Special function implementations for half/bfloat16 packets.

Current implementations fail to consider half-float packets, only
half-float scalars.  Added specializations for packets on AVX, AVX512 and
NEON.  Added tests to `special_packetmath`.

The current `special_functions` tests would fail for half and bfloat16 due to
lack of precision. The NEON tests also fail with precision issues and
due to different handling of `sqrt(inf)`, so special functions bessel, ndtri
have been disabled.

Tested with AVX, AVX512.

4 files changed, 20 insertions, 7 deletions

diff --git a/Eigen/src/Core/arch/AVX/PacketMath.h b/Eigen/src/Core/arch/AVX/PacketMath.h
index 50db0e5c0..f5c18f63f 100644
--- a/Eigen/src/Core/arch/AVX/PacketMath.h
+++ b/Eigen/src/Core/arch/AVX/PacketMath.h
@@ -147,7 +147,9 @@ struct packet_traits<Eigen::half> : default_packet_traits {
     HasRound  = 1,
     HasFloor  = 1,
     HasCeil   = 1,
-    HasRint   = 1
+    HasRint   = 1,
+    HasBessel = 1,
+    HasNdtri  = 1,
   };
 };
 
@@ -189,7 +191,9 @@ struct packet_traits<bfloat16> : default_packet_traits {
     HasRound = 1,
     HasFloor = 1,
     HasCeil = 1,
-    HasRint = 1
+    HasRint = 1,
+    HasBessel = 1,
+    HasNdtri  = 1,
   };
 };
 #endif
diff --git a/Eigen/src/Core/arch/AVX512/PacketMath.h b/Eigen/src/Core/arch/AVX512/PacketMath.h
index 2bbcd802c..a001fb186 100644
--- a/Eigen/src/Core/arch/AVX512/PacketMath.h
+++ b/Eigen/src/Core/arch/AVX512/PacketMath.h
@@ -86,7 +86,9 @@ struct packet_traits<half> : default_packet_traits {
     HasRound  = 1,
     HasFloor  = 1,
     HasCeil   = 1,
-    HasRint   = 1
+    HasRint   = 1,
+    HasBessel = 1,
+    HasNdtri  = 1,
   };
 };
 
diff --git a/Eigen/src/Core/arch/Default/Half.h b/Eigen/src/Core/arch/Default/Half.h
index b9a8a46aa..76156c416 100644
--- a/Eigen/src/Core/arch/Default/Half.h
+++ b/Eigen/src/Core/arch/Default/Half.h
@@ -58,7 +58,7 @@
 
 #define F16_PACKET_FUNCTION(PACKET_F, PACKET_F16, METHOD)           \
   template <>                                                       \
-  EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED  \
+  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_UNUSED                \
   PACKET_F16 METHOD<PACKET_F16>(const PACKET_F16& _x) {             \
     return float2half(METHOD<PACKET_F>(half2float(_x)));            \
   }
diff --git a/Eigen/src/Core/arch/NEON/PacketMath.h b/Eigen/src/Core/arch/NEON/PacketMath.h
index fd6b4f137..b60f4143f 100644
--- a/Eigen/src/Core/arch/NEON/PacketMath.h
+++ b/Eigen/src/Core/arch/NEON/PacketMath.h
@@ -192,7 +192,9 @@ struct packet_traits<float> : default_packet_traits
     HasExp  = 1,
     HasSqrt = 1,
     HasTanh = EIGEN_FAST_MATH,
-    HasErf  = EIGEN_FAST_MATH
+    HasErf  = EIGEN_FAST_MATH,
+    HasBessel = 0,  // Issues with accuracy.
+    HasNdtri = 0
   };
 };
 
@@ -3321,7 +3323,9 @@ template<> struct packet_traits<bfloat16> : default_packet_traits
     HasExp  = 1,
     HasSqrt = 0,
     HasTanh = EIGEN_FAST_MATH,
-    HasErf  = EIGEN_FAST_MATH
+    HasErf  = EIGEN_FAST_MATH,
+    HasBessel = 0,  // Issues with accuracy.
+    HasNdtri = 0,
   };
 };
 
@@ -3887,7 +3891,10 @@ struct packet_traits<Eigen::half> : default_packet_traits {
     HasCos = 0,
     HasLog = 0,
     HasExp = 0,
-    HasSqrt = 1
+    HasSqrt = 1,
+    HasErf = EIGEN_FAST_MATH,
+    HasBessel = 0,  // Issues with accuracy.
+    HasNdtri = 0,
   };
 };