Simplify more constraints and mods.

Additional mod simplification was a coincidence due to refactoring the
sum-splitting logic. I can factor this out into a separate CL if desired.

- enables additional vectorization when there is a
  constraint on the loop symbol that is redundant.
- fixes some inconsistencies in div/mod simplification (should
  lead to better code in some cases, see loop emitter test).
- replaces an ad-hoc simplification in fusion_emitter.cc with
  a more general one

Also remove most of the change detector tests in reduction_test.

PiperOrigin-RevId: 651294205

third_party/xla/xla/service/gpu/fusions/concatenate_mlir.cc

@@ -114,6 +114,7 @@ absl::Status MlirConcatenateFusion::EmitEntryFunction(
     auto thread_id_to_output_map = ComposeIndexingMaps(
         ComposeIndexingMaps(thread_id_to_input_map, input_to_output_map),
         epilogue_indexing);
+    thread_id_to_output_map.Simplify();
 
     auto loop_nest_body_builder =
         [&, operand_index = operand_index](

third_party/xla/xla/service/gpu/fusions/fusion_emitter.cc

@@ -188,13 +188,7 @@ IndexingMap KernelFusionInterface::GetDefaultThreadIdIndexingMap(
       mlir::AffineMap::get(/*dimCount=*/6,
                            /*symbolCount=*/2, output_dims, ctx),
       dim_vars, range_vars, /*rt_vars=*/{});
-  // Remove the unroll_elem_id symbol if unrolling divides num_elements.
-  if (num_elements % unroll_factor == 0) {
-    indexing_map.AddConstraint(linear_index.replace({{unroll_elem_id, c0}}),
-                               Interval{0, num_elements - unroll_factor});
-  } else {
-    indexing_map.AddConstraint(linear_index, Interval{0, num_elements - 1});
-  }
+  indexing_map.AddConstraint(linear_index, Interval{0, num_elements - 1});
   indexing_map.Simplify();
   return indexing_map;
 }

third_party/xla/xla/service/gpu/fusions/loop_mlir_test.cc

@@ -56,7 +56,7 @@ TEST_F(MlirLoopFusionTest, ThreadId_IndexingUnrolled) {
   (th_x, th_y, th_z, bl_x, bl_y, bl_z)[chunk_id, unroll_id] -> (
     ((bl_x * 128 + chunk_id * 129024 + th_x) floordiv 15000) mod 100,
     ((bl_x * 128 + chunk_id * 129024 + th_x) floordiv 75) mod 200,
-    (th_x * 4 + bl_x * 512 + chunk_id * 516096) mod 300 + unroll_id
+    ((bl_x * 128 + chunk_id * 129024 + th_x) mod 75) * 4 + unroll_id
   )
   domain:
   th_x in [0, 128)
@@ -67,7 +67,7 @@ TEST_F(MlirLoopFusionTest, ThreadId_IndexingUnrolled) {
   bl_z in [0, 1)
   chunk_id in [0, 12)
   unroll_id in [0, 4)
-  (th_x + bl_x * 128) * 4 + chunk_id * 516096 in [0, 5999997)
+  th_x + bl_x * 128 + chunk_id * 129024 in [0, 1500000)
 )"));
 }
 

third_party/xla/xla/service/gpu/fusions/loop_test.cc

@@ -90,7 +90,7 @@ TEST_F(LoopTest, ThreadIndexingUnrolled) {
   (th_x, th_y, th_z, bl_x, bl_y, bl_z)[chunk_id, unroll_id] -> (
     ((bl_x * 128 + chunk_id * 129024 + th_x) floordiv 15000) mod 100,
     ((bl_x * 128 + chunk_id * 129024 + th_x) floordiv 75) mod 200,
-    (th_x * 4 + bl_x * 512 + chunk_id * 516096) mod 300 + unroll_id
+    ((bl_x * 128 + chunk_id * 129024 + th_x) mod 75) * 4 + unroll_id
   )
   domain:
   th_x in [0, 128)
@@ -101,7 +101,7 @@ TEST_F(LoopTest, ThreadIndexingUnrolled) {
   bl_z in [0, 1)
   chunk_id in [0, 12)
   unroll_id in [0, 4)
-  (th_x + bl_x * 128) * 4 + chunk_id * 516096 in [0, 5999997)
+  th_x + bl_x * 128 + chunk_id * 129024 in [0, 1500000)
 )"));
 }
 

third_party/xla/xla/service/gpu/fusions/reduction.cc

@@ -1295,6 +1295,7 @@ std::optional<IndexingMap> ReductionInfo::ComputeThreadIdToOutputIndexing(
   }();
 
