops.size() == 1) return Ops[0];
585
586  // Sort by complexity, this groups all similar expression types together.
587  GroupByComplexity(Ops);
588
589  // If there are any constants, fold them together.
590  unsigned Idx = 0;
591  if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
592    ++Idx;
593    assert(Idx < Ops.size());
594    while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
595      // We found two constants, fold them together!
596      Constant *Fold = ConstantExpr::getAdd(LHSC->getValue(), RHSC->getValue());
597      if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
598        Ops[0] = SCEVConstant::get(CI);
599        Ops.erase(Ops.begin()+1);  // Erase the folded element
600        if (Ops.size() == 1) return Ops[0];
601        LHSC = cast<SCEVConstant>(Ops[0]);
602      } else {
603        // If we couldn't fold the expression, move to the next constant.  Note
604        // that this is impossible to happen in practice because we always
605        // constant fold constant ints to constant ints.
606        ++Idx;
607      }
608    }
609
610    // If we are left with a constant zero being added, strip it off.
611    if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) {
612      Ops.erase(Ops.begin());
613      --Idx;
614    }
615  }
616
617  if (Ops.size() == 1) return Ops[0];
618
619  // Okay, check to see if the same value occurs in the operand list twice.  If
620  // so, merge them together into an multiply expression.  Since we sorted the
621  // list, these values are required to be adjacent.
622  const Type *Ty = Ops[0]->getType();
623  for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
624    if (Ops[i] == Ops[i+1]) {      //  X + Y + Y  -->  X + Y*2
625      // Found a match, merge the two values into a multiply, and add any
626      // remaining values to the result.
627      SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty);
628      SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two);
629      if (Ops.size() == 2)
630        return Mul;
631      Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
632      Ops.push_back(Mul);
633      return SCEVAddExpr::get(Ops);
634    }
635
636  // Okay, now we know the first non-constant operand.  If there are add
637  // operands they would be next.
638  if (Idx < Ops.size()) {
639    bool DeletedAdd = false;
640    while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
641      // If we have an add, expand the add operands onto the end of the operands
642      // list.
643      Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
644      Ops.erase(Ops.begin()+Idx);
645      DeletedAdd = true;
646    }
647
648    // If we deleted at least one add, we added operands to the end of the list,
649    // and they are not necessarily sorted.  Recurse to resort and resimplify
650    // any operands we just aquired.
651    if (DeletedAdd)
652      return get(Ops);
653  }
654
655  // Skip over the add expression until we get to a multiply.
656  while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
657    ++Idx;
658
659  // If we are adding something to a multiply expression, make sure the
660  // something is not already an operand of the multiply.  If so, merge it into
661  // the multiply.
662  for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
663    SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
664    for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
665      SCEV *MulOpSCEV = Mul->getOperand(MulOp);
666      for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
667        if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
668          // Fold W + X + (X * Y * Z)  -->  W + (X * ((Y*Z)+1))
669          SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
670          if (Mul->getNumOperands() != 2) {
671            // If the multiply has more than two operands, we must get the
672            // Y*Z term.
673            std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
674            MulOps.erase(MulOps.begin()+MulOp);
675            InnerMul = SCEVMulExpr::get(MulOps);
676          }
677          SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty);
678          SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One);
679          SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]);
680          if (Ops.size() == 2) return OuterMul;
681          if (AddOp < Idx) {
682            Ops.erase(Ops.begin()+AddOp);
683            Ops.erase(Ops.begin()+Idx-1);
684          } else {
685            Ops.erase(Ops.begin()+Idx);
686            Ops.erase(Ops.begin()+AddOp-1);
687          }
688          Ops.push_back(OuterMul);
689          return SCEVAddExpr::get(Ops);
690        }
691
692      // Check this multiply against other multiplies being added together.
693      for (unsigned OtherMulIdx = Idx+1;
694           OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
695           ++OtherMulIdx) {
696        SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
697        // If MulOp occurs in OtherMul, we can fold the two multiplies
698        // together.
699        for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
700             OMulOp != e; ++OMulOp)
701          if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
702            // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
703            SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
704            if (Mul->getNumOperands() != 2) {
705              std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
706              MulOps.erase(MulOps.begin()+MulOp);
707              InnerMul1 = SCEVMulExpr::get(MulOps);
708            }
709            SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
710            if (OtherMul->getNumOperands() != 2) {
711              std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
712                                             OtherMul->op_end());
713              MulOps.erase(MulOps.begin()+OMulOp);
714              InnerMul2 = SCEVMulExpr::get(MulOps);
715            }
716            SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2);
717            SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum);
718            if (Ops.size() == 2) return OuterMul;
719            Ops.erase(Ops.begin()+Idx);
720            Ops.erase(Ops.begin()+OtherMulIdx-1);
721            Ops.push_back(OuterMul);
722            return SCEVAddExpr::get(Ops);
723          }
724      }
725    }
726  }
727
728  // If there are any add recurrences in the operands list, see if any other
729  // added values are loop invariant.  If so, we can fold them into the
730  // recurrence.
731  while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
732    ++Idx;
733
734  // Scan over all recurrences, trying to fold loop invariants into them.
735  for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
736    // Scan all of the other operands to this add and add them to the vector if
737    // they are loop invariant w.r.t. the recurrence.
738    std::vector<SCEVHandle> LIOps;
739    SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
740    for (unsigned i = 0, e = Ops.size(); i != e; ++i)
741      if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
742        LIOps.push_back(Ops[i]);
743        Ops.erase(Ops.begin()+i);
744        --i; --e;
745      }
746
747    // If we found some loop invariants, fold them into the recurrence.
748    if (!LIOps.empty()) {
749      //  NLI + LI + { Start,+,Step}  -->  NLI + { LI+Start,+,Step }
750      LIOps.push_back(AddRec->getStart());
751
752      std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
753      AddRecOps[0] = SCEVAddExpr::get(LIOps);
754
755      SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop());
756      // If all of the other operands were loop invariant, we are done.
757      if (Ops.size() == 1) return NewRec;
758
759      // Otherwise, add the folded AddRec by the non-liv parts.
760      for (unsigned i = 0;; ++i)
761        if (Ops[i] == AddRec) {
762          Ops[i] = NewRec;
763          break;
764        }
765      return SCEVAddExpr::get(Ops);
766    }
767
768    // Okay, if there weren't any loop invariants to be folded, check to see if
769    // there are multiple AddRec's with the same loop induction variable being
770    // added together.  If so, we can fold them.
771    for (unsigned OtherIdx = Idx+1;
772         OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
773      if (OtherIdx != Idx) {
774        SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
775        if (AddRec->getLoop() == OtherAddRec->getLoop()) {
776          // Other + {A,+,B} + {C,+,D}  -->  Other + {A+C,+,B+D}
777          std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
778          for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
779            if (i >= NewOps.size()) {
780              NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
781                            OtherAddRec->op_end());
782              break;
783            }
784            NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i));
785          }
786          SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
787
788          if (Ops.size() == 2) return NewAddRec;
789
790          Ops.erase(Ops.begin()+Idx);
791          Ops.erase(Ops.begin()+OtherIdx-1);
792          Ops.push_back(NewAddRec);
793          return SCEVAddExpr::get(Ops);
794        }
795      }
796
797    // Otherwise couldn't fold anything into this recurrence.  Move onto the
798    // next one.
799  }
800
801  // Okay, it looks like we really DO need an add expr.  Check to see if we
802  // already have one, otherwise create a new one.
803  std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
804  SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
805                                                                 SCEVOps)];
806  if (Result == 0) Result = new SCEVAddExpr(Ops);
807  return Result;
808}
809
810
811SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) {
812  assert(!Ops.empty() && "Cannot get empty mul!");
813
814  // Sort by complexity, this groups all similar expression types together.
815  GroupByComplexity(Ops);
816
817  // If there are any constants, fold them together.
818  unsigned Idx = 0;
819  if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
820
821    // C1*(C2+V) -> C1*C2 + C1*V
822    if (Ops.size() == 2)
823      if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
824        if (Add->getNumOperands() == 2 &&
825            isa<SCEVConstant>(Add->getOperand(0)))
826          return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)),
827                                  SCEVMulExpr::get(LHSC, Add->getOperand(1)));
828
829
830    ++Idx;
831    while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
832      // We found two constants, fold them together!
833      Constant *Fold = ConstantExpr::getMul(LHSC->getValue(), RHSC->getValue());
834      if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
835        Ops[0] = SCEVConstant::get(CI);
836        Ops.erase(Ops.begin()+1);  // Erase the folded element
837        if (Ops.size() == 1) return Ops[0];
838        LHSC = cast<SCEVConstant>(Ops[0]);
839      } else {
840        // If we couldn't fold the expression, move to the next constant.  Note
841        // that this is impossible to happen in practice because we always
842        // constant fold constant ints to constant ints.
843        ++Idx;
844      }
845    }
846
847    // If we are left with a constant one being multiplied, strip it off.
848    if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
849      Ops.erase(Ops.begin());
850      --Idx;
851    } else if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) {
852      // If we have a multiply of zero, it will always be zero.
853      return Ops[0];
854    }
855  }
856
857  // Skip over the add expression until we get to a multiply.
858  while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
859    ++Idx;
860
861  if (Ops.size() == 1)
862    return Ops[0];
863
864  // If there are mul operands inline them all into this expression.
865  if (Idx < Ops.size()) {
866    bool DeletedMul = false;
867    while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
868      // If we have an mul, expand the mul operands onto the end of the operands
869      // list.
