[mlir][sparse] extend loop emitter to emit slice driven loops

[Peiming]

code cleanup.

[Peiming]

rebase.

[Peiming]

fix check tests.

[Peiming]

code cleanup.

[Peiming]

remove useless code.

[Peiming]

address comments.

[Peiming]

use type aliases for tensor id and level

[wrengr]

mlir/include/mlir/Dialect/SparseTensor/Utils/Merger.h

444 ↗

(On Diff #507478)

What do you mean here? I'm guessing this should be "level", but I'm not sure what you mean by "favor(ing) constant levels"

mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.h

113

This should remain "/// Exits"

208–228

Can you make this class "final" (ditto for the LoopInfo). You don't need/use subclassing here, and marking it final helps the compiler generate more efficient code

212

I'm guessing this should be LoopOrd. If not, then what is it?

257

This should be Level lvl (I'm pretty sure)

327

Should this be LoopOrd? If not, then what is it?

349

What is this supposed to be: LoopOrd, LoopId, other?

[wrengr]

mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.cpp

56–60

I'd prefer these be defined as static inline functions rather than as macros, since that gives better type-safety and compiler error messages. If you need to use CMPI at several different types, then just use a template.

64–66

You should just use ValueRange::getTypes()

273–274

Please keep this as Level l

382

Please use TensorId here. I am just about to upload the CLs that make that into a newtype, so it's important to use the correct type instead of just using size_t/unsigned everywhere

383

Please define a dyn_cast variant of the getSparseTensorType function, and use that here and everywhere else. The SparseTensorType was created specifically to help avoid several code legibility and correctness concerns, so you should be using it everywhere possible.

387

You should be using SparseTensorType::getLevelRank here, since it is specifically the level-rank you want not the dim-rank

388

Please use Level for all levels. Even though it's just a typedef for now, I will be converting it to a proper type in the near future, so you should use the correct type rather than just using unsigned everywhere

468

I think it'd be clearer to just use const auto & here

622

Use "l" or "lvl" here. The name "d" is reserved for things of Dimension type, whereas this has Level type.

797–798

Why remove the const? It's clearer to know when local variables will never change

799

Please don't undo my factoring this out into a local variable. The condition is much easier to read when (1) it's all on one line, and (2) avoids repeating common expressions which forces the reader to double check if they are indeed the same or not.

1130

It would be clearer to use break in the then-branch. That keeps you from needing to indent the else-branch (which is very long), and helps the reader avoid needing to check to see if there's something else after the else-branch.

[Peiming]

mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.cpp

56–60

I will stick with this. The reason I use macro is that I want to avoid typing builder and loc.

799

Okay, it is a mistake I made during rebasing.

mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.h

327

This is unsigned index to another array (not the loop sequence). I will stick with this.

349

This is an unsigned counter.

[Peiming]

address comments + fix rebase mistakes.

mlir/include/mlir/Dialect/SparseTensor/Utils/Merger.h

444 ↗

(On Diff #507478)

I mean to pick the a static known dimension size instead of dynamic ones if there are multiple candidate. (i.e., DimOp folds to constant value). It might lead to a slightly better code.

mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.cpp

797–798

rebase mistake.

1130

I found else is easier to follow, because the control flow is more straight forward.

[Peiming]

remove useless comments.

[wrengr]

mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.cpp

65

Please don't undo this variable naming. The "mem" matches other places, and avoids confusion about whether "ptr" means MemRef vs the old "pointer" (now "position") vs llvm-pointers vs...

255–260

You should use the numTensors variable instead of calling tensors.size() repeatedly. (This is for code clarity rather than performance reasons)

273–274

It would be clearer to combine these together. Also, it would be clearer to use continue rather than extra indentation for the conditional. Putting those together, maybe use something like if (depends == 0) continue; assert(!reassoc); sliceSizes[...

mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.h

113

You want to keep the triple-slash "///", since that's what the tooling uses for generating the API documentation

[Peiming]

fix rebase mistakes.

[Peiming]

fix some TODOs.

[wrengr]

mlir/include/mlir/Dialect/SparseTensor/Utils/Merger.h

477 ↗

(On Diff #507799)

That's the wrong bound to assert; you should instead compare against levelToDependentIdx[t].size() or maxLvlRank.

For correctness you should also assert(i < numLoops && t < numTensors).

If you rebase over D146684 to get the assertion helpers, then the full assertion would be assert(isValidLevel(t, lvl) && isValidLoopId(i) && !loopToDependencies[i][t].has_value()). The nice thing about those assertion helpers is that it gives the correct bound for the level (rather than falling back to maxLvlRank), and also guards against the case where i == kInvalidId.

478 ↗

(On Diff #507799)

Isn't it redundant to store the level-type in loopToDependencies, since it's already stored in lvlTypes? That is, afaict the following code snippet should always return successfully (assuming i and t are valid):

if (const auto dep = loopToDependencies[i][t]) {
  const Level depLvl = (*dep).first;
  const auto depOptLoop = lvlToLoop[t][depLvl];
  assert(depOptLoop);
  const LoopId depLoop = *depOptLoop;
  assert(lvlTypes[t][depLoop] == (*dep).second);
}

Assuming that's correct, then you shouldn't store the level-type in loopToDependencies because it's redundant information. Or if you absolutely must store the redundant copy for some reason, then you need to verify that the level-type agrees with the one in lvlTypes (or if the one in lvlTypes is undefined, then you need to store the dlt parameter there too; and conversely you need to adjust the setLevelAndType method to also verify consistency with loopToDependencies).

I agree that it's rather convoluted to need to say lvlTypes[t][*(lvlToLoop[t][*(loopToDependencies[i][t])])], but the only solution to that is to reconsider the design of all the fields of the Merger class. For example, if we had lvlTypes : (TensorId, Level) -> LevelType instead of the current lvlTypes : (TensorId, LoopId) -> LevelType, then you wouldn't need to use lvlToLoop there. Of course, you'd have to redo the rest of the Merger code to make that work (which may end up inserting more loopToLevel uses than however many levelToLoop uses it removes). Or a different design would be to combine lvlToLoop and lvlTypes into a single lvlInfo : (TensorId, Level) -> (LevelType, optional<LoopId>); of course that would require making different changes to the rest of the Merger code. In any case, I think it would be wise to wait for D146693 to land before trying to make any of these changes, since the newtypes of that CL will greatly simplify the process of rearranging all these vectors.

598 ↗

(On Diff #507799)

This should have been named levelToDependentLoop, since we don't use "idx" in this file anymore because it causes too much confusion. I mentioned this in the previous CL that introduced this field, but you landed the CL without fixing it

mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.h

196

This comment should explain how exactly the slicedTids differs from the other tids. Also, is the same tensor allowed to occur in both fields? If so, then what does that mean? and, can the same level of the same tensor occur on both of the corresponding fields?

197–201

I think it'd be better to combine these all into a single const SmallVector<LoopLevelInfo> where struct LoopLevelInfo final { TensorId tid; Level lvl; bool isSlice; bool isReduced; }; —assuming it's okay to combine the original (tids,lvls) with the new (slicedTids,slicedLvls,sliceReduced) into a single vector/set. If that's not okay for some reason, then I still think it'd be good to use a single const SmallVector<LoopSlicedLevelInfo> field for the new stuff.

Using AOS will ensure that there's the right number of all the things that should correspond, as well as keeping the corresponding things close together. Plus it'll make it easier to add additional fields in the future as needed.

198

"levels"

200

This comment is wrong for this field

209

"...do not need to actually create a sparse..."

210

"...only need to maintain the..."

211

Is this actually the full MemRef of coordinates for all levels? If so then it should be "minCoords" (with an "s"). Whereas if it's just a single coordinate for the given level, then it should be "minCrd".

219

Given the comment, I think this would be better named something like "isFirstSlice" or "isInitialSlice".

221

If the value is just a single coordinate, then this should also be singular.

[wrengr]

mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.h

215

Given our discussion of boolean blindness, this assertion suggests that the two parameters should be combined into a single std::optional<std::pair<Level, Value>> parameter. (Albeit you'll still want to assert you didn't get a null Value.)

If that combined parameter doesn't work, why not? The only other thing that would be consistent with the assertion is union{ non-null-Value; struct{non-null-Value; Level}} but that's equivalent to struct{non-null-Value; optional<Level>}, so if that's what you want then you should assert(minCoord) instead.

296–298

This description doesn't make sense to me. Do you have a design doc that explains what exactly you mean by "slice" in this context, and explains how/why "reducing d0+d1+d2" translates into needing the two slices you mention?

302

Either "number of constraints needed to..." or "number of constraints that are needed to..."

303

"level"

308

That should be "A[i+j] => A[i+2]" to make it clear that it dereives from "j => 2".

[Peiming]

mlir/include/mlir/Dialect/SparseTensor/Utils/Merger.h

477 ↗

(On Diff #507799)

Yeah, I haven't rebase against change that introduced maxLvlRank yet.

478 ↗

(On Diff #507799)

No, it is not redundant. The lvlTypes current is a mapping for (tid, loopid) => dlt, not (tid, level) => dlt. I think storing a pair makes more sense than introducing a complete (tid, level) => dlt map here because the dlt is only required here when there are non-trivial index expressions on the level.

mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.cpp

65

Sry, probably it get overlooked during rebasing

mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.h

197–201

I agree with you on this, in fact, see my comment at L222, I will do it in a separate patch though.

219

I will change the comment, it means whether it is the initial tensor that has not yet been sliced.

296–298

Yeah, I am writing a paper on this (but still at very early stage), I will share it with you later when it is more or less complete.

[Peiming]

rebase + address comments.

mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.h

215

It should work, I will add a TODO here and submit the change in a separate patch.

[Peiming]

fix windows building errors.

[Peiming]

fix variable's name.

[Peiming]

rebase.

[Peiming]

split up complicated functions

[Peiming]

rebase.

[aartbik]

mlir/include/mlir/Dialect/SparseTensor/Utils/Merger.h

444 ↗

(On Diff #507478)

As a TODO?

444 ↗

(On Diff #507478)

Please mark such comments with a TODO, since you clearly have an idea on how to to it better. That way we can periodically grep for TODO's and fix them. Unless you think we will never do that, and then this is a note to self that should not be here.

453 ↗

(On Diff #510849)

since you added a parameter, you also need to update this comment

458 ↗

(On Diff #510849)

Top level comments usually apply to the block of code, I find e.g.

assert(!loopToDependencies[i][t].has_value()); // must be first definition

a lot more readable, since you follow it direclty with the make pair/pushback

470 ↗

(On Diff #510849)

The non-trivial concept is used more widely now, but it would still be nice to define this per file, or at least per first occurrence what non-trivial really means. Or perhaps we should start using more standard terminology on affine expressions?

503 ↗

(On Diff #510849)

tensor level with index expression on it, reads awkward

how about

must be a tensor level that contains a non-trivial index expression

mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.cpp

651

If the slice

653

I find this block of code extremely hard to read.
Any way to factor this into slightly smaller methods and combine these?

789

A note "make sure" is very ambiguous. Is that a note to self, or something that the code actively does.
Much better is to use an affirmative statement

790

appears first than normal tensors

appears before normal tensors?

1130

I agree the else is very long and deep

Why not

if (!resolved) {

genSlice
 continue;

}
....

1181

Ok, this block is where all the magic happens ;-)
I need to do one more careful pass over this...

1652

The next

1730

Sets (or Increment), but use one style

mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.h

60

comments with should or must are a bit dangling unless you say what happens when this assumption is not true

113

Why did you change Exits -> exit? Original seems okay

180–181

since we have several nested structs, can you give each a short comment (as documentation, and to improve readability(

196

Here and below (and above), period at end

300

const ref?

mlir/lib/Dialect/SparseTensor/Transforms/Sparsification.cpp

1536

I would start with the same comment as in the else, and state it in the affirmative rather than the speculative

// End either a for-loop or a while-loop that iterates over a slice.

[Peiming]

address some comments.

[Peiming]

simplify code.

mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.cpp

653

better now?

[Peiming]

fix rebase issues.

[Peiming]

fix typos.

[aartbik]

mlir/include/mlir/Dialect/SparseTensor/Utils/Merger.h

457 ↗

(On Diff #512264)

can we make this lvl < .... part also a helper method
(that way, all our asserts read almost like english ;-)

mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.cpp

92

This computation does not match my mental interpretation of the text above (L79)

96

// offset

adds very little, Either use a sentence or remove

258

why the empty lines here?

274

We need depends - 1 slices

to make sure you don't read depends as part of the sentence

390

The comment applies to the assert, but the declaration is in between

470

Please elaborate. "Pop out" is not at all representative for what follows

653

Yes, although it could still use a bit more doc on what each block does (on entry of each block).
Also, I would not overuse the "NOTE" part, in principle, all comments are NOTEs and we should only
use them when something really should jump out

737

isn't that always the case here? Should that not be part of the method description then?

1184

I think this still needs some work to make reading the block easier. The problem is that you have very concise comments in the header
(Generates .....), which is okay, since i don't want to see more there, but very few comments here, where it matters.

So I would still give every implementation function here an entry comment, but one that shows what is generated, using some pseudo-code of the output
That way, on entry of each method, I know what to expect, and dive into the various blocks with more pre-knowledge on what they do

WDYT?

1197

this one seems out of place (all others generate stuff)
perhaps move it up or down in the method order (also in header)

1254

here and a few other place, no period at end, please make once last pass over all new comments here

mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.h

60

I think what is still missing is whether it is enforced (viz. asserts fail when trying to set it)
or whether clients are responsible.

So, something like

Clients are responsible for ensuring that the order of the returned

(I think my original comment was really on when I see "should" or "must", who is to blame in the end ;-)

225

Wren can correct me if I am wrong, but I think this needs to be minimum, right (as in smallest value, and not the lowest according to some other measure)?

264

is exceeds -> exceeds

but more importantly, I would state this,

We break out of the loop when the coordindate exceeds the slideSize.

296

the most recent slice (singular)

304

perhaps we should discuss somewhere else, but we use "unsigned" at most places, and size_t only for local operations, or inside casts and asserts
Since this is part of the API, I would prefer keeping it to unsigned, unless you have very strong reasons for this

362

period at end.

"to allocate top level local"

makes very little sense when read in isolation. Just say what code fragment this points to

368

as follows?

mlir/lib/Dialect/SparseTensor/Transforms/Sparsification.cpp

62

I know this was already there, but can we use override here to make it more clear that we implementing the base visitor class?
Or at the very least group all overrides into a

// Visitor method overrides.
...

section?

mlir/lib/Dialect/SparseTensor/Utils/Merger.cpp

418 ↗

(On Diff #512264)

has the locate property as well

[wrengr]

mlir/include/mlir/Dialect/SparseTensor/Utils/Merger.h

457 ↗

(On Diff #512264)

Why do you need this extra assertion? The isValidLevel assertion already ensures that the lvl is valid for the tensor t. Therefore, rather than checking the lvl twice, the rest of the code should instead maintain the invariant that levelToDependentLoop[t].size() == lvlTypes[t].size().

[wrengr]

mlir/include/mlir/Dialect/SparseTensor/Utils/Merger.h

478 ↗

(On Diff #507799)

There is a lot of unnecessary complexity and redundancy in storing all of:

• lvlToLoop: (tid, lvl) -> optional<loopid>
• loopToLvl: (tid, loopid) -> optional<lvl>
• lvlTypes : (tid, loopid) -> dlt
• loopToDependencies : (loopid, tid) -> (lvl, dlt)
• levelToDependentLoop : (tid, lvl) -> set<loopid>

As I mentioned in my earlier comment, we can easily reconstruct the desired (tid, lvl) -> dlt map via [](t, l) { auto i = lvlToLoop[t][l]; return i ? lvlTypes[t][*i] : Undef; }. Therefore, we always have that loopToDependencies[i][t] == make_pair(l, reconstructedLvlTypes[t][l]). Consequently: since the first part of loopToDependencies has that every (t,i) pair determines l, it is trivial to construct the required (t,l) pair for passing to reconstructedLvlTypes; and since it's trivial to define reconstructedLvlTypes, therefore there is no benefit to storing this redundant information. And as I said before, whenever we store redundant information that means we must also therefore take pains to ensure that all the copies of that information remain consistent.

I agree that it would be nice to store the (tid, lvl) -> dlt map directly, and to use that in lieu of the current (tid, loopid) -> dlt map. Especially since the former can be quickly constructed from the types of the tensors, and doesn't require knowing anything about lvlToLoop/loopToLvl. However, regardless of which one we store, the point remains the same: there's no benefit to loopToDependencies storing this information redundantly, and if it stores redundant information anyways then it needs to ensure that it remains consistent with the (tid, {lvl,loopid}) -> dlt map.

[Peiming]

address comments.

mlir/include/mlir/Dialect/SparseTensor/Utils/Merger.h

457 ↗

(On Diff #512264)

I found this is actually a redundant check, if the lvl is valid then it is definitely inbound.

mlir/lib/Dialect/SparseTensor/Transforms/Sparsification.cpp

62

I added a comment, this is non-vritual function, so I did not use override here.

[Peiming]

mlir/include/mlir/Dialect/SparseTensor/Utils/Merger.h

478 ↗

(On Diff #507799)

I agree that we can probably clean it up, but I will address this in separate patches through ;-)

[aartbik]

mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.cpp

1437

I first though this was commented out code ;-)

So make it

Generate:

code

[Peiming]

address comment.

[Peiming]

fix test case memory leakage.

[vzakhari]

Hi @Peiming, the buildbots are failing (e.g. https://lab.llvm.org/buildbot/#/builders/160/builds/19165) - could you please fix it?

[Peiming]

In D142930#4319290, @vzakhari wrote:

Hi @Peiming, the buildbots are failing (e.g. https://lab.llvm.org/buildbot/#/builders/160/builds/19165) - could you please fix it?

Yeah, I saw it. but the warning seems to be unrelated to this change... I will take a look

[vzakhari]

In D142930#4319294, @Peiming wrote:

In D142930#4319290, @vzakhari wrote:

Hi @Peiming, the buildbots are failing (e.g. https://lab.llvm.org/buildbot/#/builders/160/builds/19165) - could you please fix it?

Yeah, I saw it. but the warning seems to be unrelated to this change... I will take a look

Yes, sorry, I posted it in the wrong diff. The failures started with D148565.

[Peiming]

@vzakhari this is not the patch that triggers the complaining. If you are going to revert, please make sure you revert the right one, which is https://reviews.llvm.org/D148565

[Peiming]

In D142930#4319326, @vzakhari wrote:

In D142930#4319294, @Peiming wrote:

In D142930#4319290, @vzakhari wrote:

Hi @Peiming, the buildbots are failing (e.g. https://lab.llvm.org/buildbot/#/builders/160/builds/19165) - could you please fix it?

Yeah, I saw it. but the warning seems to be unrelated to this change... I will take a look

Yes, sorry, I posted it in the wrong diff. The failures started with D148565.

I can not see any related file in D148565 either....

[Peiming]

@vzakhari I do not think my patch caused the error, see https://lab.llvm.org/buildbot/#/builders/160/builds/19161, there was already the same warning (but I do not know why it was not treated as errors).

