Add reciprocal packet op and fast specializations for float with SSE, AVX, and AVX512.

Eigen/src/Core/arch/SSE/MathFunctions.h

@@ -148,21 +148,13 @@ Packet4f prsqrt<Packet4f>(const Packet4f& _x) {
   return pselect<Packet4f>(not_normal_finite_mask, y_approx, y_newton);
 }
 
-#else
-
-template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
-Packet4f prsqrt<Packet4f>(const Packet4f& x) {
-  // Unfortunately we can't use the much faster mm_rsqrt_ps since it only provides an approximation.
-  return _mm_div_ps(pset1<Packet4f>(1.0f), _mm_sqrt_ps(x));
-}
-
 #endif
 
-template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
-Packet2d prsqrt<Packet2d>(const Packet2d& x) {
-  return _mm_div_pd(pset1<Packet2d>(1.0), _mm_sqrt_pd(x));
+template<> EIGEN_STRONG_INLINE Packet4f preciprocal<Packet4f>(const Packet4f& a) {
+  return generic_reciprocal_newton_step<Packet4f, /*Steps=*/1>::run(a, _mm_rcp_ps(a));
 }
 
+
 // Hyperbolic Tangent function.
 template <>
 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f

Eigen/src/Core/arch/SSE/PacketMath.h

@@ -136,6 +136,7 @@ struct packet_traits<float> : default_packet_traits {
 
     HasCmp  = 1,
     HasDiv = 1,
+    HasReciprocal = EIGEN_FAST_MATH,
     HasSin = EIGEN_FAST_MATH,
     HasCos = EIGEN_FAST_MATH,
     HasLog = 1,