Loop Cache Analysis

[etiotto]

Summary

Implement a new analysis to estimate the number of cache lines required by a loop nest.
The analysis is largely based on the following paper:

Compiler Optimizations for Improving Data Locality
By: Steve Carr, Katherine S. McKinley, Chau-Wen Tseng
http://www.cs.utexas.edu/users/mckinley/papers/asplos-1994.pdf

The analysis considers temporal reuse (accesses to the same memory location) and spatial reuse (accesses to memory locations within a cache line). For simplicity the analysis considers memory accesses in the innermost loop in a loop nest, and thus determines the number of cache lines used when the loop L in loop nest LN is placed in the innermost position.

The result of the analysis can be used to drive several transformations. As an example, loop interchange could use it determine which loops in a perfect loop nest should be interchanged to maximize cache reuse. Similarly, loop distribution could be enhanced to take into consideration cache reuse between arrays when distributing a loop to eliminate vectorization inhibiting dependencies.

The general approach taken to estimate the number of cache lines used by the memory references in the inner loop of a loop nest is:

• Partition memory references that exhibit temporal or spatial reuse into reference groups.
• For each loop L in the a loop nest LN: a. Compute the cost of the reference group b. Compute the 'cache cost' of the loop nest by summing up the reference groups costs

For further details of the algorithm please refer to the paper.

[Meinersbur]

What do you plan as the first use of this transformation?

llvm/include/llvm/Analysis/LoopCacheAnalysis.h

31–32

[style] The current code base most often uses a Ty suffix for typedefs.

175

[suggestion] Make these magic numbers cl::opt options?

llvm/lib/Analysis/LoopCacheAnalysis.cpp

64–65

Is passing a single innermost loop a precondition or a what this function computes? It seems the only loop that this function might return is Loops.back() and kind-of verifies that the loop vector is in the right order?!?

308

[nit] double space

320

[style] Subscripts.empty(). Sizes.empty()

333

[style] Did you mean break/return here? The next iteration might add elements to it. I'd structure this as

if (!isOneDimensionalArray(AccessFn, L)) {
   ...
  break;
}

...

conforming https://llvm.org/docs/CodingStandards.html#use-early-exits-and-continue-to-simplify-code.

337

[style] return all_of(Subcripts, ...

387

Why not using getBackedgeTakenCount()?

524–532

Since this only has code that executes in assert-builds, it should be guarded entirely by an LLVM_DEBUG.

591–592

If the intention is to provide analysis for innermost loops only, why this limitation? Could it just return an analysis result for each innermost loop?

If the analysis requires a global view to determine the cost for each loop, wouldn't a FunctionPass be more appropriate? Currently, it seems users first need get the LoopCacheAnalysis for a topmost loops, the ask it for one of its nested loops.

Are such loop nests not analyzable at all?

while (repeat) {
  for (int i = ...)
    for (int j = ...)
      B[i][j] = ... A[i+1][j+1] ... // stencil
  for (int i = ...)
    for (int j = ...)
      A[i][j] = ... B[i+1][j+1] ... // stencil
}

llvm/test/Analysis/LoopCacheAnalysis/a.ll

1 ↗

(On Diff #205185)

[serious] Can you give a more descriptive file names that a.ll and b.ll etc?

4 ↗

(On Diff #205185)

[suggestion] Is it possible to leave the triple unspecified to the test case?

[etiotto]

llvm/include/llvm/Analysis/LoopCacheAnalysis.h

31–32

OK I'll use the Ty suffix.

175

Added cl::opt for the default loop trip count and the temporal reuse threshold (see the .cpp file)

llvm/lib/Analysis/LoopCacheAnalysis.cpp

64–65

This function attempts to retrieve the innermost loop in the given loop vector. It returns a nullptr if any loops in the loop vector supplied has more than one sibling. The loop vector is expected to contain loops collected in breadth-first order. I'll improve the comment.

387

I'll do that.

591–592

The current scope of this PR is to analyze loop nests that have a single innermost loop. The analysis returns a vector of loop costs for each loop in a loop nest. This is not a hard requirement, however I would like to extend the scope of the transformation in a future PR. One of the scenario I had in mind, at least initially, as a consumer of this analysis is loop interchange which operates on perfect nests and therefore the current implementation of the analysis is sufficient for that use.

If we were to make the analysis a function pass that would force consumers to become function passes (or use the cached version of this analysis). That seems overly restrictive especially considering that loop interchange is currently a loop pass.

llvm/test/Analysis/LoopCacheAnalysis/a.ll

1 ↗

(On Diff #205185)

Ooops, yes I'll rename those files.

4 ↗

(On Diff #205185)

Unfortunately is not easily removed because the target triple is necessary to determine the target architecture cache line size, which is used in the analysis.

[etiotto]

Addressed review comment from M. Kruse.

[xbolva00]

llvm/include/llvm/Analysis/LoopCacheAnalysis.h

221

llvm::sort

llvm/lib/Analysis/LoopCacheAnalysis.cpp

366

llvm::all_of

[fhahn]

llvm/lib/Analysis/LoopCacheAnalysis.cpp

591–592

I'll try to have a closer look in a few days, but I think for the use in LoopInterchange, it would not need to be an analysis pass (I suppose there won't be a big benefit to preserve this as an analysis?).

I think a lightweight interface to query the cost for certain valid permutations would be sufficient. I think it would be great if we only compute the information when directly required (i.e. we only need to compute the costs for loops we can interchange, for the permutations valid to interchange)

[Meinersbur]

How would a pass use this analysis? It computes a cost for the current IR, but there is nothing to compare it to unless the transformation pass emits the transformed loop nest next to the original pass such that the LoopCacheAnalysis can compute its cost.

llvm/lib/Analysis/LoopCacheAnalysis.cpp

565

Would it be useful to make CacheCostTy an int64_t? At least with UBSan we could diagnose an overflow.

[etiotto]

llvm/lib/Analysis/LoopCacheAnalysis.cpp

591–592

Looking forward to you comments. You are correct, we could teach loop interchange about the locality of accesses in a loop nest. There are several other loop transformations that can benefit from it. The paper that introduces the analysis (Compiler Optimizations for Improving Data Locality - http://www.cs.utexas.edu/users/mckinley/papers/asplos-1994.pdf) illustrates how the analysis was used to guide several other loop transformation, namely loop reversal, loop fusion, and loop distribution. Given the applicability of the analysis to several transformation I think it would make sense to centralize the code as an analysis pass.

[etiotto]

llvm/include/llvm/Analysis/LoopCacheAnalysis.h

221

Yup agree, thanks for pointing this out.

llvm/lib/Analysis/LoopCacheAnalysis.cpp

565

Ok.

[etiotto]

In D63459#1549307, @Meinersbur wrote:

How would a pass use this analysis? It computes a cost for the current IR, but there is nothing to compare it to unless the transformation pass emits the transformed loop nest next to the original pass such that the LoopCacheAnalysis can compute its cost.

The result of the analysis will be a vector of costs for each loop in a loop nest. The cost associated with a loop estimates the number of cache line used if the loop was placed in the innermost position in the nest. Therefore sorting the cost vector in descending order correspond to minimizing the number of data cache misses in the nest. For example loop distribution can use the sorted vector and work out a set of permutation moves (assuming legality constraint are satisfied) to maximize cache locality.

[etiotto]

ping

[Meinersbur]

@fhahn Do you still want to look over this patch?

llvm/include/llvm/Analysis/LoopCacheAnalysis.h

55

Should return size_t

159

It does not make sense to have owning pointers to SmallVector's. This just adds another level of indirection compared to containing std::vector (or SmallVector to have a single allocation for all elements if none exceeds the small size) directly.

llvm/lib/Analysis/LoopCacheAnalysis.cpp

52

Before const_cast why not removing the const from the parameter list?

56

WL is used as a stack, a (Small)Vector could do this as well.

103

Don’t “almost always” use auto

for (const SCEV *Subscript : R.subscripts)

You seem to have applied the coding standard for auto everywhere except in foreach-loops.

117

No need for Subscripts(), Sizes()

Prefer default member initializer at declaration over IsValid(false), BaserPointer(nullptr)

121

[subjective] I'd prefer a function that either returns an nullptr/ErrorOr<IndexedReference> than an IsValid flag for ever object.

146

Nice, this is where the coding standard recommends auto.

173–176

Some compilers may complain about empty statements in non-debug builds. Alternative:

LLVM_DEBUG({
 if (InSameCacheLine)
    dbgs().indent(2) << "Found spacial reuse.\n";
  else
    dbgs().indent(2) << "No spacial reuse.\n";
});

208

Prefer int over unsigned

499–500

The LLVM code base does not use const for stack variables.

538

Do you need wrapping behavior? int instead of unsigned.

591–592

If we were to make the analysis a function pass that would force consumers to become function passes (or use the cached version of this analysis). That seems overly restrictive especially considering that loop interchange is currently a loop pass.

I don't think the new pass manager has this restriction. Passes can ask for analyses of any level using OuterAnalysisManagerProxy. The new pass manager caches everything.

[etiotto]

llvm/lib/Analysis/LoopCacheAnalysis.cpp

52

I dropped the const qualifier in the parameter declaration and adjusted the code accordingly.

103

OK I'll fix the use of auto in foreach-loops.

146

Thanks.

173–176

Agree. Is cleaner the way you propose as there is only one LLVM_DEBUG.

499–500

const qualifying local variables preempts unintended modifications later in the function... but I do not feel strongly about it. I'll change it.

591–592

Yes it is also my understanding (from the comments in PassManager.h) that the new pass manager does allows an "inner" pass (e.g. a Loop Pass) to ask for an "outer" analysis (e.g. a Function Analysis). However, at least from the comments in PassManager.h, the inner pass cannot cause the outer analysis to run and can only rely on the cached version which may give back a nullptr.

[etiotto]

Addressed Michael Kruse comments.

[fhahn]

llvm/include/llvm/Analysis/LoopCacheAnalysis.h

220

Do you anticipate most users relying on the loops to be ordered by cost? If not, it might be worth switching to a map to avoid using find_if at multiple places (even though not too common in user-written C/C++ code, I've encountered various (auto-generated) sources, which have very deep nesting levels of loops).

LoopInterhcange for example would be interested in comparing just the total cache cost of a various re-orderings of a loop nest.

llvm/lib/Analysis/LoopCacheAnalysis.cpp

591–592

. Given the applicability of the analysis to several transformation I think it would make sense to centralize the code as an analysis pass.

I agree it is a useful utility to have, I am just wondering what the benefit of exposing it as an analysis pass would be, as it is unlikely that the result would be used for most loops or could be cached between interested transforms frequently.

IMO it would be fine as a utility class/function, i.e. just provide a getLoopCacheCost() function that takes a root loop and maybe a potential re-ordering of loops, which the interested transforms can use only on the loops that they can transform. I think that would reduce the size of the patch a bit and focus on the important bits.

[Meinersbur]

llvm/lib/Analysis/LoopCacheAnalysis.cpp

591–592

I convinced myself that indeed a FunctionPass might not be that nice, because any LoopPass would need to preserve it. As @fhahn points out, wanting to preserve/reuse the analysis might be rare.

[etiotto]

llvm/include/llvm/Analysis/LoopCacheAnalysis.h

220

I was envisioning Loop Interchange wanting to get a sorted vector of cache costs for a nest and then using it to determine the optimal reordering of the loop in the nest (loop with smaller cost in the innermost position, larger cost in the outermost position). Having the cache cost vector sorted is also handy when printing it.

llvm/lib/Analysis/LoopCacheAnalysis.cpp

48

Will remove this static function and instead use the breadth_first(&Root) iterator from ADT/BreadthFirstIterator.h

591–592

I was thinking that having it as an analysis pass would allow loop transformations that do not modify the memory references in a loop nest to preserve the analysis...
I am OK with just adding a member function to the CacheCost class to construct and return the cache cost for a loop nested root by a given loop.
I will upstream a path to make that change and for the time being avoid making this an analysis pass.

591–592

I will upstream a path as suggested by @fhahn to just provide a member function to the CacheCost class to construct and return the cache cost for a loop nested rooted by a given loop.

[etiotto]

Addressed suggestions from @fhahn and dropped the pass as an analysis. Instead I provided a static member function in the CacheCost class to compute the cache cost of a nest rooted by a given loop.

[etiotto]

Note: Because I removed the getLoops static function in the last path older comments in LoopCacheAnalysis.cpp are unfortunately no longer attached to the correct line :-(

[etiotto]

@fhahn @Meinersbur do you have further comments? If not can this be approved?

[Meinersbur]

LGTM, some nitpicks left.

llvm/include/llvm/Analysis/LoopCacheAnalysis.h

182

CacheCostTy is int64_t; did you mean to assign -1?

