[TIR] Affine utility support iter lowerbound and diagnostics

include/tvm/arith/iter_affine_map.h

@@ -49,6 +49,7 @@
 #define TVM_ARITH_ITER_AFFINE_MAP_H_
 
 #include <tvm/arith/analyzer.h>
+#include <tvm/ir/diagnostic.h>
 #include <tvm/ir/expr.h>
 #include <tvm/tir/var.h>
 
@@ -275,13 +276,14 @@ class IterSumExpr : public IterMapExpr {
  * \param predicate The predicate constraints on the input iterators
  * \param require_bijective A boolean flag that indicates whether the mapping should be bijective.
  * \param analyzer Analyzer used to get context information.
+ * \param diag_ctx Diagnostic context.
  *
  * \return The detected pattern if a match exists,
  *         otherwise return an empty array.
  */
 Array<IterSumExpr> DetectIterMap(const Array<PrimExpr>& indices, const Map<Var, Range>& input_iters,
                                  const PrimExpr& predicate, bool require_bijective,
-                                 arith::Analyzer* analyzer);
+                                 arith::Analyzer* analyzer, DiagnosticContext diag_ctx);
 /*!
  * \brief Use IterVarMap detector to rewrite and simplify the indices
  *
@@ -333,6 +335,7 @@ Map<Var, PrimExpr> InverseAffineIterMap(const Array<IterSumExpr>& iter_map,
  * \param predicate The predicate constraints on the input iterators
  * \param require_bijective A boolean flag that indicates whether the mapping should be bijective.
  * \param analyzer Analyzer used to get context information.
+ * \param diag_ctx Diagnostic context.
  *
  * \return The result list has length len(bindings) + 1
         [0, len(bindings)): The iter map matching result. The inner list is of length 2.
@@ -344,7 +347,8 @@ Map<Var, PrimExpr> InverseAffineIterMap(const Array<IterSumExpr>& iter_map,
 Array<Array<IterMark>> SubspaceDivide(const Array<PrimExpr>& bindings,
                                       const Map<Var, Range>& input_iters,
                                       const Array<Var>& sub_iters, const PrimExpr& predicate,
-                                      bool require_bijective, arith::Analyzer* analyzer);
+                                      bool require_bijective, arith::Analyzer* analyzer,
+                                      DiagnosticContext diag_ctx);
 
 }  // namespace arith
 }  // namespace tvm

src/arith/int_set.cc

@@ -835,9 +835,10 @@ Optional<Array<IntSet>> EstimateRegionLowerBound(const Array<Range>& region,
     for (const Range& range : region) {
       affine_indices.push_back(range->min);
     }
+    DiagnosticContext diag_ctx(DiagnosticContext::Default(IRModule()));
     iter_sum_exprs = DetectIterMap(
         /*indices=*/affine_indices, /*input_iters=*/var_dom,
-        /*predicate=*/predicate, /*require_bijective=*/false, analyzer);
+        /*predicate=*/predicate, /*require_bijective=*/false, analyzer, diag_ctx);
   }
   if (iter_sum_exprs.empty()) {
     return NullOpt;
@@ -857,6 +858,7 @@ Optional<Array<IntSet>> EstimateRegionLowerBound(const Array<Range>& region,
     if (!analyzer->CanProve(range->extent >= split->scale)) {
       return NullOpt;
     }
+
     const PrimExpr& base = sum_expr->base;
     // IterSplitExpr: (source // lower_factor) % extent * scale
     // where `(source // lower_factor) % extent` is within [0, extent - 1]

src/tir/schedule/analysis/analysis.cc

@@ -415,12 +415,14 @@ bool IsAffineBinding(const BlockRealize& realize, const Map<Var, Range>& loop_va
   if (loop_var_ranges.empty()) {
     return true;
   }
+  DiagnosticContext diag_ctx(DiagnosticContext::Default(IRModule()));
   Array<arith::IterSumExpr> results = arith::DetectIterMap(
       /*indices=*/realize->iter_values,
       /*input_iters=*/loop_var_ranges,
       /*predicate=*/realize->predicate,
       /*require_bijective=*/false,
-      /*analyzer=*/analyzer);
+      /*analyzer=*/analyzer,
+      /*diag_ctx*/ diag_ctx);
   if (results.empty()) {
     return false;
   }

tests/python/unittest/test_arith_intset.py

@@ -16,6 +16,8 @@
 # under the License.
 import tvm
 from tvm import te
+from tvm import tir
+from tvm.ir.base import structural_equal
 
 
 class IntSetChecker:
@@ -233,6 +235,90 @@ def test_region_lower_bound_negative_scale():
     assert int_set_1.max_value.value == 35
 
