diff --git a/mlir/lib/Dialect/Math/Transforms/PolynomialApproximation.cpp b/mlir/lib/Dialect/Math/Transforms/PolynomialApproximation.cpp
--- a/mlir/lib/Dialect/Math/Transforms/PolynomialApproximation.cpp
+++ b/mlir/lib/Dialect/Math/Transforms/PolynomialApproximation.cpp
@@ -182,16 +182,21 @@
 // Helper functions to build math functions approximations.
 //----------------------------------------------------------------------------//
 
-static Value min(ImplicitLocOpBuilder &builder, Value a, Value b) {
+// Return the minimum of the two values or NaN if value is NaN
+static Value min(ImplicitLocOpBuilder &builder, Value value, Value bound) {
   return builder.create<arith::SelectOp>(
-      builder.create<arith::CmpFOp>(arith::CmpFPredicate::OLT, a, b), a, b);
+      builder.create<arith::CmpFOp>(arith::CmpFPredicate::ULT, value, bound),
+      value, bound);
 }
 
-static Value max(ImplicitLocOpBuilder &builder, Value a, Value b) {
+// Return the maximum of the two values or NaN if value is NaN
+static Value max(ImplicitLocOpBuilder &builder, Value value, Value bound) {
   return builder.create<arith::SelectOp>(
-      builder.create<arith::CmpFOp>(arith::CmpFPredicate::OGT, a, b), a, b);
+      builder.create<arith::CmpFOp>(arith::CmpFPredicate::UGT, value, bound),
+      value, bound);
 }
 
+// Return the clamped value or NaN if value is NaN
 static Value clamp(ImplicitLocOpBuilder &builder, Value value, Value lowerBound,
                    Value upperBound) {
   return max(builder, min(builder, value, upperBound), lowerBound);
diff --git a/mlir/test/Dialect/Math/polynomial-approximation.mlir b/mlir/test/Dialect/Math/polynomial-approximation.mlir
--- a/mlir/test/Dialect/Math/polynomial-approximation.mlir
+++ b/mlir/test/Dialect/Math/polynomial-approximation.mlir
@@ -225,7 +225,7 @@
 // CHECK:           %[[VAL_20:.*]] = arith.constant 1056964608 : i32
 // CHECK:           %[[VAL_21:.*]] = arith.constant 23 : i32
 // CHECK:           %[[VAL_22:.*]] = arith.constant 0.693147182 : f32
-// CHECK:           %[[VAL_23:.*]] = arith.cmpf ogt, %[[X]], %[[VAL_4]] : f32
+// CHECK:           %[[VAL_23:.*]] = arith.cmpf ugt, %[[X]], %[[VAL_4]] : f32
 // CHECK:           %[[VAL_24:.*]] = arith.select %[[VAL_23]], %[[X]], %[[VAL_4]] : f32
 // CHECK-NOT:       frexp
 // CHECK:           %[[VAL_25:.*]] = arith.bitcast %[[VAL_24]] : f32 to i32
@@ -355,9 +355,9 @@
 // CHECK:           %[[VAL_12:.*]] = arith.constant 0.00226843474 : f32
 // CHECK:           %[[VAL_13:.*]] = arith.constant 1.18534706E-4 : f32
 // CHECK:           %[[VAL_14:.*]] = arith.constant 1.19825836E-6 : f32
-// CHECK:           %[[VAL_15:.*]] = arith.cmpf olt, %[[VAL_0]], %[[VAL_2]] : f32
+// CHECK:           %[[VAL_15:.*]] = arith.cmpf ult, %[[VAL_0]], %[[VAL_2]] : f32
 // CHECK:           %[[VAL_16:.*]] = arith.select %[[VAL_15]], %[[VAL_0]], %[[VAL_2]] : f32
-// CHECK:           %[[VAL_17:.*]] = arith.cmpf ogt, %[[VAL_16]], %[[VAL_1]] : f32
+// CHECK:           %[[VAL_17:.*]] = arith.cmpf ugt, %[[VAL_16]], %[[VAL_1]] : f32
 // CHECK:           %[[VAL_18:.*]] = arith.select %[[VAL_17]], %[[VAL_16]], %[[VAL_1]] : f32
 // CHECK:           %[[VAL_19:.*]] = math.abs %[[VAL_0]] : f32
 // CHECK:           %[[VAL_20:.*]] = arith.cmpf olt, %[[VAL_19]], %[[VAL_3]] : f32
diff --git a/mlir/test/mlir-cpu-runner/math-polynomial-approx.mlir b/mlir/test/mlir-cpu-runner/math-polynomial-approx.mlir
--- a/mlir/test/mlir-cpu-runner/math-polynomial-approx.mlir
+++ b/mlir/test/mlir-cpu-runner/math-polynomial-approx.mlir
@@ -29,6 +29,11 @@
   %5 = math.tanh %4 : vector<8xf32>
   vector.print %5 : vector<8xf32>
 
+  // CHECK-NEXT: nan
+  %nan = arith.constant 0x7fc00000 : f32
+  %6 = math.tanh %nan : f32
+  vector.print %6 : f32
+
   return
 }