870      Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
871      Ops.erase(Ops.begin()+Idx);
872      DeletedMul = true;
873    }
874
875    // If we deleted at least one mul, we added operands to the end of the list,
876    // and they are not necessarily sorted.  Recurse to resort and resimplify
877    // any operands we just aquired.
878    if (DeletedMul)
879      return get(Ops);
880  }
881
882  // If there are any add recurrences in the operands list, see if any other
883  // added values are loop invariant.  If so, we can fold them into the
884  // recurrence.
885  while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
886    ++Idx;
887
888  // Scan over all recurrences, trying to fold loop invariants into them.
889  for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
890    // Scan all of the other operands to this mul and add them to the vector if
891    // they are loop invariant w.r.t. the recurrence.
892    std::vector<SCEVHandle> LIOps;
893    SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
894    for (unsigned i = 0, e = Ops.size(); i != e; ++i)
895      if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
896        LIOps.push_back(Ops[i]);
897        Ops.erase(Ops.begin()+i);
898        --i; --e;
899      }
900
901    // If we found some loop invariants, fold them into the recurrence.
902    if (!LIOps.empty()) {
903      //  NLI * LI * { Start,+,Step}  -->  NLI * { LI*Start,+,LI*Step }
904      std::vector<SCEVHandle> NewOps;
905      NewOps.reserve(AddRec->getNumOperands());
906      if (LIOps.size() == 1) {
907        SCEV *Scale = LIOps[0];
908        for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
909          NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i)));
910      } else {
911        for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
912          std::vector<SCEVHandle> MulOps(LIOps);
913          MulOps.push_back(AddRec->getOperand(i));
914          NewOps.push_back(SCEVMulExpr::get(MulOps));
915        }
916      }
917
918      SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
919
920      // If all of the other operands were loop invariant, we are done.
921      if (Ops.size() == 1) return NewRec;
922
923      // Otherwise, multiply the folded AddRec by the non-liv parts.
924      for (unsigned i = 0;; ++i)
925        if (Ops[i] == AddRec) {
926          Ops[i] = NewRec;
927          break;
928        }
929      return SCEVMulExpr::get(Ops);
930    }
931
932    // Okay, if there weren't any loop invariants to be folded, check to see if
933    // there are multiple AddRec's with the same loop induction variable being
934    // multiplied together.  If so, we can fold them.
935    for (unsigned OtherIdx = Idx+1;
936         OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
937      if (OtherIdx != Idx) {
938        SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
939        if (AddRec->getLoop() == OtherAddRec->getLoop()) {
940          // F * G  -->  {A,+,B} * {C,+,D}  -->  {A*C,+,F*D + G*B + B*D}
941          SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
942          SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(),
943                                                 G->getStart());
944          SCEVHandle B = F->getStepRecurrence();
945          SCEVHandle D = G->getStepRecurrence();
946          SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D),
947                                                SCEVMulExpr::get(G, B),
948                                                SCEVMulExpr::get(B, D));
949          SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep,
950                                                     F->getLoop());
951          if (Ops.size() == 2) return NewAddRec;
952
953          Ops.erase(Ops.begin()+Idx);
954          Ops.erase(Ops.begin()+OtherIdx-1);
955          Ops.push_back(NewAddRec);
956          return SCEVMulExpr::get(Ops);
957        }
958      }
959
960    // Otherwise couldn't fold anything into this recurrence.  Move onto the
961    // next one.
962  }
963
964  // Okay, it looks like we really DO need an mul expr.  Check to see if we
965  // already have one, otherwise create a new one.
966  std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
967  SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
968                                                                 SCEVOps)];
969  if (Result == 0)
970    Result = new SCEVMulExpr(Ops);
971  return Result;
972}
973
974SCEVHandle SCEVSDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) {
975  if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
976    if (RHSC->getValue()->equalsInt(1))
977      return LHS;                            // X sdiv 1 --> x
978    if (RHSC->getValue()->isAllOnesValue())
979      return SCEV::getNegativeSCEV(LHS);           // X sdiv -1  -->  -x
980
981    if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
982      Constant *LHSCV = LHSC->getValue();
983      Constant *RHSCV = RHSC->getValue();
984      return SCEVUnknown::get(ConstantExpr::getSDiv(LHSCV, RHSCV));
985    }
986  }
987
988  // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
989
990  SCEVSDivExpr *&Result = (*SCEVSDivs)[std::make_pair(LHS, RHS)];
991  if (Result == 0) Result = new SCEVSDivExpr(LHS, RHS);
992  return Result;
993}
994
995
996/// SCEVAddRecExpr::get - Get a add recurrence expression for the
997/// specified loop.  Simplify the expression as much as possible.
998SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start,
999                               const SCEVHandle &Step, const Loop *L) {
1000  std::vector<SCEVHandle> Operands;
1001  Operands.push_back(Start);
1002  if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1003    if (StepChrec->getLoop() == L) {
1004      Operands.insert(Operands.end(), StepChrec->op_begin(),
1005                      StepChrec->op_end());
1006      return get(Operands, L);
1007    }
1008
1009  Operands.push_back(Step);
1010  return get(Operands, L);
1011}
1012
1013/// SCEVAddRecExpr::get - Get a add recurrence expression for the
1014/// specified loop.  Simplify the expression as much as possible.
1015SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands,
1016                               const Loop *L) {
1017  if (Operands.size() == 1) return Operands[0];
1018
1019  if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back()))
1020    if (StepC->getValue()->isNullValue()) {
1021      Operands.pop_back();
1022      return get(Operands, L);             // { X,+,0 }  -->  X
1023    }
1024
1025  SCEVAddRecExpr *&Result =
1026    (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(),
1027                                                            Operands.end()))];
1028  if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1029  return Result;
1030}
1031
1032SCEVHandle SCEVUnknown::get(Value *V) {
1033  if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1034    return SCEVConstant::get(CI);
1035  SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1036  if (Result == 0) Result = new SCEVUnknown(V);
1037  return Result;
1038}
1039
1040
1041//===----------------------------------------------------------------------===//
1042//             ScalarEvolutionsImpl Definition and Implementation
1043//===----------------------------------------------------------------------===//
1044//
1045/// ScalarEvolutionsImpl - This class implements the main driver for the scalar
1046/// evolution code.
1047///
1048namespace {
1049  struct VISIBILITY_HIDDEN ScalarEvolutionsImpl {
1050    /// F - The function we are analyzing.
1051    ///
1052    Function &F;
1053
1054    /// LI - The loop information for the function we are currently analyzing.
1055    ///
1056    LoopInfo &LI;
1057
1058    /// UnknownValue - This SCEV is used to represent unknown trip counts and
1059    /// things.
1060    SCEVHandle UnknownValue;
1061
1062    /// Scalars - This is a cache of the scalars we have analyzed so far.
1063    ///
1064    std::map<Value*, SCEVHandle> Scalars;
1065
1066    /// IterationCounts - Cache the iteration count of the loops for this
1067    /// function as they are computed.
1068    std::map<const Loop*, SCEVHandle> IterationCounts;
1069
1070    /// ConstantEvolutionLoopExitValue - This map contains entries for all of
1071    /// the PHI instructions that we attempt to compute constant evolutions for.
1072    /// This allows us to avoid potentially expensive recomputation of these
1073    /// properties.  An instruction maps to null if we are unable to compute its
1074    /// exit value.
1075    std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
1076
1077  public:
1078    ScalarEvolutionsImpl(Function &f, LoopInfo &li)
1079      : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {}
1080
1081    /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1082    /// expression and create a new one.
1083    SCEVHandle getSCEV(Value *V);
1084
1085    /// hasSCEV - Return true if the SCEV for this value has already been
1086    /// computed.
1087    bool hasSCEV(Value *V) const {
1088      return Scalars.count(V);
1089    }
1090
1091    /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
1092    /// the specified value.
1093    void setSCEV(Value *V, const SCEVHandle &H) {
1094      bool isNew = Scalars.insert(std::make_pair(V, H)).second;
1095      assert(isNew && "This entry already existed!");
1096    }
1097
1098
1099    /// getSCEVAtScope - Compute the value of the specified expression within
1100    /// the indicated loop (which may be null to indicate in no loop).  If the
1101    /// expression cannot be evaluated, return UnknownValue itself.
1102    SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L);
1103
1104
1105    /// hasLoopInvariantIterationCount - Return true if the specified loop has
1106    /// an analyzable loop-invariant iteration count.
1107    bool hasLoopInvariantIterationCount(const Loop *L);
1108
1109    /// getIterationCount - If the specified loop has a predictable iteration
1110    /// count, return it.  Note that it is not valid to call this method on a
1111    /// loop without a loop-invariant iteration count.
1112    SCEVHandle getIterationCount(const Loop *L);
1113
1114    /// deleteInstructionFromRecords - This method should be called by the
1115    /// client before it removes an instruction from the program, to make sure
1116    /// that no dangling references are left around.
1117    void deleteInstructionFromRecords(Instruction *I);
1118
1119  private:
1120    /// createSCEV - We know that there is no SCEV for the specified value.
1121    /// Analyze the expression.
1122    SCEVHandle createSCEV(Value *V);
1123
1124    /// createNodeForPHI - Provide the special handling we need to analyze PHI
1125    /// SCEVs.
1126    SCEVHandle createNodeForPHI(PHINode *PN);
1127
1128    /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value
1129    /// for the specified instruction and replaces any references to the
1130    /// symbolic value SymName with the specified value.  This is used during
1131    /// PHI resolution.