201

To not leak the internal list implementation, return ArrayRef<LoopCacheCostTy>.

llvm/lib/Analysis/LoopCacheAnalysis.cpp

168

Don’t “almost always” use auto

[fhahn]

I would like to take another look, but do not want to block this for too long. Please feel free to commit if you don't hear from me by Monday.

llvm/test/Analysis/LoopCacheAnalysis/loads-store.ll

4 ↗

(On Diff #208836)

We need to make sure that the PPC backend was built when running those tests. usually we put target-specific tests in target subdirectories, with a local lit.local.cfg, checking for the backend (e.g. see llvm/test/Transforms/LoopVectorize/PowerPC/lit.local.cfg)

[greened]

llvm/include/llvm/Analysis/LoopCacheAnalysis.h

77

Referencing a cl:opt defined in the .cpp? It's a little confusing.

108

Why is this part of IndexedReference?

llvm/lib/Analysis/LoopCacheAnalysis.cpp

45

What units is this in? What does "2" mean?

190

This seems a bit dangerous to me. Depending on the client, we might want to assume reuse if we don't know the distance. Could this function return a tribool of (yes/no/unknown)?

[greened]

llvm/test/Analysis/LoopCacheAnalysis/loads-store.ll

1 ↗

(On Diff #208836)

I'd like to see block comments at the top of all of these tests explaining what they are testing. It will be much easier to understand what's going on when these tests fail.

[fhahn]

llvm/lib/Analysis/LoopCacheAnalysis.cpp

257

RefCost is guaranteed to be a SCEVConstant here, so it would be better to use cast<> instead. Or even better

if (auto ConstantCost = dyn_cast<SCEVCOnstant>(RefCost))
  return return ConstantCost->getValue()->getSExtValue();

LLVM_DEBUG(dbgs().indent(4)
             << "RefCost is not a constant! Setting to RefCost=InvalidCost "
                "(invalid value).\n");
return CacheCost::InvalidCost;

268

It looks like this function does not capture much and might be better as a separate member function?

275

nit: Capitalize start of sentence.

281

nit: Capitalize start of sentence.

457

\n at the end?

472

This should be passed in I think and the users should request it via the pass manager.

[etiotto]

Addressing code review comments given by @Meinersbur and @fhahn.

[etiotto]

In D63459#1590173, @fhahn wrote:

I would like to take another look, but do not want to block this for too long. Please feel free to commit if you don't hear from me by Monday.

Done.

[etiotto]

Address remaining comments from @fhahn

[etiotto]

llvm/include/llvm/Analysis/LoopCacheAnalysis.h

77

I'll pass it as an argument.

108

I changed into a static function in the .cpp file instead.

llvm/lib/Analysis/LoopCacheAnalysis.cpp

45

I clarified the description.

268

OK I'll make it a private member function.

[greened]

llvm/lib/Analysis/LoopCacheAnalysis.cpp

45

I'm still a bit confused. Does this mean the a[i] and a[i+1] will be considered to have temporal reuse with a value of 2? Perhaps "temporal reuse" itself needs a definition. Are we talking about referencing the same exact memory location, the same cache line, the same page, ...? It seems odd to me that "temporal reuse" would mean anything other than accessing exactly the same memory location. Everything else I would consider to be "spacial reuse."

At the very least this deserves a longer comment block about what it means and its implications. Some clients want the definition of "temporal reuse" to be "access the exact same memory location" and this default value seems to mean something very different.

240

The debug message should reference MaxDistance and not hard-code the value 2.

[etiotto]

llvm/lib/Analysis/LoopCacheAnalysis.cpp

45

That's correct, a[i] and a[i+1] are consider to have temporal reuse when the threshold is 2. A threshold of 1 would cause only references to the same memory location have temporal reuse. The analysis attempts to implement the algorithm in the paper mentioned in the summary, and
I agree that this is a bit confusing. I will add a comment to attempt to clarify better.

190

If the dependence distance is unknown at compile time the references are conservatively considered to have no spacial reuse, and consequently the analysis will overestimate the number of cache lines used by the loop (when it is in the innermost position in the nest).

For now I can return an Optional<bool> (didn't find a tribool data type readily available in LLVM). This will make it easier to place references with 'unknow' distance in the same reference group if we find a motivating test case that needs it.

[etiotto]

Addressing review comment from @reames

[etiotto]

I addressed all pending review comments, @fhahn @reames does it look ok to you guys now?

[fhahn]

Can you re-run clang-format on the latest version of the patch? I think it would be good to get an in-tree user of this soon, to make sure the modeling works as expected on real hardware/benchmarks. Do you have a timeline to get this used? I think you mentioned LoopFusion as one of the first planned users?

llvm/include/llvm/Analysis/LoopCacheAnalysis.h

199

IIRC this returns the ordered loop costs, right? Please document.

llvm/test/Analysis/LoopCacheAnalysis/PowerPC/matvecmul.ll

18

IIRC the costs should be ordered. If so, please use check next for entries with differing costs. (here and at other places)

[etiotto]

Run clang-format, address comments from @fhahn.

[etiotto]

In D63459#1605923, @fhahn wrote:

Can you re-run clang-format on the latest version of the patch? I think it would be good to get an in-tree user of this soon, to make sure the modeling works as expected on real hardware/benchmarks. Do you have a timeline to get this used? I think you mentioned LoopFusion as one of the first planned users?

I reformatted the patch and addressed inline comments. The paper reports that the analysis was used to guide both loop fusion and loop interchange. I used it myself profitably on loop interchange (not yet in tree), and the lit tests provided are based in part on that experiment.

If there are not further comments and/or concerns I'll commit the patch on Thursday.

[fhahn]

In D63459#1607143, @etiotto wrote:

In D63459#1605923, @fhahn wrote:

Can you re-run clang-format on the latest version of the patch? I think it would be good to get an in-tree user of this soon, to make sure the modeling works as expected on real hardware/benchmarks. Do you have a timeline to get this used? I think you mentioned LoopFusion as one of the first planned users?

I reformatted the patch and addressed inline comments. The paper reports that the analysis was used to guide both loop fusion and loop interchange. I used it myself profitably on loop interchange (not yet in tree), and the lit tests provided are based in part on that experiment.

Right, are you planning on submitting a patch for loop interchange upstream?

I used the printer on some of the loop interchange tests, but the delinearization does not support some cases there yet. I hope I find some time to look into that next week and maybe also integrating it into loop interchange unless you plan to do so.

If there are not further comments and/or concerns I'll commit the patch on Thursday.

[etiotto]

Right, are you planning on submitting a patch for loop interchange upstream?

I used the printer on some of the loop interchange tests, but the delinearization does not support some cases there yet. I hope I find some time to look into that next week and maybe also integrating it into loop interchange unless you plan to do so.

If you have time to integrate the analysis in loop interchange next week go ahead. I will need to work through other work in progress I am doing, and upstream those pieces before I can get to loop interchange. I think we can discuss details during the biweekly loop meetings.

In D63459#1607411, @fhahn wrote:

In D63459#1607143, @etiotto wrote:

In D63459#1605923, @fhahn wrote:

Can you re-run clang-format on the latest version of the patch? I think it would be good to get an in-tree user of this soon, to make sure the modeling works as expected on real hardware/benchmarks. Do you have a timeline to get this used? I think you mentioned LoopFusion as one of the first planned users?

I reformatted the patch and addressed inline comments. The paper reports that the analysis was used to guide both loop fusion and loop interchange. I used it myself profitably on loop interchange (not yet in tree), and the lit tests provided are based in part on that experiment.

Right, are you planning on submitting a patch for loop interchange upstream?

I used the printer on some of the loop interchange tests, but the delinearization does not support some cases there yet. I hope I find some time to look into that next week and maybe also integrating it into loop interchange unless you plan to do so.

If there are not further comments and/or concerns I'll commit the patch on Thursday.

In D63459#1607411, @fhahn wrote:

In D63459#1607143, @etiotto wrote:

In D63459#1605923, @fhahn wrote:

Can you re-run clang-format on the latest version of the patch? I think it would be good to get an in-tree user of this soon, to make sure the modeling works as expected on real hardware/benchmarks. Do you have a timeline to get this used? I think you mentioned LoopFusion as one of the first planned users?

I reformatted the patch and addressed inline comments. The paper reports that the analysis was used to guide both loop fusion and loop interchange. I used it myself profitably on loop interchange (not yet in tree), and the lit tests provided are based in part on that experiment.

Right, are you planning on submitting a patch for loop interchange upstream?

I used the printer on some of the loop interchange tests, but the delinearization does not support some cases there yet. I hope I find some time to look into that next week and maybe also integrating it into loop interchange unless you plan to do so.

If there are not further comments and/or concerns I'll commit the patch on Thursday.

[greened]

llvm/lib/Analysis/LoopCacheAnalysis.cpp

45

So how will clients with different needs use this analysis? Some might want the definition in the paper but others might want to restrict it to exact memory locations only. A cl::opt doesn't allow configuration by clients.

[etiotto]

Added a command line option to specify the threshold for temporal reuse.

[etiotto]

llvm/lib/Analysis/LoopCacheAnalysis.cpp

45

I added a optional parameter to allow users to specify the temporal reuse threshold.

[xbolva00]

/home/xbolva00/LLVM/llvm/lib/Analysis/LoopCacheAnalysis.cpp:110:14: warning: ‘llvm::raw_ostream& llvm::operator<<(llvm::raw_ostream&, const llvm::IndexedReference&)’ has not been declared within llvm
raw_ostream &llvm::operator<<(raw_ostream &OS, const IndexedReference &R) {

^~~~

In file included from /home/xbolva00/LLVM/llvm/lib/Analysis/LoopCacheAnalysis.cpp:28:0:
/home/xbolva00/LLVM/llvm/include/llvm/Analysis/LoopCacheAnalysis.h:45:23: note: only here as a friend

friend raw_ostream &operator<<(raw_ostream &OS, const IndexedReference &R);
                    ^~~~~~~~

/home/xbolva00/LLVM/llvm/lib/Analysis/LoopCacheAnalysis.cpp:443:14: warning: ‘llvm::raw_ostream& llvm::operator<<(llvm::raw_ostream&, const llvm::CacheCost&)’ has not been declared within llvm
raw_ostream &llvm::operator<<(raw_ostream &OS, const CacheCost &CC) {

^~~~

In file included from /home/xbolva00/LLVM/llvm/lib/Analysis/LoopCacheAnalysis.cpp:28:0:
/home/xbolva00/LLVM/llvm/include/llvm/Analysis/LoopCacheAnalysis.h:174:23: note: only here as a friend

friend raw_ostream &operator<<(raw_ostream &OS, const CacheCost &CC);

GCC 7 Linux.

[etiotto]

Fix build warning for operator<< when using GCC 7.

[etiotto]

In D63459#1625843, @xbolva00 wrote:

/home/xbolva00/LLVM/llvm/lib/Analysis/LoopCacheAnalysis.cpp:110:14: warning: ‘llvm::raw_ostream& llvm::operator<<(llvm::raw_ostream&, const llvm::IndexedReference&)’ has not been declared within llvm
raw_ostream &llvm::operator<<(raw_ostream &OS, const IndexedReference &R) {

^~~~

In file included from /home/xbolva00/LLVM/llvm/lib/Analysis/LoopCacheAnalysis.cpp:28:0:
/home/xbolva00/LLVM/llvm/include/llvm/Analysis/LoopCacheAnalysis.h:45:23: note: only here as a friend

friend raw_ostream &operator<<(raw_ostream &OS, const IndexedReference &R);
                    ^~~~~~~~

/home/xbolva00/LLVM/llvm/lib/Analysis/LoopCacheAnalysis.cpp:443:14: warning: ‘llvm::raw_ostream& llvm::operator<<(llvm::raw_ostream&, const llvm::CacheCost&)’ has not been declared within llvm
raw_ostream &llvm::operator<<(raw_ostream &OS, const CacheCost &CC) {

^~~~

In file included from /home/xbolva00/LLVM/llvm/lib/Analysis/LoopCacheAnalysis.cpp:28:0:
/home/xbolva00/LLVM/llvm/include/llvm/Analysis/LoopCacheAnalysis.h:174:23: note: only here as a friend

friend raw_ostream &operator<<(raw_ostream &OS, const CacheCost &CC);

GCC 7 Linux.

I uploaded a fix for this warning. I use clang to build sigh, apologies for the problem.