 
+def test_region_lower_bound_for_non_perfect_tile():
+    h1 = tvm.tir.Var("h1", "int32")
+    h2 = tvm.tir.Var("h2", "int32")
+    h3 = tvm.tir.Var("h3", "int32")
+    analyzer = tvm.arith.Analyzer()
+
+    def do_test_point_access(point, predicates, var_dom, expect):
+        regions = tvm.arith.estimate_region_lower_bound(
+            region=[
+                tvm.ir.Range.from_min_extent(min_value=point, extent=1),
+            ],
+            var_dom=var_dom,
+            predicate=tvm.tir.all(*predicates),
+        )
+        if expect is None:  # expect a failure
+            assert regions is None
+        else:
+            assert len(regions) == 1
+            for binding, expect_min, expect_max in expect:
+                min_diff = expect_min - regions[0].min_value
+                assert analyzer.simplify(tir.stmt_functor.substitute(min_diff, binding), 3) == 0
+                max_diff = expect_max - regions[0].max_value
+                assert analyzer.simplify(tir.stmt_functor.substitute(max_diff, binding), 3) == 0
+
+    # non-uniform tiling, single inner variable
+    # h3 == 0: region is [1, 9]
+    # 0 < h3 <= 26: region is [h3 * 8, h3 * 8 + 9]
+    # h3 > 26: region is [h3 * 8, 223]
+    do_test_point_access(
+        point=h3 * 8 + h2,
+        predicates=[1 <= h3 * 8 + h2, h3 * 8 + h2 < 224],
+        var_dom={
+            h2: tvm.ir.Range(begin=0, end=10),
+        },
+        expect=[
+            (
+                {},
+                tvm.tir.max(h3 * 8, 1),
+                tvm.tir.max(h3 * 8, 1)
+                - tvm.tir.max(h3 * 8, 214)
+                - tvm.tir.max(1 - h3 * 8, 0)
+                + 223,
+            ),
+            ({h3: 0}, 1, 9),
+            ({h3: 10}, h3 * 8, h3 * 8 + 9),
+            ({h3: 27}, h3 * 8, 223),
+        ],
+    )
+
+    # non-uniform tiling, two inner variables
+    do_test_point_access(
+        point=h3 * 8 + h2 * 5 + h1,
+        predicates=[1 <= h3 * 8 + h2 * 5 + h1, h3 * 8 + h2 * 5 + h1 < 224],
+        var_dom={
+            h2: tvm.ir.Range(begin=0, end=2),
+            h1: tvm.ir.Range(begin=0, end=5),
+        },
+        expect=[
+            (
+                {},
+                tvm.tir.max(h3 * 8, 1),
+                tvm.tir.max(h3 * 8, 1)
+                - tvm.tir.max(h3 * 8, 214)
+                - tvm.tir.max(1 - h3 * 8, 0)
+                + 223,
+            ),
+            ({h3: 0}, 1, 9),
+            ({h3: 10}, h3 * 8, h3 * 8 + 9),
+            ({h3: 27}, h3 * 8, 223),
+        ],
+    )
+
+    # should fail on incompatible predicates
+    do_test_point_access(
+        point=h3 * 8 + h2 * 5 + h1,
+        predicates=[1 <= h3 * 8 + h2 * 5 + h1, h3 * 8 + h1 * 2 + h2 < 224],
+        var_dom={
+            h2: tvm.ir.Range(begin=0, end=2),
+            h1: tvm.ir.Range(begin=0, end=5),
+        },
+        expect=None,
+    )
+
+
 def test_union_lower_bound():
     neg_inf = tvm.arith.int_set.neg_inf()
     pos_inf = tvm.arith.int_set.pos_inf()
@@ -257,4 +343,5 @@ def test_union_lower_bound():
     test_region_lower_bound_split_predicate()
     test_region_lower_bound_multiple_variables()
     test_region_lower_bound_negative_scale()
+    test_region_lower_bound_for_non_perfect_tile()
     test_union_lower_bound()