diff --git a/exla/lib/exla/defn.ex b/exla/lib/exla/defn.ex
index 5e8b94c5ab..d2f2fd7357 100644
--- a/exla/lib/exla/defn.ex
+++ b/exla/lib/exla/defn.ex
@@ -1367,30 +1367,42 @@ defmodule EXLA.Defn do
 
   ## Computation helpers
 
-  defp sort_computation(op, type, arg_typespecs, %{builder: %EXLA.MLIR.Function{} = function}) do
+  defp sort_computation(operator, type, arg_typespecs, %{
+         builder: %EXLA.MLIR.Function{} = function
+       }) do
     {region, [lhs, rhs | _]} = Function.push_region(function, arg_typespecs)
 
     typespec = Typespec.tensor({:pred, 8}, {})
 
-    op =
-      cond do
-        Nx.Type.integer?(type) ->
-          apply(Value, op, [lhs, rhs, typespec])
-
-        op == :less ->
-          is_nan = Value.is_nan(rhs, typespec)
-          Value.bitwise_or(is_nan, Value.less(lhs, rhs, typespec), typespec)
-
-        op == :greater ->
-          is_nan = Value.is_nan(lhs, typespec)
-          Value.bitwise_or(is_nan, Value.greater(lhs, rhs, typespec), typespec)
+    {lhs, rhs} =
+      if Nx.Type.integer?(type) do
+        {lhs, rhs}
+      else
+        {sort_computation_canonicalize_float(lhs), sort_computation_canonicalize_float(rhs)}
       end
 
+    op = apply(Value, operator, [lhs, rhs, typespec, [total_order: true]])
+
     Value.return(function, [op])
     Function.pop_region(function)
     region
   end
 
+  defp sort_computation_canonicalize_float(%Value{function: func} = op) do
+    # Standardize the representation of NaNs (-NaN, NaN) and zeros (-0, 0).
+    # See https://github.com/google/jax/blob/e81c82605f0e1813080cfe1037d043b27b38291d/jax/_src/lax/lax.py#L4248-L4253
+
+    op_typespec = Value.get_typespec(op)
+
+    zero = Value.constant(func, [0], Typespec.to_shape(op_typespec, {}))
+    zeros = Value.constant(func, [0], op_typespec)
+    nans = Value.constant(func, [:nan], op_typespec)
+
+    pred_typespec = Typespec.tensor({:pred, 8}, {})
+    op = Value.select(Value.equal(op, zero, pred_typespec), zeros, op, op_typespec)
+    Value.select(Value.is_nan(op, pred_typespec), nans, op, op_typespec)
+  end
+
   defp op_computation(
          op,
          arg_typespecs,
diff --git a/exla/lib/exla/mlir/value.ex b/exla/lib/exla/mlir/value.ex
index e38d09fc0b..2b25c6f8f6 100644
--- a/exla/lib/exla/mlir/value.ex
+++ b/exla/lib/exla/mlir/value.ex
@@ -54,31 +54,40 @@ defmodule EXLA.MLIR.Value do
   }
 
   for {op, direction} <- @bin_comparison_ops do
-    def unquote(op)(%Value{function: func} = lhs, %Value{function: func} = rhs, typespec) do
-      compare_and_return_bool(func, lhs, rhs, typespec, unquote(direction))
+    def unquote(op)(
+          %Value{function: func} = lhs,
+          %Value{function: func} = rhs,
+          typespec,
+          opts \\ []
+        ) do
+      compare_and_return_bool(func, lhs, rhs, typespec, unquote(direction), opts[:total_order])
     end
   end
 
-  defp compare_and_return_bool(func, lhs, rhs, typespec, direction) do
+  defp compare_and_return_bool(func, lhs, rhs, typespec, direction, total_order? \\ false) do
     %{type: lhs_type} = get_typespec(lhs)
     %{type: rhs_type} = get_typespec(rhs)
 
     comparison_type =
       cond do
         Nx.Type.complex?(lhs_type) or Nx.Type.complex?(rhs_type) ->
-          attr_comparison_type(:float)
+          [compare_type: attr_comparison_type(:float)]
 
         Nx.Type.float?(lhs_type) or Nx.Type.float?(rhs_type) ->
-          attr_comparison_type(:float)
+          attr =
+            if total_order? do
+              attr_comparison_type(:totalorder)
+            else
+              attr_comparison_type(:float)
+            end
+
+          [compare_type: attr]
 
         true ->
-          attr_comparison_type(:notype)
+          []
       end
 
-    attributes = [
-      comparison_direction: attr_comparison_direction(direction),
-      compare_type: comparison_type
-    ]
+    attributes = [comparison_direction: attr_comparison_direction(direction)] ++ comparison_type
 
     result_types = typespecs_to_mlir_types([Typespec.to_type(typespec, {:pred, 8})])
 
@@ -1072,7 +1081,7 @@ defmodule EXLA.MLIR.Value do
   defp attr_comparison_direction(value) when value in [:eq, :lt, :le, :gt, :ge, :ne],
     do: attr_enum("stablehlo", "comparison_direction", value)
 
-  defp attr_comparison_type(value) when value in [:float, :totalorder, :notype],
+  defp attr_comparison_type(value) when value in [:float, :totalorder],
     do: attr_enum("stablehlo", "comparison_type", value)
 
   defp attr_precision(value) when value in [:default, :high, :highest],