[xbolva00]

No problem, it was just warning :)

[fhahn]

In D63459#1626024, @etiotto wrote:

In D63459#1625843, @xbolva00 wrote:

/home/xbolva00/LLVM/llvm/lib/Analysis/LoopCacheAnalysis.cpp:110:14: warning: ‘llvm::raw_ostream& llvm::operator<<(llvm::raw_ostream&, const llvm::IndexedReference&)’ has not been declared within llvm
raw_ostream &llvm::operator<<(raw_ostream &OS, const IndexedReference &R) {

^~~~

In file included from /home/xbolva00/LLVM/llvm/lib/Analysis/LoopCacheAnalysis.cpp:28:0:
/home/xbolva00/LLVM/llvm/include/llvm/Analysis/LoopCacheAnalysis.h:45:23: note: only here as a friend

friend raw_ostream &operator<<(raw_ostream &OS, const IndexedReference &R);
                    ^~~~~~~~

/home/xbolva00/LLVM/llvm/lib/Analysis/LoopCacheAnalysis.cpp:443:14: warning: ‘llvm::raw_ostream& llvm::operator<<(llvm::raw_ostream&, const llvm::CacheCost&)’ has not been declared within llvm
raw_ostream &llvm::operator<<(raw_ostream &OS, const CacheCost &CC) {

^~~~

In file included from /home/xbolva00/LLVM/llvm/lib/Analysis/LoopCacheAnalysis.cpp:28:0:
/home/xbolva00/LLVM/llvm/include/llvm/Analysis/LoopCacheAnalysis.h:174:23: note: only here as a friend

friend raw_ostream &operator<<(raw_ostream &OS, const CacheCost &CC);

GCC 7 Linux.

I uploaded a fix for this warning. I use clang to build sigh, apologies for the problem.

If the patch has not been reverted, I think it would be better to create a new patch on Phabricator with the fix, so it is easier to see the change.

[greened]

llvm/lib/Analysis/LoopCacheAnalysis.cpp

244

Can we add the value of MaxDistance to this message?

[greened]

Oops, I missed that this landed already. Perhaps a later commit can improve the debug message.

[xbolva00]

/home/xbolva00/LLVM/llvm-project/llvm/lib/Analysis/LoopCacheAnalysis.cpp 353 warn V612 An unconditional 'return' within a loop.
/home/xbolva00/LLVM/llvm-project/llvm/lib/Analysis/LoopCacheAnalysis.cpp 456 err V502 Perhaps the '?:' operator works in a different way than it was expected. The '?:' operator has a lower priority than the '==' operator.

Found by PVS Studio

[xbolva00]

I think it would be good to get an in-tree user of this soon, to make sure the modeling works as expected on real hardware/benchmarks. Do you have a timeline to get this used? I think you mentioned LoopFusion as one of the first planned users?

What about this? Or still dead code?

[Meinersbur]

In D63459#1731015, @xbolva00 wrote:

/home/xbolva00/LLVM/llvm-project/llvm/lib/Analysis/LoopCacheAnalysis.cpp 353 warn V612 An unconditional 'return' within a loop.

This indeed does not look right. There are beaks and returns in the loop, but no continue. Meaning the loop is only iterated for one element (in this case: the innermost loop). I think nothing else than the innermost loop is needed for delinearization, in which case it could be made a conditional instead of a for-statement.

/home/xbolva00/LLVM/llvm-project/llvm/lib/Analysis/LoopCacheAnalysis.cpp 456 err V502 Perhaps the '?:' operator works in a different way than it was expected. The '?:' operator has a lower priority than the '==' operator.

TRT(TRT == None ? Optional<unsigned>(TemporalReuseThreshold) : TRT),

Could add parens around TRT == None to silence the analyzer.

[etiotto]

In D63459#1731032, @Meinersbur wrote:

In D63459#1731015, @xbolva00 wrote:

/home/xbolva00/LLVM/llvm-project/llvm/lib/Analysis/LoopCacheAnalysis.cpp 353 warn V612 An unconditional 'return' within a loop.

This indeed does not look right. There are beaks and returns in the loop, but no continue. Meaning the loop is only iterated for one element (in this case: the innermost loop). I think nothing else than the innermost loop is needed for delinearization, in which case it could be made a conditional instead of a for-statement.

/home/xbolva00/LLVM/llvm-project/llvm/lib/Analysis/LoopCacheAnalysis.cpp 456 err V502 Perhaps the '?:' operator works in a different way than it was expected. The '?:' operator has a lower priority than the '==' operator.

TRT(TRT == None ? Optional<unsigned>(TemporalReuseThreshold) : TRT),

Could add parens around TRT == None to silence the analyzer.

I have submitted a patch for review in https://reviews.llvm.org/D69821.

llvm/include/llvm/Analysis/LoopCacheAnalysis.h

+//===- llvm/Analysis/LoopCacheAnalysis.h ------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+///
+/// \file
+/// This file defines the interface for the loop cache analysis.
+///
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_ANALYSIS_LOOPCACHEANALYSIS_H
+#define LLVM_ANALYSIS_LOOPCACHEANALYSIS_H
+
+#include "llvm/Analysis/AliasAnalysis.h"
+#include "llvm/Analysis/DependenceAnalysis.h"
+#include "llvm/Analysis/LoopAnalysisManager.h"
+#include "llvm/Analysis/LoopInfo.h"
+#include "llvm/Analysis/ScalarEvolution.h"
+#include "llvm/Analysis/TargetTransformInfo.h"
+#include "llvm/IR/Instructions.h"
+#include "llvm/Pass.h"
+#include "llvm/Support/raw_ostream.h"
+
+namespace llvm {
+
+class LPMUpdater;
+using CacheCostTy = int64_t;
+using LoopVectorTy = SmallVector<Loop *, 8>;
+
+/// Represents a memory reference as a base pointer and a set of indexing
+/// operations. For example given the array reference A[i][2j+1][3k+2] in a
+/// 3-dim loop nest:
+///   for(i=0;i<n;++i)
+///     for(j=0;j<m;++j)
+///       for(k=0;k<o;++k)
+///         ... A[i][2j+1][3k+2] ...
+/// We expect:
+///   BasePointer -> A
+///   Subscripts -> [{0,+,1}<%for.i>][{1,+,2}<%for.j>][{2,+,3}<%for.k>]
+///   Sizes -> [m][o][4]
+class IndexedReference {
+  friend raw_ostream &operator<<(raw_ostream &OS, const IndexedReference &R);
+
+public:
+  /// Construct an indexed reference given a \p StoreOrLoadInst instruction.
+  IndexedReference(Instruction &StoreOrLoadInst, const LoopInfo &LI,
+                   ScalarEvolution &SE);
+
+  bool isValid() const { return IsValid; }
+  const SCEV *getBasePointer() const { return BasePointer; }
+  size_t getNumSubscripts() const { return Subscripts.size(); }
+  const SCEV *getSubscript(unsigned SubNum) const {
+    assert(SubNum < getNumSubscripts() && "Invalid subscript number");
+    return Subscripts[SubNum];
+  }
+  const SCEV *getFirstSubscript() const {
+    assert(!Subscripts.empty() && "Expecting non-empty container");
+    return Subscripts.front();
+  }
+  const SCEV *getLastSubscript() const {
+    assert(!Subscripts.empty() && "Expecting non-empty container");
+    return Subscripts.back();
+  }
+
+  /// Return true/false if the current object and the indexed reference \p Other
+  /// are/aren't in the same cache line of size \p CLS. Two references are in
+  /// the same chace line iff the distance between them in the innermost
+  /// dimension is less than the cache line size. Return None if unsure.
+  Optional<bool> hasSpacialReuse(const IndexedReference &Other, unsigned CLS,
+                                 AliasAnalysis &AA) const;
+
+  /// Return true if the current object and the indexed reference \p Other
+  /// have distance smaller than \p MaxDistance in the dimension associated with
+  /// the given loop \p L. Return false if the distance is not smaller than \p
+  /// MaxDistance and None if unsure.
+  Optional<bool> hasTemporalReuse(const IndexedReference &Other,
+                                  unsigned MaxDistance, const Loop &L,
+                                  DependenceInfo &DI, AliasAnalysis &AA) const;
+
+  /// Compute the cost of the reference w.r.t. the given loop \p L when it is
+  /// considered in the innermost position in the loop nest.
+  /// The cost is defined as:
+  ///   - equal to one if the reference is loop invariant, or
+  ///   - equal to '(TripCount * stride) / cache_line_size' if:
+  ///     + the reference stride is less than the cache line size, and
+  ///     + the coefficient of this loop's index variable used in all other
+  ///       subscripts is zero
+  ///   - or otherwise equal to 'TripCount'.
+  CacheCostTy computeRefCost(const Loop &L, unsigned CLS) const;
+
+private:
+  /// Attempt to delinearize the indexed reference.
+  bool delinearize(const LoopInfo &LI);
+
+  /// Return true if the index reference is invariant with respect to loop \p L.
+  bool isLoopInvariant(const Loop &L) const;
+
+  /// Return true if the indexed reference is 'consecutive' in loop \p L.
+  /// An indexed reference is 'consecutive' if the only coefficient that uses
+  /// the loop induction variable is the rightmost one, and the access stride is
+  /// smaller than the cache line size \p CLS.
+  bool isConsecutive(const Loop &L, unsigned CLS) const;
+
+  /// Return the coefficient used in the rightmost dimension.
+  const SCEV *getLastCoefficient() const;
+
+  /// Return true if the coefficient corresponding to induction variable of
+  /// loop \p L in the given \p Subscript is zero or is loop invariant in \p L.
+  bool isCoeffForLoopZeroOrInvariant(const SCEV &Subscript,
+                                     const Loop &L) const;
+
+  /// Verify that the given \p Subscript is 'well formed' (must be a simple add
+  /// recurrence).
+  bool isSimpleAddRecurrence(const SCEV &Subscript, const Loop &L) const;
+
+  /// Return true if the given reference \p Other is definetely aliased with
+  /// the indexed reference represented by this class.
+  bool isAliased(const IndexedReference &Other, AliasAnalysis &AA) const;
+
+private:
+  /// True if the reference can be delinearized, false otherwise.
+  bool IsValid = false;
+
+  /// Represent the memory reference instruction.
+  Instruction &StoreOrLoadInst;
+
+  /// The base pointer of the memory reference.
+  const SCEV *BasePointer = nullptr;
+
+  /// The subscript (indexes) of the memory reference.
+  SmallVector<const SCEV *, 3> Subscripts;
+
+  /// The dimensions of the memory reference.
+  SmallVector<const SCEV *, 3> Sizes;
+
+  ScalarEvolution &SE;
+};
+
+/// A reference group represents a set of memory references that exhibit
+/// temporal or spacial reuse. Two references belong to the same
+/// reference group with respect to a inner loop L iff:
+/// 1. they have a loop independent dependency, or
+/// 2. they have a loop carried dependence with a small dependence distance
+///    (e.g. less than 2) carried by the inner loop, or
+/// 3. they refer to the same array, and the subscript in their innermost
+///    dimension is less than or equal to 'd' (where 'd' is less than the cache
+///    line size)
+///
+/// Intuitively a reference group represents memory references that access
+/// the same cache line. Conditions 1,2 above account for temporal reuse, while
+/// contition 3 accounts for spacial reuse.
+using ReferenceGroupTy = SmallVector<std::unique_ptr<IndexedReference>, 8>;
+using ReferenceGroupsTy = SmallVector<ReferenceGroupTy, 8>;
+
+/// \c CacheCost represents the estimated cost of a inner loop as the number of
+/// cache lines used by the memory references it contains.
+/// The 'cache cost' of a loop 'L' in a loop nest 'LN' is computed as the sum of
+/// the cache costs of all of its reference groups when the loop is considered
+/// to be in the innermost position in the nest.
+/// A reference group represents memory references that fall into the same cache
+/// line. Each reference group is analysed with respect to the innermost loop in
+/// a loop nest. The cost of a reference is defined as follow:
+///  - one if it is loop invariant w.r.t the innermost loop,
+///  - equal to the loop trip count divided by the cache line times the
+///    reference stride if the reference stride is less than the cache line
+///    size (CLS), and the coefficient of this loop's index variable used in all
+///    other subscripts is zero (e.g. RefCost = TripCount/(CLS/RefStride))
+///  - equal to the innermost loop trip count if the reference stride is greater
+///    or equal to the cache line size CLS.
+class CacheCost {
+  friend raw_ostream &operator<<(raw_ostream &OS, const CacheCost &CC);
+  using LoopTripCountTy = std::pair<const Loop *, unsigned>;
+  using LoopCacheCostTy = std::pair<const Loop *, CacheCostTy>;
+
+public:
+  static CacheCostTy constexpr InvalidCost = -1;
+
+  /// Construct a CacheCost object for the loop nest described by \p Loops.
+  /// The optional parameter \p TRT can be used to specify the max. distance
+  /// between array elements accessed in a loop so that the elements are
+  /// classified to have temporal reuse.
+  CacheCost(const LoopVectorTy &Loops, const LoopInfo &LI, ScalarEvolution &SE,
+            TargetTransformInfo &TTI, AliasAnalysis &AA, DependenceInfo &DI,
+            Optional<unsigned> TRT = None);
+
+  /// Create a CacheCost for the loop nest rooted by \p Root.
+  /// The optional parameter \p TRT can be used to specify the max. distance
+  /// between array elements accessed in a loop so that the elements are
+  /// classified to have temporal reuse.
+  static std::unique_ptr<CacheCost>
+  getCacheCost(Loop &Root, LoopStandardAnalysisResults &AR, DependenceInfo &DI,
+               Optional<unsigned> TRT = None);
+
+  /// Return the estimated cost of loop \p L if the given loop is part of the
+  /// loop nest associated with this object. Return -1 otherwise.
+  CacheCostTy getLoopCost(const Loop &L) const {
+    auto IT = std::find_if(
+        LoopCosts.begin(), LoopCosts.end(),
+        [&L](const LoopCacheCostTy &LCC) { return LCC.first == &L; });
+    return (IT != LoopCosts.end()) ? (*IT).second : -1;
+  }
+
+  /// Return the estimated ordered loop costs.
+  const ArrayRef<LoopCacheCostTy> getLoopCosts() const { return LoopCosts; }
+
+private:
+  /// Calculate the cache footprint of each loop in the nest (when it is
+  /// considered to be in the innermost position).
+  void calculateCacheFootprint();
+
+  /// Partition store/load instructions in the loop nest into reference groups.
+  /// Two or more memory accesses belong in the same reference group if they
+  /// share the same cache line.
+  bool populateReferenceGroups(ReferenceGroupsTy &RefGroups) const;
+
+  /// Calculate the cost of the given loop \p L assuming it is the innermost
+  /// loop in nest.
+  CacheCostTy computeLoopCacheCost(const Loop &L,
+                                   const ReferenceGroupsTy &RefGroups) const;
+
+  /// Compute the cost of a representative reference in reference group \p RG
+  /// when the given loop \p L is considered as the innermost loop in the nest.
+  /// The computed cost is an estimate for the number of cache lines used by the
+  /// reference group. The representative reference cost is defined as:
+  ///   - equal to one if the reference is loop invariant, or
+  ///   - equal to '(TripCount * stride) / cache_line_size' if (a) loop \p L's
+  ///     induction variable is used only in the reference subscript associated
+  ///     with loop \p L, and (b) the reference stride is less than the cache
+  ///     line size, or
+  ///   - TripCount otherwise
+  CacheCostTy computeRefGroupCacheCost(const ReferenceGroupTy &RG,
+                                       const Loop &L) const;
+
+  /// Sort the LoopCosts vector by decreasing cache cost.
+  void sortLoopCosts() {
+    sort(LoopCosts, [](const LoopCacheCostTy &A, const LoopCacheCostTy &B) {
+      return A.second > B.second;
+    });
+  }
+
+private:
+  /// Loops in the loop nest associated with this object.
+  LoopVectorTy Loops;
+
+  /// Trip counts for the loops in the loop nest associated with this object.
+  SmallVector<LoopTripCountTy, 3> TripCounts;
+
+  /// Cache costs for the loops in the loop nest associated with this object.
+  SmallVector<LoopCacheCostTy, 3> LoopCosts;
+
+  /// The max. distance between array elements accessed in a loop so that the
+  /// elements are classified to have temporal reuse.
+  Optional<unsigned> TRT;
+
+  const LoopInfo &LI;
+  ScalarEvolution &SE;
+  TargetTransformInfo &TTI;
+  AliasAnalysis &AA;
+  DependenceInfo &DI;
+};
+
+raw_ostream &operator<<(raw_ostream &OS, const IndexedReference &R);
+raw_ostream &operator<<(raw_ostream &OS, const CacheCost &CC);
+
+/// Printer pass for the \c CacheCost results.
+class LoopCachePrinterPass : public PassInfoMixin<LoopCachePrinterPass> {
+  raw_ostream &OS;
+
+public:
+  explicit LoopCachePrinterPass(raw_ostream &OS) : OS(OS) {}
+
+  PreservedAnalyses run(Loop &L, LoopAnalysisManager &AM,
+                        LoopStandardAnalysisResults &AR, LPMUpdater &U);
+};
+
+} // namespace llvm
+
+#endif // LLVM_ANALYSIS_LOOPCACHEANALYSIS_H

