Partially Vectorize Cast

Eigen/Core

@@ -186,7 +186,6 @@ using std::ptrdiff_t;
 // Generic half float support
 #include "src/Core/arch/Default/Half.h"
 #include "src/Core/arch/Default/BFloat16.h"
-#include "src/Core/arch/Default/TypeCasting.h"
 #include "src/Core/arch/Default/GenericPacketMathFunctionsFwd.h"
 
 #if defined EIGEN_VECTORIZE_AVX512

Eigen/src/Core/CoreEvaluators.h

@@ -621,6 +621,207 @@ protected:
   Data m_d;
 };
 
+// ----------------------- Casting ---------------------
+
+template <typename SrcType, typename DstType, typename ArgType>
+struct unary_evaluator<CwiseUnaryOp<core_cast_op<SrcType, DstType>, ArgType>, IndexBased> {
+  using CastOp = core_cast_op<SrcType, DstType>;
+  using XprType = CwiseUnaryOp<CastOp, ArgType>;
+
+  // Use the largest packet type by default
+  using SrcPacketType = typename packet_traits<SrcType>::type;
+  static constexpr int SrcPacketSize = unpacket_traits<SrcPacketType>::size;
+  static constexpr int SrcPacketBytes = SrcPacketSize * sizeof(SrcType);
+
+  enum {
+    CoeffReadCost = int(evaluator<ArgType>::CoeffReadCost) + int(functor_traits<CastOp>::Cost),
+    PacketAccess = functor_traits<CastOp>::PacketAccess,
+    ActualPacketAccessBit = PacketAccess ? PacketAccessBit : 0,
+    Flags = evaluator<ArgType>::Flags & (HereditaryBits | LinearAccessBit | ActualPacketAccessBit),
+    IsRowMajor = (evaluator<ArgType>::Flags & RowMajorBit),
+    Alignment = evaluator<ArgType>::Alignment
+  };
+
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit unary_evaluator(const XprType& xpr)
+      : m_argImpl(xpr.nestedExpression()), m_rows(xpr.rows()), m_cols(xpr.cols()) {
+    EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<CastOp>::Cost);
+    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+  }
+
+  template <typename DstPacketType>
+  using AltSrcScalarOp = std::enable_if_t<(unpacket_traits<DstPacketType>::size < SrcPacketSize && !find_packet_by_size<SrcType, unpacket_traits<DstPacketType>::size>::value), bool>;
+  template <typename DstPacketType>
+  using SrcPacketArgs1 = std::enable_if_t<(find_packet_by_size<SrcType, unpacket_traits<DstPacketType>::size>::value), bool>;
+  template <typename DstPacketType>
+  using SrcPacketArgs2 = std::enable_if_t<(unpacket_traits<DstPacketType>::size) == (2 * SrcPacketSize), bool>;
+  template <typename DstPacketType>
+  using SrcPacketArgs4 = std::enable_if_t<(unpacket_traits<DstPacketType>::size) == (4 * SrcPacketSize), bool>;
+  template <typename DstPacketType>
+  using SrcPacketArgs8 = std::enable_if_t<(unpacket_traits<DstPacketType>::size) == (8 * SrcPacketSize), bool>;
+
+  template <bool UseRowMajor = IsRowMajor, std::enable_if_t<UseRowMajor, bool> = true>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool check_array_bounds(Index, Index col, Index packetSize) const {
+    return col + packetSize <= cols();
+  }
+  template <bool UseRowMajor = IsRowMajor, std::enable_if_t<!UseRowMajor, bool> = true>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool check_array_bounds(Index row, Index, Index packetSize) const {
+    return row + packetSize <= rows();
+  }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool check_array_bounds(Index index, Index packetSize) const {
+    return index + packetSize <= size();
+  }
+
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE SrcType srcCoeff(Index row, Index col, Index offset) const {
+    Index actualRow = IsRowMajor ? row : row + offset;
+    Index actualCol = IsRowMajor ? col + offset : col;
+    return m_argImpl.coeff(actualRow, actualCol);
+  }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE SrcType srcCoeff(Index index, Index offset) const {
+    Index actualIndex = index + offset;
+    return m_argImpl.coeff(actualIndex);
+  }
+
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DstType coeff(Index row, Index col) const {
+    return cast<SrcType, DstType>(srcCoeff(row, col, 0));
+  }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DstType coeff(Index index) const { return cast<SrcType, DstType>(srcCoeff(index, 0)); }
+
+  template <int LoadMode, typename PacketType = SrcPacketType>
+  EIGEN_STRONG_INLINE PacketType srcPacket(Index row, Index col, Index offset) const {