1132    void ReplaceSymbolicValueWithConcrete(Instruction *I,
1133                                          const SCEVHandle &SymName,
1134                                          const SCEVHandle &NewVal);
1135
1136    /// ComputeIterationCount - Compute the number of times the specified loop
1137    /// will iterate.
1138    SCEVHandle ComputeIterationCount(const Loop *L);
1139
1140    /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
1141    /// 'setcc load X, cst', try to se if we can compute the trip count.
1142    SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI,
1143                                                        Constant *RHS,
1144                                                        const Loop *L,
1145                                                        ICmpInst::Predicate p);
1146
1147    /// ComputeIterationCountExhaustively - If the trip is known to execute a
1148    /// constant number of times (the condition evolves only from constants),
1149    /// try to evaluate a few iterations of the loop until we get the exit
1150    /// condition gets a value of ExitWhen (true or false).  If we cannot
1151    /// evaluate the trip count of the loop, return UnknownValue.
1152    SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond,
1153                                                 bool ExitWhen);
1154
1155    /// HowFarToZero - Return the number of times a backedge comparing the
1156    /// specified value to zero will execute.  If not computable, return
1157    /// UnknownValue.
1158    SCEVHandle HowFarToZero(SCEV *V, const Loop *L);
1159
1160    /// HowFarToNonZero - Return the number of times a backedge checking the
1161    /// specified value for nonzero will execute.  If not computable, return
1162    /// UnknownValue.
1163    SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L);
1164
1165    /// HowManyLessThans - Return the number of times a backedge containing the
1166    /// specified less-than comparison will execute.  If not computable, return
1167    /// UnknownValue.
1168    SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L);
1169
1170    /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1171    /// in the header of its containing loop, we know the loop executes a
1172    /// constant number of times, and the PHI node is just a recurrence
1173    /// involving constants, fold it.
1174    Constant *getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its,
1175                                                const Loop *L);
1176  };
1177}
1178
1179//===----------------------------------------------------------------------===//
1180//            Basic SCEV Analysis and PHI Idiom Recognition Code
1181//
1182
1183/// deleteInstructionFromRecords - This method should be called by the
1184/// client before it removes an instruction from the program, to make sure
1185/// that no dangling references are left around.
1186void ScalarEvolutionsImpl::deleteInstructionFromRecords(Instruction *I) {
1187  Scalars.erase(I);
1188  if (PHINode *PN = dyn_cast<PHINode>(I))
1189    ConstantEvolutionLoopExitValue.erase(PN);
1190}
1191
1192
1193/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1194/// expression and create a new one.
1195SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) {
1196  assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!");
1197
1198  std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
1199  if (I != Scalars.end()) return I->second;
1200  SCEVHandle S = createSCEV(V);
1201  Scalars.insert(std::make_pair(V, S));
1202  return S;
1203}
1204
1205/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1206/// the specified instruction and replaces any references to the symbolic value
1207/// SymName with the specified value.  This is used during PHI resolution.
1208void ScalarEvolutionsImpl::
1209ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1210                                 const SCEVHandle &NewVal) {
1211  std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
1212  if (SI == Scalars.end()) return;
1213
1214  SCEVHandle NV =
1215    SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal);
1216  if (NV == SI->second) return;  // No change.
1217
1218  SI->second = NV;       // Update the scalars map!
1219
1220  // Any instruction values that use this instruction might also need to be
1221  // updated!
1222  for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1223       UI != E; ++UI)
1224    ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1225}
1226
1227/// createNodeForPHI - PHI nodes have two cases.  Either the PHI node exists in
1228/// a loop header, making it a potential recurrence, or it doesn't.
1229///
1230SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) {
1231  if (PN->getNumIncomingValues() == 2)  // The loops have been canonicalized.
1232    if (const Loop *L = LI.getLoopFor(PN->getParent()))
1233      if (L->getHeader() == PN->getParent()) {
1234        // If it lives in the loop header, it has two incoming values, one
1235        // from outside the loop, and one from inside.
1236        unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1237        unsigned BackEdge     = IncomingEdge^1;
1238
1239        // While we are analyzing this PHI node, handle its value symbolically.
1240        SCEVHandle SymbolicName = SCEVUnknown::get(PN);
1241        assert(Scalars.find(PN) == Scalars.end() &&
1242               "PHI node already processed?");
1243        Scalars.insert(std::make_pair(PN, SymbolicName));
1244
1245        // Using this symbolic name for the PHI, analyze the value coming around
1246        // the back-edge.
1247        SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1248
1249        // NOTE: If BEValue is loop invariant, we know that the PHI node just
1250        // has a special value for the first iteration of the loop.
1251
1252        // If the value coming around the backedge is an add with the symbolic
1253        // value we just inserted, then we found a simple induction variable!
1254        if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1255          // If there is a single occurrence of the symbolic value, replace it
1256          // with a recurrence.
1257          unsigned FoundIndex = Add->getNumOperands();
1258          for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1259            if (Add->getOperand(i) == SymbolicName)
1260              if (FoundIndex == e) {
1261                FoundIndex = i;
1262                break;
1263              }
1264
1265          if (FoundIndex != Add->getNumOperands()) {
1266            // Create an add with everything but the specified operand.
1267            std::vector<SCEVHandle> Ops;
1268            for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1269              if (i != FoundIndex)
1270                Ops.push_back(Add->getOperand(i));
1271            SCEVHandle Accum = SCEVAddExpr::get(Ops);
1272
1273            // This is not a valid addrec if the step amount is varying each
1274            // loop iteration, but is not itself an addrec in this loop.
1275            if (Accum->isLoopInvariant(L) ||
1276                (isa<SCEVAddRecExpr>(Accum) &&
1277                 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1278              SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1279              SCEVHandle PHISCEV  = SCEVAddRecExpr::get(StartVal, Accum, L);
1280
1281              // Okay, for the entire analysis of this edge we assumed the PHI
1282              // to be symbolic.  We now need to go back and update all of the
1283              // entries for the scalars that use the PHI (except for the PHI
1284              // itself) to use the new analyzed value instead of the "symbolic"
1285              // value.
1286              ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1287              return PHISCEV;
1288            }
1289          }
1290        } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) {
1291          // Otherwise, this could be a loop like this:
1292          //     i = 0;  for (j = 1; ..; ++j) { ....  i = j; }
1293          // In this case, j = {1,+,1}  and BEValue is j.
1294          // Because the other in-value of i (0) fits the evolution of BEValue
1295          // i really is an addrec evolution.
1296          if (AddRec->getLoop() == L && AddRec->isAffine()) {
1297            SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1298
1299            // If StartVal = j.start - j.stride, we can use StartVal as the
1300            // initial step of the addrec evolution.
1301            if (StartVal == SCEV::getMinusSCEV(AddRec->getOperand(0),
1302                                               AddRec->getOperand(1))) {
1303              SCEVHandle PHISCEV =
1304                 SCEVAddRecExpr::get(StartVal, AddRec->getOperand(1), L);
1305
1306              // Okay, for the entire analysis of this edge we assumed the PHI
1307              // to be symbolic.  We now need to go back and update all of the
1308              // entries for the scalars that use the PHI (except for the PHI
1309              // itself) to use the new analyzed value instead of the "symbolic"
1310              // value.
1311              ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1312              return PHISCEV;
1313            }
1314          }
1315        }
1316
1317        return SymbolicName;
1318      }
1319
1320  // If it's not a loop phi, we can't handle it yet.
1321  return SCEVUnknown::get(PN);
1322}
1323
1324/// GetConstantFactor - Determine the largest constant factor that S has.  For
1325/// example, turn {4,+,8} -> 4.    (S umod result) should always equal zero.
1326static uint64_t GetConstantFactor(SCEVHandle S) {
1327  if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
1328    if (uint64_t V = C->getValue()->getZExtValue())
1329      return V;
1330    else   // Zero is a multiple of everything.
1331      return 1ULL << (S->getType()->getPrimitiveSizeInBits()-1);
1332  }
1333
1334  if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
1335    return GetConstantFactor(T->getOperand()) &
1336           cast<IntegerType>(T->getType())->getBitMask();
1337  if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S))
1338    return GetConstantFactor(E->getOperand());
1339
1340  if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
1341    // The result is the min of all operands.
1342    uint64_t Res = GetConstantFactor(A->getOperand(0));
1343    for (unsigned i = 1, e = A->getNumOperands(); i != e && Res > 1; ++i)
1344      Res = std::min(Res, GetConstantFactor(A->getOperand(i)));
1345    return Res;
1346  }
1347
1348  if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
1349    // The result is the product of all the operands.
1350    uint64_t Res = GetConstantFactor(M->getOperand(0));
1351    for (unsigned i = 1, e = M->getNumOperands(); i != e; ++i)
1352      Res *= GetConstantFactor(M->getOperand(i));
1353    return Res;
1354  }
1355
1356  if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
1357    // For now, we just handle linear expressions.
1358    if (A->getNumOperands() == 2) {
1359      // We want the GCD between the start and the stride value.
1360      uint64_t Start = GetConstantFactor(A->getOperand(0));
1361      if (Start == 1) return 1;
1362      uint64_t Stride = GetConstantFactor(A->getOperand(1));
1363      return GreatestCommonDivisor64(Start, Stride);
1364    }
1365  }
1366
1367  // SCEVSDivExpr, SCEVUnknown.
1368  return 1;
1369}
1370
1371/// createSCEV - We know that there is no SCEV for the specified value.
1372/// Analyze the expression.