llvm/lib/Analysis/CMakeLists.txt

add_llvm_library(LLVMAnalysis
   LazyBlockFrequencyInfo.cpp
   LazyCallGraph.cpp
   LazyValueInfo.cpp
   LegacyDivergenceAnalysis.cpp
   Lint.cpp
   Loads.cpp
   LoopAccessAnalysis.cpp
   LoopAnalysisManager.cpp
+  LoopCacheAnalysis.cpp
   LoopUnrollAnalyzer.cpp
   LoopInfo.cpp
   LoopPass.cpp
   MemDepPrinter.cpp
   MemDerefPrinter.cpp
   MemoryBuiltins.cpp
   MemoryDependenceAnalysis.cpp
   MemoryLocation.cpp

llvm/lib/Analysis/LoopCacheAnalysis.cpp

+//===- LoopCacheAnalysis.cpp - Loop Cache Analysis -------------------------==//
+//
+//                     The LLVM Compiler Infrastructure
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+///
+/// \file
+/// This file defines the implementation for the loop cache analysis.
+/// The implementation is largely based on the following paper:
+///
+///       Compiler Optimizations for Improving Data Locality
+///       By: Steve Carr, Katherine S. McKinley, Chau-Wen Tseng
+///       http://www.cs.utexas.edu/users/mckinley/papers/asplos-1994.pdf
+///
+/// The general approach taken to estimate the number of cache lines used by the
+/// memory references in an inner loop is:
+///    1. Partition memory references that exhibit temporal or spacial reuse
+///       into reference groups.
+///    2. For each loop L in the a loop nest LN:
+///       a. Compute the cost of the reference group
+///       b. Compute the loop cost by summing up the reference groups costs
+//===----------------------------------------------------------------------===//
+
+#include "llvm/Analysis/LoopCacheAnalysis.h"
+#include "llvm/ADT/BreadthFirstIterator.h"
+#include "llvm/ADT/Sequence.h"
+#include "llvm/ADT/SmallVector.h"
+#include "llvm/Support/Debug.h"
+
+using namespace llvm;
+
+#define DEBUG_TYPE "loop-cache-cost"
+
+static cl::opt<unsigned> DefaultTripCount(
+    "default-trip-count", cl::init(100), cl::Hidden,
+    cl::desc("Use this to specify the default trip count of a loop"));
+
+// In this analysis two array references are considered to exhibit temporal
+// reuse if they access either the same memory location, or a memory location
+// with distance smaller than a configurable threshold.
+static cl::opt<unsigned> TemporalReuseThreshold(
+    "temporal-reuse-threshold", cl::init(2), cl::Hidden,
+    cl::desc("Use this to specify the max. distance between array elements "
+             "accessed in a loop so that the elements are classified to have "
+             "temporal reuse"));
+
+/// Retrieve the innermost loop in the given loop nest \p Loops. It returns a
+/// nullptr if any loops in the loop vector supplied has more than one sibling.
+/// The loop vector is expected to contain loops collected in breadth-first
+/// order.
+static Loop *getInnerMostLoop(const LoopVectorTy &Loops) {
+  assert(!Loops.empty() && "Expecting a non-empy loop vector");
+
+  Loop *LastLoop = Loops.back();
+  Loop *ParentLoop = LastLoop->getParentLoop();
+
+  if (ParentLoop == nullptr) {
+    assert(Loops.size() == 1 && "Expecting a single loop");
+    return LastLoop;
+  }
+
+  return (std::is_sorted(Loops.begin(), Loops.end(),
+                         [](const Loop *L1, const Loop *L2) {
+                           return L1->getLoopDepth() < L2->getLoopDepth();
+                         }))
+             ? LastLoop
+             : nullptr;
+}
+
+static bool isOneDimensionalArray(const SCEV &AccessFn, const SCEV &ElemSize,
+                                  const Loop &L, ScalarEvolution &SE) {
+  const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(&AccessFn);
+  if (!AR || !AR->isAffine())
+    return false;
+
+  assert(AR->getLoop() && "AR should have a loop");
+
+  // Check that start and increment are not add recurrences.
+  const SCEV *Start = AR->getStart();
+  const SCEV *Step = AR->getStepRecurrence(SE);
+  if (isa<SCEVAddRecExpr>(Start) || isa<SCEVAddRecExpr>(Step))
+    return false;
+
+  // Check that start and increment are both invariant in the loop.
+  if (!SE.isLoopInvariant(Start, &L) || !SE.isLoopInvariant(Step, &L))
+    return false;
+
+  return AR->getStepRecurrence(SE) == &ElemSize;
+}
+
+/// Compute the trip count for the given loop \p L. Return the SCEV expression
+/// for the trip count or nullptr if it cannot be computed.
+static const SCEV *computeTripCount(const Loop &L, ScalarEvolution &SE) {
+  const SCEV *BackedgeTakenCount = SE.getBackedgeTakenCount(&L);
+  if (isa<SCEVCouldNotCompute>(BackedgeTakenCount) ||
+      !isa<SCEVConstant>(BackedgeTakenCount))
+    return nullptr;
+
+  return SE.getAddExpr(BackedgeTakenCount,
+                       SE.getOne(BackedgeTakenCount->getType()));
+}
+
+//===----------------------------------------------------------------------===//
+// IndexedReference implementation
+//
+raw_ostream &llvm::operator<<(raw_ostream &OS, const IndexedReference &R) {
+  if (!R.IsValid) {
+    OS << R.StoreOrLoadInst;
+    OS << ", IsValid=false.";
+    return OS;
+  }
+
+  OS << *R.BasePointer;
+  for (const SCEV *Subscript : R.Subscripts)
+    OS << "[" << *Subscript << "]";
+
+  OS << ", Sizes: ";
+  for (const SCEV *Size : R.Sizes)
+    OS << "[" << *Size << "]";
+
+  return OS;
+}
+
+IndexedReference::IndexedReference(Instruction &StoreOrLoadInst,
+                                   const LoopInfo &LI, ScalarEvolution &SE)
+    : StoreOrLoadInst(StoreOrLoadInst), SE(SE) {
+  assert((isa<StoreInst>(StoreOrLoadInst) || isa<LoadInst>(StoreOrLoadInst)) &&
+         "Expecting a load or store instruction");
+
+  IsValid = delinearize(LI);
+  if (IsValid)
+    LLVM_DEBUG(dbgs().indent(2) << "Succesfully delinearized: " << *this
+                                << "\n");
+}
+
+Optional<bool> IndexedReference::hasSpacialReuse(const IndexedReference &Other,
+                                                 unsigned CLS,
+                                                 AliasAnalysis &AA) const {
+  assert(IsValid && "Expecting a valid reference");
+
+  if (BasePointer != Other.getBasePointer() && !isAliased(Other, AA)) {
+    LLVM_DEBUG(dbgs().indent(2)
+               << "No spacial reuse: different base pointers\n");
+    return false;
+  }
+
+  unsigned NumSubscripts = getNumSubscripts();
+  if (NumSubscripts != Other.getNumSubscripts()) {
+    LLVM_DEBUG(dbgs().indent(2)
+               << "No spacial reuse: different number of subscripts\n");
+    return false;
+  }
+
+  // all subscripts must be equal, except the leftmost one (the last one).
+  for (auto SubNum : seq<unsigned>(0, NumSubscripts - 1)) {
+    if (getSubscript(SubNum) != Other.getSubscript(SubNum)) {
+      LLVM_DEBUG(dbgs().indent(2) << "No spacial reuse, different subscripts: "
+                                  << "\n\t" << *getSubscript(SubNum) << "\n\t"
+                                  << *Other.getSubscript(SubNum) << "\n");
+      return false;
+    }
+  }
+
+  // the difference between the last subscripts must be less than the cache line
+  // size.
+  const SCEV *LastSubscript = getLastSubscript();
+  const SCEV *OtherLastSubscript = Other.getLastSubscript();
+  const SCEVConstant *Diff = dyn_cast<SCEVConstant>(
+      SE.getMinusSCEV(LastSubscript, OtherLastSubscript));
+
+  if (Diff == nullptr) {
+    LLVM_DEBUG(dbgs().indent(2)
+               << "No spacial reuse, difference between subscript:\n\t"
+               << *LastSubscript << "\n\t" << OtherLastSubscript
+               << "\nis not constant.\n");
+    return None;
+  }
+
+  bool InSameCacheLine = (Diff->getValue()->getSExtValue() < CLS);
+
+  LLVM_DEBUG({
+    if (InSameCacheLine)
+      dbgs().indent(2) << "Found spacial reuse.\n";
+    else
+      dbgs().indent(2) << "No spacial reuse.\n";
+  });
+
+  return InSameCacheLine;
+}
+
+Optional<bool> IndexedReference::hasTemporalReuse(const IndexedReference &Other,
+                                                  unsigned MaxDistance,
+                                                  const Loop &L,
+                                                  DependenceInfo &DI,
+                                                  AliasAnalysis &AA) const {
+  assert(IsValid && "Expecting a valid reference");
+
+  if (BasePointer != Other.getBasePointer() && !isAliased(Other, AA)) {
+    LLVM_DEBUG(dbgs().indent(2)
+               << "No temporal reuse: different base pointer\n");
+    return false;
+  }
+
+  std::unique_ptr<Dependence> D =
+      DI.depends(&StoreOrLoadInst, &Other.StoreOrLoadInst, true);
+
+  if (D == nullptr) {
+    LLVM_DEBUG(dbgs().indent(2) << "No temporal reuse: no dependence\n");
+    return false;
+  }
+
+  if (D->isLoopIndependent()) {
+    LLVM_DEBUG(dbgs().indent(2) << "Found temporal reuse\n");
+    return true;
+  }
+
+  // Check the dependence distance at every loop level. There is temporal reuse
+  // if the distance at the given loop's depth is small (|d| <= MaxDistance) and
+  // it is zero at every other loop level.
+  int LoopDepth = L.getLoopDepth();
+  int Levels = D->getLevels();
+  for (int Level = 1; Level <= Levels; ++Level) {
+    const SCEV *Distance = D->getDistance(Level);
+    const SCEVConstant *SCEVConst = dyn_cast_or_null<SCEVConstant>(Distance);
+
+    if (SCEVConst == nullptr) {
+      LLVM_DEBUG(dbgs().indent(2) << "No temporal reuse: distance unknown\n");
+      return None;
+    }
+
+    const ConstantInt &CI = *SCEVConst->getValue();
+    if (Level != LoopDepth && !CI.isZero()) {
+      LLVM_DEBUG(dbgs().indent(2)
+                 << "No temporal reuse: distance is not zero at depth=" << Level
+                 << "\n");
+      return false;
+    } else if (Level == LoopDepth && CI.getSExtValue() > MaxDistance) {
+      LLVM_DEBUG(
+          dbgs().indent(2)
+          << "No temporal reuse: distance is greater than MaxDistance at depth="
+          << Level << "\n");
+      return false;
+    }
+  }
+
+  LLVM_DEBUG(dbgs().indent(2) << "Found temporal reuse\n");
+  return true;
+}
+
+CacheCostTy IndexedReference::computeRefCost(const Loop &L,
+                                             unsigned CLS) const {
+  assert(IsValid && "Expecting a valid reference");
+  LLVM_DEBUG({
+    dbgs().indent(2) << "Computing cache cost for:\n";
+    dbgs().indent(4) << *this << "\n";
+  });
+
+  // If the indexed reference is loop invariant the cost is one.
+  if (isLoopInvariant(L)) {
+    LLVM_DEBUG(dbgs().indent(4) << "Reference is loop invariant: RefCost=1\n");
+    return 1;
+  }
+
+  const SCEV *TripCount = computeTripCount(L, SE);
+  if (!TripCount) {
+    LLVM_DEBUG(dbgs() << "Trip count of loop " << L.getName()
+                      << " could not be computed, using DefaultTripCount\n");
+    const SCEV *ElemSize = Sizes.back();
+    TripCount = SE.getConstant(ElemSize->getType(), DefaultTripCount);
+  }
+  LLVM_DEBUG(dbgs() << "TripCount=" << *TripCount << "\n");
+
+  // If the indexed reference is 'consecutive' the cost is
+  // (TripCount*Stride)/CLS, otherwise the cost is TripCount.
+  const SCEV *RefCost = TripCount;
+
+  if (isConsecutive(L, CLS)) {
+    const SCEV *Coeff = getLastCoefficient();
+    const SCEV *ElemSize = Sizes.back();
+    const SCEV *Stride = SE.getMulExpr(Coeff, ElemSize);
+    const SCEV *CacheLineSize = SE.getConstant(Stride->getType(), CLS);
+    const SCEV *Numerator = SE.getMulExpr(Stride, TripCount);
+    RefCost = SE.getUDivExpr(Numerator, CacheLineSize);
+    LLVM_DEBUG(dbgs().indent(4)
+               << "Access is consecutive: RefCost=(TripCount*Stride)/CLS="
+               << *RefCost << "\n");
+  } else
+    LLVM_DEBUG(dbgs().indent(4)
+               << "Access is not consecutive: RefCost=TripCount=" << *RefCost