+    constexpr int PacketSize = unpacket_traits<PacketType>::size;
+    Index actualRow = IsRowMajor ? row : row + (offset * PacketSize);
+    Index actualCol = IsRowMajor ? col + (offset * PacketSize) : col;
+    eigen_assert(check_array_bounds(actualRow, actualCol, PacketSize) && "Array index out of bounds");
+    return m_argImpl.template packet<LoadMode, PacketType>(actualRow, actualCol);
+  }
+  template <int LoadMode, typename PacketType = SrcPacketType>
+  EIGEN_STRONG_INLINE PacketType srcPacket(Index index, Index offset) const {
+    constexpr int PacketSize = unpacket_traits<PacketType>::size;
+    Index actualIndex = index + (offset * PacketSize);
+    eigen_assert(check_array_bounds(actualIndex, PacketSize) && "Array index out of bounds");
+    return m_argImpl.template packet<LoadMode, PacketType>(actualIndex);
+  }
+
+  // There is no source packet type with equal or fewer elements than DstPacketType.
+  // This is problematic as the evaluation loop may attempt to access data outside the bounds of the array.
+  // For example, consider the cast utilizing pcast<Packet4f,Packet2d> with an array of size 4: {0.0f,1.0f,2.0f,3.0f}. 
+  // The first iteration of the evaulation loop will load 16 bytes: {0.0f,1.0f,2.0f,3.0f} and cast to {0.0,1.0}, which is acceptable.
+  // The second iteration will load 16 bytes: {2.0f,3.0f,?,?}, which is outside the bounds of the array.
+
+  // Instead, perform runtime check to determine if the load would access data outside the bounds of the array.
+  // If not, perform full load. Otherwise, revert to a scalar loop to perform a partial load.
+  // In either case, perform a vectorized cast of the source packet.
+  template <int LoadMode, typename DstPacketType, AltSrcScalarOp<DstPacketType> = true>
+  EIGEN_STRONG_INLINE DstPacketType packet(Index row, Index col) const {
+    constexpr int DstPacketSize = unpacket_traits<DstPacketType>::size;
+    constexpr int SrcBytesIncrement = DstPacketSize * sizeof(SrcType);
+    constexpr int SrcLoadMode = plain_enum_min(SrcBytesIncrement, LoadMode);
+    SrcPacketType src;
+    if (EIGEN_PREDICT_TRUE(check_array_bounds(row, col, SrcPacketSize))) {
+      src = srcPacket<SrcLoadMode>(row, col, 0);
+    } else {
+      Array<SrcType, SrcPacketSize, 1> srcArray;
+      for (size_t k = 0; k < DstPacketSize; k++) srcArray[k] = srcCoeff(row, col, k);
+      for (size_t k = DstPacketSize; k < SrcPacketSize; k++) srcArray[k] = SrcType(0);
+      src = pload<SrcPacketType>(srcArray.data());
+    }
+    return pcast<SrcPacketType, DstPacketType>(src);
+  }
+  // Use the source packet type with the same size as DstPacketType, if it exists
+  template <int LoadMode, typename DstPacketType, SrcPacketArgs1<DstPacketType> = true>
+  EIGEN_STRONG_INLINE DstPacketType packet(Index row, Index col) const {
+    constexpr int DstPacketSize = unpacket_traits<DstPacketType>::size;
+    using SizedSrcPacketType = typename find_packet_by_size<SrcType, DstPacketSize>::type;
+    constexpr int SrcBytesIncrement = DstPacketSize * sizeof(SrcType);
+    constexpr int SrcLoadMode = plain_enum_min(SrcBytesIncrement, LoadMode);
+    return pcast<SizedSrcPacketType, DstPacketType>(
+        srcPacket<SrcLoadMode, SizedSrcPacketType>(row, col, 0));
+  }
+  // unpacket_traits<DstPacketType>::size == 2 * SrcPacketSize
+  template <int LoadMode, typename DstPacketType, SrcPacketArgs2<DstPacketType> = true>
+  EIGEN_STRONG_INLINE DstPacketType packet(Index row, Index col) const {
+    constexpr int SrcLoadMode = plain_enum_min(SrcPacketBytes, LoadMode);
+    return pcast<SrcPacketType, DstPacketType>(
+        srcPacket<SrcLoadMode>(row, col, 0), srcPacket<SrcLoadMode>(row, col, 1));
+  }
+  // unpacket_traits<DstPacketType>::size == 4 * SrcPacketSize
+  template <int LoadMode, typename DstPacketType, SrcPacketArgs4<DstPacketType> = true>
+  EIGEN_STRONG_INLINE DstPacketType packet(Index row, Index col) const {
+    constexpr int SrcLoadMode = plain_enum_min(SrcPacketBytes, LoadMode);
+    return pcast<SrcPacketType, DstPacketType>(
+        srcPacket<SrcLoadMode>(row, col, 0), srcPacket<SrcLoadMode>(row, col, 1),
+        srcPacket<SrcLoadMode>(row, col, 2), srcPacket<SrcLoadMode>(row, col, 3));
