diff --git a/mlir/lib/Dialect/Arith/Transforms/EmulateWideInt.cpp b/mlir/lib/Dialect/Arith/Transforms/EmulateWideInt.cpp
--- a/mlir/lib/Dialect/Arith/Transforms/EmulateWideInt.cpp
+++ b/mlir/lib/Dialect/Arith/Transforms/EmulateWideInt.cpp
@@ -13,6 +13,7 @@
 #include "mlir/Dialect/Func/IR/FuncOps.h"
 #include "mlir/Dialect/Func/Transforms/FuncConversions.h"
 #include "mlir/Dialect/Vector/IR/VectorOps.h"
+#include "mlir/IR/BuiltinTypes.h"
 #include "mlir/Transforms/DialectConversion.h"
 #include "llvm/Support/MathExtras.h"
 #include <cassert>
@@ -640,6 +641,11 @@
     return None;
   });
 
+  // IndexType is not sized, do not emulate.
+  addConversion([](IndexType ty) -> Optional<Type> { return ty; });
+  // FlatType is not an integer type, do not emulate.
+  addConversion([](FloatType ty) -> Optional<Type> { return ty; });
+
   // Vector case.
   addConversion([this](VectorType ty) -> Optional<Type> {
     auto intTy = ty.getElementType().dyn_cast<IntegerType>();
diff --git a/mlir/test/Dialect/Arith/emulate-wide-int.mlir b/mlir/test/Dialect/Arith/emulate-wide-int.mlir
--- a/mlir/test/Dialect/Arith/emulate-wide-int.mlir
+++ b/mlir/test/Dialect/Arith/emulate-wide-int.mlir
@@ -10,6 +10,24 @@
     return %x : i32
 }
 
+// Expect no conversions, index is not sized.
+// CHECK-LABEL: func @addi_same_index
+// CHECK-SAME:    ([[ARG:%.+]]: index) -> index
+// CHECK-NEXT:    [[X:%.+]] = arith.addi [[ARG]], [[ARG]] : index
+// CHECK-NEXT:    return [[X]] : index
+func.func @addi_same_index(%a : index) -> index {
+    %x = arith.addi %a, %a : index
+    return %x : index
+}
+
+// Expect no conversions, f64 is not an integer type.
+// CHECK-LABEL: func @addi_same_f64
+// CHECK-SAME:    ([[ARG:%.+]]: f64) -> f64
+// CHECK-NEXT:    return [[ARG]] : f64
+func.func @addi_same_f64(%a : f64) -> f64 {
+    return %a : f64
+}
+
 // Expect no conversions, i32 is supported.
 // CHECK-LABEL: func @addi_same_vector_i32
 // CHECK-SAME:    ([[ARG:%.+]]: vector<2xi32>) -> vector<2xi32>