+               << "\n");
+
+  // Attempt to fold RefCost into a constant.
+  if (auto ConstantCost = dyn_cast<SCEVConstant>(RefCost))
+    return ConstantCost->getValue()->getSExtValue();
+
+  LLVM_DEBUG(dbgs().indent(4)
+             << "RefCost is not a constant! Setting to RefCost=InvalidCost "
+                "(invalid value).\n");
+
+  return CacheCost::InvalidCost;
+}
+
+bool IndexedReference::delinearize(const LoopInfo &LI) {
+  assert(Subscripts.empty() && "Subscripts should be empty");
+  assert(Sizes.empty() && "Sizes should be empty");
+  assert(!IsValid && "Should be called once from the constructor");
+  LLVM_DEBUG(dbgs() << "Delinearizing: " << StoreOrLoadInst << "\n");
+
+  const SCEV *ElemSize = SE.getElementSize(&StoreOrLoadInst);
+  const BasicBlock *BB = StoreOrLoadInst.getParent();
+
+  for (Loop *L = LI.getLoopFor(BB); L != nullptr; L = L->getParentLoop()) {
+    const SCEV *AccessFn =
+        SE.getSCEVAtScope(getPointerOperand(&StoreOrLoadInst), L);
+
+    BasePointer = dyn_cast<SCEVUnknown>(SE.getPointerBase(AccessFn));
+    if (BasePointer == nullptr) {
+      LLVM_DEBUG(
+          dbgs().indent(2)
+          << "ERROR: failed to delinearize, can't identify base pointer\n");
+      return false;
+    }
+
+    AccessFn = SE.getMinusSCEV(AccessFn, BasePointer);
+
+    LLVM_DEBUG(dbgs().indent(2) << "In Loop '" << L->getName()
+                                << "', AccessFn: " << *AccessFn << "\n");
+
+    SE.delinearize(AccessFn, Subscripts, Sizes,
+                   SE.getElementSize(&StoreOrLoadInst));
+
+    if (Subscripts.empty() || Sizes.empty() ||
+        Subscripts.size() != Sizes.size()) {
+      // Attempt to determine whether we have a single dimensional array access.
+      // before giving up.
+      if (!isOneDimensionalArray(*AccessFn, *ElemSize, *L, SE)) {
+        LLVM_DEBUG(dbgs().indent(2)
+                   << "ERROR: failed to delinearize reference\n");
+        Subscripts.clear();
+        Sizes.clear();
+        break;
+      }
+
+      const SCEV *Div = SE.getUDivExactExpr(AccessFn, ElemSize);
+      Subscripts.push_back(Div);
+      Sizes.push_back(ElemSize);
+    }
+
+    return all_of(Subscripts, [&](const SCEV *Subscript) {
+      return isSimpleAddRecurrence(*Subscript, *L);
+    });
+  }
+
+  return false;
+}
+
+bool IndexedReference::isLoopInvariant(const Loop &L) const {
+  Value *Addr = getPointerOperand(&StoreOrLoadInst);
+  assert(Addr != nullptr && "Expecting either a load or a store instruction");
+  assert(SE.isSCEVable(Addr->getType()) && "Addr should be SCEVable");
+
+  if (SE.isLoopInvariant(SE.getSCEV(Addr), &L))
+    return true;
+
+  // The indexed reference is loop invariant if none of the coefficients use
+  // the loop induction variable.
+  bool allCoeffForLoopAreZero = all_of(Subscripts, [&](const SCEV *Subscript) {
+    return isCoeffForLoopZeroOrInvariant(*Subscript, L);
+  });
+
+  return allCoeffForLoopAreZero;
+}
+
+bool IndexedReference::isConsecutive(const Loop &L, unsigned CLS) const {
+  // The indexed reference is 'consecutive' if the only coefficient that uses
+  // the loop induction variable is the last one...
+  const SCEV *LastSubscript = Subscripts.back();
+  for (const SCEV *Subscript : Subscripts) {
+    if (Subscript == LastSubscript)
+      continue;
+    if (!isCoeffForLoopZeroOrInvariant(*Subscript, L))
+      return false;
+  }
+
+  // ...and the access stride is less than the cache line size.
+  const SCEV *Coeff = getLastCoefficient();
+  const SCEV *ElemSize = Sizes.back();
+  const SCEV *Stride = SE.getMulExpr(Coeff, ElemSize);
+  const SCEV *CacheLineSize = SE.getConstant(Stride->getType(), CLS);
+
+  return SE.isKnownPredicate(ICmpInst::ICMP_ULT, Stride, CacheLineSize);
+}
+
+const SCEV *IndexedReference::getLastCoefficient() const {
+  const SCEV *LastSubscript = getLastSubscript();
+  assert(isa<SCEVAddRecExpr>(LastSubscript) &&
+         "Expecting a SCEV add recurrence expression");
+  const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LastSubscript);
+  return AR->getStepRecurrence(SE);
+}
+
+bool IndexedReference::isCoeffForLoopZeroOrInvariant(const SCEV &Subscript,
+                                                     const Loop &L) const {
+  const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(&Subscript);
+  return (AR != nullptr) ? AR->getLoop() != &L
+                         : SE.isLoopInvariant(&Subscript, &L);
+}
+
+bool IndexedReference::isSimpleAddRecurrence(const SCEV &Subscript,
+                                             const Loop &L) const {
+  if (!isa<SCEVAddRecExpr>(Subscript))
+    return false;
+
+  const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(&Subscript);
+  assert(AR->getLoop() && "AR should have a loop");
+
+  if (!AR->isAffine())
+    return false;
+
+  const SCEV *Start = AR->getStart();
+  const SCEV *Step = AR->getStepRecurrence(SE);
+
+  if (!SE.isLoopInvariant(Start, &L) || !SE.isLoopInvariant(Step, &L))
+    return false;
+
+  return true;
+}
+
+bool IndexedReference::isAliased(const IndexedReference &Other,
+                                 AliasAnalysis &AA) const {
+  const auto &Loc1 = MemoryLocation::get(&StoreOrLoadInst);
+  const auto &Loc2 = MemoryLocation::get(&Other.StoreOrLoadInst);
+  return AA.isMustAlias(Loc1, Loc2);
+}
+
+//===----------------------------------------------------------------------===//
+// CacheCost implementation
+//
+raw_ostream &llvm::operator<<(raw_ostream &OS, const CacheCost &CC) {
+  for (const auto &LC : CC.LoopCosts) {
+    const Loop *L = LC.first;
+    OS << "Loop '" << L->getName() << "' has cost = " << LC.second << "\n";
+  }
+  return OS;
+}
+
+CacheCost::CacheCost(const LoopVectorTy &Loops, const LoopInfo &LI,
+                     ScalarEvolution &SE, TargetTransformInfo &TTI,
+                     AliasAnalysis &AA, DependenceInfo &DI,
+                     Optional<unsigned> TRT)
+    : Loops(Loops), TripCounts(), LoopCosts(),
+      TRT(TRT == None ? Optional<unsigned>(TemporalReuseThreshold) : TRT),
+      LI(LI), SE(SE), TTI(TTI), AA(AA), DI(DI) {
+  assert(!Loops.empty() && "Expecting a non-empty loop vector.");
+
+  for (const Loop *L : Loops) {
+    unsigned TripCount = SE.getSmallConstantTripCount(L);
+    TripCount = (TripCount == 0) ? DefaultTripCount : TripCount;
+    TripCounts.push_back({L, TripCount});
+  }
+
+  calculateCacheFootprint();
+}
+
+std::unique_ptr<CacheCost>
+CacheCost::getCacheCost(Loop &Root, LoopStandardAnalysisResults &AR,
+                        DependenceInfo &DI, Optional<unsigned> TRT) {
+  if (Root.getParentLoop()) {
+    LLVM_DEBUG(dbgs() << "Expecting the outermost loop in a loop nest\n");
+    return nullptr;
+  }
+
+  LoopVectorTy Loops;
+  for (Loop *L : breadth_first(&Root))
+    Loops.push_back(L);
+
+  if (!getInnerMostLoop(Loops)) {
+    LLVM_DEBUG(dbgs() << "Cannot compute cache cost of loop nest with more "
+                         "than one innermost loop\n");
+    return nullptr;
+  }
+
+  return make_unique<CacheCost>(Loops, AR.LI, AR.SE, AR.TTI, AR.AA, DI, TRT);
+}
+
+void CacheCost::calculateCacheFootprint() {
+  LLVM_DEBUG(dbgs() << "POPULATING REFERENCE GROUPS\n");
+  ReferenceGroupsTy RefGroups;
+  if (!populateReferenceGroups(RefGroups))
+    return;
+
+  LLVM_DEBUG(dbgs() << "COMPUTING LOOP CACHE COSTS\n");
+  for (const Loop *L : Loops) {
+    assert((std::find_if(LoopCosts.begin(), LoopCosts.end(),
+                         [L](const LoopCacheCostTy &LCC) {
+                           return LCC.first == L;
+                         }) == LoopCosts.end()) &&
+           "Should not add duplicate element");
+    CacheCostTy LoopCost = computeLoopCacheCost(*L, RefGroups);
+    LoopCosts.push_back(std::make_pair(L, LoopCost));
+  }
+
+  sortLoopCosts();
+  RefGroups.clear();
+}
+
+bool CacheCost::populateReferenceGroups(ReferenceGroupsTy &RefGroups) const {
+  assert(RefGroups.empty() && "Reference groups should be empty");
+
+  unsigned CLS = TTI.getCacheLineSize();
+  Loop *InnerMostLoop = getInnerMostLoop(Loops);
+  assert(InnerMostLoop != nullptr && "Expecting a valid innermost loop");
+
+  for (BasicBlock *BB : InnerMostLoop->getBlocks()) {
+    for (Instruction &I : *BB) {
+      if (!isa<StoreInst>(I) && !isa<LoadInst>(I))
+        continue;
+
+      std::unique_ptr<IndexedReference> R(new IndexedReference(I, LI, SE));
+      if (!R->isValid())
+        continue;
+
+      bool Added = false;
+      for (ReferenceGroupTy &RefGroup : RefGroups) {
+        const IndexedReference &Representative = *RefGroup.front().get();
+        LLVM_DEBUG({
+          dbgs() << "References:\n";
+          dbgs().indent(2) << *R << "\n";
+          dbgs().indent(2) << Representative << "\n";
+        });
+
+        Optional<bool> HasTemporalReuse =
+            R->hasTemporalReuse(Representative, *TRT, *InnerMostLoop, DI, AA);
+        Optional<bool> HasSpacialReuse =
+            R->hasSpacialReuse(Representative, CLS, AA);
+
+        if ((HasTemporalReuse.hasValue() && *HasTemporalReuse) ||
+            (HasSpacialReuse.hasValue() && *HasSpacialReuse)) {
+          RefGroup.push_back(std::move(R));
+          Added = true;
+          break;
+        }
+      }
+
+      if (!Added) {
+        ReferenceGroupTy RG;
+        RG.push_back(std::move(R));
+        RefGroups.push_back(std::move(RG));
+      }
+    }
+  }
+
+  if (RefGroups.empty())
+    return false;
+
+  LLVM_DEBUG({
+    dbgs() << "\nIDENTIFIED REFERENCE GROUPS:\n";
+    int n = 1;
+    for (const ReferenceGroupTy &RG : RefGroups) {
+      dbgs().indent(2) << "RefGroup " << n << ":\n";
+      for (const auto &IR : RG)
+        dbgs().indent(4) << *IR << "\n";
+      n++;
+    }
+    dbgs() << "\n";
+  });
+
+  return true;
+}
+
+CacheCostTy
+CacheCost::computeLoopCacheCost(const Loop &L,
+                                const ReferenceGroupsTy &RefGroups) const {
+  if (!L.isLoopSimplifyForm())
+    return InvalidCost;
+
+  LLVM_DEBUG(dbgs() << "Considering loop '" << L.getName()
+                    << "' as innermost loop.\n");
+
+  // Compute the product of the trip counts of each other loop in the nest.
+  CacheCostTy TripCountsProduct = 1;
+  for (const auto &TC : TripCounts) {
+    if (TC.first == &L)
+      continue;
+    TripCountsProduct *= TC.second;
+  }
+
+  CacheCostTy LoopCost = 0;
+  for (const ReferenceGroupTy &RG : RefGroups) {
+    CacheCostTy RefGroupCost = computeRefGroupCacheCost(RG, L);
+    LoopCost += RefGroupCost * TripCountsProduct;
+  }
+
+  LLVM_DEBUG(dbgs().indent(2) << "Loop '" << L.getName()
+                              << "' has cost=" << LoopCost << "\n");
+
+  return LoopCost;
+}
+
+CacheCostTy CacheCost::computeRefGroupCacheCost(const ReferenceGroupTy &RG,
+                                                const Loop &L) const {
+  assert(!RG.empty() && "Reference group should have at least one member.");
+
+  const IndexedReference *Representative = RG.front().get();
+  return Representative->computeRefCost(L, TTI.getCacheLineSize());
+}
+
+//===----------------------------------------------------------------------===//
+// LoopCachePrinterPass implementation
+//
+PreservedAnalyses LoopCachePrinterPass::run(Loop &L, LoopAnalysisManager &AM,
+                                            LoopStandardAnalysisResults &AR,
+                                            LPMUpdater &U) {
+  Function *F = L.getHeader()->getParent();
+  DependenceInfo DI(F, &AR.AA, &AR.SE, &AR.LI);
+
+  if (auto CC = CacheCost::getCacheCost(L, AR, DI))
+    OS << *CC;
+
+  return PreservedAnalyses::all();
+}