+  }
+  // unpacket_traits<DstPacketType>::size == 8 * SrcPacketSize
+  template <int LoadMode, typename DstPacketType, SrcPacketArgs8<DstPacketType> = true>
+  EIGEN_STRONG_INLINE DstPacketType packet(Index row, Index col) const {
+    constexpr int SrcLoadMode = plain_enum_min(SrcPacketBytes, LoadMode);
+    return pcast<SrcPacketType, DstPacketType>(
+        srcPacket<SrcLoadMode>(row, col, 0), srcPacket<SrcLoadMode>(row, col, 1), 
+        srcPacket<SrcLoadMode>(row, col, 2), srcPacket<SrcLoadMode>(row, col, 3), 
+        srcPacket<SrcLoadMode>(row, col, 4), srcPacket<SrcLoadMode>(row, col, 5),
+        srcPacket<SrcLoadMode>(row, col, 6), srcPacket<SrcLoadMode>(row, col, 7));
+  }
+
+  // Analagous routines for linear access.
+  template <int LoadMode, typename DstPacketType, AltSrcScalarOp<DstPacketType> = true>
+  EIGEN_STRONG_INLINE DstPacketType packet(Index index) const {
+    constexpr int DstPacketSize = unpacket_traits<DstPacketType>::size;
+    constexpr int SrcBytesIncrement = DstPacketSize * sizeof(SrcType);
+    constexpr int SrcLoadMode = plain_enum_min(SrcBytesIncrement, LoadMode);
+    SrcPacketType src;
+    if (EIGEN_PREDICT_TRUE(check_array_bounds(index, SrcPacketSize))) {
+      src = srcPacket<SrcLoadMode>(index, 0);
+    } else {
+      Array<SrcType, SrcPacketSize, 1> srcArray;
+      for (size_t k = 0; k < DstPacketSize; k++) srcArray[k] = srcCoeff(index, k);
+      for (size_t k = DstPacketSize; k < SrcPacketSize; k++) srcArray[k] = SrcType(0);
+      src = pload<SrcPacketType>(srcArray.data());
+    }
+    return pcast<SrcPacketType, DstPacketType>(src);
+  }
+  template <int LoadMode, typename DstPacketType, SrcPacketArgs1<DstPacketType> = true>
+  EIGEN_STRONG_INLINE DstPacketType packet(Index index) const {
+    constexpr int DstPacketSize = unpacket_traits<DstPacketType>::size;
+    using SizedSrcPacketType = typename find_packet_by_size<SrcType, DstPacketSize>::type;
+    constexpr int SrcBytesIncrement = DstPacketSize * sizeof(SrcType);
+    constexpr int SrcLoadMode = plain_enum_min(SrcBytesIncrement, LoadMode);
+    return pcast<SizedSrcPacketType, DstPacketType>(
+        srcPacket<SrcLoadMode, SizedSrcPacketType>(index, 0));
+  }
+  template <int LoadMode, typename DstPacketType, SrcPacketArgs2<DstPacketType> = true>
+  EIGEN_STRONG_INLINE DstPacketType packet(Index index) const {
+    constexpr int SrcLoadMode = plain_enum_min(SrcPacketBytes, LoadMode);
+    return pcast<SrcPacketType, DstPacketType>(
+        srcPacket<SrcLoadMode>(index, 0), srcPacket<SrcLoadMode>(index, 1));
+  }
+  template <int LoadMode, typename DstPacketType, SrcPacketArgs4<DstPacketType> = true>
+  EIGEN_STRONG_INLINE DstPacketType packet(Index index) const {
+    constexpr int SrcLoadMode = plain_enum_min(SrcPacketBytes, LoadMode);
+    return pcast<SrcPacketType, DstPacketType>(
+        srcPacket<SrcLoadMode>(index, 0), srcPacket<SrcLoadMode>(index, 1),
+        srcPacket<SrcLoadMode>(index, 2), srcPacket<SrcLoadMode>(index, 3));
+  }
+  template <int LoadMode, typename DstPacketType, SrcPacketArgs8<DstPacketType> = true>
+  EIGEN_STRONG_INLINE DstPacketType packet(Index index) const {
+    constexpr int SrcLoadMode = plain_enum_min(SrcPacketBytes, LoadMode);
+    return pcast<SrcPacketType, DstPacketType>(
+        srcPacket<SrcLoadMode>(index, 0), srcPacket<SrcLoadMode>(index, 1),
+        srcPacket<SrcLoadMode>(index, 2), srcPacket<SrcLoadMode>(index, 3),
+        srcPacket<SrcLoadMode>(index, 4), srcPacket<SrcLoadMode>(index, 5),
+        srcPacket<SrcLoadMode>(index, 6), srcPacket<SrcLoadMode>(index, 7));
+  }
+
+  constexpr EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index rows() const { return m_rows; }
+  constexpr EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index cols() const { return m_cols; }
+  constexpr EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index size() const { return m_rows * m_cols; }
+
+ protected:
+  const evaluator<ArgType> m_argImpl;
+  const variable_if_dynamic<Index, XprType::RowsAtCompileTime> m_rows;
+  const variable_if_dynamic<Index, XprType::ColsAtCompileTime> m_cols;
+};
+
 // -------------------- CwiseTernaryOp --------------------
 