[vzakhari]

In D142930#4319341, @Peiming wrote:

In D142930#4319326, @vzakhari wrote:

In D142930#4319294, @Peiming wrote:

In D142930#4319290, @vzakhari wrote:

Hi @Peiming, the buildbots are failing (e.g. https://lab.llvm.org/buildbot/#/builders/160/builds/19165) - could you please fix it?

Yeah, I saw it. but the warning seems to be unrelated to this change... I will take a look

Yes, sorry, I posted it in the wrong diff. The failures started with D148565.

I can not see any related file in D148565 either....

let me explain what I see: I looked at https://lab.llvm.org/buildbot/#/builders/160 and the first failing build was 19162: https://lab.llvm.org/buildbot/#/builders/160/builds/19162; it points to D148565. The build issue is shown in stdio section:

FAILED: tools/mlir/lib/Dialect/SparseTensor/Transforms/CMakeFiles/obj.MLIRSparseTensorTransforms.dir/SparseGPUCodegen.cpp.o 
/usr/local/bin/c++ -DGTEST_HAS_RTTI=0 -DMLIR_CUDA_CONVERSIONS_ENABLED=0 -DMLIR_ROCM_CONVERSIONS_ENABLED=0 -D_DEBUG -D_GLIBCXX_ASSERTIONS -D_GNU_SOURCE -D_LIBCPP_ENABLE_ASSERTIONS -D__STDC_CONSTANT_MACROS -D__STDC_FORMAT_MACROS -D__STDC_LIMIT_MACROS -I/home/tcwg-buildbot/worker/flang-aarch64-latest-gcc/build/tools/mlir/lib/Dialect/SparseTensor/Transforms -I/home/tcwg-buildbot/worker/flang-aarch64-latest-gcc/llvm-project/mlir/lib/Dialect/SparseTensor/Transforms -I/home/tcwg-buildbot/worker/flang-aarch64-latest-gcc/build/include -I/home/tcwg-buildbot/worker/flang-aarch64-latest-gcc/llvm-project/llvm/include -I/home/tcwg-buildbot/worker/flang-aarch64-latest-gcc/llvm-project/mlir/include -I/home/tcwg-buildbot/worker/flang-aarch64-latest-gcc/build/tools/mlir/include -fPIC -fno-semantic-interposition -fvisibility-inlines-hidden -Werror=date-time -Wall -Wextra -Wno-unused-parameter -Wwrite-strings -Wcast-qual -Wno-missing-field-initializers -pedantic -Wno-long-long -Wimplicit-fallthrough -Wno-maybe-uninitialized -Wno-class-memaccess -Wno-redundant-move -Wno-pessimizing-move -Wno-noexcept-type -Wdelete-non-virtual-dtor -Wsuggest-override -Wno-comment -Wno-misleading-indentation -Wctad-maybe-unsupported -fdiagnostics-color -ffunction-sections -fdata-sections -O3 -DNDEBUG  -fno-exceptions -funwind-tables -fno-rtti -UNDEBUG -std=c++17 -MD -MT tools/mlir/lib/Dialect/SparseTensor/Transforms/CMakeFiles/obj.MLIRSparseTensorTransforms.dir/SparseGPUCodegen.cpp.o -MF tools/mlir/lib/Dialect/SparseTensor/Transforms/CMakeFiles/obj.MLIRSparseTensorTransforms.dir/SparseGPUCodegen.cpp.o.d -o tools/mlir/lib/Dialect/SparseTensor/Transforms/CMakeFiles/obj.MLIRSparseTensorTransforms.dir/SparseGPUCodegen.cpp.o -c /home/tcwg-buildbot/worker/flang-aarch64-latest-gcc/llvm-project/mlir/lib/Dialect/SparseTensor/Transforms/SparseGPUCodegen.cpp
In file included from ../llvm-project/mlir/lib/Dialect/SparseTensor/Transforms/SparseGPUCodegen.cpp:17:
../llvm-project/mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.h: In member function ‘constexpr mlir::sparse_tensor::TensorLevel mlir::sparse_tensor::LoopEmitter::makeTensorLevel(mlir::sparse_tensor::TensorId, mlir::sparse_tensor::Level) const’:
../llvm-project/mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.h:199:29: error: call to non-‘constexpr’ function ‘unsigned int mlir::sparse_tensor::LoopEmitter::getNumTensors() const’
  199 |     return l * getNumTensors() + t;
      |                ~~~~~~~~~~~~~^~
../llvm-project/mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.h:195:12: note: ‘unsigned int mlir::sparse_tensor::LoopEmitter::getNumTensors() const’ declared here
  195 |   unsigned getNumTensors() const { return tensors.size(); }
      |            ^~~~~~~~~~~~~
90.309 [1754/1/4349] Linking CXX shared library lib/libclang-cpp.so.17git
ninja: build stopped: subcommand failed.

So it does point to the change from D148565.

[Peiming]

Thanks! Now I see it! https://reviews.llvm.org/D149874 should fix it.

mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.h

public:
   using OutputUpdater = function_ref<Value(OpBuilder &builder, Location loc,
                                            Value memref, Value tensor)>;
   // Map from [tid, dim] to a list of dependent [tid, dim] for affine expression
   // index on sparse tensors.
   // E.g., for affine index (d0 + d1), it depends on two [tid, dim] that defines
   // d0 and d1 (for affine expression reduction).
   // If the list is empty, it means that there is no affine expression on the
   // input [tid, dim].
+  // NOTE: the order of the returned list should be consistent with the
+  // topological order of the iteration graph.
   using DependentDimGetter =
       function_ref<std::vector<std::pair<unsigned, unsigned>>(unsigned,
                                                               unsigned)>;
 
   LoopEmitter() = default;
 
   /// Takes an array of tensors inputs, on which the generated loops will
   /// iterate on. The index of the tensor in the array is also the tensor id
public:
   ///   for (i = p0; i < end; i++)
   ///     ...
   ///   // loop sequence end.
   /// }
   void enterNewLoopSeq(OpBuilder &builder, Location loc, ArrayRef<size_t> tids,
                        ArrayRef<size_t> dims);
 
   // exit the current loop sequence, this will reset universal index to 0.
-  void exitCurrentLoopSeq() {
-    assert(loopSeqStack.size() == loopStack.size() + 1);
-    loopSeqStack.pop_back();
-  }
+  void exitCurrentLoopSeq(OpBuilder &builder, Location loc);
 
   // TODO: Gets rid of `dim` in the argument list? Track the dimension we
   // are currently at internally. Then it would be enterNextDimForTensor.
   // Still need a way to specify the dim for non annoated dense tensor though,
   // as it can be accessed out of order.
   /// Emits loop over tensor_tid_dim, it assumes that loops between
   /// tensor_tid_[0, dim - 1] have already been generated.
   /// The function will also perform in-place update on the `reduc` vector to
const std::vector<std::vector<Value>> &getIdxBuffer() const {
     return idxBuffer;
   };
   const std::vector<Value> &getValBuffer() const { return valBuffer; };
 
   constexpr static llvm::StringLiteral getLoopEmitterLoopAttrName() {
     return llvm::StringLiteral("Emitted from");
   }
 
 private:
   struct LoopLevelInfo {
-    LoopLevelInfo(ArrayRef<size_t> tids, ArrayRef<size_t> dims, Operation *loop,
+    LoopLevelInfo(ArrayRef<size_t> tids, ArrayRef<size_t> dims,
+                  ArrayRef<size_t> slicedTids, ArrayRef<size_t> slicedDims,
+                  ArrayRef<bool> sliceResolved, Operation *loop,
                   Block *userBlock, Value iv, StringAttr loopTag)
-        : tids(tids), dims(dims), loop(loop), userCodeBlock(userBlock), iv(iv) {
+        : tids(tids), dims(dims), slicedTids(slicedTids),
+          slicedDims(slicedDims), sliceResolved(sliceResolved), loop(loop),
+          userCodeBlock(userBlock), iv(iv) {
       // Attached a special tag to loop emitter generated loop.
       if (loopTag)
         loop->setAttr(LoopEmitter::getLoopEmitterLoopAttrName(), loopTag);
     }
     // TODO: maybe use a vector<pair> for tid and dim?
     // The set of tensors that the loop is operating on
     const llvm::SmallVector<size_t> tids;
     // The corresponding dims for the tensors
     const llvm::SmallVector<size_t> dims;
+    // The set of tensors that the loop is operating on
+    const llvm::SmallVector<size_t> slicedTids;
+    // The corresponding dims for the tensors
+    const llvm::SmallVector<size_t> slicedDims;
+    // The corresponding dims for the tensors
+    const llvm::SmallVector<bool> sliceResolved;
     const Operation *loop;      // the loop operation
     Block *const userCodeBlock; // the block holding user' generated code.
     const Value iv;             // the induction variable for the loop
   };
 
+  struct SliceInfo {
+    SliceInfo(Value baseSlice, Value minCoord, Value offset, Value isNonEmpty,
+              std::optional<unsigned> slicedOnLvl, unsigned depth)
+        : baseSlice(baseSlice), minCoord(minCoord), offset(offset),
+          isNonEmpty(isNonEmpty), slicedOnLvl(slicedOnLvl), depth(depth) {
+      assert(!slicedOnLvl || minCoord);
+    }
+
+    // Whether this is the first slice
+    bool isInitialTensor() const { return !slicedOnLvl.has_value(); }
+
+    Value baseSlice;  // the current slices being reduced
+    Value minCoord;   // the minimal coordinates of the slice on lvl.
+    Value offset;     // the offset of the current slice.
+    Value isNonEmpty; // whether the slice is empty.
+    std::optional<unsigned> slicedOnLvl; // the level on which the slice is done
+    unsigned depth; // the depth (relative to dependentDimMap[tid][lvl]).
+  };
+
   /// Linearizes address for dense dimension (i.e., p = (i * d0) + j).
   Value genAddress(OpBuilder &builder, Location loc, size_t tid, size_t dim,
                    Value iv);
 
   /// Generate a predicate to determine whether the tranformed coordinates is
   /// on the given slice.
   /// Returns std::pair<Transformed coordinates, Predicate>
   std::pair<Value, Value> genSliceLegitPredicate(OpBuilder &builder,
                                                  Location loc, Value coord,
private:
 
   /// Emits extra locals, since the locals might not be in simplified lattices
   /// point used to generate the loops, but are still required to generates
   /// expressions.
   void emitExtraLocalsForTensorsAtDenseDims(OpBuilder &builder, Location loc,
                                             ArrayRef<size_t> tids,
                                             ArrayRef<size_t> dims);
 
+  Operation *emitForLoopOverTensorAtDim(OpBuilder &builder, Location loc,
+                                        size_t tid, size_t dim,
+                                        MutableArrayRef<Value> reduc,
+                                        bool isParallel);
+
   /// Exits a for loop, returns the reduction results, e.g.,
   /// For sequential for loops:
   /// %ret = for () {
   ///   ...
   ///   %val = addi %args, %c
   ///   yield %val
   /// }
   /// For parallel loops, the following generated code by users:
   /// %ret = parallel () init(%args) {
   ///   ...
   ///   %val = op %args, %c
   /// }
private:
   /// users (`reduc`).
   void exitForLoop(RewriterBase &rewriter, Location loc,
                    MutableArrayRef<Value> reduc);
 
   /// Exits a while loop, returns the reduction results.
   void exitWhileLoop(OpBuilder &builder, Location loc,
                      MutableArrayRef<Value> reduc);
 
+  //
+  // Slice-driven loop related methods.
+  //
+
+  /// Retrieves the most recent slices on lvl. To reduce affine expression like
+  /// d0 + d1 + d2, we need two slices (one of size d1 + d2, and the other of
+  /// size d2). This methods returns the latter slice (of size d2), which is
+  /// also the final slice on the level.
+  SliceInfo &getFinalSliceOnLvl(size_t tid, size_t lvl);
+
+  /// Get the total number of constraints that needed to fully resolve the
+  /// dependent dimension on tensor[tid].
+  size_t sliceTotalConstraints(size_t tid);
+
+  /// Whether the tid is fully resolved, i.e., all the dependent dimension are
+  /// reduced by slices offsets.
+  bool sliceFullyResolved(size_t tid);
+
+  /// Generates a whileOp to iterate over a subset of coordinates on tid on lvl
+  /// using the pHi and pLo provided, the loop break on the first coordinate
+  /// that exceeds the slice boundary (i.e., coord >= slice.offset +
+  /// slice.size).
+  std::pair<Operation *, ValueRange>
+  genSliceLvlTraverseLoop(OpBuilder &builder, Location loc, Value pLo,
+                          Value pHi, Value offset, size_t tid, size_t lvl,
+                          size_t depth, ValueRange userReduc, bool genYield,
+                          /*bodyBody=*/
+                          llvm::function_ref<void(OpBuilder &, Location, Value,
+                                                  MutableArrayRef<Value>)>);
+
+  /// Generates a nested loop that iterates over tid on all the coordinates on
+  /// lvl.
+  ValueRange genSliceAllLvlTraverseLoop(
+      OpBuilder &builder, Location loc, Value offset, size_t tid, size_t lvl,
+      size_t depth, ValueRange userReduc,
+      /*bodyBody=*/
+      llvm::function_ref<void(OpBuilder &, Location, Value,
+                              MutableArrayRef<Value>)>);
+
+  /// Generates code to get the first non-empty slice of tid on lvl.
+  /// return true if has already been resolved.
+  bool genSliceBegin(OpBuilder &builder, Location loc, size_t tid, size_t lvl);
+
+  /// Generates code to get the next non-empty slices of tid on lvl.
+  void genSliceNextInduction(OpBuilder &builder, Location loc,
+                             const Operation *whileOp, size_t tid, size_t lvl,
+                             SmallVectorImpl<Value> &operands,
+                             unsigned &retIdx);
+
+  /// Generates a slice-driven while loop like follows.
+  ///
+  /// curSlice = getFirstNonEmptySlice(tensor).
+  ///
+  /// while(isNonEmpty) {
+  ///   ..user code..
+  ///   isNonEmpty, curSlice = getNextNonEmptySlice(curSlice)
+  /// }
+  Operation *emitSliceDrivenLoopOverTensorAtDim(OpBuilder &builder,
+                                                Location loc, size_t tid,
+                                                size_t lvl,
+                                                MutableArrayRef<Value> reduc);
+
   /// A optional string attribute that should be attached to the loop
   /// generated by loop emitter, it might help following passes to identify
   /// loops that operates on sparse tensors more easily.
   StringAttr loopTag;
   /// Whether the loop emitter needs to treat the last tensor as the output
   /// tensor.
   bool hasOutput;
   bool isSparseOut;
   /// Input and (optional) output tensors.
   std::vector<Value> tensors;
   /// Values realted to slices.
   std::vector<bool> isSparseSlices;
   std::vector<std::vector<Value>> sliceOffsets;
   std::vector<std::vector<Value>> sliceStrides;
   /// The dim and dim type array for each tensor.
   std::vector<std::vector<Value>> dims;
   std::vector<std::vector<DimLevelType>> dimTypes;
   /// Sparse iteration information (by tensor and dim). These arrays
   /// are updated to remain current within the current loop.
   std::vector<std::vector<Value>> pidxs;
   std::vector<std::vector<Value>> coord;
   std::vector<std::vector<Value>> highs;
   std::vector<std::vector<Value>> ptrBuffer; // to_pointers
   std::vector<std::vector<Value>> idxBuffer; // to_indices
   std::vector<Value> valBuffer;              // to_value
-
-  // Map from [tid, dim] to a list of dependent [tid, dim].
-  // See comments for `DependentDimGetter`.
-  std::vector<std::vector<std::vector<std::pair<unsigned, unsigned>>>>
-      dependentDimMap;
-
   // Loop Stack, stores the information of all the nested loops that are
   // alive.
   std::vector<LoopLevelInfo> loopStack;
 
   // Loop Sequence Stack, stores the unversial index for the current loop
-  // sequence.
-  std::vector<Value> loopSeqStack;
+  // sequence. and a list of tids which was taken sliced.
+  // TODO: maybe we should have a LoopSeqInfo
+  std::vector<
+      std::pair<Value, std::vector<std::tuple<unsigned, unsigned, bool>>>>
+      loopSeqStack;
 
   // Maps AffineDimExpr to the index of the loop in loopStack.
   // TODO: We should probably use a callback function here to make it more
   // general.
   std::vector<unsigned> sparsiferLoopLvlMap;
 
+  //
+  // Slice-driven loops related fields.
+  //
+
+  // Map from [tid, dim] to a list of dependent [tid, dim].
+  // See comments for `DependentDimGetter`.
+  std::vector<std::vector<std::vector<std::pair<unsigned, unsigned>>>>
+      dependentDimMap;
+
+  // The cached pointer buffer for the slices, they serve the same purpose as
+  // ptrBuffer for compressed dimensions. But they always starts with the first
+  // pidx pointing to coord > slice.offset to avoid iteration from the
+  // beginning.
+  std::vector<std::vector<std::vector<Value>>> slicePtrBuffer;
+
+  // The cached size for each slices.
+  std::vector<std::vector<std::vector<Value>>> sliceSizes;
+
+  // The number of resolved constraints so far.
+  std::vector<unsigned> sliceResolvedConstraints;
+
+  // sliceStack[tid] holds the generated slice stack on tid.
+  std::vector<std::vector<SliceInfo>> sliceStack;
+
   // TODO: not yet used, it should track the current level for each tensor
   // to help eliminate `dim` paramters from above APIs.
   // std::vector<size_t> curLv;
 };
 
 } // namespace sparse_tensor
 } // namespace mlir
 
 #endif // MLIR_DIALECT_SPARSETENSOR_TRANSFORMS_SPARSETENSORLOOPEMITTER_H_

mlir/lib/Dialect/SparseTensor/Transforms/LoopEmitter.cpp

 #include "CodegenUtils.h"
 
 #include "mlir/Dialect/Arith/IR/Arith.h"
 #include "mlir/Dialect/Bufferization/IR/Bufferization.h"
 #include "mlir/Dialect/Linalg/IR/Linalg.h"
 #include "mlir/Dialect/Linalg/Utils/Utils.h"
 #include "mlir/Dialect/MemRef/IR/MemRef.h"
 #include "mlir/Dialect/SCF/IR/SCF.h"
+#include "mlir/Dialect/Tensor/IR/Tensor.h"
 
 using namespace mlir;
 using namespace mlir::sparse_tensor;
 
 //===----------------------------------------------------------------------===//
 // File local helper functions.
 //===----------------------------------------------------------------------===//
 