llvm/lib/Passes/PassBuilder.cpp

 #include "llvm/Analysis/DemandedBits.h"
 #include "llvm/Analysis/DependenceAnalysis.h"
 #include "llvm/Analysis/DominanceFrontier.h"
 #include "llvm/Analysis/GlobalsModRef.h"
 #include "llvm/Analysis/IVUsers.h"
 #include "llvm/Analysis/LazyCallGraph.h"
 #include "llvm/Analysis/LazyValueInfo.h"
 #include "llvm/Analysis/LoopAccessAnalysis.h"
+#include "llvm/Analysis/LoopCacheAnalysis.h"
 #include "llvm/Analysis/LoopInfo.h"
 #include "llvm/Analysis/MemoryDependenceAnalysis.h"
 #include "llvm/Analysis/MemorySSA.h"
 #include "llvm/Analysis/ModuleSummaryAnalysis.h"
 #include "llvm/Analysis/OptimizationRemarkEmitter.h"
 #include "llvm/Analysis/PhiValues.h"
 #include "llvm/Analysis/PostDominators.h"
 #include "llvm/Analysis/ProfileSummaryInfo.h"

llvm/lib/Passes/PassRegistry.def

 LOOP_PASS("simplify-cfg", LoopSimplifyCFGPass())
 LOOP_PASS("strength-reduce", LoopStrengthReducePass())
 LOOP_PASS("indvars", IndVarSimplifyPass())
 LOOP_PASS("irce", IRCEPass())
 LOOP_PASS("unroll-and-jam", LoopUnrollAndJamPass())
 LOOP_PASS("unroll-full", LoopFullUnrollPass())
 LOOP_PASS("print-access-info", LoopAccessInfoPrinterPass(dbgs()))
 LOOP_PASS("print<ivusers>", IVUsersPrinterPass(dbgs()))
+LOOP_PASS("print<loop-cache-cost>", LoopCachePrinterPass(dbgs()))
 LOOP_PASS("loop-predication", LoopPredicationPass())
 LOOP_PASS("guard-widening", GuardWideningPass())
 #undef LOOP_PASS
 
 #ifndef LOOP_PASS_WITH_PARAMS
 #define LOOP_PASS_WITH_PARAMS(NAME, CREATE_PASS, PARSER)
 #endif
 LOOP_PASS_WITH_PARAMS("unswitch",
                            [](bool NonTrivial) {
                              return SimpleLoopUnswitchPass(NonTrivial);
                            },
                            parseLoopUnswitchOptions)
 #undef LOOP_PASS_WITH_PARAMS

llvm/test/Analysis/LoopCacheAnalysis/PowerPC/lit.local.cfg

+if not 'PowerPC' in config.root.targets:
+    config.unsupported = True

llvm/test/Analysis/LoopCacheAnalysis/PowerPC/loads-store.ll

+; RUN: opt < %s -passes='print<loop-cache-cost>' -disable-output 2>&1 | FileCheck %s
+
+target datalayout = "e-m:e-i64:64-n32:64"
+target triple = "powerpc64le-unknown-linux-gnu"
+
+; void foo(long n, long m, long o, int A[n][m][o], int B[n][m][o], int C[n][m][o]) {
+;   for (long i = 0; i < n; i++)
+;     for (long j = 0; j < m; j++)
+;       for (long k = 0; k < o; k++)
+;         A[i][k][j] += B[i][k][j] + C[i][j][k];
+; }
+
+; CHECK-DAG: Loop 'for.i' has cost = 3000000
+; CHECK-DAG: Loop 'for.k' has cost = 2030000
+; CHECK-DAG: Loop 'for.j' has cost = 1060000
+
+define void @foo(i64 %n, i64 %m, i64 %o, i32* %A, i32* %B, i32* %C) {
+entry:
+  %cmp32 = icmp sgt i64 %n, 0
+  %cmp230 = icmp sgt i64 %m, 0
+  %cmp528 = icmp sgt i64 %o, 0
+  br i1 %cmp32, label %for.cond1.preheader.lr.ph, label %for.end
+
+for.cond1.preheader.lr.ph:                        ; preds = %entry
+  br i1 %cmp230, label %for.i.preheader, label %for.end
+
+for.i.preheader:                                  ; preds = %for.cond1.preheader.lr.ph
+  br i1 %cmp528, label %for.i.preheader.split, label %for.end
+
+for.i.preheader.split:                            ; preds = %for.i.preheader
+  br label %for.i
+
+for.i:                                            ; preds = %for.inci, %for.i.preheader.split
+  %i = phi i64 [ %inci, %for.inci ], [ 0, %for.i.preheader.split ]
+  %muli = mul i64 %i, %m
+  br label %for.j
+
+for.j:                                            ; preds = %for.incj, %for.i
+  %j = phi i64 [ %incj, %for.incj ], [ 0, %for.i ]
+  %addj = add i64 %muli, %j
+  %mulj = mul i64 %addj, %o
+  br label %for.k
+
+for.k:                                            ; preds = %for.k, %for.j
+  %k = phi i64 [ 0, %for.j ], [ %inck, %for.k ]
+
+  ; B[i][k][j]
+  %addk = add i64 %muli, %k
+  %mulk = mul i64 %addk, %o
+  %arrayidx1 = add i64 %j, %mulk
+  %arrayidx2 = getelementptr inbounds i32, i32* %B, i64 %arrayidx1
+  %elem_B = load i32, i32* %arrayidx2, align 4
+
+  ; C[i][j][k]
+  %arrayidx3 = add i64 %k, %mulj
+  %arrayidx4 = getelementptr inbounds i32, i32* %C, i64 %arrayidx3
+  %elem_C = load i32, i32* %arrayidx4, align 4
+
+  ; A[i][k][j]
+  %arrayidx5 = getelementptr inbounds i32, i32* %A, i64 %arrayidx1
+  %elem_A = load i32, i32* %arrayidx5, align 4
+
+  ; A[i][k][j] += B[i][k][j] + C[i][j][k]
+  %add1 = add i32 %elem_B, %elem_C
+  %add2 = add i32 %add1, %elem_A
+  %arrayidx6 = getelementptr inbounds i32, i32* %A, i64 %arrayidx1
+  store i32 %add2, i32* %arrayidx6, align 4
+
+  %inck = add nsw i64 %k, 1
+  %exitcond.us = icmp eq i64 %inck, %o
+  br i1 %exitcond.us, label %for.incj, label %for.k
+
+for.incj:                                         ; preds = %for.k
+  %incj = add nsw i64 %j, 1
+  %exitcond54.us = icmp eq i64 %incj, %m
+  br i1 %exitcond54.us, label %for.inci, label %for.j
+
+for.inci:                                         ; preds = %for.incj
+  %inci = add nsw i64 %i, 1
+  %exitcond55.us = icmp eq i64 %inci, %n
+  br i1 %exitcond55.us, label %for.end.loopexit, label %for.i
+
+for.end.loopexit:                                 ; preds = %for.inci
+  br label %for.end
+
+for.end:                                          ; preds = %for.end.loopexit, %for.cond1.preheader.lr.ph, %entry
+  ret void
+}