1373///
1374SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) {
1375  if (Instruction *I = dyn_cast<Instruction>(V)) {
1376    switch (I->getOpcode()) {
1377    case Instruction::Add:
1378      return SCEVAddExpr::get(getSCEV(I->getOperand(0)),
1379                              getSCEV(I->getOperand(1)));
1380    case Instruction::Mul:
1381      return SCEVMulExpr::get(getSCEV(I->getOperand(0)),
1382                              getSCEV(I->getOperand(1)));
1383    case Instruction::SDiv:
1384      return SCEVSDivExpr::get(getSCEV(I->getOperand(0)),
1385                              getSCEV(I->getOperand(1)));
1386      break;
1387
1388    case Instruction::Sub:
1389      return SCEV::getMinusSCEV(getSCEV(I->getOperand(0)),
1390                                getSCEV(I->getOperand(1)));
1391    case Instruction::Or:
1392      // If the RHS of the Or is a constant, we may have something like:
1393      // X*4+1 which got turned into X*4|1.  Handle this as an add so loop
1394      // optimizations will transparently handle this case.
1395      if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) {
1396        SCEVHandle LHS = getSCEV(I->getOperand(0));
1397        uint64_t CommonFact = GetConstantFactor(LHS);
1398        assert(CommonFact && "Common factor should at least be 1!");
1399        if (CommonFact > CI->getZExtValue()) {
1400          // If the LHS is a multiple that is larger than the RHS, use +.
1401          return SCEVAddExpr::get(LHS,
1402                                  getSCEV(I->getOperand(1)));
1403        }
1404      }
1405      break;
1406
1407    case Instruction::Shl:
1408      // Turn shift left of a constant amount into a multiply.
1409      if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) {
1410        Constant *X = ConstantInt::get(V->getType(), 1);
1411        X = ConstantExpr::getShl(X, SA);
1412        return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X));
1413      }
1414      break;
1415
1416    case Instruction::Trunc:
1417      return SCEVTruncateExpr::get(getSCEV(I->getOperand(0)), I->getType());
1418
1419    case Instruction::ZExt:
1420      return SCEVZeroExtendExpr::get(getSCEV(I->getOperand(0)), I->getType());
1421
1422    case Instruction::BitCast:
1423      // BitCasts are no-op casts so we just eliminate the cast.
1424      if (I->getType()->isInteger() &&
1425          I->getOperand(0)->getType()->isInteger())
1426        return getSCEV(I->getOperand(0));
1427      break;
1428
1429    case Instruction::PHI:
1430      return createNodeForPHI(cast<PHINode>(I));
1431
1432    default: // We cannot analyze this expression.
1433      break;
1434    }
1435  }
1436
1437  return SCEVUnknown::get(V);
1438}
1439
1440
1441
1442//===----------------------------------------------------------------------===//
1443//                   Iteration Count Computation Code
1444//
1445
1446/// getIterationCount - If the specified loop has a predictable iteration
1447/// count, return it.  Note that it is not valid to call this method on a
1448/// loop without a loop-invariant iteration count.
1449SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) {
1450  std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L);
1451  if (I == IterationCounts.end()) {
1452    SCEVHandle ItCount = ComputeIterationCount(L);
1453    I = IterationCounts.insert(std::make_pair(L, ItCount)).first;
1454    if (ItCount != UnknownValue) {
1455      assert(ItCount->isLoopInvariant(L) &&
1456             "Computed trip count isn't loop invariant for loop!");
1457      ++NumTripCountsComputed;
1458    } else if (isa<PHINode>(L->getHeader()->begin())) {
1459      // Only count loops that have phi nodes as not being computable.
1460      ++NumTripCountsNotComputed;
1461    }
1462  }
1463  return I->second;
1464}
1465
1466/// ComputeIterationCount - Compute the number of times the specified loop
1467/// will iterate.
1468SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) {
1469  // If the loop has a non-one exit block count, we can't analyze it.
1470  std::vector<BasicBlock*> ExitBlocks;
1471  L->getExitBlocks(ExitBlocks);
1472  if (ExitBlocks.size() != 1) return UnknownValue;
1473
1474  // Okay, there is one exit block.  Try to find the condition that causes the
1475  // loop to be exited.
1476  BasicBlock *ExitBlock = ExitBlocks[0];
1477
1478  BasicBlock *ExitingBlock = 0;
1479  for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
1480       PI != E; ++PI)
1481    if (L->contains(*PI)) {
1482      if (ExitingBlock == 0)
1483        ExitingBlock = *PI;
1484      else
1485        return UnknownValue;   // More than one block exiting!
1486    }
1487  assert(ExitingBlock && "No exits from loop, something is broken!");
1488
1489  // Okay, we've computed the exiting block.  See what condition causes us to
1490  // exit.
1491  //
1492  // FIXME: we should be able to handle switch instructions (with a single exit)
1493  BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
1494  if (ExitBr == 0) return UnknownValue;
1495  assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
1496
1497  // At this point, we know we have a conditional branch that determines whether
1498  // the loop is exited.  However, we don't know if the branch is executed each
1499  // time through the loop.  If not, then the execution count of the branch will
1500  // not be equal to the trip count of the loop.
1501  //
1502  // Currently we check for this by checking to see if the Exit branch goes to
1503  // the loop header.  If so, we know it will always execute the same number of
1504  // times as the loop.  We also handle the case where the exit block *is* the
1505  // loop header.  This is common for un-rotated loops.  More extensive analysis
1506  // could be done to handle more cases here.
1507  if (ExitBr->getSuccessor(0) != L->getHeader() &&
1508      ExitBr->getSuccessor(1) != L->getHeader() &&
1509      ExitBr->getParent() != L->getHeader())
1510    return UnknownValue;
1511
1512  ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
1513
1514  // If its not an integer comparison then compute it the hard way.
1515  // Note that ICmpInst deals with pointer comparisons too so we must check
1516  // the type of the operand.
1517  if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType()))
1518    return ComputeIterationCountExhaustively(L, ExitBr->getCondition(),
1519                                          ExitBr->getSuccessor(0) == ExitBlock);
1520
1521  // If the condition was exit on true, convert the condition to exit on false
1522  ICmpInst::Predicate Cond;
1523  if (ExitBr->getSuccessor(1) == ExitBlock)
1524    Cond = ExitCond->getPredicate();
1525  else
1526    Cond = ExitCond->getInversePredicate();
1527
1528  // Handle common loops like: for (X = "string"; *X; ++X)
1529  if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
1530    if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
1531      SCEVHandle ItCnt =
1532        ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond);
1533      if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
1534    }
1535
1536  SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
1537  SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
1538
1539  // Try to evaluate any dependencies out of the loop.
1540  SCEVHandle Tmp = getSCEVAtScope(LHS, L);
1541  if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
1542  Tmp = getSCEVAtScope(RHS, L);
1543  if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
1544
1545  // At this point, we would like to compute how many iterations of the
1546  // loop the predicate will return true for these inputs.
1547  if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) {
1548    // If there is a constant, force it into the RHS.
1549    std::swap(LHS, RHS);
1550    Cond = ICmpInst::getSwappedPredicate(Cond);
1551  }
1552
1553  // FIXME: think about handling pointer comparisons!  i.e.:
1554  // while (P != P+100) ++P;
1555
1556  // If we have a comparison of a chrec against a constant, try to use value
1557  // ranges to answer this query.
1558  if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
1559    if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
1560      if (AddRec->getLoop() == L) {
1561        // Form the comparison range using the constant of the correct type so
1562        // that the ConstantRange class knows to do a signed or unsigned
1563        // comparison.
1564        ConstantInt *CompVal = RHSC->getValue();
1565        const Type *RealTy = ExitCond->getOperand(0)->getType();
1566        CompVal = dyn_cast<ConstantInt>(
1567          ConstantExpr::getBitCast(CompVal, RealTy));
1568        if (CompVal) {
1569          // Form the constant range.
1570          ConstantRange CompRange(Cond, CompVal);
1571
1572          SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange,
1573              false /*Always treat as unsigned range*/);
1574          if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
1575        }
1576      }
1577
1578  switch (Cond) {
1579  case ICmpInst::ICMP_NE: {                     // while (X != Y)
1580    // Convert to: while (X-Y != 0)
1581    SCEVHandle TC = HowFarToZero(SCEV::getMinusSCEV(LHS, RHS), L);
1582    if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1583    break;
1584  }
1585  case ICmpInst::ICMP_EQ: {
1586    // Convert to: while (X-Y == 0)           // while (X == Y)
1587    SCEVHandle TC = HowFarToNonZero(SCEV::getMinusSCEV(LHS, RHS), L);
1588    if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1589    break;
1590  }
1591  case ICmpInst::ICMP_SLT: {
1592    SCEVHandle TC = HowManyLessThans(LHS, RHS, L);
1593    if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1594    break;
1595  }
1596  case ICmpInst::ICMP_SGT: {
1597    SCEVHandle TC = HowManyLessThans(RHS, LHS, L);
1598    if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1599    break;
1600  }
1601  default:
1602#if 0
1603    cerr << "ComputeIterationCount ";
1604    if (ExitCond->getOperand(0)->getType()->isUnsigned())
1605      cerr << "[unsigned] ";
1606    cerr << *LHS << "   "
1607         << Instruction::getOpcodeName(Instruction::ICmp)
1608         << "   " << *RHS << "\n";
1609#endif
1610    break;
1611  }
1612  return ComputeIterationCountExhaustively(L, ExitCond,
1613                                       ExitBr->getSuccessor(0) == ExitBlock);
1614}
1615
1616static ConstantInt *
1617EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) {
1618  SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C));
1619  SCEVHandle Val = AddRec->evaluateAtIteration(InVal);
1620  assert(isa<SCEVConstant>(Val) &&
1621         "Evaluation of SCEV at constant didn't fold correctly?");
1622  return cast<SCEVConstant>(Val)->getValue();
1623}
1624
1625/// GetAddressedElementFromGlobal - Given a global variable with an initializer
1626/// and a GEP expression (missing the pointer index) indexing into it, return
1627/// the addressed element of the initializer or null if the index expression is
1628/// invalid.