+#define CMPI(predicate)                                                        \
+  LLVM_ATTRIBUTE_UNUSED                                                        \
+  inline static Value predicate##I(OpBuilder &b, Location loc, Value l,        \
+                                   Value r) {                                  \
+    return b.create<arith::CmpIOp>(loc, arith::CmpIPredicate::predicate, l,    \
+                                   r);                                         \
+  }
+
+CMPI(eq)
+CMPI(ne)
+CMPI(slt)
+CMPI(sle)
+CMPI(sgt)
+CMPI(sge)
+CMPI(ult)
+CMPI(ule)
+CMPI(ugt)
+CMPI(uge)
+
+#undef CMPI
+
+/// Extracts a corresponding vector of type from a ValueRange.
+static SmallVector<Type> getTypesFromValues(ValueRange vs) {
+  SmallVector<Type> ret;
+  for (auto v : vs)
+    ret.push_back(v.getType());
+  return ret;
+}
+
 /// Generates a pointer/index load from the sparse storage scheme. Narrower
 /// data types need to be zero extended before casting the value into the
 /// index type used for looping and indexing.
 static Value genIndexLoad(OpBuilder &builder, Location loc, Value ptr,
                           Value s) {
   // For the scalar case, we simply zero extend narrower indices into 64-bit
   // values before casting to index without a performance penalty. Here too,
   // however, indices that already are 64-bit, in theory, cannot express the
   // full range as explained above.
   Value load = builder.create<memref::LoadOp>(loc, ptr, s);
   if (!load.getType().isa<IndexType>()) {
     if (load.getType().getIntOrFloatBitWidth() < 64)
       load = builder.create<arith::ExtUIOp>(loc, builder.getI64Type(), load);
     load =
         builder.create<arith::IndexCastOp>(loc, builder.getIndexType(), load);
   }
   return load;
 }
 
static Value genSliceStride(OpBuilder &builder, Location loc, Value tensor,
   return createOrFoldSliceStrideOp(builder, loc, tensor, toOrigDim(enc, lvl));
 }
 
 static Value toSliceCoord(OpBuilder &builder, Location loc, Value v,
                           Value offset, Value stride, Value tensor,
                           unsigned lvl) {
   // iv = iv * stride + offset
   v = builder.create<arith::MulIOp>(loc, v, stride);
   v = builder.create<arith::AddIOp>(loc, v, offset);
   return v;
 }
 
 static std::pair<Value, Value> fromSliceCoord(OpBuilder &builder, Location loc,
                                               Value iv, Value offset,
                                               Value stride, Value tensor,
                                               unsigned lvl) {
   // iv = (iv - offset) / stride
   iv = builder.create<arith::SubIOp>(loc, iv, offset);
   Value rem = builder.create<arith::RemUIOp>(loc, iv, stride);
   iv = builder.create<arith::DivUIOp>(loc, iv, stride);
   return std::make_pair(iv, rem);
 }
 
+/// Helper method the generate a tensor.extract_slice operation with the given
+/// offset and size on dim.
+static Value genExtractSliceWithOffsetOnDim(OpBuilder &builder, Location loc,
+                                            Value src, Value dynOffset,
+                                            Value sz, unsigned dim) {
+
+  RankedTensorType srcTp = src.getType().cast<RankedTensorType>();
+  int rank = srcTp.getRank();
+
+  SmallVector<int64_t> offsets(rank, 0);
+  SmallVector<int64_t> strides(rank, 1);
+  SmallVector<int64_t> sizes(srcTp.getShape());
+  SmallVector<Value> dynSizes;
+
+  offsets[dim] = ShapedType::kDynamic;
+  sizes[dim] = ShapedType::kDynamic;
+
+  auto srcEncoding = getSparseTensorEncoding(srcTp);
+  SmallVector<SparseTensorDimSliceAttr> sliceAttrs;
+
+  for (unsigned i = 0, e = sizes.size(); i < e; i++) {
+    // Infers the slice attribute array (sets offset/size to dynamic on the
+    // slicing dimension).
+    int offset = i == dim ? SparseTensorDimSliceAttr::kDynamic : 0;
+    int size = (i == dim || ShapedType::isDynamic(sizes[i]))
+                   ? SparseTensorDimSliceAttr::kDynamic
+                   : sizes[i];
+    sliceAttrs.push_back(SparseTensorDimSliceAttr::get(srcTp.getContext(),
+                                                       /*offset=*/offset,
+                                                       /*size=*/size,
+                                                       /*stride=*/1));
+    if (ShapedType::isDynamic(sizes[i])) {
+      if (dim == i)
+        dynSizes.push_back(sz);
+      else
+        dynSizes.push_back(linalg::createOrFoldDimOp(builder, loc, src, dim));
+    }
+  }
+
+  // Keeps original encodings but attaches slice attribute.
+  auto encoding = SparseTensorEncodingAttr::get(
+      srcTp.getContext(), srcEncoding.getDimLevelType(),
+      srcEncoding.getDimOrdering(), srcEncoding.getHigherOrdering(),
+      srcEncoding.getPointerBitWidth(), srcEncoding.getIndexBitWidth(),
+      sliceAttrs);
+
+  auto retTp = RankedTensorType::get(sizes, srcTp.getElementType(), encoding);
+  return builder
+      .create<tensor::ExtractSliceOp>(loc, retTp, src, ValueRange{dynOffset},
+                                      dynSizes, ValueRange{}, offsets, sizes,
+                                      strides)
+      .getResult();
+}
+
 std::pair<Value, Value>
 LoopEmitter::genSliceLegitPredicate(OpBuilder &builder, Location loc,
                                     Value coord, unsigned tid, unsigned lvl) {
   assert(isSparseSlices[tid]);
   Value slice = tensors[tid];
   Value offset = sliceOffsets[tid][lvl];
   Value stride = sliceStrides[tid][lvl];
   auto enc = getSparseTensorEncoding(slice.getType());
 
   std::pair<Value, Value> trans =
       fromSliceCoord(builder, loc, coord, offset, stride, slice, lvl);
 
   SmallVector<Value, 3> conds; // at most 3 conditions
 
   if (auto staticOffset = enc.getStaticLvlSliceOffset(lvl);
       !(staticOffset.has_value() && *staticOffset == 0)) {
     // 1st, coord >= offset (skip the check if offset is known to be 0).
-    auto geOffset = builder.create<arith::CmpIOp>(
-        loc, arith::CmpIPredicate::uge, coord, offset);
+    auto geOffset = ugeI(builder, loc, coord, offset);
     conds.push_back(geOffset);
   }
 
   // 2nd, coord_in_slice < length
-  auto ltLength = builder.create<arith::CmpIOp>(loc, arith::CmpIPredicate::ult,
-                                                trans.first, dims[tid][lvl]);
+  auto ltLength = ultI(builder, loc, trans.first, dims[tid][lvl]);
   conds.push_back(ltLength);
 
   if (auto staticStride = enc.getStaticLvlSliceStride(lvl);
       !(staticStride.has_value() && *staticStride == 1)) {
     // 3rd, rem == 0 (skip the check if stride is known to be 1).
-    auto fitStride = builder.create<arith::CmpIOp>(
-        loc, arith::CmpIPredicate::eq, trans.second,
-        constantIndex(builder, loc, 0));
+    auto fitStride =
+        eqI(builder, loc, trans.second, constantIndex(builder, loc, 0));
     conds.push_back(fitStride);
   }
 
   // Must meet all condition to be a valid coordinate in slice.
   auto pred = conds.front();
   for (unsigned i = 1, e = conds.size(); i < e; i++)
     pred = builder.create<arith::AndIOp>(loc, pred, conds[i]);
 
   return {trans.first, pred};
 }
 
 //===----------------------------------------------------------------------===//
 // Sparse tensor loop emitter class implementations
 //===----------------------------------------------------------------------===//
 
 Value LoopEmitter::genAddress(OpBuilder &builder, Location loc, size_t tid,
                               size_t dim, Value iv) {
   Value p = dim == 0 ? constantIndex(builder, loc, 0) : pidxs[tid][dim - 1];
   Value mul = builder.create<arith::MulIOp>(loc, highs[tid][dim], p);
-  if (isSparseSlices[tid])
+  if (isSparseSlices[tid]) {
     iv = toSliceCoord(builder, loc, iv, sliceOffsets[tid][dim],
                       sliceStrides[tid][dim], tensors[tid], dim);
+  }
   Value add = builder.create<arith::AddIOp>(loc, mul, iv);
   return add;
 }
 
 LoopEmitter::LoopEmitter(ValueRange tensors, StringAttr loopTag, bool hasOutput,
                          bool isSparseOut, ArrayRef<unsigned> topSort,
                          DependentDimGetter getter) {
   initialize(tensors, loopTag, hasOutput, isSparseOut, topSort, getter);
void LoopEmitter::initialize(ValueRange tensors, StringAttr loopTag,
   this->ptrBuffer.assign(tensors.size(), std::vector<Value>());
   this->idxBuffer.assign(tensors.size(), std::vector<Value>());
   this->valBuffer.assign(tensors.size(), nullptr);
   this->loopStack.reserve(topSort.size());
   this->sparsiferLoopLvlMap.assign(topSort.size(), 0);
   this->dependentDimMap.assign(
       tensors.size(),
       std::vector<std::vector<std::pair<unsigned, unsigned>>>());
+  this->slicePtrBuffer.assign(tensors.size(),
+                              std::vector<std::vector<Value>>());
+  this->sliceSizes.assign(tensors.size(), std::vector<std::vector<Value>>());
+  this->sliceStack.assign(tensors.size(), std::vector<SliceInfo>());
+  this->sliceResolvedConstraints.assign(tensors.size(), 0);
 
   for (size_t tid = 0, e = tensors.size(); tid < e; tid++) {
 
     auto t = tensors[tid];
     // a scalar or 0-dimension tensors
     if (isZeroRankedTensorOrScalar(t.getType()))
       continue;
     auto rtp = getRankedTensorType(t);
     auto rank = static_cast<size_t>(rtp.getRank());
     auto enc = getSparseTensorEncoding(rtp);
     // We always treat sparse output tensor as dense so that we always iterate
     // it based on dim size.
     if (enc && !(isOutputTensor(tid) && isSparseOut)) {
       isSparseSlices[tid] = enc.isSlice();
       for (auto dimTp : enc.getDimLevelType())
         dimTypes[tid].push_back(dimTp);
     } else
       dimTypes[tid].assign(rank, DimLevelType::Dense);
 
     // Initialize using empty value.
     sliceOffsets[tid].assign(rank, Value());
     sliceStrides[tid].assign(rank, Value());
     dims[tid].assign(rank, Value());
     pidxs[tid].assign(rank, Value());
     coord[tid].assign(rank, Value());
     highs[tid].assign(rank, Value());
     ptrBuffer[tid].assign(rank, Value());
     idxBuffer[tid].assign(rank, Value());
 
+    // Slice-driven loops related initialization.
     dependentDimMap[tid].assign(rank,
                                 std::vector<std::pair<unsigned, unsigned>>());
-    if (dimGetter)
-      for (unsigned i = 0; i < rank; i++)
+    slicePtrBuffer[tid].assign(rank, std::vector<Value>());
+    sliceSizes[tid].assign(rank, std::vector<Value>());
+    sliceStack[tid].emplace_back(tensors[tid], /*minCoord=*/Value(),
+                                 /*offset=*/Value(), /*isNonEmpty*/ Value(),
+                                 std::nullopt, 0);
+    if (dimGetter) {
+      for (unsigned i = 0; i < rank; i++) {
         dependentDimMap[tid][i] = dimGetter(tid, i);
+        unsigned depends = dependentDimMap[tid][i].size();
+        if (depends != 0) {
+          // We need depends - 1 slices to fully resolve the affine expression.
+          slicePtrBuffer[tid][i].assign(depends - 1, nullptr);
+          sliceSizes[tid][i].assign(depends - 1, nullptr);
+        }
+      }
+    }
   }
 
   // FIXME: This map should be maintained outside loop emitter.
   for (unsigned i = 0, e = topSort.size(); i < e; i++) {
     // This is an inverse map of the topologically sorted loop index from
     // sparsifier. This is needed to map the AffineDimExpr back to the
     // loopStack index used in loop emitter.
     sparsiferLoopLvlMap[topSort[i]] = i;
if (!enc) {
       // Annotated sparse tensors.
       // We also need the value buffer for annotated all dense `sparse` tensor.
       valBuffer[t] = genToValues(builder, loc, tensor);
     }
     // NOTE: we can also prepare for 0 dim here in advance, this will hosit
     // some loop preparation from tensor iteration, but will also
     // (undesirably) hosit the code ouside if conditions.
   }
+
+  Type indexType = builder.getIndexType();
+  Value c0 = constantZero(builder, loc, indexType);
+  Value c2 = constantIndex(builder, loc, 2);
+  // TODO: We should probably use integer with pointer bitwidth for the cache.
+  MemRefType cacheTp = MemRefType::get({ShapedType::kDynamic}, indexType);
+  // Generate caches required to fast compute next-non-empty slices with
+  // increasing offset for slice-base loop.
+  // We need to start a separate loop here because the cache size depends on the
+  // dimension size computed in the aboves loops.
+  for (size_t t = 0, e = tensors.size(); t < e; t++) {
+    auto rtp = tensors[t].getType().dyn_cast<RankedTensorType>();
+    if (!rtp)
+      continue;
+
+    // for a pair of [pLo, pHi]. Note that we can not compress pHi because slice
+    // creates segments in the index buffer so that the pHi for the current dim
+    // is no longer the pLo for the next dim.
+    Value pIdxSize = c2;
+    auto rank = rtp.getRank();
+    for (unsigned lvl = 0; lvl < rank; lvl++) {
+      if (!dependentDimMap[t][lvl].empty()) {
+        // Needs at least two operands to form a non-trivial affine expression.
+        ArrayRef<std::pair<unsigned, unsigned>> dependedDim =
+            dependentDimMap[t][lvl];
+        assert(dependedDim.size() > 1);
+
+        Value size = c0;
+        for (unsigned e = dependedDim.size() - 1; e >= 1; e--) {
+          auto [dt, dd] = dependedDim[e];
+          size = builder.create<arith::AddIOp>(loc, size, dims[dt][dd]);
+          sliceSizes[t][lvl][e - 1] = size;
+        }
+
+        // No cache for dense level, they can be simply increased by one.
+        auto dlt = dimTypes[t][lvl];
+
+        if (!isDenseDLT(dlt)) {
+          llvm::for_each(slicePtrBuffer[t][lvl], [cacheTp, pIdxSize, c2, loc,
+                                                  &builder](Value &cache) {
+            cache = builder.create<memref::AllocaOp>(
+                loc, cacheTp,
+                // Additional two metadata {memSize, idx} at head.
+                builder.create<arith::AddIOp>(loc, pIdxSize, c2).getResult());
+          });
+        }
+
+        // Accumlates the size required to cache the pLo for the slice.
+        // E.g., if we want to cache the pIdx for slice<d0xd1xf64> on the second
+        // level. We at most need to a memref<d0xindex>.
+        // NOTE: this is apperantly an over-approximation when the previous
+        // level is compressed, and we can compute a precise memory size
+        // inside the loops. But that would also requires us to allocate/free
+        // memorys in loops.
+        // TODO: Maybe using allocaScopOp inside the loop to resolve the issue?
+        if (!dependentDimMap[t][lvl].empty()) {
+          auto [dt, dd] = dependentDimMap[t][lvl].back();
+          pIdxSize = builder.create<arith::MulIOp>(loc, pIdxSize, dims[dt][dd]);
+        } else {
+          // This level does not need to be sliced, the final size of the slice
+          // on the level will be the same as the current size.
+          pIdxSize = builder.create<arith::MulIOp>(loc, pIdxSize, dims[t][lvl]);
+        }
+      }
+    }
+  }
 }
 
 void LoopEmitter::enterNewLoopSeq(OpBuilder &builder, Location loc,
                                   ArrayRef<size_t> tids,
                                   ArrayRef<size_t> dims) {
   assert(loopSeqStack.size() == loopStack.size());
-  // Universal Index starts from 0.
-  loopSeqStack.emplace_back(constantIndex(builder, loc, 0));
   // Prepares for all the tensors used in the current loop sequence.
-  for (auto [tid, dim] : llvm::zip(tids, dims))
+  std::vector<std::tuple<unsigned, unsigned, bool>> slicedTids;
+  for (auto [tid, dim] : llvm::zip(tids, dims)) {
+    if (!dependentDimMap[tid][dim].empty()) {
+      bool fullyRes = genSliceBegin(builder, loc, tid, dim);
+      slicedTids.emplace_back(tid, dim, fullyRes);
+    } else {
       prepareLoopOverTensorAtDim(builder, loc, tid, dim);
     }
+  }
+
+  // Universal Index starts from 0.
+  loopSeqStack.emplace_back(constantIndex(builder, loc, 0),
+                            std::move(slicedTids));
+}
+
+void LoopEmitter::exitCurrentLoopSeq(OpBuilder &builder, Location loc) {
+  assert(loopSeqStack.size() == loopStack.size() + 1);
+
+  const std::vector<std::tuple<unsigned, unsigned, bool>> &slicedTids =
+      loopSeqStack.back().second;
+
+  // Pop out outdated slices.
+  for (auto [tid, lvl, res] : slicedTids) {
+    if (!res) {
+      assert(sliceStack[tid].back().slicedOnLvl == lvl);
+      sliceStack[tid].pop_back();
+      // There is an additional item in sliceStack for the input tensor.
+      assert(sliceResolvedConstraints[tid] + 1 == sliceStack[tid].size());
+    } else {
+      Value c1 = constantIndex(builder, loc, 1);
+      Value c2 = constantIndex(builder, loc, 2);
+
+      // pIdx += 2, we finished the current lvl, advance the pointer index of
+      // the previous level by two to skip the [pLo, pHi] for current level.
+      // TODO: we could probably use an SSA value for it.
+      Value sPtrBuf = slicePtrBuffer[tid][lvl].back();
+      Value curP = genIndexLoad(builder, loc, sPtrBuf, c1);
+      Value nexP = builder.create<arith::AddIOp>(loc, curP, c2);
+      builder.create<memref::StoreOp>(loc, nexP, sPtrBuf, c1);
+    }
+  }
+  loopSeqStack.pop_back();
+}
 
 Value LoopEmitter::genAffine(OpBuilder &builder, AffineExpr a, Location loc) {
   switch (a.getKind()) {
   case AffineExprKind::DimId: {
     unsigned idx = a.cast<AffineDimExpr>().getPosition();
     return loopStack[sparsiferLoopLvlMap[idx]].iv;
   }
   case AffineExprKind::Add: {
case AffineExprKind::Constant: {
     int64_t c = a.cast<AffineConstantExpr>().getValue();
     return constantIndex(builder, loc, c);
   }
   default:
     llvm_unreachable("unexpected affine subscript");
   }
 }
 
