diff --git a/mlir/include/mlir/Dialect/Arithmetic/IR/ArithmeticOps.td b/mlir/include/mlir/Dialect/Arithmetic/IR/ArithmeticOps.td
--- a/mlir/include/mlir/Dialect/Arithmetic/IR/ArithmeticOps.td
+++ b/mlir/include/mlir/Dialect/Arithmetic/IR/ArithmeticOps.td
@@ -594,7 +594,7 @@
 // AddFOp
 //===----------------------------------------------------------------------===//
 
-def Arith_AddFOp : Arith_FloatBinaryOp<"addf"> {
+def Arith_AddFOp : Arith_FloatBinaryOp<"addf", [Commutative]> {
   let summary = "floating point addition operation";
   let description = [{
     The `addf` operation takes two operands and returns one result, each of
@@ -627,6 +627,28 @@
 
 def Arith_SubFOp : Arith_FloatBinaryOp<"subf"> {
   let summary = "floating point subtraction operation";
+  let description = [{
+    The `subf` operation takes two operands and returns one result, each of
+    these is required to be the same type. This type may be a floating point
+    scalar type, a vector whose element type is a floating point type, or a
+    floating point tensor.
+
+    Example:
+
+    ```mlir
+    // Scalar subtraction.
+    %a = arith.subf %b, %c : f64
+
+    // SIMD vector subtraction, e.g. for Intel SSE.
+    %f = arith.subf %g, %h : vector<4xf32>
+
+    // Tensor subtraction.
+    %x = arith.subf %y, %z : tensor<4x?xbf16>
+    ```
+
+    TODO: In the distant future, this will accept optional attributes for fast
+    math, contraction, rounding mode, and other controls.
+  }];
   let hasFolder = 1;
 }
 
@@ -723,7 +745,7 @@
 // MulFOp
 //===----------------------------------------------------------------------===//
 
-def Arith_MulFOp : Arith_FloatBinaryOp<"mulf"> {
+def Arith_MulFOp : Arith_FloatBinaryOp<"mulf", [Commutative]> {
   let summary = "floating point multiplication operation";
   let description = [{
     The `mulf` operation takes two operands and returns one result, each of
diff --git a/mlir/lib/Dialect/Arithmetic/IR/ArithmeticOps.cpp b/mlir/lib/Dialect/Arithmetic/IR/ArithmeticOps.cpp
--- a/mlir/lib/Dialect/Arithmetic/IR/ArithmeticOps.cpp
+++ b/mlir/lib/Dialect/Arithmetic/IR/ArithmeticOps.cpp
@@ -580,10 +580,6 @@
   if (matchPattern(getRhs(), m_NegZeroFloat()))
     return getLhs();
 
-  // addf(-0, x) -> x
-  if (matchPattern(getLhs(), m_NegZeroFloat()))
-    return getRhs();
-
   return constFoldBinaryOp<FloatAttr>(
       operands, [](const APFloat &a, const APFloat &b) { return a + b; });
 }
diff --git a/mlir/test/Dialect/Arithmetic/canonicalize.mlir b/mlir/test/Dialect/Arithmetic/canonicalize.mlir
--- a/mlir/test/Dialect/Arithmetic/canonicalize.mlir
+++ b/mlir/test/Dialect/Arithmetic/canonicalize.mlir
@@ -658,7 +658,7 @@
   %c0 = arith.constant 0.0 : f32
   %c-0 = arith.constant -0.0 : f32
   %c1 = arith.constant 1.0 : f32
-  %0 = arith.addf %arg0, %c0 : f32
+  %0 = arith.addf %c0, %arg0 : f32
   %1 = arith.addf %arg0, %c-0 : f32
   %2 = arith.addf %c-0, %arg0 : f32
   %3 = arith.addf %c1, %c1 : f32
@@ -685,15 +685,18 @@
 // -----
 
 // CHECK-LABEL: @test_mulf(
-func @test_mulf(%arg0 : f32) -> (f32, f32, f32) {
-  // CHECK-NEXT:  %[[C4:.+]] = arith.constant 4.0
-  // CHECK-NEXT:   return %arg0, %arg0, %[[C4]]
+func @test_mulf(%arg0 : f32) -> (f32, f32, f32, f32) {
+  // CHECK-DAG:   %[[C2:.+]] = arith.constant 2.0
+  // CHECK-DAG:   %[[C4:.+]] = arith.constant 4.0
+  // CHECK-NEXT:  %[[X:.+]] = arith.mulf %arg0, %[[C2]]
+  // CHECK-NEXT:  return %[[X]], %arg0, %arg0, %[[C4]]
   %c1 = arith.constant 1.0 : f32
   %c2 = arith.constant 2.0 : f32
-  %0 = arith.mulf %arg0, %c1 : f32
-  %1 = arith.mulf %c1, %arg0 : f32
-  %2 = arith.mulf %c2, %c2 : f32
-  return %0, %1, %2 : f32, f32, f32
+  %0 = arith.mulf %c2, %arg0 : f32
+  %1 = arith.mulf %arg0, %c1 : f32
+  %2 = arith.mulf %c1, %arg0 : f32
+  %3 = arith.mulf %c2, %c2 : f32
+  return %0, %1, %2, %3 : f32, f32, f32, f32
 }
 
 // -----