1629static Constant *
1630GetAddressedElementFromGlobal(GlobalVariable *GV,
1631                              const std::vector<ConstantInt*> &Indices) {
1632  Constant *Init = GV->getInitializer();
1633  for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
1634    uint64_t Idx = Indices[i]->getZExtValue();
1635    if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
1636      assert(Idx < CS->getNumOperands() && "Bad struct index!");
1637      Init = cast<Constant>(CS->getOperand(Idx));
1638    } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
1639      if (Idx >= CA->getNumOperands()) return 0;  // Bogus program
1640      Init = cast<Constant>(CA->getOperand(Idx));
1641    } else if (isa<ConstantAggregateZero>(Init)) {
1642      if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
1643        assert(Idx < STy->getNumElements() && "Bad struct index!");
1644        Init = Constant::getNullValue(STy->getElementType(Idx));
1645      } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
1646        if (Idx >= ATy->getNumElements()) return 0;  // Bogus program
1647        Init = Constant::getNullValue(ATy->getElementType());
1648      } else {
1649        assert(0 && "Unknown constant aggregate type!");
1650      }
1651      return 0;
1652    } else {
1653      return 0; // Unknown initializer type
1654    }
1655  }
1656  return Init;
1657}
1658
1659/// ComputeLoadConstantCompareIterationCount - Given an exit condition of
1660/// 'setcc load X, cst', try to se if we can compute the trip count.
1661SCEVHandle ScalarEvolutionsImpl::
1662ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS,
1663                                         const Loop *L,
1664                                         ICmpInst::Predicate predicate) {
1665  if (LI->isVolatile()) return UnknownValue;
1666
1667  // Check to see if the loaded pointer is a getelementptr of a global.
1668  GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
1669  if (!GEP) return UnknownValue;
1670
1671  // Make sure that it is really a constant global we are gepping, with an
1672  // initializer, and make sure the first IDX is really 0.
1673  GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
1674  if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
1675      GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
1676      !cast<Constant>(GEP->getOperand(1))->isNullValue())
1677    return UnknownValue;
1678
1679  // Okay, we allow one non-constant index into the GEP instruction.
1680  Value *VarIdx = 0;
1681  std::vector<ConstantInt*> Indexes;
1682  unsigned VarIdxNum = 0;
1683  for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
1684    if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
1685      Indexes.push_back(CI);
1686    } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
1687      if (VarIdx) return UnknownValue;  // Multiple non-constant idx's.
1688      VarIdx = GEP->getOperand(i);
1689      VarIdxNum = i-2;
1690      Indexes.push_back(0);
1691    }
1692
1693  // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
1694  // Check to see if X is a loop variant variable value now.
1695  SCEVHandle Idx = getSCEV(VarIdx);
1696  SCEVHandle Tmp = getSCEVAtScope(Idx, L);
1697  if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
1698
1699  // We can only recognize very limited forms of loop index expressions, in
1700  // particular, only affine AddRec's like {C1,+,C2}.
1701  SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
1702  if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
1703      !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
1704      !isa<SCEVConstant>(IdxExpr->getOperand(1)))
1705    return UnknownValue;
1706
1707  unsigned MaxSteps = MaxBruteForceIterations;
1708  for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
1709    ConstantInt *ItCst =
1710      ConstantInt::get(IdxExpr->getType(), IterationNum);
1711    ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst);
1712
1713    // Form the GEP offset.
1714    Indexes[VarIdxNum] = Val;
1715
1716    Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
1717    if (Result == 0) break;  // Cannot compute!
1718
1719    // Evaluate the condition for this iteration.
1720    Result = ConstantExpr::getICmp(predicate, Result, RHS);
1721    if (!isa<ConstantInt>(Result)) break;  // Couldn't decide for sure
1722    if (cast<ConstantInt>(Result)->getZExtValue() == false) {
1723#if 0
1724      cerr << "\n***\n*** Computed loop count " << *ItCst
1725           << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
1726           << "***\n";
1727#endif
1728      ++NumArrayLenItCounts;
1729      return SCEVConstant::get(ItCst);   // Found terminating iteration!
1730    }
1731  }
1732  return UnknownValue;
1733}
1734
1735
1736/// CanConstantFold - Return true if we can constant fold an instruction of the
1737/// specified type, assuming that all operands were constants.
1738static bool CanConstantFold(const Instruction *I) {
1739  if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
1740      isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
1741    return true;
1742
1743  if (const CallInst *CI = dyn_cast<CallInst>(I))
1744    if (const Function *F = CI->getCalledFunction())
1745      return canConstantFoldCallTo((Function*)F);  // FIXME: elim cast
1746  return false;
1747}
1748
1749/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
1750/// in the loop that V is derived from.  We allow arbitrary operations along the
1751/// way, but the operands of an operation must either be constants or a value
1752/// derived from a constant PHI.  If this expression does not fit with these
1753/// constraints, return null.
1754static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
1755  // If this is not an instruction, or if this is an instruction outside of the
1756  // loop, it can't be derived from a loop PHI.
1757  Instruction *I = dyn_cast<Instruction>(V);
1758  if (I == 0 || !L->contains(I->getParent())) return 0;
1759
1760  if (PHINode *PN = dyn_cast<PHINode>(I))
1761    if (L->getHeader() == I->getParent())
1762      return PN;
1763    else
1764      // We don't currently keep track of the control flow needed to evaluate
1765      // PHIs, so we cannot handle PHIs inside of loops.
1766      return 0;
1767
1768  // If we won't be able to constant fold this expression even if the operands
1769  // are constants, return early.
1770  if (!CanConstantFold(I)) return 0;
1771
1772  // Otherwise, we can evaluate this instruction if all of its operands are
1773  // constant or derived from a PHI node themselves.
1774  PHINode *PHI = 0;
1775  for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
1776    if (!(isa<Constant>(I->getOperand(Op)) ||
1777          isa<GlobalValue>(I->getOperand(Op)))) {
1778      PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
1779      if (P == 0) return 0;  // Not evolving from PHI
1780      if (PHI == 0)
1781        PHI = P;
1782      else if (PHI != P)
1783        return 0;  // Evolving from multiple different PHIs.
1784    }
1785
1786  // This is a expression evolving from a constant PHI!
1787  return PHI;
1788}
1789
1790/// EvaluateExpression - Given an expression that passes the
1791/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
1792/// in the loop has the value PHIVal.  If we can't fold this expression for some
1793/// reason, return null.
1794static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
1795  if (isa<PHINode>(V)) return PHIVal;
1796  if (GlobalValue *GV = dyn_cast<GlobalValue>(V))
1797    return GV;
1798  if (Constant *C = dyn_cast<Constant>(V)) return C;
1799  Instruction *I = cast<Instruction>(V);
1800
1801  std::vector<Constant*> Operands;
1802  Operands.resize(I->getNumOperands());
1803
1804  for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
1805    Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
1806    if (Operands[i] == 0) return 0;
1807  }
1808
1809  return ConstantFoldInstOperands(I, &Operands[0], Operands.size());
1810}
1811
1812/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1813/// in the header of its containing loop, we know the loop executes a
1814/// constant number of times, and the PHI node is just a recurrence
1815/// involving constants, fold it.
1816Constant *ScalarEvolutionsImpl::
1817getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, const Loop *L) {
1818  std::map<PHINode*, Constant*>::iterator I =
1819    ConstantEvolutionLoopExitValue.find(PN);
1820  if (I != ConstantEvolutionLoopExitValue.end())
1821    return I->second;
1822
1823  if (Its > MaxBruteForceIterations)
1824    return ConstantEvolutionLoopExitValue[PN] = 0;  // Not going to evaluate it.
1825
1826  Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
1827
1828  // Since the loop is canonicalized, the PHI node must have two entries.  One
1829  // entry must be a constant (coming in from outside of the loop), and the
1830  // second must be derived from the same PHI.
1831  bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
1832  Constant *StartCST =
1833    dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
1834  if (StartCST == 0)
1835    return RetVal = 0;  // Must be a constant.
1836
1837  Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
1838  PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
1839  if (PN2 != PN)
1840    return RetVal = 0;  // Not derived from same PHI.
1841
1842  // Execute the loop symbolically to determine the exit value.
1843  unsigned IterationNum = 0;
1844  unsigned NumIterations = Its;
1845  if (NumIterations != Its)
1846    return RetVal = 0;  // More than 2^32 iterations??
1847
1848  for (Constant *PHIVal = StartCST; ; ++IterationNum) {
1849    if (IterationNum == NumIterations)
1850      return RetVal = PHIVal;  // Got exit value!
1851
1852    // Compute the value of the PHI node for the next iteration.
1853    Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
1854    if (NextPHI == PHIVal)
1855      return RetVal = NextPHI;  // Stopped evolving!
1856    if (NextPHI == 0)
1857      return 0;        // Couldn't evaluate!