-Operation *LoopEmitter::enterLoopOverTensorAtDim(
-    OpBuilder &builder, Location loc, ArrayRef<size_t> tids,
-    ArrayRef<size_t> dims, MutableArrayRef<Value> reduc, bool isParallel) {
-  // TODO: support multiple return on parallel for?
-  assert(!isParallel || reduc.size() <= 1);
-  bool isSparseInput = false;
-  size_t tid = tids.front(), dim = dims.front();
-  for (auto [t, d] : llvm::zip(tids, dims)) {
-    assert(dimTypes[t].size() > d); // Must be a valid tid, dim pair
-    assert(!coord[t][d]);           // We cannot re-enter the same level
-    auto dimType = dimTypes[t][d];
-    // Must be a recognizable DLT.
-    assert(isDenseDLT(dimType) || isCompressedDLT(dimType) ||
-           isSingletonDLT(dimType));
-    bool isSparse = isCompressedDLT(dimType) || isSingletonDLT(dimType);
-    // We can at most have one sparse input, otherwise, a while loop is
-    // required to co-iterate multiple sparse tensors.
-    assert(!isSparseInput || !isSparse);
-    if (isSparse) {
-      tid = t;
-      dim = d;
-    }
-    isSparseInput = isSparseInput || isSparse;
-  }
+Operation *LoopEmitter::emitForLoopOverTensorAtDim(OpBuilder &builder,
+                                                   Location loc, size_t tid,
+                                                   size_t dim,
+                                                   MutableArrayRef<Value> reduc,
+                                                   bool isParallel) {
+  bool isSparseCond =
+      isCompressedDLT(dimTypes[tid][dim]) || isSingletonDLT(dimTypes[tid][dim]);
 
   // TODO: support dynamic slices.
   Value step = constantIndex(builder, loc, 1);
-  Value lo = isSparseInput ? pidxs[tid][dim]      // current offset
-                           : loopSeqStack.back(); // universal index
+  Value lo = isSparseCond ? pidxs[tid][dim]            // current offset
+                          : loopSeqStack.back().first; // universal index
   Value hi = highs[tid][dim];
 
   Operation *loop = nullptr;
   Value iv;
   if (isParallel) {
     scf::ParallelOp parOp =
         builder.create<scf::ParallelOp>(loc, lo, hi, step, reduc);
     builder.setInsertionPointToStart(parOp.getBody());
if (isParallel) {
     assert(forOp.getNumRegionIterArgs() == reduc.size());
     for (int i = 0, e = reduc.size(); i < e; i++)
       reduc[i] = forOp.getRegionIterArg(i);
     loop = forOp;
   }
   assert(loop && iv);
 
   Value c;
-  if (isSparseInput) {
+  if (isSparseCond) {
     pidxs[tid][dim] = iv;
     // Generating a load on the indices array yields the coordinate.
     Value ptr = idxBuffer[tid][dim];
     c = genIndexLoad(builder, loc, ptr, iv);
   } else {
     // Dense tensor, the coordinates is the inducation variable.
     c = iv;
   }
 
-  if (isSparseSlices[tid] && isSparseInput) {
+  if (isSparseSlices[tid] && isSparseCond) {
     // For sparse level slices, we need to filter out invalid coordinates that
     // are not included in the slice.
     SmallVector<Type> types;
     for (Value red : reduc)
       types.push_back(red.getType());
 
     auto [trans, pred] = genSliceLegitPredicate(builder, loc, c, tid, dim);
     bool hasReduc = !types.empty();
if (isSparseSlices[tid] && isSparseCond) {
     }
     // Set the insert point to matched branch.
     builder.setInsertionPointToStart(&ifOp.getThenRegion().front());
     c = trans;
   }
 
   assert(c);
   coord[tid][dim] = c;
+  return loop;
+}
+
+Operation *LoopEmitter::enterLoopOverTensorAtDim(
+    OpBuilder &builder, Location loc, ArrayRef<size_t> tids,
+    ArrayRef<size_t> dims, MutableArrayRef<Value> reduc, bool isParallel) {
+  // TODO: support multiple return on parallel for?
+  assert(!isParallel || reduc.size() <= 1);
+  bool isSparseCond = false, isSliceCond = false;
+  size_t tid = tids.front(), dim = dims.front();
+
+  for (auto [t, d] : llvm::zip(tids, dims)) {
+    assert(dimTypes[t].size() > d);         // Must be a valid tid, dim pair
+    assert(!coord[t][d] ||                  // We cannot re-enter the same level
+           !dependentDimMap[t][d].empty()); // unless it is a slice-driver loop
+    auto dimType = dimTypes[t][d];
+    // Must be a recognizable DLT.
+    assert(isDenseDLT(dimType) || isCompressedDLT(dimType) ||
+           isSingletonDLT(dimType));
+
+    // This is a slice-driven loop.
+    if (!dependentDimMap[t][d].empty()) {
+      assert(!isSliceCond && !isSparseCond);
+      isSliceCond = true;
+      tid = t;
+      dim = d;
+      continue;
+    }
+
+    bool isSparse = isCompressedDLT(dimType) || isSingletonDLT(dimType);
+    // We can at most have one sparse input, otherwise, a while loop is
+    // required to co-iterate multiple sparse tensors.
+    assert(!isSparseCond || !isSparse);
+    assert(!isSliceCond || !isSparseCond);
+    if (isSparse) {
+      tid = t;
+      dim = d;
+    }
+    isSparseCond = isSparseCond || isSparse;
+  }
+
+  // if the slice is fully reduced, we can now use TACO-based algorithm to
+  // iterate it.
+  Operation *l = nullptr;
+  if (isSliceCond) {
+    bool fullyResolved = sliceFullyResolved(tid);
+    if (!fullyResolved) {
+      l = emitSliceDrivenLoopOverTensorAtDim(builder, loc, tid, dim, reduc);
+    } else {
+      const SliceInfo &info = getFinalSliceOnLvl(tid, dim);
+      Value offset = info.offset;
+      unsigned depth = info.depth - 1;
+      Operation *insertPoint = nullptr;
+      // TODO: we should generalize the method to support iteration over for
+      // normal slices as well to allow early break.
+      l = genSliceLvlTraverseLoop(
+              builder, loc, pidxs[tid][dim], highs[tid][dim], offset, tid, dim,
+              depth, reduc,
+              /*genYield=*/false, // unaware of the yield values from user yet
+              [this, tid, dim, reduc, offset,
+               &insertPoint](OpBuilder &builder, Location loc, Value iv,
+                             MutableArrayRef<Value> innerReduc) {
+                assert(innerReduc.size() == reduc.size());
+                // Updates users' reduction variable inplace
+                for (unsigned i = 0, e = reduc.size(); i < e; i++)
+                  reduc[i] = innerReduc[i];
+                // Loads the coordinates.
+                Value absC =
+                    genIndexLoad(builder, loc, idxBuffer[tid][dim], iv);
+
+                // We need to substract the offset to get relative coordinates.
+                // TODO: how to assert relC >=0 during runtime?
+                insertPoint = builder.create<arith::SubIOp>(loc, absC, offset);
+                pidxs[tid][dim] = iv;
+                coord[tid][dim] = insertPoint->getResult(0);
+              })
+              .first;
+      // We did not finish the loop body, reset the insertion point and delegate
+      // to user.
+      builder.setInsertionPointAfter(insertPoint);
+    }
     // NOTE: we can also prepare for next dim here in advance
-  // Push the loop into stack
-  loopStack.emplace_back(ArrayRef<size_t>(tid), ArrayRef<size_t>(dim), loop,
-                         builder.getInsertionBlock(), coord[tid][dim], loopTag);
+    // Pushes the loop into stack.
+    loopStack.emplace_back(
+        ArrayRef<size_t>(), ArrayRef<size_t>(), ArrayRef<size_t>(tid),
+        ArrayRef<size_t>(dim), ArrayRef<bool>(fullyResolved), l,
+  } else {
+    l = emitForLoopOverTensorAtDim(builder, loc, tid, dim, reduc, isParallel);
+    // NOTE: we can also prepare for next dim here in advance
+    // Pushes the loop into stack.
+    loopStack.emplace_back(ArrayRef<size_t>(tid), ArrayRef<size_t>(dim),
+                           ArrayRef<size_t>(), ArrayRef<size_t>(),
+                           ArrayRef<bool>(), l, builder.getInsertionBlock(),
+                           coord[tid][dim], loopTag);
+  }
+
   // Emit extra locals.
   emitExtraLocalsForTensorsAtDenseDims(builder, loc, tids, dims);
-
-  return loop;
+  return l;
 }
 
 Operation *LoopEmitter::enterFilterLoopOverTensorAtDim(
     OpBuilder &builder, Location loc, size_t tid, size_t dim, AffineExpr affine,
     MutableArrayRef<Value> reduc) {
   assert(!affine.isa<AffineDimExpr>() && !isDenseDLT(dimTypes[tid][dim]));
   assert(dimTypes[tid].size() > dim);
   // We can not re-enter the same level.
Operation *LoopEmitter::enterFilterLoopOverTensorAtDim(
   // index.
   scf::ForOp forOp = builder.create<scf::ForOp>(loc, lo, hi, step, reduc);
 
   // In-place update on the reduction variable vector.
   assert(forOp.getNumRegionIterArgs() == reduc.size());
   for (int i = 0, e = reduc.size(); i < e; i++)
     reduc[i] = forOp.getRegionIterArg(i);
 
   builder.setInsertionPointToStart(forOp.getBody());
   Value iv = forOp.getInductionVar();
 
   pidxs[tid][dim] = iv;
   // Generating a load on the indices array yields the coordinate.
   Value ptr = idxBuffer[tid][dim];
   coord[tid][dim] = genIndexLoad(builder, loc, ptr, iv);
 
   // Generate an if condition to filter out indices that is not equal to the
   // result of the affine expression.
   Value expected = genAffine(builder, affine, loc);
-  auto pred = builder.create<arith::CmpIOp>(loc, arith::CmpIPredicate::eq,
-                                            coord[tid][dim], expected);
+  auto pred = eqI(builder, loc, coord[tid][dim], expected);
   SmallVector<Type> types;
   for (Value red : reduc) {
     types.push_back(red.getType());
   }
 
   bool hasReduc = !types.empty();
   scf::IfOp ifOp =
       builder.create<scf::IfOp>(loc, types, pred, /*else*/ hasReduc);
if (hasReduc) {
     // On mismatch.
     builder.create<scf::YieldOp>(loc, reduc);
   }
   // Set the insert point to matched branch.
   builder.setInsertionPointToStart(&ifOp.getThenRegion().front());
 
   // NOTE: we can also prepare for next dim here in advance
   // Push the loop into stack
-  loopStack.emplace_back(ArrayRef<size_t>(tid), ArrayRef<size_t>(dim), forOp,
-                         builder.getInsertionBlock(), coord[tid][dim], nullptr);
+  loopStack.emplace_back(ArrayRef<size_t>(tid), ArrayRef<size_t>(dim),
+                         ArrayRef<size_t>(), ArrayRef<size_t>(),
+                         ArrayRef<bool>(), forOp, builder.getInsertionBlock(),
+                         coord[tid][dim], nullptr);
   return forOp;
 }
 
 void LoopEmitter::genDenseAffineAddressAtCurLevel(OpBuilder &builder,
                                                   Location loc, size_t tid,
                                                   size_t dim,
                                                   AffineExpr affine) {
   Value affineV = genAffine(builder, affine, loc);
   pidxs[tid][dim] = genAddress(builder, loc, tid, dim, affineV);
 }
 
 Operation *LoopEmitter::enterCoIterationOverTensorsAtDims(
     OpBuilder &builder, Location loc, ArrayRef<size_t> tids,
     ArrayRef<size_t> dims, bool needsUniv, MutableArrayRef<Value> reduc) {
+
+  // NOTE: make sure that the slice driven tensor-related reduction variable
+  // appears first than normal tensors.
   assert(tids.size() == dims.size());
   SmallVector<Type> types;
   SmallVector<Value> operands;
   // Construct the while-loop with a parameter for each index.
   Type indexType = builder.getIndexType();
   for (auto [tid, dim] : llvm::zip(tids, dims)) {
+    // TODO: support coiteration with slice driven tensors.
+    assert(dependentDimMap[tid][dim].empty() && "TODO: not yet implemented");
     if (isCompressedDLT(dimTypes[tid][dim]) ||
         isSingletonDLT(dimTypes[tid][dim])) {
       assert(pidxs[tid][dim]);
       types.push_back(indexType);
       operands.push_back(pidxs[tid][dim]);
     }
   }
   // The position where user-supplied reduction variable starts.
   for (Value rec : reduc) {
     types.push_back(rec.getType());
     operands.push_back(rec);
   }
   if (needsUniv) {
     types.push_back(indexType);
     // Update universal index.
-    operands.push_back(loopSeqStack.back());
+    operands.push_back(loopSeqStack.back().first);
   }
   assert(types.size() == operands.size());
   scf::WhileOp whileOp = builder.create<scf::WhileOp>(loc, types, operands);
 
   SmallVector<Location> locs(types.size(), loc);
   Block *before = builder.createBlock(&whileOp.getBefore(), {}, types, locs);
   Block *after = builder.createBlock(&whileOp.getAfter(), {}, types, locs);
 
   // Build the "before" region, which effectively consists
   // of a conjunction of "i < upper" tests on all induction.
   builder.setInsertionPointToStart(&whileOp.getBefore().front());
   Value cond;
   unsigned o = 0;
   for (auto [tid, dim] : llvm::zip(tids, dims)) {
     if (isCompressedDLT(dimTypes[tid][dim]) ||
         isSingletonDLT(dimTypes[tid][dim])) {
       Value op1 = before->getArgument(o);
       Value op2 = highs[tid][dim];
-      Value opc = builder.create<arith::CmpIOp>(loc, arith::CmpIPredicate::ult,
-                                                op1, op2);
+      Value opc = ultI(builder, loc, op1, op2);
       cond = cond ? builder.create<arith::AndIOp>(loc, cond, opc) : opc;
       // Update
       pidxs[tid][dim] = after->getArgument(o++);
     }
   }
   builder.create<scf::ConditionOp>(loc, cond, before->getArguments());
 
   // Generates while body.
Operation *LoopEmitter::enterCoIterationOverTensorsAtDims(
 
   Value min;
   // Finds the minimum coordinate
   if (!needsUniv) {
     for (auto [tid, dim] : llvm::zip(tids, dims)) {
       if (isCompressedDLT(dimTypes[tid][dim]) ||
           isSingletonDLT(dimTypes[tid][dim])) {
         if (min) {
-          Value cmp = builder.create<arith::CmpIOp>(
-              loc, arith::CmpIPredicate::ult, coord[tid][dim], min);
+          Value cmp = ultI(builder, loc, coord[tid][dim], min);
           min = builder.create<arith::SelectOp>(loc, cmp, coord[tid][dim], min);
         } else {
           min = coord[tid][dim];
         }
       }
     }
   } else {
     assert(!min);
     // Otherwise, universal index is the minimal pidx.
     min = after->getArguments().back();
   }
 
   // Sets up the loop stack.
-  loopStack.emplace_back(tids, dims, whileOp, builder.getInsertionBlock(), min,
-                         loopTag);
+  loopStack.emplace_back(tids, dims, ArrayRef<size_t>(), ArrayRef<size_t>(),
+                         ArrayRef<bool>(), whileOp, builder.getInsertionBlock(),
+                         min, loopTag);
   assert(loopStack.size() == loopSeqStack.size());
 
   // Emits extra locals
   emitExtraLocalsForTensorsAtDenseDims(builder, loc, tids, dims);
 
   // Updates reduction variables
   assert(after->getNumArguments() == o + reduc.size() + (needsUniv ? 1 : 0));
   // In-place update on reduction variable.

 void LoopEmitter::exitWhileLoop(OpBuilder &builder, Location loc,
                                 MutableArrayRef<Value> reduc) {
   const LoopLevelInfo &loopInfo = loopStack.back();
   auto whileOp = llvm::cast<scf::WhileOp>(loopInfo.loop);
   builder.setInsertionPointToEnd(loopInfo.userCodeBlock);
   auto &dims = loopInfo.dims;
   auto &tids = loopInfo.tids;
   Value iv = loopInfo.iv;
+
   // Finalize the induction. Note that the induction could be performed
   // in the individual if-branches to avoid re-evaluating the conditions.
   // However, that would result in a rather elaborate forest of yield
   // instructions during code generation. Moreover, performing the induction
   // after the if-statements more closely resembles code generated by TACO.
   unsigned o = 0;
   SmallVector<Value> operands;
+  unsigned delta = 0;
+  for (auto [tid, dim, resolved] : llvm::zip(
+           loopInfo.slicedTids, loopInfo.slicedDims, loopInfo.sliceResolved)) {
+    if (!resolved) {
+      genSliceNextInduction(builder, loc, whileOp, tid, dim, operands, o);
+      sliceResolvedConstraints[tid]--;
+    } else {
+      // TODO: We need to distinguish coiterate loop with slice-driven loop and
+      // fully reduced while op for iterating one slices.
+      // since we didn't implement coiteration, this must be iteration just
+      // on fully resolved slice.
+      assert(loopInfo.slicedTids.size() == 1 && loopInfo.tids.empty());
+      // The if guard to filter out out-range coordinates.
+      assert(llvm::isa<scf::IfOp>(builder.getInsertionBlock()->getParentOp()));
+      pidxs[tid][dim] = whileOp->getResult(o++);
+      // FIXME: we are not using continue here since we do not support
+      // coiteration on slices. But it need to be treated similarly as the
+      // universal index.
+      o++; // skip continue flag.
+      // Since we did not push two results from whileOp. The size of the
+      // operands vector is smaller than the actual number of return values from
+      // the whileOp.
+      // It is because we are actually generate yield in the IfOp inside the
+      // whileOp to only iterates over inbound coordinates within the slices.
+      delta += 2;
+    }
+  };
+
   Value one = constantIndex(builder, loc, 1);
   for (auto [tid, dim] : llvm::zip(tids, dims)) {
     if (isCompressedDLT(dimTypes[tid][dim]) ||
         isSingletonDLT(dimTypes[tid][dim])) {
       Value op1 = coord[tid][dim];
       Value op3 = pidxs[tid][dim];
-      Value cmp =
-          builder.create<arith::CmpIOp>(loc, arith::CmpIPredicate::eq, op1, iv);
+      Value cmp = eqI(builder, loc, op1, iv);
       Value add = builder.create<arith::AddIOp>(loc, op3, one);
       operands.push_back(builder.create<arith::SelectOp>(loc, cmp, add, op3));
       // Following loops continue iteration from the break point of the
       // current while loop.
       pidxs[tid][dim] = whileOp->getResult(o++);
       // The coordinates are invalid now.
       coord[tid][dim] = nullptr;
       // highs remains unchanged.
     }
   }
 
   // Reduction value from users.
   for (auto &i : reduc) {
     operands.push_back(i);
     // In place update reduction variable.
     i = whileOp->getResult(o++);
   }
 
   // An (optional) universal index.
-  if (operands.size() < whileOp.getNumResults()) {
-    assert(operands.size() + 1 == whileOp.getNumResults());
+  if (operands.size() + delta < whileOp.getNumResults()) {
+    assert(operands.size() + delta + 1 == whileOp.getNumResults());
     // The last one is the universial index.
     operands.push_back(builder.create<arith::AddIOp>(loc, iv, one));
     // update the loop starting point of current loop sequence
-    loopSeqStack.back() = whileOp->getResult(o++);
+    loopSeqStack.back().first = whileOp->getResult(o++);
   }
 