llvm/test/Analysis/LoopCacheAnalysis/PowerPC/matmul.ll

+; RUN: opt < %s -passes='print<loop-cache-cost>' -disable-output 2>&1 | FileCheck %s
+
+target datalayout = "e-m:e-i64:64-n32:64"
+target triple = "powerpc64le-unknown-linux-gnu"
+
+; void matmul(long n, long m, long o, int A[n][m], int B[n][m], int C[n]) {
+;   for (long i = 0; i < n; i++) 
+;     for (long j = 0; j < m; j++) 
+;       for (long k = 0; k < o; k++) 
+;         C[i][j] = C[i][j] + A[i][k] * B[k][j];
+; }
+
+; CHECK-DAG:Loop 'for.i' has cost = 2010000
+; CHECK-DAG:Loop 'for.k' has cost = 1040000
+; CHECK-DAG:Loop 'for.j' has cost = 70000
+    
+define void @matmul(i64 %n, i64 %m, i64 %o, i32* %A, i32* %B, i32* %C) {
+entry:
+  br label %for.i
+
+for.i:                                         ; preds = %entry, %for.inc.i
+  %i = phi i64 [ 0, %entry ], [ %i.next, %for.inc.i ]
+  %muli = mul i64 %i, %m
+  br label %for.j
+
+for.j:                                        ; preds = %for.i, %for.inc.j
+  %j = phi i64 [ 0, %for.i ], [ %j.next, %for.inc.j ]
+  %addj = add i64 %muli, %j
+  %mulj = mul i64 %addj, %o
+  br label %for.k
+
+for.k:                                        ; preds = %for.j, %for.inc.k
+  %k = phi i64 [ 0, %for.j ], [ %k.next, %for.inc.k ]
+
+  ; A[i][k]
+  %arrayidx3 = add i64 %k, %muli
+  %arrayidx4 = getelementptr inbounds i32, i32* %A, i64 %arrayidx3
+  %elem_A = load i32, i32* %arrayidx4, align 4
+
+  ; B[k][j]
+  %mulk = mul i64 %k, %o
+  %arrayidx5 = add i64 %j, %mulk
+  %arrayidx6 = getelementptr inbounds i32, i32* %B, i64 %arrayidx5
+  %elem_B = load i32, i32* %arrayidx6, align 4
+
+  ; C[i][k]
+  %arrayidx7 = add i64 %j, %muli
+  %arrayidx8 = getelementptr inbounds i32, i32* %C, i64 %arrayidx7
+  %elem_C = load i32, i32* %arrayidx8, align 4
+
+  ; C[i][j] = C[i][j] + A[i][k] * B[k][j];
+  %mul = mul nsw i32 %elem_A, %elem_B
+  %add = add nsw i32 %elem_C, %mul
+  store i32 %add, i32* %arrayidx8, align 4
+
+  br label %for.inc.k
+
+for.inc.k:                                          ; preds = %for.k
+  %k.next = add nuw nsw i64 %k, 1
+  %exitcond = icmp ne i64 %k.next, %o
+  br i1 %exitcond, label %for.k, label %for.end
+
+for.end:                                          ; preds = %for.inc
+  br label %for.inc.j
+
+for.inc.j:                                        ; preds = %for.end
+  %j.next = add nuw nsw i64 %j, 1
+  %exitcond5 = icmp ne i64 %j.next, %m
+  br i1 %exitcond5, label %for.j, label %for.end23
+
+for.end23:                                        ; preds = %for.inc.j
+  br label %for.inc.i
+
+for.inc.i:                                        ; preds = %for.end23
+  %i.next = add nuw nsw i64 %i, 1
+  %exitcond8 = icmp ne i64 %i.next, %n
+  br i1 %exitcond8, label %for.i, label %for.end26
+
+for.end26:                                        ; preds = %for.inc.i
+  ret void
+}

llvm/test/Analysis/LoopCacheAnalysis/PowerPC/matvecmul.ll

+; RUN: opt < %s -passes='print<loop-cache-cost>' -disable-output 2>&1 | FileCheck %s
+
+target datalayout = "e-m:e-i64:64-n32:64"
+target triple = "powerpc64le-unknown-linux-gnu"
+
+; void matvecmul(const double *__restrict y, const double * __restrict x, const double * __restrict b,
+;    const int * __restrict nb, const int * __restrict nx, const int * __restrict ny, const int * __restrict nz) {
+;
+;   for (int k=1;k<nz,++k) 
+;      for (int j=1;j<ny,++j)
+;        for (int i=1;i<nx,++i)
+;          for (int l=1;l<nb,++l)
+;            for (int m=1;m<nb,++m)
+;                 y[k+1][j][i][l] = y[k+1][j][i][l] + b[k][j][i][m][l]*x[k][j][i][m]
+; }
+
+; CHECK-DAG: Loop 'k_loop' has cost = 30000000000
+; CHECK-DAG: Loop 'j_loop' has cost = 30000000000
+; CHECK-DAG: Loop 'i_loop' has cost = 30000000000
+; CHECK-DAG: Loop 'm_loop' has cost = 10700000000
+; CHECK-DAG: Loop 'l_loop' has cost = 1300000000
+
+%_elem_type_of_double = type <{ double }>
+
+; Function Attrs: norecurse nounwind
+define void @mat_vec_mpy([0 x %_elem_type_of_double]* noalias %y, [0 x %_elem_type_of_double]* noalias readonly %x,
+    [0 x %_elem_type_of_double]* noalias readonly %b, i32* noalias readonly %nb, i32* noalias readonly %nx, 
+    i32* noalias readonly %ny, i32* noalias readonly %nz) {
+mat_times_vec_entry:
+  %_ind_val = load i32, i32* %nb, align 4
+  %_conv = sext i32 %_ind_val to i64
+  %_grt_tmp.i = icmp sgt i64 %_conv, 0
+  %a_b.i = select i1 %_grt_tmp.i, i64 %_conv, i64 0
+  %_ind_val1 = load i32, i32* %nx, align 4
+  %_conv2 = sext i32 %_ind_val1 to i64
+  %_grt_tmp.i266 = icmp sgt i64 %_conv2, 0
+  %a_b.i267 = select i1 %_grt_tmp.i266, i64 %_conv2, i64 0
+  %_ind_val3 = load i32, i32* %ny, align 4
+  %_conv4 = sext i32 %_ind_val3 to i64
+  %_grt_tmp.i264 = icmp sgt i64 %_conv4, 0
+  %a_b.i265 = select i1 %_grt_tmp.i264, i64 %_conv4, i64 0
+  %_ind_val5 = load i32, i32* %nz, align 4
+  %_mult_tmp = shl nsw i64 %a_b.i, 3
+  %_mult_tmp7 = mul i64 %_mult_tmp, %a_b.i267
+  %_mult_tmp8 = mul i64 %_mult_tmp7, %a_b.i265
+  %_sub_tmp = sub nuw nsw i64 -8, %_mult_tmp
+  %_sub_tmp21 = sub i64 %_sub_tmp, %_mult_tmp7
+  %_sub_tmp23 = sub i64 %_sub_tmp21, %_mult_tmp8
+  %_mult_tmp73 = mul i64 %_mult_tmp, %a_b.i
+  %_mult_tmp74 = mul i64 %_mult_tmp73, %a_b.i267
+  %_mult_tmp75 = mul i64 %_mult_tmp74, %a_b.i265
+  %_sub_tmp93 = sub i64 %_sub_tmp, %_mult_tmp73
+  %_sub_tmp95 = sub i64 %_sub_tmp93, %_mult_tmp74
+  %_sub_tmp97 = sub i64 %_sub_tmp95, %_mult_tmp75
+  %_grt_tmp853288 = icmp slt i32 %_ind_val5, 1
+  br i1 %_grt_tmp853288, label %_return_bb, label %k_loop.lr.ph
+
+k_loop.lr.ph:                                     ; preds = %mat_times_vec_entry
+  %_grt_tmp851279 = icmp slt i32 %_ind_val3, 1
+  %_grt_tmp847270 = icmp slt i32 %_ind_val, 1
+  %_aa_conv = bitcast [0 x %_elem_type_of_double]* %y to i8*
+  %_adda_ = getelementptr inbounds i8, i8* %_aa_conv, i64 %_sub_tmp23
+  %_aa_conv434 = bitcast [0 x %_elem_type_of_double]* %x to i8*
+  %_adda_435 = getelementptr inbounds i8, i8* %_aa_conv434, i64 %_sub_tmp23
+  %_aa_conv785 = bitcast [0 x %_elem_type_of_double]* %b to i8*
+  %_adda_786 = getelementptr inbounds i8, i8* %_aa_conv785, i64 %_sub_tmp97
+  br i1 %_grt_tmp851279, label %k_loop.us.preheader, label %k_loop.lr.ph.split
+
+k_loop.us.preheader:                              ; preds = %k_loop.lr.ph
+  br label %_return_bb.loopexit
+
+k_loop.lr.ph.split:                               ; preds = %k_loop.lr.ph
+  %_grt_tmp849273 = icmp slt i32 %_ind_val1, 1
+  br i1 %_grt_tmp849273, label %k_loop.us291.preheader, label %k_loop.lr.ph.split.split
+
+k_loop.us291.preheader:                           ; preds = %k_loop.lr.ph.split
+  br label %_return_bb.loopexit300
+
+k_loop.lr.ph.split.split:                         ; preds = %k_loop.lr.ph.split
+  br i1 %_grt_tmp847270, label %k_loop.us294.preheader, label %k_loop.preheader
+
+k_loop.preheader:                                 ; preds = %k_loop.lr.ph.split.split
+  %0 = add i32 %_ind_val, 1
+  %1 = add i32 %_ind_val1, 1
+  %2 = add i32 %_ind_val3, 1
+  %3 = add i32 %_ind_val5, 1
+  br label %k_loop
+
+k_loop.us294.preheader:                           ; preds = %k_loop.lr.ph.split.split
+  br label %_return_bb.loopexit301
+
+k_loop:                                           ; preds = %k_loop._label_18_crit_edge.split.split.split, %k_loop.preheader
+  %indvars.iv316 = phi i64 [ 1, %k_loop.preheader ], [ %indvars.iv.next317, %k_loop._label_18_crit_edge.split.split.split ]
+  %indvars.iv.next317 = add nuw nsw i64 %indvars.iv316, 1
+  %_ix_x_len = mul i64 %_mult_tmp8, %indvars.iv.next317
+  %_ix_x_len410 = mul i64 %_mult_tmp75, %indvars.iv316
+  %_ix_x_len822 = mul i64 %_mult_tmp8, %indvars.iv316
+  br label %j_loop
+
+j_loop:                                           ; preds = %j_loop._label_15_crit_edge.split.split, %k_loop
+  %indvars.iv312 = phi i64 [ %indvars.iv.next313, %j_loop._label_15_crit_edge.split.split ], [ 1, %k_loop ]
+  %_ix_x_len371 = mul i64 %_mult_tmp7, %indvars.iv312
+  %_ix_x_len415 = mul i64 %_mult_tmp74, %indvars.iv312
+  br label %i_loop
+
+i_loop:                                           ; preds = %i_loop._label_12_crit_edge.split, %j_loop
+  %indvars.iv307 = phi i64 [ %indvars.iv.next308, %i_loop._label_12_crit_edge.split ], [ 1, %j_loop ]
+  %_ix_x_len375 = mul i64 %_mult_tmp, %indvars.iv307
+  %_ix_x_len420 = mul i64 %_mult_tmp73, %indvars.iv307
+  br label %l_loop
+
+l_loop:                                           ; preds = %l_loop._label_9_crit_edge, %i_loop
+  %indvars.iv303 = phi i64 [ %indvars.iv.next304, %l_loop._label_9_crit_edge ], [ 1, %i_loop ]
+  %_ix_x_len378 = shl nuw nsw i64 %indvars.iv303, 3
+  br label %m_loop
+
+m_loop:                                           ; preds = %m_loop, %l_loop
+  %indvars.iv = phi i64 [ %indvars.iv.next, %m_loop ], [ 1, %l_loop ]
+  %_ix_x_len424 = mul i64 %_mult_tmp, %indvars.iv
+  %_ix_x_len454 = shl nuw nsw i64 %indvars.iv, 3
+  %_ixa_gep = getelementptr inbounds i8, i8* %_adda_, i64 %_ix_x_len
+  %_ixa_gep791 = getelementptr inbounds i8, i8* %_adda_786, i64 %_ix_x_len410
+  %_ixa_gep823 = getelementptr inbounds i8, i8* %_adda_435, i64 %_ix_x_len822
+  %_ixa_gep372 = getelementptr inbounds i8, i8* %_ixa_gep, i64 %_ix_x_len371
+  %_ixa_gep376 = getelementptr inbounds i8, i8* %_ixa_gep372, i64 %_ix_x_len375
+  %_ixa_gep796 = getelementptr inbounds i8, i8* %_ixa_gep791, i64 %_ix_x_len415
+  %_ixa_gep828 = getelementptr inbounds i8, i8* %_ixa_gep823, i64 %_ix_x_len371
+  %_ixa_gep379 = getelementptr inbounds i8, i8* %_ixa_gep376, i64 %_ix_x_len378
+  %_ixa_gep801 = getelementptr inbounds i8, i8* %_ixa_gep796, i64 %_ix_x_len420
+  %_ixa_gep833 = getelementptr inbounds i8, i8* %_ixa_gep828, i64 %_ix_x_len375
+  %_ixa_gep806 = getelementptr inbounds i8, i8* %_ixa_gep801, i64 %_ix_x_len378
+  %_ixa_gep810 = getelementptr inbounds i8, i8* %_ixa_gep806, i64 %_ix_x_len424
+  %_gepp = bitcast i8* %_ixa_gep379 to double*
+  %_gepp813 = bitcast i8* %_ixa_gep810 to double*
+  %_ind_val814 = load double, double* %_gepp813, align 8
+  %_ixa_gep837 = getelementptr inbounds i8, i8* %_ixa_gep833, i64 %_ix_x_len454
+  %_gepp840 = bitcast i8* %_ixa_gep837 to double*
+  %_ind_val841 = load double, double* %_gepp840, align 8
+  %_mult_tmp842 = fmul double %_ind_val814, %_ind_val841
+  store double %_mult_tmp842, double* %_gepp, align 8
+  %indvars.iv.next = add nuw nsw i64 %indvars.iv, 1
+  %wide.trip.count = zext i32 %0 to i64
+  %wide.trip.count305 = zext i32 %0 to i64
+  %wide.trip.count309 = zext i32 %1 to i64
+  %wide.trip.count314 = zext i32 %2 to i64
+  %wide.trip.count319 = zext i32 %3 to i64
+  %exitcond = icmp ne i64 %indvars.iv.next, %wide.trip.count
+  br i1 %exitcond, label %m_loop, label %l_loop._label_9_crit_edge
+
+l_loop._label_9_crit_edge:                        ; preds = %m_loop
+  %indvars.iv.next304 = add nuw nsw i64 %indvars.iv303, 1
+  %exitcond306 = icmp ne i64 %indvars.iv.next304, %wide.trip.count305
+  br i1 %exitcond306, label %l_loop, label %i_loop._label_12_crit_edge.split
+
+i_loop._label_12_crit_edge.split:                 ; preds = %l_loop._label_9_crit_edge
+  %indvars.iv.next308 = add nuw nsw i64 %indvars.iv307, 1
+  %exitcond310 = icmp ne i64 %indvars.iv.next308, %wide.trip.count309
+  br i1 %exitcond310, label %i_loop, label %j_loop._label_15_crit_edge.split.split
+
+j_loop._label_15_crit_edge.split.split:           ; preds = %i_loop._label_12_crit_edge.split
+  %indvars.iv.next313 = add nuw nsw i64 %indvars.iv312, 1
+  %exitcond315 = icmp ne i64 %indvars.iv.next313, %wide.trip.count314
+  br i1 %exitcond315, label %j_loop, label %k_loop._label_18_crit_edge.split.split.split
+
+k_loop._label_18_crit_edge.split.split.split:     ; preds = %j_loop._label_15_crit_edge.split.split
+  %exitcond320 = icmp ne i64 %indvars.iv.next317, %wide.trip.count319
+  br i1 %exitcond320, label %k_loop, label %_return_bb.loopexit302
+
+_return_bb.loopexit:                              ; preds = %k_loop.us.preheader
+  br label %_return_bb
+
+_return_bb.loopexit300:                           ; preds = %k_loop.us291.preheader
+  br label %_return_bb
+
+_return_bb.loopexit301:                           ; preds = %k_loop.us294.preheader
+  br label %_return_bb
+
+_return_bb.loopexit302:                           ; preds = %k_loop._label_18_crit_edge.split.split.split
+  br label %_return_bb
+
+_return_bb:                                       ; preds = %_return_bb.loopexit302, %_return_bb.loopexit301, %_return_bb.loopexit300, %_return_bb.loopexit, %mat_times_vec_entry
+  ret void
+}
+
+