1858    PHIVal = NextPHI;
1859  }
1860}
1861
1862/// ComputeIterationCountExhaustively - If the trip is known to execute a
1863/// constant number of times (the condition evolves only from constants),
1864/// try to evaluate a few iterations of the loop until we get the exit
1865/// condition gets a value of ExitWhen (true or false).  If we cannot
1866/// evaluate the trip count of the loop, return UnknownValue.
1867SCEVHandle ScalarEvolutionsImpl::
1868ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
1869  PHINode *PN = getConstantEvolvingPHI(Cond, L);
1870  if (PN == 0) return UnknownValue;
1871
1872  // Since the loop is canonicalized, the PHI node must have two entries.  One
1873  // entry must be a constant (coming in from outside of the loop), and the
1874  // second must be derived from the same PHI.
1875  bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
1876  Constant *StartCST =
1877    dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
1878  if (StartCST == 0) return UnknownValue;  // Must be a constant.
1879
1880  Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
1881  PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
1882  if (PN2 != PN) return UnknownValue;  // Not derived from same PHI.
1883
1884  // Okay, we find a PHI node that defines the trip count of this loop.  Execute
1885  // the loop symbolically to determine when the condition gets a value of
1886  // "ExitWhen".
1887  unsigned IterationNum = 0;
1888  unsigned MaxIterations = MaxBruteForceIterations;   // Limit analysis.
1889  for (Constant *PHIVal = StartCST;
1890       IterationNum != MaxIterations; ++IterationNum) {
1891    ConstantInt *CondVal =
1892      dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
1893
1894    // Couldn't symbolically evaluate.
1895    if (!CondVal) return UnknownValue;
1896
1897    if (CondVal->getZExtValue() == uint64_t(ExitWhen)) {
1898      ConstantEvolutionLoopExitValue[PN] = PHIVal;
1899      ++NumBruteForceTripCountsComputed;
1900      return SCEVConstant::get(ConstantInt::get(Type::Int32Ty, IterationNum));
1901    }
1902
1903    // Compute the value of the PHI node for the next iteration.
1904    Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
1905    if (NextPHI == 0 || NextPHI == PHIVal)
1906      return UnknownValue;  // Couldn't evaluate or not making progress...
1907    PHIVal = NextPHI;
1908  }
1909
1910  // Too many iterations were needed to evaluate.
1911  return UnknownValue;
1912}
1913
1914/// getSCEVAtScope - Compute the value of the specified expression within the
1915/// indicated loop (which may be null to indicate in no loop).  If the
1916/// expression cannot be evaluated, return UnknownValue.
1917SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) {
1918  // FIXME: this should be turned into a virtual method on SCEV!
1919
1920  if (isa<SCEVConstant>(V)) return V;
1921
1922  // If this instruction is evolves from a constant-evolving PHI, compute the
1923  // exit value from the loop without using SCEVs.
1924  if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
1925    if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
1926      const Loop *LI = this->LI[I->getParent()];
1927      if (LI && LI->getParentLoop() == L)  // Looking for loop exit value.
1928        if (PHINode *PN = dyn_cast<PHINode>(I))
1929          if (PN->getParent() == LI->getHeader()) {
1930            // Okay, there is no closed form solution for the PHI node.  Check
1931            // to see if the loop that contains it has a known iteration count.
1932            // If so, we may be able to force computation of the exit value.
1933            SCEVHandle IterationCount = getIterationCount(LI);
1934            if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) {
1935              // Okay, we know how many times the containing loop executes.  If
1936              // this is a constant evolving PHI node, get the final value at
1937              // the specified iteration number.
1938              Constant *RV = getConstantEvolutionLoopExitValue(PN,
1939                                               ICC->getValue()->getZExtValue(),
1940                                                               LI);
1941              if (RV) return SCEVUnknown::get(RV);
1942            }
1943          }
1944
1945      // Okay, this is an expression that we cannot symbolically evaluate
1946      // into a SCEV.  Check to see if it's possible to symbolically evaluate
1947      // the arguments into constants, and if so, try to constant propagate the
1948      // result.  This is particularly useful for computing loop exit values.
1949      if (CanConstantFold(I)) {
1950        std::vector<Constant*> Operands;
1951        Operands.reserve(I->getNumOperands());
1952        for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
1953          Value *Op = I->getOperand(i);
1954          if (Constant *C = dyn_cast<Constant>(Op)) {
1955            Operands.push_back(C);
1956          } else {
1957            SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
1958            if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
1959              Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(),
1960                                                              Op->getType(),
1961                                                              false));
1962            else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
1963              if (Constant *C = dyn_cast<Constant>(SU->getValue()))
1964                Operands.push_back(ConstantExpr::getIntegerCast(C,
1965                                                                Op->getType(),
1966                                                                false));
1967              else
1968                return V;
1969            } else {
1970              return V;
1971            }
1972          }
1973        }
1974        Constant *C =ConstantFoldInstOperands(I, &Operands[0], Operands.size());
1975        return SCEVUnknown::get(C);
1976      }
1977    }
1978
1979    // This is some other type of SCEVUnknown, just return it.
1980    return V;
1981  }
1982
1983  if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
1984    // Avoid performing the look-up in the common case where the specified
1985    // expression has no loop-variant portions.
1986    for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
1987      SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
1988      if (OpAtScope != Comm->getOperand(i)) {
1989        if (OpAtScope == UnknownValue) return UnknownValue;
1990        // Okay, at least one of these operands is loop variant but might be
1991        // foldable.  Build a new instance of the folded commutative expression.
1992        std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
1993        NewOps.push_back(OpAtScope);
1994
1995        for (++i; i != e; ++i) {
1996          OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
1997          if (OpAtScope == UnknownValue) return UnknownValue;
1998          NewOps.push_back(OpAtScope);
1999        }
2000        if (isa<SCEVAddExpr>(Comm))
2001          return SCEVAddExpr::get(NewOps);
2002        assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!");
2003        return SCEVMulExpr::get(NewOps);
2004      }
2005    }
2006    // If we got here, all operands are loop invariant.
2007    return Comm;
2008  }
2009
2010  if (SCEVSDivExpr *Div = dyn_cast<SCEVSDivExpr>(V)) {
2011    SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
2012    if (LHS == UnknownValue) return LHS;
2013    SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
2014    if (RHS == UnknownValue) return RHS;
2015    if (LHS == Div->getLHS() && RHS == Div->getRHS())
2016      return Div;   // must be loop invariant
2017    return SCEVSDivExpr::get(LHS, RHS);
2018  }
2019
2020  // If this is a loop recurrence for a loop that does not contain L, then we
2021  // are dealing with the final value computed by the loop.
2022  if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
2023    if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
2024      // To evaluate this recurrence, we need to know how many times the AddRec
2025      // loop iterates.  Compute this now.
2026      SCEVHandle IterationCount = getIterationCount(AddRec->getLoop());
2027      if (IterationCount == UnknownValue) return UnknownValue;
2028      IterationCount = getTruncateOrZeroExtend(IterationCount,
2029                                               AddRec->getType());
2030
2031      // If the value is affine, simplify the expression evaluation to just
2032      // Start + Step*IterationCount.
2033      if (AddRec->isAffine())
2034        return SCEVAddExpr::get(AddRec->getStart(),
2035                                SCEVMulExpr::get(IterationCount,
2036                                                 AddRec->getOperand(1)));
2037
2038      // Otherwise, evaluate it the hard way.
2039      return AddRec->evaluateAtIteration(IterationCount);
2040    }
2041    return UnknownValue;
2042  }
2043
2044  //assert(0 && "Unknown SCEV type!");
2045  return UnknownValue;
2046}
2047
2048
2049/// SolveQuadraticEquation - Find the roots of the quadratic equation for the
2050/// given quadratic chrec {L,+,M,+,N}.  This returns either the two roots (which
2051/// might be the same) or two SCEVCouldNotCompute objects.
2052///
2053static std::pair<SCEVHandle,SCEVHandle>
2054SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) {
2055  assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
2056  SCEVConstant *L = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
2057  SCEVConstant *M = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
2058  SCEVConstant *N = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
2059
2060  // We currently can only solve this if the coefficients are constants.
2061  if (!L || !M || !N) {
2062    SCEV *CNC = new SCEVCouldNotCompute();
2063    return std::make_pair(CNC, CNC);
2064  }
2065
2066  Constant *C = L->getValue();
2067  Constant *Two = ConstantInt::get(C->getType(), 2);
2068
2069  // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
2070  // The B coefficient is M-N/2
2071  Constant *B = ConstantExpr::getSub(M->getValue(),
2072                                     ConstantExpr::getSDiv(N->getValue(),
2073                                                          Two));
2074  // The A coefficient is N/2
2075  Constant *A = ConstantExpr::getSDiv(N->getValue(), Two);
2076
2077  // Compute the B^2-4ac term.
2078  Constant *SqrtTerm =
2079    ConstantExpr::getMul(ConstantInt::get(C->getType(), 4),
2080                         ConstantExpr::getMul(A, C));
2081  SqrtTerm = ConstantExpr::getSub(ConstantExpr::getMul(B, B), SqrtTerm);
2082
2083  // Compute floor(sqrt(B^2-4ac))
2084  uint64_t SqrtValV = cast<ConstantInt>(SqrtTerm)->getZExtValue();
2085  uint64_t SqrtValV2 = (uint64_t)sqrt((double)SqrtValV);
2086  // The square root might not be precise for arbitrary 64-bit integer
2087  // values.  Do some sanity checks to ensure it's correct.