-  assert(o == operands.size());
+  assert(o == operands.size() + delta);
   builder.create<scf::YieldOp>(loc, operands);
   builder.setInsertionPointAfter(whileOp);
 }
 
 void LoopEmitter::exitCurrentLoop(RewriterBase &rewriter, Location loc,
                                   MutableArrayRef<Value> reduc) {
   // Clean up the values, it would help use to discover potential bug at a
   // earlier stage (instead of silently using a wrong value).
   LoopLevelInfo &loopInfo = loopStack.back();
   assert(loopInfo.tids.size() == loopInfo.dims.size());
   SmallVector<Value> red;
   if (llvm::isa<scf::WhileOp>(loopInfo.loop)) {
     exitWhileLoop(rewriter, loc, reduc);
   } else {
     exitForLoop(rewriter, loc, reduc);
   }
 
   assert(loopStack.size() == loopSeqStack.size());
   loopStack.pop_back();
 }
+
+//===----------------------------------------------------------------------===//
+// Slice-driven loop related methods.
+//===----------------------------------------------------------------------===//
+
+LoopEmitter::SliceInfo &LoopEmitter::getFinalSliceOnLvl(size_t tid,
+                                                        size_t lvl) {
+  for (auto it = sliceStack[tid].rbegin(), ie = sliceStack[tid].rend(); it < ie;
+       it++) {
+    if (it->slicedOnLvl == lvl) {
+      assert(it->depth == dependentDimMap[tid][lvl].size() - 1);
+      return *it;
+    }
+  }
+
+  llvm_unreachable("Failed to find sliceInfo");
+}
+
+size_t LoopEmitter::sliceTotalConstraints(size_t tid) {
+  size_t numConstraints = 0;
+  for (const auto &lvlDeps : dependentDimMap[tid]) {
+    if (!lvlDeps.empty()) {
+      assert(lvlDeps.size() >= 2);
+      numConstraints += lvlDeps.size() - 1;
+    }
+  }
+  return numConstraints;
+}
+
+bool LoopEmitter::sliceFullyResolved(size_t tid) {
+  return sliceTotalConstraints(tid) == sliceResolvedConstraints[tid];
+}
+
+std::pair<Operation *, ValueRange> LoopEmitter::genSliceLvlTraverseLoop(
+    OpBuilder &builder, Location loc, Value loopLo, Value loopHi, Value offset,
+    size_t tid, size_t lvl, size_t depth, ValueRange userReduc, bool genYield,
+    llvm::function_ref<void(OpBuilder &, Location, Value,
+                            MutableArrayRef<Value>)>
+        bodyBuilder) {
+  Value c1 = constantIndex(builder, loc, 1);
+  Value sliceHi =
+      builder.create<arith::AddIOp>(loc, offset, sliceSizes[tid][lvl].back());
+
+  SmallVector<Value> reduc = {
+      loopLo,                         // loop lower bounds
+      constantI1(builder, loc, true), // continue
+  };
+  // Append user required reduction value.
+  reduc.append(userReduc.begin(), userReduc.end());
+  SmallVector<Type> types = getTypesFromValues(reduc);
+
+  scf::WhileOp whileOp = builder.create<scf::WhileOp>(
+      loc, types, reduc,
+      /*beforeBuilder=*/
+      [loopHi](OpBuilder &builder, Location loc, ValueRange args) {
+        Value lo = args[0];
+        Value cont = args[1];
+        Value inBound = ultI(builder, loc, lo, loopHi);
+        Value cond = builder.create<arith::AndIOp>(loc, cont, inBound);
+        // continue if not yet break nor out of bound.
+        builder.create<scf::ConditionOp>(loc, cond, args);
+      },
+      /*afterBuilder=*/
+      [this, c1, tid, lvl, sliceHi, genYield,
+       bodyBuilder](OpBuilder &builder, Location loc, ValueRange args) {
+        Value iv = args[0];
+        Value coord = genIndexLoad(builder, loc, idxBuffer[tid][lvl], iv);
+        // If coord < sliceHi
+        Value cont = ultI(builder, loc, coord, sliceHi);
+
+        SmallVector<Type> types = getTypesFromValues(args.drop_front(2));
+        auto ifOp = builder.create<scf::IfOp>(loc, types, cont, true);
+        {
+          // 2 reduction variable maintained by us.
+          SmallVector<Value> ifRet = args.drop_front(2);
+          assert(ifRet.size() == args.size() - 2);
+
+          OpBuilder::InsertionGuard guard(builder);
+          // If not in slice.
+          // Break the while loop (by setting continue to false)
+          builder.setInsertionPointToStart(&ifOp.getElseRegion().front());
+          builder.create<scf::YieldOp>(loc, ifRet);
+
+          // If this is a legit coordinates in slice
+          builder.setInsertionPointToStart(&ifOp.getThenRegion().front());
+          bodyBuilder(builder, loc, iv, ifRet);
+          if (genYield) {
+            builder.setInsertionPointToEnd(&ifOp.getThenRegion().front());
+            builder.create<scf::YieldOp>(loc, ifRet);
+          }
+        }
+        // Marks this speical ifOp to avoid sparisification finalizing it.
+        ifOp->setAttr(getLoopEmitterLoopAttrName(),
+                      StringAttr::get(builder.getContext(), "slice"));
+        // Insertion point restored to after ifOp.
+        SmallVector<Value> yields;
+        // Increase induction variable.
+        yields.push_back(builder.create<arith::AddIOp>(loc, iv, c1));
+        yields.push_back(cont);
+        yields.append(ifOp.getResults().begin(), ifOp.getResults().end());
+        builder.create<scf::YieldOp>(loc, yields);
+      });
+
+  builder.setInsertionPointAfter(whileOp);
+  return std::make_pair(whileOp, whileOp.getResults().drop_front(2));
+}
+
+ValueRange LoopEmitter::genSliceAllLvlTraverseLoop(
+    OpBuilder &builder, Location loc, Value offset, size_t tid, size_t lvl,
+    size_t depth, ValueRange userReduc,
+    llvm::function_ref<void(OpBuilder &, Location, Value,
+                            MutableArrayRef<Value>)>
+        bodyBuilder) {
+
+  Value c0 = constantIndex(builder, loc, 0);
+  Value c1 = constantIndex(builder, loc, 1);
+  Value c2 = constantIndex(builder, loc, 2);
+
+  // TODO: it only works on all compressed tensor.
+  Value sPtrBuf = slicePtrBuffer[tid][lvl][depth];
+  Value pSt = c2;                                      // pointer starting index
+  Value mSz = genIndexLoad(builder, loc, sPtrBuf, c0); // memSize
+
+  auto forOp =
+      scf::buildLoopNest(
+          builder, loc, pSt, mSz, c2, userReduc,
+          [this, c1, depth, tid, lvl, offset, sPtrBuf,
+           bodyBuilder](OpBuilder &builder, Location loc, ValueRange ivs,
+                        ValueRange iterArgs) -> scf::ValueVector {
+            // generate traversal for each level.
+            Value loopLo = genIndexLoad(builder, loc, sPtrBuf, ivs.front());
+            Value loopHi = genIndexLoad(
+                builder, loc, sPtrBuf,
+                builder.create<arith::AddIOp>(loc, ivs.front(), c1));
+            return genSliceLvlTraverseLoop(builder, loc, loopLo, loopHi, offset,
+                                           tid, lvl, depth, iterArgs, true,
+                                           bodyBuilder)
+                .second;
+          })
+          .loops.front();
+
+  // Insert after current while operation.
+  builder.setInsertionPointAfter(forOp);
+  return forOp.getResults();
+}
+
+bool LoopEmitter::genSliceBegin(OpBuilder &builder, Location loc, size_t tid,
+                                size_t lvl) {
+
+  Value c0 = constantIndex(builder, loc, 0);
+  Value c1 = constantIndex(builder, loc, 1);
+  Value c2 = constantIndex(builder, loc, 2);
+  Value c3 = constantIndex(builder, loc, 3);
+  Value c4 = constantIndex(builder, loc, 4);
+
+  if (sliceFullyResolved(tid)) {
+    // If constraints on the tensor is fully resolved. We do not need to
+    // generates slice begin any more, instead we fall back to TACO-based
+    // algorithm to (co)iterates over the slice.
+    Value pLoPtr =
+        genIndexLoad(builder, loc, slicePtrBuffer[tid][lvl].back(), c1);
+    pLoPtr = builder.create<arith::AddIOp>(loc, pLoPtr, c2);
+    Value pHiPtr = builder.create<arith::AddIOp>(loc, pLoPtr, c1);
+    pidxs[tid][lvl] =
+        genIndexLoad(builder, loc, slicePtrBuffer[tid][lvl].back(), pLoPtr);
+    highs[tid][lvl] =
+        genIndexLoad(builder, loc, slicePtrBuffer[tid][lvl].back(), pHiPtr);
+    return true;
+  }
+
+  // Only when the level is sorted, the next-non-empty slice can be computed
+  // efficiently.
+  assert(isOrderedDLT(dimTypes[tid][lvl]));
+  if (isDenseDLT(dimTypes[tid][lvl]) || isSingletonDLT(dimTypes[tid][lvl]))
+    llvm_unreachable("TODO: dense level should be easy to support, while "
+                     "singleton level requres more efforts");
+
+  assert(!dependentDimMap[tid][lvl].empty());
+  assert(!sliceStack[tid].empty());
+
+  const SliceInfo &sliceInfo = sliceStack[tid].back();
+  auto baseEnc = getSparseTensorEncoding(sliceInfo.baseSlice.getType());
+
+  Value size, minCoord, isNonEmpty;
+  unsigned depth = 0;
+  if (sliceInfo.isInitialTensor()) {
+    // The input tensor is slices, not yet handled.
+    if (baseEnc.isSlice())
+      llvm_unreachable("TODO: not yet implemented");
+
+    assert(lvl == 0); // must be reduing the affine expression on the first lvl.
+    // Fills out pIdxBuffer[tid][lvl][0] with [/*memSize =*/4, 0, 0, pHi]
+    Value sPtrBuf = slicePtrBuffer[tid][0][0];
+    Value pHi = genIndexLoad(builder, loc, ptrBuffer[tid][0], c1);
+    builder.create<memref::StoreOp>(loc, c4, sPtrBuf, c0);  // memSize = 4
+    builder.create<memref::StoreOp>(loc, c0, sPtrBuf, c1);  // index = 0
+    builder.create<memref::StoreOp>(loc, c0, sPtrBuf, c2);  // pLo = 0;
+    builder.create<memref::StoreOp>(loc, pHi, sPtrBuf, c3); // loaded pHi.
+
+    size = sliceSizes[tid][0][0];
+    // This is an non empty tensor if 0 < pHi.
+    isNonEmpty = ultI(builder, loc, c0, pHi);
+    // The minimal coord must be at the first on ordered level.
+    // FIXME: Technically we should load the coord only when the slice is
+    // nonempty. though we assume that even on empty sparse tensors, a non-empty
+    // ptr/idx buffer is allocated for each level so it would not cause OOB to
+    // avoid generating a ifOp here.
+    minCoord = genIndexLoad(builder, loc, idxBuffer[tid][0], c0);
+    depth = 1;
+  } else {
+    unsigned prevLvl = *sliceInfo.slicedOnLvl;
+    assert(lvl >= prevLvl);
+    if (lvl != prevLvl + 1) {
+      // Either lvl = prevSlicedLvl, i.e., t[d0 + d1 + d2,...] (more than one
+      // variable need to be reduced on the same level).
+      // Or lvl > prevSliceLvl + 1, i.e., t[..., d2, d3 + d4] (having a
+      // simple dim expression in between).
+      llvm_unreachable("TODO: not yet implemented");
+    } else {
+      assert(slicePtrBuffer[tid][prevLvl].size() == sliceInfo.depth);
+      Value sPtrBuf = slicePtrBuffer[tid][lvl][0];
+
+      SmallVector<Value, 3> reduc = {
+          constantI1(builder, loc, false), // isNonEmpty
+          dims[tid][lvl],                  // minCoord
+          c2,                              // memSize
+      };
+      ValueRange result = genSliceAllLvlTraverseLoop(
+          builder, loc, sliceInfo.offset, tid, prevLvl, sliceInfo.depth - 1,
+          reduc,
+          [this, c1, c2, tid, lvl, sPtrBuf](OpBuilder &builder, Location loc,
+                                            Value iv,
+                                            MutableArrayRef<Value> reduc) {
+            Value &isNonEmpty = reduc[0];
+            Value &minCoord = reduc[1];
+            Value &curMemSize = reduc[2];
+
+            Value pHi = builder.create<arith::AddIOp>(loc, iv, c1);
+            Value sPLo = genIndexLoad(builder, loc, ptrBuffer[tid][lvl], iv);
+            Value sPHi = genIndexLoad(builder, loc, ptrBuffer[tid][lvl], pHi);
+
+            // isNonEmpty = isNonEmpty || lvlNonEmpty
+            Value lvlNonEmpty = ultI(builder, loc, sPLo, sPHi);
+            isNonEmpty =
+                builder.create<arith::OrIOp>(loc, lvlNonEmpty, isNonEmpty);
+
+            // Update minimal coordinate.
+            auto ifNonEmpty = builder.create<scf::IfOp>(
+                loc, builder.getIndexType(), lvlNonEmpty, true);
+            {
+              OpBuilder::InsertionGuard guard(builder);
+              builder.setInsertionPointToStart(ifNonEmpty.thenBlock());
+              Value curC =
+                  genIndexLoad(builder, loc, idxBuffer[tid][lvl], sPLo);
+              Value isCurSmaller = ultI(builder, loc, curC, minCoord);
+              Value newMin = builder.create<arith::SelectOp>(loc, isCurSmaller,
+                                                             curC, minCoord);
+              builder.create<scf::YieldOp>(loc, newMin);
+              builder.setInsertionPointToStart(ifNonEmpty.elseBlock());
+              builder.create<scf::YieldOp>(loc, minCoord);
+            }
+            minCoord = ifNonEmpty.getResult(0);
+
+            // filles in
+            builder.create<memref::StoreOp>(loc, sPLo, sPtrBuf, curMemSize);
+            Value nxtMemSize =
+                builder.create<arith::AddIOp>(loc, curMemSize, c1);
+            builder.create<memref::StoreOp>(loc, sPHi, sPtrBuf, nxtMemSize);
+
+            // curMemSize += 2
+            curMemSize = builder.create<arith::AddIOp>(loc, curMemSize, c2);
+          });
+
+      size = sliceSizes[tid][lvl][0];
+      isNonEmpty = result[0];
+      minCoord = result[1];
+      depth = 1;
+
+      // Two metadata [memSize, idx].
+      // TODO: we might be able to use an SSA value for memSize here to avoid
+      // memory operation.
+      builder.create<memref::StoreOp>(loc, result[2], sPtrBuf, c0);
+      builder.create<memref::StoreOp>(loc, c0, sPtrBuf, c1);
+    }
+  }
+
+  assert(depth > 0 && size && isNonEmpty && minCoord && depth);
+  // Compute the minimal offsets viable for a non empty tensor.
+  // offset = isNonEmpty && minCoord >= size ? minCoord - size + 1 : 0;
+  // NOTE: that minCoord is invalid when isNonEmpty = false, in which case
+  // the computed slices are meaningless.
+  // FIXME: support relative offset compute.
+  Value geSize = ugeI(builder, loc, minCoord, size);
+  Value pred = builder.create<arith::AndIOp>(loc, isNonEmpty, geSize);
+
+  Value mp1 = builder.create<arith::AddIOp>(loc, minCoord, c1);
+  Value mms = builder.create<arith::SubIOp>(loc, mp1, size);
+  // This is the absolute offset related to the underly tensor.
+  Value absOffset = builder.create<arith::SelectOp>(loc, pred, mms, c0);
+  // This is the relative offset related to the base slice.
+  Value relOffset = absOffset;
+  uint64_t dim = toOrigDim(baseEnc, lvl);
+  Value newSlice = genExtractSliceWithOffsetOnDim(
+      builder, loc, sliceInfo.baseSlice, relOffset, size, dim);
+  sliceStack[tid].emplace_back(newSlice, minCoord, absOffset, isNonEmpty, lvl,
+                               depth);
+  return false;
+}
+
+void LoopEmitter::genSliceNextInduction(OpBuilder &builder, Location loc,
+                                        const Operation *op, size_t tid,
+                                        size_t lvl,
+                                        SmallVectorImpl<Value> &operands,
+                                        unsigned &retIdx) {
+  if (!isCompressedDLT(dimTypes[tid][lvl]))
+    llvm_unreachable("TODO");
+
+  // else generate code to compute next non empty slice.
+  Value c0 = constantIndex(builder, loc, 0);
+  Value c1 = constantIndex(builder, loc, 1);
+  Value c2 = constantIndex(builder, loc, 2);
+
+  auto whileOp = llvm::cast<scf::WhileOp>(op);
+  SliceInfo &info = sliceStack[tid].back();
+  assert(info.slicedOnLvl == lvl);
+
+  //
+  // We forward to the next non empty slice by
+  // if (minCoord > offset) {
+  //   offset += 1
+  // } else {
+  //    minCoord = nextMinInSlice();
+  //    offset = minCoord - size + 1;
+  // }
+  //
+  // if (offset + size > parents.size)
+  //   isNonEmpty = false;
+  //
+  Value absOffset = info.offset;
+  // Resets slices pointers as the resolved slices are invalidated after we
+  // moves forward to the next slice.
+  for (unsigned i = 0; i <= lvl; i++)
+    builder.create<memref::StoreOp>(loc, c0, slicePtrBuffer[tid][i].back(), c1);
+
+  SmallVector<Value, 3> reduc = {info.minCoord, info.isNonEmpty, absOffset};
+  SmallVector<Type, 3> types = getTypesFromValues(reduc);
+  Value sPtrBuf = slicePtrBuffer[tid][lvl][info.depth - 1];
+  Value fastPathP = ugtI(builder, loc, info.minCoord, absOffset);
+  auto ifOp = builder.create<scf::IfOp>(loc, types, fastPathP, true);
+  {
+    OpBuilder::InsertionGuard guard(builder);
+    // Take the fast path if minCoord > offset
+    builder.setInsertionPointToStart(&ifOp.getThenRegion().front());
+    reduc[2] = builder.create<arith::AddIOp>(loc, absOffset, c1);
+    // Yield offset + 1.
+    builder.create<scf::YieldOp>(loc, reduc);
+
+    // Else, take the slow path.
+    builder.setInsertionPointToStart(&ifOp.getElseRegion().front());
+    reduc[2] = absOffset; // restore value.
+    Value pSt = c2;       // pointer starting index
+    Value mSz = genIndexLoad(builder, loc, sPtrBuf, c0); // memSize
+    reduc[0] = dims[tid][lvl];                           // next min coord
+    reduc[1] = constantI1(builder, loc, false);          // isNonEmpty
+    auto loopArgs = static_cast<ValueRange>(reduc).drop_back();
+    auto forOp = scf::buildLoopNest(
+        builder, loc, pSt, mSz, c2, loopArgs,
+        [this, tid, lvl, c1, sPtrBuf,
+         &info](OpBuilder &builder, Location loc, ValueRange ivs,
+                ValueRange iterArgs) -> scf::ValueVector {
+          Value curMinCoord = iterArgs[0];
+          Value isNonEmpty = iterArgs[1];
+
+          Type idxTp = builder.getIndexType();
+          Value pLo = genIndexLoad(builder, loc, sPtrBuf, ivs.front());
+          Value pHi =
+              genIndexLoad(builder, loc, sPtrBuf,
+                           builder.create<arith::AddIOp>(loc, ivs.front(), c1));
+          //
+          // if pLo < pHi
+          //   coord = load[pLo]
+          //   if coord == minCoord
+          //     pLo += 1
+          //
+          // if pLo < pHi
+          //   curMinCoord = min(curMinCoord, load[pLo])
+          //
+          Value pred = ultI(builder, loc, pLo, pHi);
+          auto advPLo = builder.create<scf::IfOp>(loc, idxTp, pred, true);
+          /* if pLo < pHi */ {
+            builder.setInsertionPointToStart(&advPLo.getThenRegion().front());
+            // coord = load[pLo]
+            Value coord = genIndexLoad(builder, loc, idxBuffer[tid][lvl], pLo);
+            Value pred = eqI(builder, loc, coord, info.minCoord);
+            auto ifEqual = builder.create<scf::IfOp>(loc, idxTp, pred, true);
+            /* if coord == minCoord */ {
+              builder.setInsertionPointToStart(
+                  &ifEqual.getThenRegion().front());
+              Value newPlo = builder.create<arith::AddIOp>(loc, pLo, c1);
+              // Updates the cache.
+              builder.create<memref::StoreOp>(loc, newPlo, sPtrBuf,
+                                              ivs.front());
+              builder.create<scf::YieldOp>(loc, newPlo);
+            }
+            /* else coord != minCoord */ {
+              builder.setInsertionPointToStart(
+                  &ifEqual.getElseRegion().front());
+              builder.create<scf::YieldOp>(loc, pLo);
+            }
+            builder.setInsertionPointAfter(ifEqual);
+            builder.create<scf::YieldOp>(loc, ifEqual.getResults());
+          }
+          /* else pLo >= pHi */ {
+            builder.setInsertionPointToStart(&advPLo.getElseRegion().front());
+            builder.create<scf::YieldOp>(loc, pLo);
+          }
+
+          builder.setInsertionPointAfter(advPLo);
+          pLo = advPLo.getResult(0);
+          Value lvlNonEmpty = ultI(builder, loc, pLo, pHi);
+          // Update minCoords
+          auto newMin =
+              builder.create<scf::IfOp>(loc, idxTp, lvlNonEmpty, true);
+          builder.setInsertionPointToStart(&newMin.getThenRegion().front());
+          builder.create<scf::YieldOp>(
+              loc, genIndexLoad(builder, loc, idxBuffer[tid][lvl], pLo));
+
+          builder.setInsertionPointToStart(&newMin.getElseRegion().front());
+          builder.create<scf::YieldOp>(loc, curMinCoord);
+          builder.setInsertionPointAfter(newMin);
+
+          // isNonEmpty = isNonEmpty || lvlNonEmpty
+          isNonEmpty =
+              builder.create<arith::OrIOp>(loc, lvlNonEmpty, isNonEmpty);
+          curMinCoord = builder.create<arith::SelectOp>(
+              loc, ultI(builder, loc, newMin.getResult(0), curMinCoord),
+              newMin.getResult(0), curMinCoord);
+          return {curMinCoord, isNonEmpty};
+        });
+
+    builder.setInsertionPointAfter(forOp.loops.front());
+    // minOffset = minCoord + 1 >= size ? minCoord + 1 - size : c0
+    Value tmp = builder.create<arith::AddIOp>(loc, forOp.results.front(), c1);
+    Value minOffset = builder.create<arith::SubIOp>(
+        loc, tmp, sliceSizes[tid][lvl][info.depth - 1]);
+    Value p = ugeI(builder, loc, tmp, sliceSizes[tid][lvl][info.depth - 1]);
+    minOffset = builder.create<arith::SelectOp>(loc, p, minOffset, c0);
+    SmallVector<Value, 3> yields;
+    yields.assign(forOp.results.begin(), forOp.results.end());
+    yields.push_back(minOffset);
+    builder.create<scf::YieldOp>(loc, yields);
+  }
+
+  Value nextMinCoord = ifOp.getResults()[0];
+  //// builder.create<vector::PrintOp>(loc, nextMinCoord);
+  Value nextNonEmpty = ifOp.getResults()[1];
+
+  // the next offset should at least be offset + 1;
+  Value minOffset = ifOp.getResults()[2];
+  Value nxOffset = builder.create<arith::AddIOp>(loc, info.offset, c1);
+  Value maxPred = ugtI(builder, loc, minOffset, nxOffset);
+  Value nextAbsOffset =
+      builder.create<arith::SelectOp>(loc, maxPred, minOffset, nxOffset);
+
+  Value sliceUB = builder.create<arith::AddIOp>(
+      loc, nextAbsOffset, sliceSizes[tid][lvl][info.depth - 1]);
+
+  // FIXME: this only works if the parsent is the tensor, we should use the
+  // parents slice size + parent offset.
+  assert(info.depth - 1 == 0);
+  // nextNonEmpty = nextNonEmpty && slice upper bound <= parent upperbound.
+  nextNonEmpty = builder.create<arith::AndIOp>(
+      loc, nextNonEmpty, uleI(builder, loc, sliceUB, dims[tid][lvl]));
+
+  // FIXME: compute relative offset.
+  assert(info.depth - 1 == 0);
+  Value nextRelOffset = nextAbsOffset;
+  nextRelOffset =
+      builder.create<arith::SelectOp>(loc, nextNonEmpty, nextRelOffset, c0);
+
+  uint64_t dim =
+      toOrigDim(getSparseTensorEncoding(tensors[tid].getType()), lvl);
+
+  Value nextSlice = genExtractSliceWithOffsetOnDim(
+      builder, loc, sliceStack[tid][sliceStack.size() - 2].baseSlice,
+      nextRelOffset, sliceSizes[tid][lvl][info.depth - 1], dim);
+
+  operands.push_back(nextNonEmpty);
+  operands.push_back(nextSlice);
+  operands.push_back(nextMinCoord);
+  operands.push_back(nextAbsOffset); // we push the absolute offset.
+
+  // Update the slice stack.
+  info.isNonEmpty = whileOp.getResult(retIdx++);
+  info.baseSlice = whileOp.getResult(retIdx++);
+  info.minCoord = whileOp.getResult(retIdx++);
+  info.offset = whileOp.getResult(retIdx++);
+}
+
+Operation *LoopEmitter::emitSliceDrivenLoopOverTensorAtDim(
+    OpBuilder &builder, Location loc, size_t tid, size_t lvl,
+    MutableArrayRef<Value> reduc) {
+  assert(!sliceFullyResolved(tid));
+  SliceInfo &sliceInfo = sliceStack[tid].back();
+  assert(sliceInfo.slicedOnLvl == lvl);
+
+  // NOTE: The order matters!
+  constexpr size_t numMetaReduc = 4; // number of reduction maintained by us.
+  SmallVector<Value> operands{sliceInfo.isNonEmpty, sliceInfo.baseSlice,
+                              sliceInfo.minCoord, sliceInfo.offset};
+  // Append user-required reduction values.
+  operands.append(reduc.begin(), reduc.end());
+  assert(operands.size() == numMetaReduc + reduc.size());
+
+  SmallVector<Type> types = getTypesFromValues(operands);
+
+  auto whileOp = builder.create<scf::WhileOp>(
+      loc, types, operands,
+      /*beforeBuilder=*/
+      [](OpBuilder &builder, Location loc, ValueRange args) {
+        builder.create<scf::ConditionOp>(loc, /*isNonEmpty*/ args[0], args);
+      },
+      /*afterBuilder=*/
+      [this, tid, lvl, reduc, &sliceInfo](OpBuilder &builder, Location loc,
+                                          ValueRange args) {
+        assert(args.size() == reduc.size() + numMetaReduc);
+        sliceInfo.isNonEmpty = args[0];
+        sliceInfo.baseSlice = args[1];
+        sliceInfo.minCoord = args[2];
+        sliceInfo.offset = args[3];
+        // The slice offset is the coordinate.
+        Value c = sliceInfo.offset;
+        if (sliceInfo.depth > 1) {
+          // Coord is the relative offset related to its parents.
+          // Update c = absOffset[lvl][depth] - absOffset[lvl][depth - 1]
+          llvm_unreachable("TODO: not yet implement");
+        }
+        coord[tid][lvl] = c;
+
+        for (unsigned i = 0, e = reduc.size(); i < e; i++)
+          reduc[i] = args[i + numMetaReduc];
+      });
+
+  // Increments the number of resolved constraints on tid.
+  sliceResolvedConstraints[tid]++;
+  // Set the insertion point to while loop body.
+  builder.setInsertionPointToEnd(&whileOp.getAfter().front());
+  return whileOp;
+}