   AddGroupIdConstraint(map, root_index, groups_);
+  map.Simplify();
   return map;
 }
 
@@ -1321,6 +1322,7 @@ std::optional<IndexingMap> ReductionInfo::ComputeThreadIdToInputIndexing(
       GetBitcastMap(tiling_.GetXlaShape(),
                     hero.operand(hero_operand_index)->shape(), ctx));
   AddGroupIdConstraint(map, root_index, groups_);
+  map.Simplify();
   return map;
 }
 

third_party/xla/xla/service/gpu/fusions/reduction_mlir.cc

@@ -564,10 +564,13 @@ std::optional<IndexingMap> MlirReductionFusion::ComputeThreadIdToInputIndexing(
              .indexing_maps[hero_operand_index]
              .begin());
   }
-  auto map = ComputeReductionInputIndexing(ctx);
-  AddGroupIdConstraint(map, root_index, groups_);
-  return map * GetBitcastMap(input_shape_,
-                             hero.operand(hero_operand_index)->shape(), ctx);
+  auto projected_map = ComputeReductionInputIndexing(ctx);
+  AddGroupIdConstraint(projected_map, root_index, groups_);
+  auto map = projected_map *
+             GetBitcastMap(input_shape_,
+                           hero.operand(hero_operand_index)->shape(), ctx);
+  map.Simplify();
+  return map;
 }
 
 std::optional<IndexingMap> MlirReductionFusion::ComputeThreadIdToOutputIndexing(
@@ -578,6 +581,7 @@ std::optional<IndexingMap> MlirReductionFusion::ComputeThreadIdToOutputIndexing(
         GetBitcastMap(input_shape_, analysis_.fusion_root(root_index).shape(),
                       ctx));
     AddGroupIdConstraint(map, root_index, groups_);
+    map.Simplify();
     return map;
   }
 
@@ -594,10 +598,12 @@ std::optional<IndexingMap> MlirReductionFusion::ComputeThreadIdToOutputIndexing(
   const auto& hero = analysis_.fusion_hero(root_index).instruction();
   auto physical_shape =
       ShapeUtil::DeleteDimensions(hero.dimensions(), hero.operand(0)->shape());
-  return projected_indexing *
-         GetBitcastMap(ShapeUtil::MakeShapeWithDescendingLayout(
-                           PrimitiveType::U8, output_shape),
-                       physical_shape, ctx);
+  auto map = projected_indexing *
+             GetBitcastMap(ShapeUtil::MakeShapeWithDescendingLayout(
+                               PrimitiveType::U8, output_shape),
+                           physical_shape, ctx);
+  map.Simplify();
+  return map;
 }
 
 SmallVector<Value> MlirReductionFusion::EvaluateEpilogue(

third_party/xla/xla/service/gpu/fusions/reduction_mlir_test.cc

@@ -670,7 +670,7 @@ TEST_F(MlirColumnReductionTest, ColumnReduction) {
         (d0, d1, d2, d3, d4, d5)[s0, s1] -> (
           d3 floordiv 11,
           d0 floordiv 32 + s0 * 32,
-          (d3 mod 11) * 32 + d0 mod 32 + s1
+          (d3 mod 11) * 32 + d0 mod 32
         )
         domain:
         d0 in [0, 1024)
@@ -681,24 +681,24 @@ TEST_F(MlirColumnReductionTest, ColumnReduction) {
         d5 in [0, 1)
         s0 in [0, 33)
         s1 in [0, 1)
-        (d3 mod 11) * 32 + d0 mod 32 + s1 in [0, 321)
+        (d3 mod 11) * 32 + d0 mod 32 in [0, 321)
         d0 floordiv 32 + s0 * 32 in [0, 1051)
       )"));
   EXPECT_THAT(
       fusion.ComputeThreadIdToOutputIndexing(0, &mlir_context_)->ToString(),
       MatchIndexingString(R"(
         (d0, d1, d2, d3, d4, d5)[s0] -> (
-          d3 floordiv 11, (d3 mod 11) * 32 + d0 floordiv 32 + s0
+          d3 floordiv 11, (d3 mod 11) * 32 + d0 floordiv 32
         )
         domain:
-        d0 in [0, 1024)
+        d0 in [0, 993)
         d1 in [0, 1)
         d2 in [0, 1)
         d3 in [0, 143)
         d4 in [0, 1)
         d5 in [0, 1)
         s0 in [0, 1)
-        (d3 mod 11) * 32 + d0 floordiv 32 + s0 in [0, 321)
+        (d3 mod 11) * 32 + d0 floordiv 32 in [0, 321)
         d0 mod 32 in [0, 1)
       )"));
   TF_ASSERT_OK(EmitAndCheckIR(kHloString, R"(