2088  if (SqrtValV2*SqrtValV2 > SqrtValV ||
2089      (SqrtValV2+1)*(SqrtValV2+1) <= SqrtValV) {
2090    SCEV *CNC = new SCEVCouldNotCompute();
2091    return std::make_pair(CNC, CNC);
2092  }
2093
2094  ConstantInt *SqrtVal = ConstantInt::get(Type::Int64Ty, SqrtValV2);
2095  SqrtTerm = ConstantExpr::getTruncOrBitCast(SqrtVal, SqrtTerm->getType());
2096
2097  Constant *NegB = ConstantExpr::getNeg(B);
2098  Constant *TwoA = ConstantExpr::getMul(A, Two);
2099
2100  // The divisions must be performed as signed divisions.
2101  Constant *Solution1 =
2102    ConstantExpr::getSDiv(ConstantExpr::getAdd(NegB, SqrtTerm), TwoA);
2103  Constant *Solution2 =
2104    ConstantExpr::getSDiv(ConstantExpr::getSub(NegB, SqrtTerm), TwoA);
2105  return std::make_pair(SCEVUnknown::get(Solution1),
2106                        SCEVUnknown::get(Solution2));
2107}
2108
2109/// HowFarToZero - Return the number of times a backedge comparing the specified
2110/// value to zero will execute.  If not computable, return UnknownValue
2111SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) {
2112  // If the value is a constant
2113  if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2114    // If the value is already zero, the branch will execute zero times.
2115    if (C->getValue()->isNullValue()) return C;
2116    return UnknownValue;  // Otherwise it will loop infinitely.
2117  }
2118
2119  SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
2120  if (!AddRec || AddRec->getLoop() != L)
2121    return UnknownValue;
2122
2123  if (AddRec->isAffine()) {
2124    // If this is an affine expression the execution count of this branch is
2125    // equal to:
2126    //
2127    //     (0 - Start/Step)    iff   Start % Step == 0
2128    //
2129    // Get the initial value for the loop.
2130    SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
2131    if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
2132    SCEVHandle Step = AddRec->getOperand(1);
2133
2134    Step = getSCEVAtScope(Step, L->getParentLoop());
2135
2136    // Figure out if Start % Step == 0.
2137    // FIXME: We should add DivExpr and RemExpr operations to our AST.
2138    if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
2139      if (StepC->getValue()->equalsInt(1))      // N % 1 == 0
2140        return SCEV::getNegativeSCEV(Start);  // 0 - Start/1 == -Start
2141      if (StepC->getValue()->isAllOnesValue())  // N % -1 == 0
2142        return Start;                   // 0 - Start/-1 == Start
2143
2144      // Check to see if Start is divisible by SC with no remainder.
2145      if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
2146        ConstantInt *StartCC = StartC->getValue();
2147        Constant *StartNegC = ConstantExpr::getNeg(StartCC);
2148        Constant *Rem = ConstantExpr::getSRem(StartNegC, StepC->getValue());
2149        if (Rem->isNullValue()) {
2150          Constant *Result =ConstantExpr::getSDiv(StartNegC,StepC->getValue());
2151          return SCEVUnknown::get(Result);
2152        }
2153      }
2154    }
2155  } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
2156    // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
2157    // the quadratic equation to solve it.
2158    std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec);
2159    SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2160    SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2161    if (R1) {
2162#if 0
2163      cerr << "HFTZ: " << *V << " - sol#1: " << *R1
2164           << "  sol#2: " << *R2 << "\n";
2165#endif
2166      // Pick the smallest positive root value.
2167      if (ConstantInt *CB =
2168          dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2169                                   R1->getValue(), R2->getValue()))) {
2170        if (CB->getZExtValue() == false)
2171          std::swap(R1, R2);   // R1 is the minimum root now.
2172
2173        // We can only use this value if the chrec ends up with an exact zero
2174        // value at this index.  When solving for "X*X != 5", for example, we
2175        // should not accept a root of 2.
2176        SCEVHandle Val = AddRec->evaluateAtIteration(R1);
2177        if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val))
2178          if (EvalVal->getValue()->isNullValue())
2179            return R1;  // We found a quadratic root!
2180      }
2181    }
2182  }
2183
2184  return UnknownValue;
2185}
2186
2187/// HowFarToNonZero - Return the number of times a backedge checking the
2188/// specified value for nonzero will execute.  If not computable, return
2189/// UnknownValue
2190SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) {
2191  // Loops that look like: while (X == 0) are very strange indeed.  We don't
2192  // handle them yet except for the trivial case.  This could be expanded in the
2193  // future as needed.
2194
2195  // If the value is a constant, check to see if it is known to be non-zero
2196  // already.  If so, the backedge will execute zero times.
2197  if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2198    Constant *Zero = Constant::getNullValue(C->getValue()->getType());
2199    Constant *NonZero =
2200      ConstantExpr::getICmp(ICmpInst::ICMP_NE, C->getValue(), Zero);
2201    if (NonZero == ConstantInt::getTrue())
2202      return getSCEV(Zero);
2203    return UnknownValue;  // Otherwise it will loop infinitely.
2204  }
2205
2206  // We could implement others, but I really doubt anyone writes loops like
2207  // this, and if they did, they would already be constant folded.
2208  return UnknownValue;
2209}
2210
2211/// HowManyLessThans - Return the number of times a backedge containing the
2212/// specified less-than comparison will execute.  If not computable, return
2213/// UnknownValue.
2214SCEVHandle ScalarEvolutionsImpl::
2215HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L) {
2216  // Only handle:  "ADDREC < LoopInvariant".
2217  if (!RHS->isLoopInvariant(L)) return UnknownValue;
2218
2219  SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
2220  if (!AddRec || AddRec->getLoop() != L)
2221    return UnknownValue;
2222
2223  if (AddRec->isAffine()) {
2224    // FORNOW: We only support unit strides.
2225    SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, RHS->getType());
2226    if (AddRec->getOperand(1) != One)
2227      return UnknownValue;
2228
2229    // The number of iterations for "[n,+,1] < m", is m-n.  However, we don't
2230    // know that m is >= n on input to the loop.  If it is, the condition return
2231    // true zero times.  What we really should return, for full generality, is
2232    // SMAX(0, m-n).  Since we cannot check this, we will instead check for a
2233    // canonical loop form: most do-loops will have a check that dominates the
2234    // loop, that only enters the loop if [n-1]<m.  If we can find this check,
2235    // we know that the SMAX will evaluate to m-n, because we know that m >= n.
2236
2237    // Search for the check.
2238    BasicBlock *Preheader = L->getLoopPreheader();
2239    BasicBlock *PreheaderDest = L->getHeader();
2240    if (Preheader == 0) return UnknownValue;
2241
2242    BranchInst *LoopEntryPredicate =
2243      dyn_cast<BranchInst>(Preheader->getTerminator());
2244    if (!LoopEntryPredicate) return UnknownValue;
2245
2246    // This might be a critical edge broken out.  If the loop preheader ends in
2247    // an unconditional branch to the loop, check to see if the preheader has a
2248    // single predecessor, and if so, look for its terminator.
2249    while (LoopEntryPredicate->isUnconditional()) {
2250      PreheaderDest = Preheader;
2251      Preheader = Preheader->getSinglePredecessor();
2252      if (!Preheader) return UnknownValue;  // Multiple preds.
2253
2254      LoopEntryPredicate =
2255        dyn_cast<BranchInst>(Preheader->getTerminator());
2256      if (!LoopEntryPredicate) return UnknownValue;
2257    }
2258
2259    // Now that we found a conditional branch that dominates the loop, check to
2260    // see if it is the comparison we are looking for.
2261    if (ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition())){
2262      Value *PreCondLHS = ICI->getOperand(0);
2263      Value *PreCondRHS = ICI->getOperand(1);
2264      ICmpInst::Predicate Cond;
2265      if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest)
2266        Cond = ICI->getPredicate();
2267      else
2268        Cond = ICI->getInversePredicate();
2269
2270      switch (Cond) {
2271      case ICmpInst::ICMP_UGT:
2272        std::swap(PreCondLHS, PreCondRHS);
2273        Cond = ICmpInst::ICMP_ULT;
2274        break;
2275      case ICmpInst::ICMP_SGT:
2276        std::swap(PreCondLHS, PreCondRHS);
2277        Cond = ICmpInst::ICMP_SLT;
2278        break;
2279      default: break;
2280      }
2281
2282      if (Cond == ICmpInst::ICMP_SLT) {
2283        if (PreCondLHS->getType()->isInteger()) {
2284          if (RHS != getSCEV(PreCondRHS))
2285            return UnknownValue;  // Not a comparison against 'm'.
2286
2287          if (SCEV::getMinusSCEV(AddRec->getOperand(0), One)
2288                      != getSCEV(PreCondLHS))
2289            return UnknownValue;  // Not a comparison against 'n-1'.
2290        }
2291        else return UnknownValue;
2292      } else if (Cond == ICmpInst::ICMP_ULT)
2293        return UnknownValue;
2294
2295      // cerr << "Computed Loop Trip Count as: "
2296      //      << //  *SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)) << "\n";
2297      return SCEV::getMinusSCEV(RHS, AddRec->getOperand(0));
2298    }
2299    else
2300      return UnknownValue;
2301  }
2302
2303  return UnknownValue;
2304}
2305
2306/// getNumIterationsInRange - Return the number of iterations of this loop that
2307/// produce values in the specified constant range.  Another way of looking at
2308/// this is that it returns the first iteration number where the value is not in
2309/// the condition, thus computing the exit count. If the iteration count can't
2310/// be computed, an instance of SCEVCouldNotCompute is returned.