mlir/lib/Dialect/SparseTensor/Transforms/SparseTensorRewriting.cpp

if (!reducValue.empty()) {
       // merge the block *before* the yield op.
       rewriter.mergeBlockBefore(srcBlock, &*rewriter.getInsertionPoint(), args);
     }
 
     for (int64_t i = 0; i < rank; i++) {
       // Link the reduction chain. Note that loop emitter update the reducValue
       // in place.
       loopEmitter.exitCurrentLoop(rewriter, loc, reducValue);
-      loopEmitter.exitCurrentLoopSeq();
+      loopEmitter.exitCurrentLoopSeq(rewriter, loc);
     }
 
     // Replace the foreach operator with the value returned by the outtermost
     // for loop.
     rewriter.replaceOp(op, reducValue);
     return success();
   }
 };

mlir/lib/Dialect/SparseTensor/Transforms/Sparsification.cpp

 };
 
 /// A helper class that visits an affine expression and tries to find an
 /// AffineDimExpr to which the corresponding iterator from a GenericOp matches
 /// the desired iterator type.
 class AffineDimFinder : public AffineExprVisitor<AffineDimFinder> {
 public:
   explicit AffineDimFinder(linalg::GenericOp op)
-      : iterTypes(op.getIteratorTypesArray()) {}
+      : iterTypes(op.getIteratorTypes()) {}
   void visitDimExpr(AffineDimExpr expr) {
-    if (pickedDim == nullptr || pickIterType == iterTypes[expr.getPosition()]) {
+    if (pickedDim == nullptr ||
+        pickIterType == iterTypes[expr.getPosition()]
+                            .cast<linalg::IteratorTypeAttr>()
+                            .getValue()) {
       pickedDim = expr;
     }
   }
 
   /// Set the desired iterator type that we want to pick.
   void setPickedIterType(utils::IteratorType iterType) {
     pickIterType = iterType;
   }
 
   /// Get the desired AffineDimExpr.
   AffineDimExpr getDimExpr() const { return pickedDim.cast<AffineDimExpr>(); }
 
 private:
   /// The picked AffineDimExpr after visit.
   AffineExpr pickedDim;
   /// The iterator type that we want.
   utils::IteratorType pickIterType;
   /// The mapping between dim=>iterator type.
-  SmallVector<utils::IteratorType> iterTypes;
+  ArrayAttr iterTypes;
 };
 
 /// A helper class that visits an affine expression and tries to find an
 /// AffineDimExpr to which the corresponding iterator from a GenericOp matches
 /// the desired iterator type.
-struct AffineDimCollector : public AffineExprVisitor<AffineDimFinder> {
+struct AffineDimCollector : public AffineExprVisitor<AffineDimCollector> {
   void visitDimExpr(AffineDimExpr expr) { dims.push_back(expr); }
   SmallVector<AffineDimExpr> dims;
 };
 
 } // namespace
 
 //===----------------------------------------------------------------------===//
 // Sparse compiler analysis methods.

 /// Ends a single loop in current sequence. Returns new values for needsUniv.
 static bool endLoop(CodegenEnv &env, RewriterBase &rewriter, Operation *loop,
                     unsigned idx, unsigned li, bool needsUniv) {
   // End a while-loop.
   if (auto whileOp = dyn_cast<scf::WhileOp>(loop)) {
     finalizeWhileOp(env, rewriter, idx, needsUniv, env.lat(li).bits, whileOp);
   } else {
     needsUniv = false;
   }
 
   env.genLoopBoundary([&](MutableArrayRef<Value> reduc) {
     env.emitter().exitCurrentLoop(rewriter, env.op().getLoc(), reduc);
     return std::nullopt;
   });
 
   return needsUniv;
 }
 
 /// Ends a loop sequence at given level.
 static void endLoopSeq(CodegenEnv &env, OpBuilder &builder, unsigned exp,
                        unsigned at, unsigned idx, unsigned ldx) {
   assert(env.getLoopIdxValue(idx) == nullptr);
-  env.emitter().exitCurrentLoopSeq();
+  env.emitter().exitCurrentLoopSeq(builder, env.op().getLoc());
   // Unmark bookkeeping of invariants and loop index.
   genInvariants(env, builder, exp, ldx, /*atStart=*/false);
   // Finalize access pattern expansion for sparse tensor output.
   genExpand(env, builder, at, /*atStart=*/false);
 }
 
 /// Recursively generates code while computing iteration lattices in order
 /// to manage the complexity of implementing co-iteration over unions