llvm/test/Analysis/LoopCacheAnalysis/PowerPC/single-store.ll

+; RUN: opt < %s -passes='print<loop-cache-cost>' -disable-output 2>&1 | FileCheck %s
+
+target datalayout = "e-m:e-i64:64-n32:64"
+target triple = "powerpc64le-unknown-linux-gnu"
+
+; void foo(long n, long m, long o, int A[n][m][o]) {
+;   for (long i = 0; i < n; i++)
+;     for (long j = 0; j < m; j++)
+;       for (long k = 0; k < o; k++)
+;         A[2*i+3][3*j-4][2*k+7] = 1;
+; }
+
+; CHECK-DAG: Loop 'for.i' has cost = 1000000
+; CHECK-DAG: Loop 'for.j' has cost = 1000000
+; CHECK-DAG: Loop 'for.k' has cost = 60000
+
+define void @foo(i64 %n, i64 %m, i64 %o, i32* %A) {
+entry:
+  %cmp32 = icmp sgt i64 %n, 0
+  %cmp230 = icmp sgt i64 %m, 0
+  %cmp528 = icmp sgt i64 %o, 0
+  br i1 %cmp32, label %for.cond1.preheader.lr.ph, label %for.end
+
+for.cond1.preheader.lr.ph:                        ; preds = %entry
+  br i1 %cmp230, label %for.i.preheader, label %for.end
+
+for.i.preheader:                                  ; preds = %for.cond1.preheader.lr.ph
+  br i1 %cmp528, label %for.i.preheader.split, label %for.end
+
+for.i.preheader.split:                            ; preds = %for.i.preheader
+  br label %for.i
+
+for.i:                                            ; preds = %for.inci, %for.i.preheader.split
+  %i = phi i64 [ %inci, %for.inci ], [ 0, %for.i.preheader.split ]
+  %mul8 = shl i64 %i, 1
+  %add9 = add nsw i64 %mul8, 3
+  %0 = mul i64 %add9, %m
+  %sub = add i64 %0, -4
+  br label %for.j
+
+for.j:                                            ; preds = %for.incj, %for.i
+  %j = phi i64 [ %incj, %for.incj ], [ 0, %for.i ]
+  %mul7 = mul nsw i64 %j, 3
+  %tmp = add i64 %sub, %mul7
+  %tmp27 = mul i64 %tmp, %o
+  br label %for.k
+
+for.k:                                            ; preds = %for.k, %for.j.us
+  %k = phi i64 [ 0, %for.j ], [ %inck, %for.k ]
+
+  %mul = mul nsw i64 %k, 2
+  %arrayidx.sum = add i64 %mul, 7
+  %arrayidx10.sum = add i64 %arrayidx.sum, %tmp27
+  %arrayidx11 = getelementptr inbounds i32, i32* %A, i64 %arrayidx10.sum
+  store i32 1, i32* %arrayidx11, align 4
+
+  %inck = add nsw i64 %k, 1
+  %exitcond.us = icmp eq i64 %inck, %o
+  br i1 %exitcond.us, label %for.incj, label %for.k
+
+for.incj:                                         ; preds = %for.k
+  %incj = add nsw i64 %j, 1
+  %exitcond54.us = icmp eq i64 %incj, %m
+  br i1 %exitcond54.us, label %for.inci, label %for.j
+
+for.inci:                                         ; preds = %for.incj
+  %inci = add nsw i64 %i, 1
+  %exitcond55.us = icmp eq i64 %inci, %n
+  br i1 %exitcond55.us, label %for.end.loopexit, label %for.i
+
+for.end.loopexit:                                 ; preds = %for.inci
+  br label %for.end
+
+for.end:                                          ; preds = %for.end.loopexit, %for.cond1.preheader.lr.ph, %entry
+  ret void
+}
+

llvm/test/Analysis/LoopCacheAnalysis/PowerPC/stencil.ll

+; RUN: opt < %s -passes='print<loop-cache-cost>' -disable-output 2>&1 | FileCheck %s
+
+target datalayout = "e-m:e-i64:64-n32:64"
+target triple = "powerpc64le-unknown-linux-gnu"
+
+; void foo(long n, long m, long o, int A[n][m], int B[n][m], int C[n]) {
+;   for (long i = 0; i < n; i++)
+;     for (long j = 0; j < m; j++) {
+;         A[i][j] = A[i][j+1] + B[i-1][j] + B[i+1][j+1] + C[i];
+;         A[i][j] += B[i][i];
+;     }   
+; }
+
+; CHECK-DAG: Loop 'for.i' has cost = 20600
+; CHECK-DAG: Loop 'for.j' has cost = 800
+
+define void @foo(i64 %n, i64 %m, i32* %A, i32* %B, i32* %C) {
+entry:
+  %cmp32 = icmp sgt i64 %n, 0
+  %cmp230 = icmp sgt i64 %m, 0
+  br i1 %cmp32, label %for.cond1.preheader.lr.ph, label %for.end
+
+for.cond1.preheader.lr.ph:                        ; preds = %entry
+  br i1 %cmp230, label %for.i.preheader, label %for.end
+
+for.i.preheader:                                  ; preds = %for.cond1.preheader.lr.ph
+  br label %for.i
+
+for.i:                                            ; preds = %for.inci, %for.i.preheader.split
+  %i = phi i64 [ %inci, %for.inci ], [ 0, %for.i.preheader ]
+  %subione = sub i64 %i, 1
+  %addione = add i64 %i, 1
+  %muli = mul i64 %i, %m
+  %muliminusone = mul i64 %subione, %m
+  %muliplusone = mul i64 %addione, %m
+  br label %for.j
+
+for.j:                                            ; preds = %for.incj, %for.i
+  %j = phi i64 [ %incj, %for.incj ], [ 0, %for.i ]
+  %addj = add i64 %muli, %j
+
+  ; B[i-1][j]
+  %arrayidx1 = add i64 %j, %muliminusone
+  %arrayidx2 = getelementptr inbounds i32, i32* %B, i64 %arrayidx1
+  %elem_B1 = load i32, i32* %arrayidx2, align 4
+
+  ; B[i-1][j+1]
+  %addjone = add i64 %j, 1
+  %arrayidx3 = add i64 %addjone, %muliminusone
+  %arrayidx4 = getelementptr inbounds i32, i32* %B, i64 %arrayidx3
+  %elem_B2 = load i32, i32* %arrayidx4, align 4
+
+  ; C[i]
+  %arrayidx6 = getelementptr inbounds i32, i32* %C, i64 %i
+  %elem_C = load i32, i32* %arrayidx6, align 4
+
+  ; A[i][j+1]
+  %arrayidx7 = add i64 %addjone, %muli
+  %arrayidx8 = getelementptr inbounds i32, i32* %A, i64 %arrayidx7
+  %elem_A = load i32, i32* %arrayidx8, align 4
+
+  ; A[i][j] = A[i][j+1] + B[i-1][j] + B[i-1][j+1] + C[i]
+  %addB = add i32 %elem_B1, %elem_B2
+  %addC = add i32 %addB, %elem_C
+  %addA = add i32 %elem_A, %elem_C
+  %arrayidx9 = add i64 %j, %muli
+  %arrayidx10 = getelementptr inbounds i32, i32* %A, i64 %arrayidx9
+  store i32 %addA, i32* %arrayidx10, align 4
+
+  ; A[i][j] += B[i][i];
+  %arrayidx11 = add i64 %j, %muli
+  %arrayidx12 = getelementptr inbounds i32, i32* %A, i64 %arrayidx11
+  %elem_A1 = load i32, i32* %arrayidx12, align 4
+  %arrayidx13 = add i64 %i, %muli
+  %arrayidx14 = getelementptr inbounds i32, i32* %B, i64 %arrayidx13
+  %elem_B3 = load i32, i32* %arrayidx14, align 4
+  %addA1 = add i32 %elem_A1, %elem_B3
+  store i32 %addA1, i32* %arrayidx12, align 4
+
+  br label %for.incj
+
+for.incj:                                         ; preds = %for.j
+  %incj = add nsw i64 %j, 1
+  %exitcond54.us = icmp eq i64 %incj, %m
+  br i1 %exitcond54.us, label %for.inci, label %for.j
+
+for.inci:                                         ; preds = %for.incj
+  %inci = add nsw i64 %i, 1
+  %exitcond55.us = icmp eq i64 %inci, %n
+  br i1 %exitcond55.us, label %for.end.loopexit, label %for.i
+
+for.end.loopexit:                                 ; preds = %for.inci
+  br label %for.end
+
+for.end:                                          ; preds = %for.end.loopexit, %for.cond1.preheader.lr.ph, %entry
+  ret void
+}
+