2311SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
2312                                                   bool isSigned) const {
2313  if (Range.isFullSet())  // Infinite loop.
2314    return new SCEVCouldNotCompute();
2315
2316  // If the start is a non-zero constant, shift the range to simplify things.
2317  if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
2318    if (!SC->getValue()->isNullValue()) {
2319      std::vector<SCEVHandle> Operands(op_begin(), op_end());
2320      Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType());
2321      SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop());
2322      if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
2323        return ShiftedAddRec->getNumIterationsInRange(
2324                                      Range.subtract(SC->getValue()),isSigned);
2325      // This is strange and shouldn't happen.
2326      return new SCEVCouldNotCompute();
2327    }
2328
2329  // The only time we can solve this is when we have all constant indices.
2330  // Otherwise, we cannot determine the overflow conditions.
2331  for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
2332    if (!isa<SCEVConstant>(getOperand(i)))
2333      return new SCEVCouldNotCompute();
2334
2335
2336  // Okay at this point we know that all elements of the chrec are constants and
2337  // that the start element is zero.
2338
2339  // First check to see if the range contains zero.  If not, the first
2340  // iteration exits.
2341  ConstantInt *Zero = ConstantInt::get(getType(), 0);
2342  if (!Range.contains(Zero, isSigned)) return SCEVConstant::get(Zero);
2343
2344  if (isAffine()) {
2345    // If this is an affine expression then we have this situation:
2346    //   Solve {0,+,A} in Range  ===  Ax in Range
2347
2348    // Since we know that zero is in the range, we know that the upper value of
2349    // the range must be the first possible exit value.  Also note that we
2350    // already checked for a full range.
2351    ConstantInt *Upper = cast<ConstantInt>(Range.getUpper());
2352    ConstantInt *A     = cast<SCEVConstant>(getOperand(1))->getValue();
2353    ConstantInt *One   = ConstantInt::get(getType(), 1);
2354
2355    // The exit value should be (Upper+A-1)/A.
2356    Constant *ExitValue = Upper;
2357    if (A != One) {
2358      ExitValue = ConstantExpr::getSub(ConstantExpr::getAdd(Upper, A), One);
2359      ExitValue = ConstantExpr::getSDiv(ExitValue, A);
2360    }
2361    assert(isa<ConstantInt>(ExitValue) &&
2362           "Constant folding of integers not implemented?");
2363
2364    // Evaluate at the exit value.  If we really did fall out of the valid
2365    // range, then we computed our trip count, otherwise wrap around or other
2366    // things must have happened.
2367    ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue);
2368    if (Range.contains(Val, isSigned))
2369      return new SCEVCouldNotCompute();  // Something strange happened
2370
2371    // Ensure that the previous value is in the range.  This is a sanity check.
2372    assert(Range.contains(EvaluateConstantChrecAtConstant(this,
2373                          ConstantExpr::getSub(ExitValue, One)), isSigned) &&
2374           "Linear scev computation is off in a bad way!");
2375    return SCEVConstant::get(cast<ConstantInt>(ExitValue));
2376  } else if (isQuadratic()) {
2377    // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
2378    // quadratic equation to solve it.  To do this, we must frame our problem in
2379    // terms of figuring out when zero is crossed, instead of when
2380    // Range.getUpper() is crossed.
2381    std::vector<SCEVHandle> NewOps(op_begin(), op_end());
2382    NewOps[0] = SCEV::getNegativeSCEV(SCEVUnknown::get(Range.getUpper()));
2383    SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop());
2384
2385    // Next, solve the constructed addrec
2386    std::pair<SCEVHandle,SCEVHandle> Roots =
2387      SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec));
2388    SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2389    SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2390    if (R1) {
2391      // Pick the smallest positive root value.
2392      if (ConstantInt *CB =
2393          dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2394                                   R1->getValue(), R2->getValue()))) {
2395        if (CB->getZExtValue() == false)
2396          std::swap(R1, R2);   // R1 is the minimum root now.
2397
2398        // Make sure the root is not off by one.  The returned iteration should
2399        // not be in the range, but the previous one should be.  When solving
2400        // for "X*X < 5", for example, we should not return a root of 2.
2401        ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
2402                                                             R1->getValue());
2403        if (Range.contains(R1Val, isSigned)) {
2404          // The next iteration must be out of the range...
2405          Constant *NextVal =
2406            ConstantExpr::getAdd(R1->getValue(),
2407                                 ConstantInt::get(R1->getType(), 1));
2408
2409          R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
2410          if (!Range.contains(R1Val, isSigned))
2411            return SCEVUnknown::get(NextVal);
2412          return new SCEVCouldNotCompute();  // Something strange happened
2413        }
2414
2415        // If R1 was not in the range, then it is a good return value.  Make
2416        // sure that R1-1 WAS in the range though, just in case.
2417        Constant *NextVal =
2418          ConstantExpr::getSub(R1->getValue(),
2419                               ConstantInt::get(R1->getType(), 1));
2420        R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
2421        if (Range.contains(R1Val, isSigned))
2422          return R1;
2423        return new SCEVCouldNotCompute();  // Something strange happened
2424      }
2425    }
2426  }
2427
2428  // Fallback, if this is a general polynomial, figure out the progression
2429  // through brute force: evaluate until we find an iteration that fails the
2430  // test.  This is likely to be slow, but getting an accurate trip count is
2431  // incredibly important, we will be able to simplify the exit test a lot, and
2432  // we are almost guaranteed to get a trip count in this case.
2433  ConstantInt *TestVal = ConstantInt::get(getType(), 0);
2434  ConstantInt *One     = ConstantInt::get(getType(), 1);
2435  ConstantInt *EndVal  = TestVal;  // Stop when we wrap around.
2436  do {
2437    ++NumBruteForceEvaluations;
2438    SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal));
2439    if (!isa<SCEVConstant>(Val))  // This shouldn't happen.
2440      return new SCEVCouldNotCompute();
2441
2442    // Check to see if we found the value!
2443    if (!Range.contains(cast<SCEVConstant>(Val)->getValue(), isSigned))
2444      return SCEVConstant::get(TestVal);
2445
2446    // Increment to test the next index.
2447    TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One));
2448  } while (TestVal != EndVal);
2449
2450  return new SCEVCouldNotCompute();
2451}
2452
2453
2454
2455//===----------------------------------------------------------------------===//
2456//                   ScalarEvolution Class Implementation
2457//===----------------------------------------------------------------------===//
2458
2459bool ScalarEvolution::runOnFunction(Function &F) {
2460  Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>());
2461  return false;
2462}
2463
2464void ScalarEvolution::releaseMemory() {
2465  delete (ScalarEvolutionsImpl*)Impl;
2466  Impl = 0;
2467}
2468
2469void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
2470  AU.setPreservesAll();
2471  AU.addRequiredTransitive<LoopInfo>();
2472}
2473
2474SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
2475  return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
2476}
2477
2478/// hasSCEV - Return true if the SCEV for this value has already been
2479/// computed.
2480bool ScalarEvolution::hasSCEV(Value *V) const {
2481  return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V);
2482}
2483
2484
2485/// setSCEV - Insert the specified SCEV into the map of current SCEVs for
2486/// the specified value.
2487void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) {
2488  ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H);
2489}
2490
2491
2492SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const {
2493  return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L);
2494}
2495
2496bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const {
2497  return !isa<SCEVCouldNotCompute>(getIterationCount(L));
2498}
2499
2500SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const {
2501  return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L);
2502}
2503
2504void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const {
2505  return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I);
2506}
2507
2508static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE,
2509                          const Loop *L) {
2510  // Print all inner loops first
2511  for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
2512    PrintLoopInfo(OS, SE, *I);
2513
2514  cerr << "Loop " << L->getHeader()->getName() << ": ";
2515
2516  std::vector<BasicBlock*> ExitBlocks;
2517  L->getExitBlocks(ExitBlocks);
2518  if (ExitBlocks.size() != 1)
2519    cerr << "<multiple exits> ";
2520
2521  if (SE->hasLoopInvariantIterationCount(L)) {
2522    cerr << *SE->getIterationCount(L) << " iterations! ";
2523  } else {
2524    cerr << "Unpredictable iteration count. ";
2525  }
2526
2527  cerr << "\n";
2528}
2529
2530void ScalarEvolution::print(std::ostream &OS, const Module* ) const {
2531  Function &F = ((ScalarEvolutionsImpl*)Impl)->F;
2532  LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI;
2533
2534  OS << "Classifying expressions for: " << F.getName() << "\n";
2535  for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
2536    if (I->getType()->isInteger()) {
2537      OS << *I;
2538      OS << "  --> ";
2539      SCEVHandle SV = getSCEV(&*I);
2540      SV->print(OS);
2541      OS << "\t\t";
2542
2543      if ((*I).getType()->isInteger()) {
2544        ConstantRange Bounds = SV->getValueRange();
2545        if (!Bounds.isFullSet())
2546          OS << "Bounds: " << Bounds << " ";
2547      }
2548
2549      if (const Loop *L = LI.getLoopFor((*I).getParent())) {
2550        OS << "Exits: ";
2551        SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop());
2552        if (isa<SCEVCouldNotCompute>(ExitValue)) {
2553          OS << "<<Unknown>>";
2554        } else {
2555          OS << *ExitValue;
2556        }
2557      }
2558
2559
2560      OS << "\n";
2561    }
2562
2563  OS << "Determining loop execution counts for: " << F.getName() << "\n";
2564  for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
2565    PrintLoopInfo(OS, this, *I);
2566}
2567
2568