mlir/test/Dialect/SparseTensor/sparse_conv_2d_slice_based.mlir

+// RUN: mlir-opt %s --sparsification="enable-slice-affine=true" --cse | FileCheck %s
+
+#map = affine_map<(d0, d1, d2, d3) -> (d0 + d2, d1 + d3)>
+#map1 = affine_map<(d0, d1, d2, d3) -> (d2, d3)>
+#map2 = affine_map<(d0, d1, d2, d3) -> (d0, d1)>
+
+#DCSR = #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>
+// CHECK-LABEL:   func.func @conv2d_all_sparse_CSR(
+// CHECK-SAME:      %[[VAL_0:.*]]: tensor<8x8xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>,
+// CHECK-SAME:      %[[VAL_1:.*]]: tensor<3x3xi32>) -> tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>> {
+// CHECK:           %[[VAL_2:.*]] = arith.constant 8 : index
+// CHECK:           %[[VAL_3:.*]] = arith.constant 3 : index
+// CHECK:           %[[VAL_4:.*]] = arith.constant 4 : index
+// CHECK:           %[[VAL_5:.*]] = arith.constant 0 : index
+// CHECK:           %[[VAL_6:.*]] = arith.constant 1 : index
+// CHECK:           %[[VAL_7:.*]] = arith.constant 2 : index
+// CHECK:           %[[VAL_8:.*]] = arith.constant 0 : i32
+// CHECK:           %[[VAL_9:.*]] = arith.constant true
+// CHECK:           %[[VAL_10:.*]] = arith.constant false
+// CHECK:           %[[VAL_11:.*]] = bufferization.alloc_tensor() : tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>
+// CHECK:           %[[VAL_12:.*]] = sparse_tensor.pointers %[[VAL_0]] {dimension = 0 : index}
+// CHECK:           %[[VAL_13:.*]] = sparse_tensor.indices %[[VAL_0]] {dimension = 0 : index}
+// CHECK:           %[[VAL_14:.*]] = sparse_tensor.pointers %[[VAL_0]] {dimension = 1 : index}
+// CHECK:           %[[VAL_15:.*]] = sparse_tensor.indices %[[VAL_0]] {dimension = 1 : index}
+// CHECK:           %[[VAL_16:.*]] = sparse_tensor.values %[[VAL_0]]
+// CHECK:           %[[VAL_17:.*]] = bufferization.to_memref %[[VAL_1]] : memref<3x3xi32>
+// CHECK:           %[[VAL_18:.*]] = memref.alloca(%[[VAL_4]]) : memref<?xindex>
+// CHECK:           %[[VAL_19:.*]] = memref.alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK:           %[[VAL_20:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_6]]] : memref<?xindex>
+// CHECK:           memref.store %[[VAL_4]], %[[VAL_18]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:           memref.store %[[VAL_5]], %[[VAL_18]]{{\[}}%[[VAL_6]]] : memref<?xindex>
+// CHECK:           memref.store %[[VAL_5]], %[[VAL_18]]{{\[}}%[[VAL_7]]] : memref<?xindex>
+// CHECK:           memref.store %[[VAL_20]], %[[VAL_18]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK:           %[[VAL_21:.*]] = arith.cmpi ugt, %[[VAL_20]], %[[VAL_5]] : index
+// CHECK:           %[[VAL_22:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:           %[[VAL_23:.*]] = arith.cmpi uge, %[[VAL_22]], %[[VAL_3]] : index
+// CHECK:           %[[VAL_24:.*]] = arith.andi %[[VAL_21]], %[[VAL_23]] : i1
+// CHECK:           %[[VAL_25:.*]] = arith.addi %[[VAL_22]], %[[VAL_6]] : index
+// CHECK:           %[[VAL_26:.*]] = arith.subi %[[VAL_25]], %[[VAL_3]] : index
+// CHECK:           %[[VAL_27:.*]] = arith.select %[[VAL_24]], %[[VAL_26]], %[[VAL_5]] : index
+// CHECK:           %[[VAL_28:.*]] = tensor.extract_slice %[[VAL_0]]{{\[}}%[[VAL_27]], 0] {{\[}}%[[VAL_3]], 8] [1, 1]
+// CHECK:           %[[VAL_29:.*]]:5 = scf.while (%[[VAL_30:.*]] = %[[VAL_21]],
+// CHECK-SAME:                                    %[[VAL_31:.*]] = %[[VAL_28]],
+// CHECK-SAME:                                    %[[VAL_32:.*]] = %[[VAL_22]],
+// CHECK-SAME:                                    %[[VAL_33:.*]] = %[[VAL_27]],
+// CHECK-SAME:                                    %[[VAL_34:.*]] = %[[VAL_11]])
+// CHECK:             scf.condition(%[[VAL_30]]) %[[VAL_30]], %[[VAL_31]], %[[VAL_32]], %[[VAL_33]], %[[VAL_34]]
+// CHECK:           } do {
+// CHECK:           ^bb0(%[[VAL_35:.*]]: i1,
+// CHECK-SAME:           %[[VAL_36:.*]]: tensor<?x8xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ], slice = [ (?, ?, 1), (0, 8, 1) ] }>>,
+// CHECK-SAME:           %[[VAL_37:.*]]: index, %[[VAL_38:.*]]: index,
+// CHECK-SAME:           %[[VAL_39:.*]]: tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>):
+// CHECK:             %[[VAL_40:.*]] = memref.load %[[VAL_18]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+//
+// !!!!! Code below is for slice non empty begin.
+//
+// CHECK:             %[[VAL_41:.*]]:3 = scf.for %[[VAL_42:.*]] = %[[VAL_7]] to %[[VAL_40]] step %[[VAL_7]] iter_args(%[[VAL_43:.*]] = %[[VAL_10]], %[[VAL_44:.*]] = %[[VAL_2]], %[[VAL_45:.*]] = %[[VAL_7]]) -> (i1, index, index) {
+// CHECK:               %[[VAL_46:.*]] = memref.load %[[VAL_18]]{{\[}}%[[VAL_42]]] : memref<?xindex>
+// CHECK:               %[[VAL_47:.*]] = arith.addi %[[VAL_42]], %[[VAL_6]] : index
+// CHECK:               %[[VAL_48:.*]] = memref.load %[[VAL_18]]{{\[}}%[[VAL_47]]] : memref<?xindex>
+// CHECK:               %[[VAL_49:.*]] = arith.addi %[[VAL_38]], %[[VAL_3]] : index
+// CHECK:               %[[VAL_50:.*]]:5 = scf.while (%[[VAL_51:.*]] = %[[VAL_46]], %[[VAL_52:.*]] = %[[VAL_9]], %[[VAL_53:.*]] = %[[VAL_43]], %[[VAL_54:.*]] = %[[VAL_44]], %[[VAL_55:.*]] = %[[VAL_45]]) : (index, i1, i1, index, index) -> (index, i1, i1, index, index) {
+// CHECK:                 %[[VAL_56:.*]] = arith.cmpi ult, %[[VAL_51]], %[[VAL_48]] : index
+// CHECK:                 %[[VAL_57:.*]] = arith.andi %[[VAL_52]], %[[VAL_56]] : i1
+// CHECK:                 scf.condition(%[[VAL_57]]) %[[VAL_51]], %[[VAL_52]], %[[VAL_53]], %[[VAL_54]], %[[VAL_55]] : index, i1, i1, index, index
+// CHECK:               } do {
+// CHECK:               ^bb0(%[[VAL_58:.*]]: index, %[[VAL_59:.*]]: i1, %[[VAL_60:.*]]: i1, %[[VAL_61:.*]]: index, %[[VAL_62:.*]]: index):
+// CHECK:                 %[[VAL_63:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_58]]] : memref<?xindex>
+// CHECK:                 %[[VAL_64:.*]] = arith.cmpi ult, %[[VAL_63]], %[[VAL_49]] : index
+// CHECK:                 %[[VAL_65:.*]]:3 = scf.if %[[VAL_64]] -> (i1, index, index) {
+// CHECK:                   %[[VAL_66:.*]] = arith.addi %[[VAL_58]], %[[VAL_6]] : index
+// CHECK:                   %[[VAL_67:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_58]]] : memref<?xindex>
+// CHECK:                   %[[VAL_68:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_66]]] : memref<?xindex>
+// CHECK:                   %[[VAL_69:.*]] = arith.cmpi ult, %[[VAL_67]], %[[VAL_68]] : index
+// CHECK:                   %[[VAL_70:.*]] = arith.ori %[[VAL_69]], %[[VAL_60]] : i1
+// CHECK:                   %[[VAL_71:.*]] = scf.if %[[VAL_69]] -> (index) {
+// CHECK:                     %[[VAL_72:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_67]]] : memref<?xindex>
+// CHECK:                     %[[VAL_73:.*]] = arith.cmpi ult, %[[VAL_72]], %[[VAL_61]] : index
+// CHECK:                     %[[VAL_74:.*]] = arith.select %[[VAL_73]], %[[VAL_72]], %[[VAL_61]] : index
+// CHECK:                     scf.yield %[[VAL_74]] : index
+// CHECK:                   } else {
+// CHECK:                     scf.yield %[[VAL_61]] : index
+// CHECK:                   }
+// CHECK:                   memref.store %[[VAL_67]], %[[VAL_19]]{{\[}}%[[VAL_62]]] : memref<?xindex>
+// CHECK:                   %[[VAL_75:.*]] = arith.addi %[[VAL_62]], %[[VAL_6]] : index
+// CHECK:                   memref.store %[[VAL_68]], %[[VAL_19]]{{\[}}%[[VAL_75]]] : memref<?xindex>
+// CHECK:                   %[[VAL_76:.*]] = arith.addi %[[VAL_62]], %[[VAL_7]] : index
+// CHECK:                   scf.yield %[[VAL_70]], %[[VAL_77:.*]], %[[VAL_76]] : i1, index, index
+// CHECK:                 } else {
+// CHECK:                   scf.yield %[[VAL_60]], %[[VAL_61]], %[[VAL_62]] : i1, index, index
+// CHECK:                 } {"Emitted from" = "slice"}
+// CHECK:                 %[[VAL_78:.*]] = arith.addi %[[VAL_58]], %[[VAL_6]] : index
+// CHECK:                 scf.yield %[[VAL_78]], %[[VAL_64]], %[[VAL_79:.*]]#0, %[[VAL_79]]#1, %[[VAL_79]]#2 : index, i1, i1, index, index
+// CHECK:               }
+// CHECK:               scf.yield %[[VAL_80:.*]]#2, %[[VAL_80]]#3, %[[VAL_80]]#4 : i1, index, index
+// CHECK:             }
+// CHECK:             memref.store %[[VAL_81:.*]]#2, %[[VAL_19]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:             memref.store %[[VAL_5]], %[[VAL_19]]{{\[}}%[[VAL_6]]] : memref<?xindex>
+// CHECK:             %[[VAL_82:.*]] = arith.cmpi uge, %[[VAL_81]]#1, %[[VAL_3]] : index
+// CHECK:             %[[VAL_83:.*]] = arith.andi %[[VAL_81]]#0, %[[VAL_82]] : i1
+// CHECK:             %[[VAL_84:.*]] = arith.addi %[[VAL_81]]#1, %[[VAL_6]] : index
+// CHECK:             %[[VAL_85:.*]] = arith.subi %[[VAL_84]], %[[VAL_3]] : index
+// CHECK:             %[[VAL_86:.*]] = arith.select %[[VAL_83]], %[[VAL_85]], %[[VAL_5]] : index
+// CHECK:             %[[VAL_87:.*]] = tensor.extract_slice %[[VAL_36]][0, %[[VAL_86]]] {{\[}}%[[VAL_2]], %[[VAL_3]]] [1, 1] : tensor<?x8xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ], slice = [ (?, ?, 1), (0, 8, 1) ] }>> to tensor<?x?xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ], slice = [ (0, ?, 1), (?, ?, 1) ] }>>
+// CHECK:             %[[VAL_88:.*]]:5 = scf.while (%[[VAL_89:.*]] = %[[VAL_81]]#0, %[[VAL_90:.*]] = %[[VAL_87]], %[[VAL_91:.*]] = %[[VAL_81]]#1, %[[VAL_92:.*]] = %[[VAL_86]], %[[VAL_93:.*]] = %[[VAL_39]]) : (i1, tensor<?x?xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ], slice = [ (0, ?, 1), (?, ?, 1) ] }>>, index, index, tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>) -> (i1, tensor<?x?xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ], slice = [ (0, ?, 1), (?, ?, 1) ] }>>, index, index, tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>) {
+// CHECK:               scf.condition(%[[VAL_89]]) %[[VAL_89]], %[[VAL_90]], %[[VAL_91]], %[[VAL_92]], %[[VAL_93]] : i1, tensor<?x?xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ], slice = [ (0, ?, 1), (?, ?, 1) ] }>>, index, index, tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>
+// CHECK:             } do {
+// CHECK:             ^bb0(%[[VAL_94:.*]]: i1, %[[VAL_95:.*]]: tensor<?x?xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ], slice = [ (0, ?, 1), (?, ?, 1) ] }>>, %[[VAL_96:.*]]: index, %[[VAL_97:.*]]: index, %[[VAL_98:.*]]: tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>):
+// CHECK:               %[[VAL_99:.*]] = memref.load %[[VAL_18]]{{\[}}%[[VAL_6]]] : memref<?xindex>
+// CHECK:               %[[VAL_100:.*]] = arith.addi %[[VAL_99]], %[[VAL_7]] : index
+// CHECK:               %[[VAL_101:.*]] = arith.addi %[[VAL_100]], %[[VAL_6]] : index
+// CHECK:               %[[VAL_102:.*]] = memref.load %[[VAL_18]]{{\[}}%[[VAL_100]]] : memref<?xindex>
+// CHECK:               %[[VAL_103:.*]] = memref.load %[[VAL_18]]{{\[}}%[[VAL_101]]] : memref<?xindex>
+// CHECK:               %[[VAL_104:.*]] = arith.addi %[[VAL_38]], %[[VAL_3]] : index
+// CHECK:               %[[VAL_105:.*]]:4 = scf.while (%[[VAL_106:.*]] = %[[VAL_102]], %[[VAL_107:.*]] = %[[VAL_9]], %[[VAL_108:.*]] = %[[VAL_8]], %[[VAL_109:.*]] = %[[VAL_98]]) : (index, i1, i32, tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>) -> (index, i1, i32, tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>) {
+// CHECK:                 %[[VAL_110:.*]] = arith.cmpi ult, %[[VAL_106]], %[[VAL_103]] : index
+// CHECK:                 %[[VAL_111:.*]] = arith.andi %[[VAL_107]], %[[VAL_110]] : i1
+// CHECK:                 scf.condition(%[[VAL_111]]) %[[VAL_106]], %[[VAL_107]], %[[VAL_108]], %[[VAL_109]] : index, i1, i32, tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>
+// CHECK:               } do {
+// CHECK:               ^bb0(%[[VAL_112:.*]]: index, %[[VAL_113:.*]]: i1, %[[VAL_114:.*]]: i32, %[[VAL_115:.*]]: tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>):
+// CHECK:                 %[[VAL_116:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_112]]] : memref<?xindex>
+// CHECK:                 %[[VAL_117:.*]] = arith.cmpi ult, %[[VAL_116]], %[[VAL_104]] : index
+// CHECK:                 %[[VAL_118:.*]]:2 = scf.if %[[VAL_117]] -> (i32, tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>) {
+// CHECK:                   %[[VAL_119:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_112]]] : memref<?xindex>
+// CHECK:                   %[[VAL_120:.*]] = arith.subi %[[VAL_119]], %[[VAL_38]] : index
+// CHECK:                   %[[VAL_121:.*]] = memref.load %[[VAL_19]]{{\[}}%[[VAL_6]]] : memref<?xindex>
+// CHECK:                   %[[VAL_122:.*]] = arith.addi %[[VAL_121]], %[[VAL_7]] : index
+// CHECK:                   %[[VAL_123:.*]] = arith.addi %[[VAL_122]], %[[VAL_6]] : index
+// CHECK:                   %[[VAL_124:.*]] = memref.load %[[VAL_19]]{{\[}}%[[VAL_122]]] : memref<?xindex>
+// CHECK:                   %[[VAL_125:.*]] = memref.load %[[VAL_19]]{{\[}}%[[VAL_123]]] : memref<?xindex>
+// CHECK:                   %[[VAL_126:.*]] = arith.addi %[[VAL_97]], %[[VAL_3]] : index
+// CHECK:                   %[[VAL_127:.*]]:4 = scf.while (%[[VAL_128:.*]] = %[[VAL_124]], %[[VAL_129:.*]] = %[[VAL_9]], %[[VAL_130:.*]] = %[[VAL_114]], %[[VAL_131:.*]] = %[[VAL_115]]) : (index, i1, i32, tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>) -> (index, i1, i32, tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>) {
+// CHECK:                     %[[VAL_132:.*]] = arith.cmpi ult, %[[VAL_128]], %[[VAL_125]] : index
+// CHECK:                     %[[VAL_133:.*]] = arith.andi %[[VAL_129]], %[[VAL_132]] : i1
+// CHECK:                     scf.condition(%[[VAL_133]]) %[[VAL_128]], %[[VAL_129]], %[[VAL_130]], %[[VAL_131]] : index, i1, i32, tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>
+// CHECK:                   } do {
+//
+// !!!!! Code below is the actually convolution kernel
+//
+// CHECK:                   ^bb0(%[[VAL_134:.*]]: index, %[[VAL_135:.*]]: i1, %[[VAL_136:.*]]: i32, %[[VAL_137:.*]]: tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>):
+// CHECK:                     %[[VAL_138:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_134]]] : memref<?xindex>
+// CHECK:                     %[[VAL_139:.*]] = arith.cmpi ult, %[[VAL_138]], %[[VAL_126]] : index
+// CHECK:                     %[[VAL_140:.*]]:2 = scf.if %[[VAL_139]] -> (i32, tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>) {
+// CHECK:                       %[[VAL_141:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_134]]] : memref<?xindex>
+// CHECK:                       %[[VAL_142:.*]] = arith.subi %[[VAL_141]], %[[VAL_97]] : index
+// CHECK:                       %[[VAL_143:.*]] = memref.load %[[VAL_16]]{{\[}}%[[VAL_134]]] : memref<?xi32>
+// CHECK:                       %[[VAL_144:.*]] = memref.load %[[VAL_17]]{{\[}}%[[VAL_120]], %[[VAL_142]]] : memref<3x3xi32>
+// CHECK:                       %[[VAL_145:.*]] = arith.muli %[[VAL_143]], %[[VAL_144]] : i32
+// CHECK:                       %[[VAL_146:.*]] = arith.addi %[[VAL_136]], %[[VAL_145]] : i32
+// CHECK:                       scf.yield %[[VAL_146]], %[[VAL_137]] : i32, tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>
+// CHECK:                     } else {
+// CHECK:                       scf.yield %[[VAL_136]], %[[VAL_137]] : i32, tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>
+// CHECK:                     } {"Emitted from" = "slice"}
+// CHECK:                     %[[VAL_147:.*]] = arith.addi %[[VAL_134]], %[[VAL_6]] : index
+// CHECK:                     scf.yield %[[VAL_147]], %[[VAL_139]], %[[VAL_148:.*]]#0, %[[VAL_148]]#1 : index, i1, i32, tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>
+// CHECK:                   } attributes {"Emitted from" = "linalg.generic"}
+// CHECK:                   %[[VAL_149:.*]] = memref.load %[[VAL_19]]{{\[}}%[[VAL_6]]] : memref<?xindex>
+// CHECK:                   %[[VAL_150:.*]] = arith.addi %[[VAL_149]], %[[VAL_7]] : index
+// CHECK:                   memref.store %[[VAL_150]], %[[VAL_19]]{{\[}}%[[VAL_6]]] : memref<?xindex>
+// CHECK:                   scf.yield %[[VAL_151:.*]]#2, %[[VAL_151]]#3 : i32, tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>
+// CHECK:                 } else {
+// CHECK:                   scf.yield %[[VAL_114]], %[[VAL_115]] : i32, tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>
+// CHECK:                 } {"Emitted from" = "slice"}
+// CHECK:                 %[[VAL_152:.*]] = arith.addi %[[VAL_112]], %[[VAL_6]] : index
+// CHECK:                 scf.yield %[[VAL_152]], %[[VAL_117]], %[[VAL_153:.*]]#0, %[[VAL_153]]#1 : index, i1, i32, tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>
+// CHECK:               } attributes {"Emitted from" = "linalg.generic"}
+// CHECK:               %[[VAL_154:.*]] = memref.load %[[VAL_18]]{{\[}}%[[VAL_6]]] : memref<?xindex>
+// CHECK:               %[[VAL_155:.*]] = arith.addi %[[VAL_154]], %[[VAL_7]] : index
+// CHECK:               memref.store %[[VAL_155]], %[[VAL_18]]{{\[}}%[[VAL_6]]] : memref<?xindex>
+// CHECK:               %[[VAL_156:.*]] = sparse_tensor.insert %[[VAL_157:.*]]#2 into %[[VAL_157]]#3{{\[}}%[[VAL_38]], %[[VAL_97]]] : tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>
+//
+// !!!!! Code below is for slice non empty next.
+//
+// CHECK:               memref.store %[[VAL_5]], %[[VAL_18]]{{\[}}%[[VAL_6]]] : memref<?xindex>
+// CHECK:               memref.store %[[VAL_5]], %[[VAL_19]]{{\[}}%[[VAL_6]]] : memref<?xindex>
+// CHECK:               %[[VAL_158:.*]] = arith.cmpi ugt, %[[VAL_96]], %[[VAL_97]] : index
+// CHECK:               %[[VAL_159:.*]]:3 = scf.if %[[VAL_158]] -> (index, i1, index) {
+// CHECK:                 %[[VAL_160:.*]] = arith.addi %[[VAL_97]], %[[VAL_6]] : index
+// CHECK:                 scf.yield %[[VAL_96]], %[[VAL_94]], %[[VAL_160]] : index, i1, index
+// CHECK:               } else {
+// CHECK:                 %[[VAL_161:.*]] = memref.load %[[VAL_19]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:                 %[[VAL_162:.*]]:2 = scf.for %[[VAL_163:.*]] = %[[VAL_7]] to %[[VAL_161]] step %[[VAL_7]] iter_args(%[[VAL_164:.*]] = %[[VAL_2]], %[[VAL_165:.*]] = %[[VAL_10]]) -> (index, i1) {
+// CHECK:                   %[[VAL_166:.*]] = memref.load %[[VAL_19]]{{\[}}%[[VAL_163]]] : memref<?xindex>
+// CHECK:                   %[[VAL_167:.*]] = arith.addi %[[VAL_163]], %[[VAL_6]] : index
+// CHECK:                   %[[VAL_168:.*]] = memref.load %[[VAL_19]]{{\[}}%[[VAL_167]]] : memref<?xindex>
+// CHECK:                   %[[VAL_169:.*]] = arith.cmpi ult, %[[VAL_166]], %[[VAL_168]] : index
+// CHECK:                   %[[VAL_170:.*]] = scf.if %[[VAL_169]] -> (index) {
+// CHECK:                     %[[VAL_171:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_166]]] : memref<?xindex>
+// CHECK:                     %[[VAL_172:.*]] = arith.cmpi eq, %[[VAL_171]], %[[VAL_96]] : index
+// CHECK:                     %[[VAL_173:.*]] = scf.if %[[VAL_172]] -> (index) {
+// CHECK:                       %[[VAL_174:.*]] = arith.addi %[[VAL_166]], %[[VAL_6]] : index
+// CHECK:                       memref.store %[[VAL_174]], %[[VAL_19]]{{\[}}%[[VAL_163]]] : memref<?xindex>
+// CHECK:                       scf.yield %[[VAL_174]] : index
+// CHECK:                     } else {
+// CHECK:                       scf.yield %[[VAL_166]] : index
+// CHECK:                     }
+// CHECK:                     scf.yield %[[VAL_175:.*]] : index
+// CHECK:                   } else {
+// CHECK:                     scf.yield %[[VAL_166]] : index
+// CHECK:                   }
+// CHECK:                   %[[VAL_176:.*]] = arith.cmpi ult, %[[VAL_177:.*]], %[[VAL_168]] : index
+// CHECK:                   %[[VAL_178:.*]] = scf.if %[[VAL_176]] -> (index) {
+// CHECK:                     %[[VAL_179:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_177]]] : memref<?xindex>
+// CHECK:                     scf.yield %[[VAL_179]] : index
+// CHECK:                   } else {
+// CHECK:                     scf.yield %[[VAL_164]] : index
+// CHECK:                   }
+// CHECK:                   %[[VAL_180:.*]] = arith.ori %[[VAL_176]], %[[VAL_165]] : i1
+// CHECK:                   %[[VAL_181:.*]] = arith.cmpi ult, %[[VAL_182:.*]], %[[VAL_164]] : index
+// CHECK:                   %[[VAL_183:.*]] = arith.select %[[VAL_181]], %[[VAL_182]], %[[VAL_164]] : index
+// CHECK:                   scf.yield %[[VAL_183]], %[[VAL_180]] : index, i1
+// CHECK:                 }
+// CHECK:                 %[[VAL_184:.*]] = arith.addi %[[VAL_185:.*]]#0, %[[VAL_6]] : index
+// CHECK:                 %[[VAL_186:.*]] = arith.subi %[[VAL_184]], %[[VAL_3]] : index
+// CHECK:                 %[[VAL_187:.*]] = arith.cmpi uge, %[[VAL_184]], %[[VAL_3]] : index
+// CHECK:                 %[[VAL_188:.*]] = arith.select %[[VAL_187]], %[[VAL_186]], %[[VAL_5]] : index
+// CHECK:                 scf.yield %[[VAL_185]]#0, %[[VAL_185]]#1, %[[VAL_188]] : index, i1, index
+// CHECK:               }
+// CHECK:               %[[VAL_189:.*]] = arith.addi %[[VAL_97]], %[[VAL_6]] : index
+// CHECK:               %[[VAL_190:.*]] = arith.cmpi ugt, %[[VAL_191:.*]]#2, %[[VAL_189]] : index
+// CHECK:               %[[VAL_192:.*]] = arith.select %[[VAL_190]], %[[VAL_191]]#2, %[[VAL_189]] : index
+// CHECK:               %[[VAL_193:.*]] = arith.addi %[[VAL_192]], %[[VAL_3]] : index
+// CHECK:               %[[VAL_194:.*]] = arith.cmpi ule, %[[VAL_193]], %[[VAL_2]] : index
+// CHECK:               %[[VAL_195:.*]] = arith.andi %[[VAL_191]]#1, %[[VAL_194]] : i1
+// CHECK:               %[[VAL_196:.*]] = arith.select %[[VAL_195]], %[[VAL_192]], %[[VAL_5]] : index
+// CHECK:               %[[VAL_197:.*]] = tensor.extract_slice %[[VAL_36]][0, %[[VAL_196]]] {{\[}}%[[VAL_2]], %[[VAL_3]]] [1, 1] : tensor<?x8xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ], slice = [ (?, ?, 1), (0, 8, 1) ] }>> to tensor<?x?xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ], slice = [ (0, ?, 1), (?, ?, 1) ] }>>
+// CHECK:               scf.yield %[[VAL_195]], %[[VAL_197]], %[[VAL_191]]#0, %[[VAL_192]], %[[VAL_156]] : i1, tensor<?x?xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ], slice = [ (0, ?, 1), (?, ?, 1) ] }>>, index, index, tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>
+// CHECK:             } attributes {"Emitted from" = "linalg.generic"}
+// CHECK:             memref.store %[[VAL_5]], %[[VAL_18]]{{\[}}%[[VAL_6]]] : memref<?xindex>
+// CHECK:             %[[VAL_198:.*]] = arith.cmpi ugt, %[[VAL_37]], %[[VAL_38]] : index
+// CHECK:             %[[VAL_199:.*]]:3 = scf.if %[[VAL_198]] -> (index, i1, index) {
+// CHECK:               %[[VAL_200:.*]] = arith.addi %[[VAL_38]], %[[VAL_6]] : index
+// CHECK:               scf.yield %[[VAL_37]], %[[VAL_35]], %[[VAL_200]] : index, i1, index
+// CHECK:             } else {
+// CHECK:               %[[VAL_201:.*]] = memref.load %[[VAL_18]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:               %[[VAL_202:.*]]:2 = scf.for %[[VAL_203:.*]] = %[[VAL_7]] to %[[VAL_201]] step %[[VAL_7]] iter_args(%[[VAL_204:.*]] = %[[VAL_2]], %[[VAL_205:.*]] = %[[VAL_10]]) -> (index, i1) {
+// CHECK:                 %[[VAL_206:.*]] = memref.load %[[VAL_18]]{{\[}}%[[VAL_203]]] : memref<?xindex>
+// CHECK:                 %[[VAL_207:.*]] = arith.addi %[[VAL_203]], %[[VAL_6]] : index
+// CHECK:                 %[[VAL_208:.*]] = memref.load %[[VAL_18]]{{\[}}%[[VAL_207]]] : memref<?xindex>
+// CHECK:                 %[[VAL_209:.*]] = arith.cmpi ult, %[[VAL_206]], %[[VAL_208]] : index
+// CHECK:                 %[[VAL_210:.*]] = scf.if %[[VAL_209]] -> (index) {
+// CHECK:                   %[[VAL_211:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_206]]] : memref<?xindex>
+// CHECK:                   %[[VAL_212:.*]] = arith.cmpi eq, %[[VAL_211]], %[[VAL_37]] : index
+// CHECK:                   %[[VAL_213:.*]] = scf.if %[[VAL_212]] -> (index) {
+// CHECK:                     %[[VAL_214:.*]] = arith.addi %[[VAL_206]], %[[VAL_6]] : index
+// CHECK:                     memref.store %[[VAL_214]], %[[VAL_18]]{{\[}}%[[VAL_203]]] : memref<?xindex>
+// CHECK:                     scf.yield %[[VAL_214]] : index
+// CHECK:                   } else {
+// CHECK:                     scf.yield %[[VAL_206]] : index
+// CHECK:                   }
+// CHECK:                   scf.yield %[[VAL_215:.*]] : index
+// CHECK:                 } else {
+// CHECK:                   scf.yield %[[VAL_206]] : index
+// CHECK:                 }
+// CHECK:                 %[[VAL_216:.*]] = arith.cmpi ult, %[[VAL_217:.*]], %[[VAL_208]] : index
+// CHECK:                 %[[VAL_218:.*]] = scf.if %[[VAL_216]] -> (index) {
+// CHECK:                   %[[VAL_219:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_217]]] : memref<?xindex>
+// CHECK:                   scf.yield %[[VAL_219]] : index
+// CHECK:                 } else {
+// CHECK:                   scf.yield %[[VAL_204]] : index
+// CHECK:                 }
+// CHECK:                 %[[VAL_220:.*]] = arith.ori %[[VAL_216]], %[[VAL_205]] : i1
+// CHECK:                 %[[VAL_221:.*]] = arith.cmpi ult, %[[VAL_222:.*]], %[[VAL_204]] : index
+// CHECK:                 %[[VAL_223:.*]] = arith.select %[[VAL_221]], %[[VAL_222]], %[[VAL_204]] : index
+// CHECK:                 scf.yield %[[VAL_223]], %[[VAL_220]] : index, i1
+// CHECK:               }
+// CHECK:               %[[VAL_224:.*]] = arith.addi %[[VAL_225:.*]]#0, %[[VAL_6]] : index
+// CHECK:               %[[VAL_226:.*]] = arith.subi %[[VAL_224]], %[[VAL_3]] : index
+// CHECK:               %[[VAL_227:.*]] = arith.cmpi uge, %[[VAL_224]], %[[VAL_3]] : index
+// CHECK:               %[[VAL_228:.*]] = arith.select %[[VAL_227]], %[[VAL_226]], %[[VAL_5]] : index
+// CHECK:               scf.yield %[[VAL_225]]#0, %[[VAL_225]]#1, %[[VAL_228]] : index, i1, index
+// CHECK:             }
+// CHECK:             %[[VAL_229:.*]] = arith.addi %[[VAL_38]], %[[VAL_6]] : index
+// CHECK:             %[[VAL_230:.*]] = arith.cmpi ugt, %[[VAL_231:.*]]#2, %[[VAL_229]] : index
+// CHECK:             %[[VAL_232:.*]] = arith.select %[[VAL_230]], %[[VAL_231]]#2, %[[VAL_229]] : index
+// CHECK:             %[[VAL_233:.*]] = arith.addi %[[VAL_232]], %[[VAL_3]] : index
+// CHECK:             %[[VAL_234:.*]] = arith.cmpi ule, %[[VAL_233]], %[[VAL_2]] : index
+// CHECK:             %[[VAL_235:.*]] = arith.andi %[[VAL_231]]#1, %[[VAL_234]] : i1
+// CHECK:             %[[VAL_236:.*]] = arith.select %[[VAL_235]], %[[VAL_232]], %[[VAL_5]] : index
+// CHECK:             %[[VAL_237:.*]] = tensor.extract_slice %[[VAL_36]]{{\[}}%[[VAL_236]], 0] {{\[}}%[[VAL_3]], 8] [1, 1] : tensor<?x8xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ], slice = [ (?, ?, 1), (0, 8, 1) ] }>> to tensor<?x8xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ], slice = [ (?, ?, 1), (0, 8, 1) ] }>>
+// CHECK:             scf.yield %[[VAL_235]], %[[VAL_237]], %[[VAL_231]]#0, %[[VAL_232]], %[[VAL_238:.*]]#4 : i1, tensor<?x8xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ], slice = [ (?, ?, 1), (0, 8, 1) ] }>>, index, index, tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>
+// CHECK:           } attributes {"Emitted from" = "linalg.generic"}
+// CHECK:           %[[VAL_239:.*]] = sparse_tensor.load %[[VAL_240:.*]]#4 hasInserts : tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>
+// CHECK:           return %[[VAL_239]] : tensor<6x6xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>
+// CHECK:         }
+func.func @conv2d_all_sparse_CSR(%arg0: tensor<8x8xi32, #DCSR>,
+                                 %arg1: tensor<3x3xi32>) -> tensor<6x6xi32, #DCSR> {
+  %0 = bufferization.alloc_tensor() : tensor<6x6xi32, #DCSR>
+  %1 = linalg.generic {
+         indexing_maps = [#map, #map1, #map2],
+         iterator_types = ["parallel", "parallel", "reduction", "reduction"]}
+         ins(%arg0, %arg1 : tensor<8x8xi32, #DCSR>, tensor<3x3xi32>)
+         outs(%0 : tensor<6x6xi32, #DCSR>) {
+    ^bb0(%in: i32, %in_0: i32, %out: i32):
+      %2 = arith.muli %in, %in_0 : i32
+      %3 = arith.addi %out, %2 : i32
+      linalg.yield %3 : i32
+    } -> tensor<6x6xi32, #DCSR>
+  return %1 : tensor<6x6xi32, #DCSR>
+}

mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conv_2d_slice_based.mlir

+// DEFINE: %{option} = "enable-slice-affine=true enable-runtime-library=false"
+// DEFINE: %{command} = mlir-opt %s --sparse-compiler=%{option} | \
+// DEFINE: mlir-cpu-runner \
+// DEFINE:  -e entry -entry-point-result=void  \
+// DEFINE:  -shared-libs=%mlir_lib_dir/libmlir_c_runner_utils%shlibext | \
+// DEFINE: FileCheck %s
+//
+// RUN: %{command}
+
+#map = affine_map<(d0, d1, d2, d3) -> (d0 + d2, d1 + d3)>
+#map1 = affine_map<(d0, d1, d2, d3) -> (d2, d3)>
+#map2 = affine_map<(d0, d1, d2, d3) -> (d0, d1)>
+
+#DCSR = #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>
+
+module {
+  func.func @conv2d_all_sparse_CSR(%arg0: tensor<8x8xi32, #DCSR>, %arg1: tensor<3x3xi32>) -> tensor<6x6xi32, #DCSR> {
+    %0 = bufferization.alloc_tensor() : tensor<6x6xi32, #DCSR>
+    %1 = linalg.generic {
+    indexing_maps = [#map, #map1, #map2],
+    iterator_types = ["parallel", "parallel", "reduction", "reduction"]}
+    ins(%arg0, %arg1 : tensor<8x8xi32, #DCSR>, tensor<3x3xi32>)
+    outs(%0 : tensor<6x6xi32, #DCSR>) {
+    ^bb0(%in: i32, %in_0: i32, %out: i32):
+      %2 = arith.muli %in, %in_0 : i32
+      %3 = arith.addi %out, %2 : i32
+      linalg.yield %3 : i32
+    } -> tensor<6x6xi32, #DCSR>
+    return %1 : tensor<6x6xi32, #DCSR>
+  }
+
+  func.func @entry() {
+    %c0 = arith.constant 0 : index
+    %i0 = arith.constant 0 : i32
+
+    // A typical edge detection filter.
+    %filter = arith.constant dense<[
+      [  1,  0, -1 ],
+      [  0,  0,  0 ],
+      [ -1,  0,  1 ]
+    ]> : tensor<3x3xi32>
+
+    %input = arith.constant dense<[
+      [  1,  2,  3,  4,  0,  6,  7,  8 ],
+      [  2,  2,  4,  4,  0,  0,  6,  8 ],
+      [  2,  2,  4,  4,  0,  0,  6,  8 ],
+      [  2,  2,  3,  4,  0,  0,  7,  8 ],
+      [  1,  3,  3,  4,  0,  0,  6,  8 ],
+      [  3,  2,  3,  4,  0,  0,  7,  8 ],
+      [  1,  3,  3,  4,  3,  6,  6,  8 ],
+      [  1,  3,  3,  4,  3,  0,  7,  8 ]
+    ]> : tensor<8x8xi32>
+
+    %sparse_filter_CSR = sparse_tensor.convert %filter
+      : tensor<3x3xi32> to tensor<3x3xi32>
+
+    %sparse_input_CSR = sparse_tensor.convert %input
+      : tensor<8x8xi32> to tensor<8x8xi32, #DCSR>
+
+    %3 = call @conv2d_all_sparse_CSR(%sparse_input_CSR, %sparse_filter_CSR)
+         : (tensor<8x8xi32, #DCSR>,
+            tensor<3x3xi32>) -> tensor<6x6xi32, #DCSR>
+
+    %out = sparse_tensor.convert %3
+      : tensor<6x6xi32, #DCSR> to tensor<6x6xi32>
+    //
+    // CHECK:    ( ( 0, 0, -1, -6, -1, 6 ),
+    // CHECK-SAME: ( -1, 0, 1, 0, 1, 0 ),
+    // CHECK-SAME: ( 0, -1, 1, 0, 0, 0 ),
+    // CHECK-SAME: ( -1, 0, 0, 0, 0, 0 ),
+    // CHECK-SAME: ( 0, 0, 3, 6, -3, -6 ),
+    // CHECK-SAME: ( 2, -1, 3, 0, -3, 0 ) )
+    //
+    %v2 = vector.transfer_read %out[%c0, %c0], %i0
+      : tensor<6x6xi32>, vector<6x6xi32>
+    vector.print %v2 : vector<6x6xi32>
+
+    return
+  }
+
+}

mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conv_3d_slice_based.mlir

+// DEFINE: %{option} = "enable-slice-affine=true enable-runtime-library=false"
+// DEFINE: %{command} = mlir-opt %s --sparse-compiler=%{option} | \
+// DEFINE: mlir-cpu-runner \
+// DEFINE:  -e entry -entry-point-result=void  \
+// DEFINE:  -shared-libs=%mlir_lib_dir/libmlir_c_runner_utils%shlibext | \
+// DEFINE: FileCheck %s
+//
+// RUN: %{command}
+
+#CCC = #sparse_tensor.encoding<{
+  dimLevelType = [ "compressed", "compressed", "compressed" ]
+}>
+
+func.func @alloc_3d_filled_f32(%s1 : index, %s2 : index, %s3 : index, %f : f32) -> tensor<?x?x?xf32> {
+  %buf = bufferization.alloc_tensor(%s1, %s2, %s3) : tensor<?x?x?xf32>
+  %ret = linalg.fill ins(%f : f32) outs(%buf : tensor<?x?x?xf32>) -> tensor<?x?x?xf32>
+  return %ret : tensor<?x?x?xf32>
+}
+
+func.func @conv_3d_CCC(%arg0: tensor<?x?x?xf32, #CCC>, %arg1: tensor<?x?x?xf32>) -> tensor<?x?x?xf32, #CCC> {
+  %c6 = arith.constant 6 : index
+  %s = bufferization.alloc_tensor(%c6, %c6, %c6) : tensor<?x?x?xf32, #CCC>
+  %ret = linalg.conv_3d
+     ins (%arg0, %arg1: tensor<?x?x?xf32, #CCC>, tensor<?x?x?xf32>)
+    outs (%s: tensor<?x?x?xf32, #CCC>) -> tensor<?x?x?xf32, #CCC>
+  return %ret : tensor<?x?x?xf32, #CCC>
+}
+
+func.func @entry() {
+  %c0 = arith.constant 0 : index
+  %c1 = arith.constant 1 : index
+  %c3 = arith.constant 3 : index
+  %c6 = arith.constant 6 : index
+  %c8 = arith.constant 8 : index
+  %f10 = arith.constant 10.00000e+00 : f32
+  %val = arith.constant 2.00000e+00 : f32
+  %zero = arith.constant 0.00000e+00 : f32
+
+  %filter3D = call @alloc_3d_filled_f32(%c3, %c3, %c3, %val) : (index, index, index, f32) -> (tensor<?x?x?xf32>)
+  %in3D_tmp = call @alloc_3d_filled_f32(%c8, %c8, %c8, %val) : (index, index, index, f32) -> (tensor<?x?x?xf32>)
+  %in3D = tensor.insert %f10 into %in3D_tmp[%c0, %c3, %c0] : tensor<?x?x?xf32>
+  %out3D = call @alloc_3d_filled_f32(%c6, %c6, %c6, %zero) : (index, index, index, f32) -> (tensor<?x?x?xf32>)
+
+  %in3D_CCC = sparse_tensor.convert %in3D
+    : tensor<?x?x?xf32> to tensor<?x?x?xf32, #CCC>
+  %CCC_ret = call @conv_3d_CCC(%in3D_CCC, %filter3D) : (tensor<?x?x?xf32, #CCC>, tensor<?x?x?xf32>) -> (tensor<?x?x?xf32, #CCC>)
+  // CHECK:     ( ( ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 124, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 124, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 124, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ) ),
+  // CHECK-SAME:  ( ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ) ),
+  // CHECK-SAME:  ( ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ) ),
+  // CHECK-SAME:  ( ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ) ),
+  // CHECK-SAME:  ( ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ) ),
+  // CHECK-SAME:  ( ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ),
+  // CHECK-SAME:    ( 108, 108, 108, 108, 108, 108 ) ) )
+  %1 = sparse_tensor.convert %CCC_ret
+    : tensor<?x?x?xf32, #CCC> to tensor<?x?x?xf32>
+  %v1 = vector.transfer_read %1[%c0, %c0, %c0], %zero
+      : tensor<?x?x?xf32>, vector<6x6x6xf32>
+  vector.print %v1 : vector<6x6x6xf32>
+
+  // Free the resources
+  bufferization.dealloc_tensor %in3D : tensor<?x?x?xf32>
+  bufferization.dealloc_tensor %filter3D : tensor<?x?x?xf32>
+
+  bufferization.dealloc_tensor %in3D_CCC : tensor<?x?x?xf32, #CCC>
+  bufferization.dealloc_tensor %CCC_ret : tensor<?x?x?xf32, #CCC>
+
+  return
+}