diff --git a/Eigen/src/Core/functors/BinaryFunctors.h b/Eigen/src/Core/functors/BinaryFunctors.h
index 38f123cff..eaa4352b8 100644
--- a/Eigen/src/Core/functors/BinaryFunctors.h
+++ b/Eigen/src/Core/functors/BinaryFunctors.h
@@ -518,22 +518,26 @@ struct scalar_atan2_op {
     return static_cast<Scalar>(atan2(y, x));
   }
   template <typename Packet>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::enable_if_t<is_same<LhsScalar,RhsScalar>::value, Packet> packetOp(const Packet& y,
-                                                        const Packet& x) const {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+      std::enable_if_t<is_same<LhsScalar, RhsScalar>::value, Packet>
+      packetOp(const Packet& y, const Packet& x) const {
     // See https://en.cppreference.com/w/cpp/numeric/math/atan2
     // for how corner cases are supposed to be handled according to the
     // IEEE floating-point standard (IEC 60559).
-    const Packet kSignMask = pset1<Packet>(-Scalar(0.0));
+    const Packet kSignMask = pset1<Packet>(-Scalar(0));
     const Packet kPi = pset1<Packet>(Scalar(EIGEN_PI));
     const Packet kPiO2 = pset1<Packet>(Scalar(EIGEN_PI / 2));
     const Packet kPiO4 = pset1<Packet>(Scalar(EIGEN_PI / 4));
-    constexpr Scalar k3PiO4f = Scalar(3.0 * (EIGEN_PI / 4));
-    const Packet k3PiO4 = pset1<Packet>(k3PiO4f);
-    Packet x_neg = pcmp_lt(x, pzero(x));
-    Packet x_sign = pand(x, kSignMask);
-    Packet y_sign = pand(y, kSignMask);
-    Packet x_zero = pcmp_eq(x, pzero(x));
-    Packet y_zero = pcmp_eq(y, pzero(y));
+    const Packet k3PiO4 = pset1<Packet>(Scalar(3.0 * (EIGEN_PI / 4)));
+
+    // Various predicates about the inputs.
+    Packet x_signbit = pand(x, kSignMask);
+    Packet x_has_signbit = pcmp_lt(por(x_signbit, kPi), pzero(x));
+    Packet x_is_zero = pcmp_eq(x, pzero(x));
+    Packet x_neg = pandnot(x_has_signbit, x_is_zero);
+
+    Packet y_signbit = pand(y, kSignMask);
+    Packet y_is_zero = pcmp_eq(y, pzero(y));
     Packet x_is_not_nan = pcmp_eq(x, x);
     Packet y_is_not_nan = pcmp_eq(y, y);
 
@@ -542,20 +546,22 @@ struct scalar_atan2_op {
     Packet result = patan(pdiv(y, x));
 
     // Compute shift for when x != 0 and y != 0.
-    Packet shift = pselect(x_neg, por(kPi, y_sign), pzero(x));
+    Packet shift = pselect(x_neg, por(kPi, y_signbit), pzero(x));
 
     // Special cases:
     //   Handle  x = +/-inf && y = +/-inf.
     Packet is_not_nan = pcmp_eq(result, result);
-    result = pselect(is_not_nan, padd(shift, result),
-                     pselect(x_neg, por(k3PiO4, y_sign), por(kPiO4, y_sign)));
-    //   Handle x == +/-0.
     result =
-        pselect(x_zero, pselect(y_zero, pzero(y), por(y_sign, kPiO2)), result);
+        pselect(is_not_nan, padd(shift, result),
+                pselect(x_neg, por(k3PiO4, y_signbit), por(kPiO4, y_signbit)));
+    //   Handle x == +/-0.
+    result = pselect(
+        x_is_zero, pselect(y_is_zero, pzero(y), por(y_signbit, kPiO2)), result);
     //   Handle y == +/-0.
-    result = pselect(y_zero,
-                     pselect(x_sign, por(y_sign, kPi), por(y_sign, pzero(y))),
-                     result);
+    result = pselect(
+        y_is_zero,
+        pselect(x_has_signbit, por(y_signbit, kPi), por(y_signbit, pzero(y))),
+        result);
     // Handle NaN inputs.
     Packet kQNaN = pset1<Packet>(NumTraits<Scalar>::quiet_NaN());
     return pselect(pand(x_is_not_nan, y_is_not_nan), result, kQNaN);