 // this is a ternary expression

Eigen/src/Core/GenericPacketMath.h

@@ -146,14 +146,67 @@ template<typename T> struct unpacket_traits
 
 template<typename T> struct unpacket_traits<const T> : unpacket_traits<T> { };
 
-template <typename Src, typename Tgt> struct type_casting_traits {
+/** \internal A convenience utility for determining if the type is a scalar.
+ * This is used to enable some generic packet implementations.
+ */
+template <typename Packet>
+struct is_scalar {
+  using Scalar = typename unpacket_traits<Packet>::type;
+  enum { value = internal::is_same<Packet, Scalar>::value };
+};
+
+// automatically and succinctly define combinations of pcast<SrcPacket,TgtPacket> when 
+// 1) the packets are the same type, or
+// 2) the packets differ only in sign. 
+// In both of these cases, preinterpret (bit_cast) is equivalent to pcast (static_cast)
+template <typename SrcPacket, typename TgtPacket,
+          bool Scalar = is_scalar<SrcPacket>::value && is_scalar<TgtPacket>::value>
+struct is_degenerate_helper : is_same<SrcPacket, TgtPacket> {};
+template <>
+struct is_degenerate_helper<int8_t, uint8_t, true> : std::true_type {};
+template <>
+struct is_degenerate_helper<int16_t, uint16_t, true> : std::true_type {};
+template <>
+struct is_degenerate_helper<int32_t, uint32_t, true> : std::true_type {};
+template <>
+struct is_degenerate_helper<int64_t, uint64_t, true> : std::true_type {};
+
+template <typename SrcPacket, typename TgtPacket>
+struct is_degenerate_helper<SrcPacket, TgtPacket, false> {
+  using SrcScalar = typename unpacket_traits<SrcPacket>::type;
+  static constexpr int SrcSize = unpacket_traits<SrcPacket>::size;
+  using TgtScalar = typename unpacket_traits<TgtPacket>::type;
+  static constexpr int TgtSize = unpacket_traits<TgtPacket>::size;
+  static constexpr bool value = is_degenerate_helper<SrcScalar, TgtScalar, true>::value && (SrcSize == TgtSize);
+};
+
+// is_degenerate<T1,T2>::value == is_degenerate<T2,T1>::value
+template <typename SrcPacket, typename TgtPacket>
+struct is_degenerate {
+  static constexpr bool value =
+      is_degenerate_helper<SrcPacket, TgtPacket>::value || is_degenerate_helper<TgtPacket, SrcPacket>::value;
+};
+
+template <typename Packet>
+struct is_half {
+  using Scalar = typename unpacket_traits<Packet>::type;
+  static constexpr int Size = unpacket_traits<Packet>::size;
+  using DefaultPacket = typename packet_traits<Scalar>::type;
+  static constexpr int DefaultSize = unpacket_traits<DefaultPacket>::size;
+  static constexpr bool value = Size < DefaultSize;
+};
+
+template <typename Src, typename Tgt>
+struct type_casting_traits {
   enum {
-    VectorizedCast = 0,
+    VectorizedCast =
+        is_degenerate<Src, Tgt>::value && packet_traits<Src>::Vectorizable && packet_traits<Tgt>::Vectorizable,
     SrcCoeffRatio = 1,
     TgtCoeffRatio = 1
   };
 };
 
+
 /** \internal Wrapper to ensure that multiple packet types can map to the same
     same underlying vector type. */
 template<typename T, int unique_id = 0>
@@ -171,45 +224,84 @@ struct eigen_packet_wrapper
   T m_val;
 };
 
+template <typename Target, typename Packet, bool IsSame = is_same<Target, Packet>::value>
+struct preinterpret_generic;
 
-/** \internal A convenience utility for determining if the type is a scalar.
+template <typename Target, typename Packet>
- * This is used to enable some generic packet implementations.
+struct preinterpret_generic<Target, Packet, false> {
- */
+  // the packets are not the same, attempt scalar bit_cast
-template<typename Packet>
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Target run(const Packet& a) {
-struct is_scalar {
+    return numext::bit_cast<Target, Packet>(a);
-  using Scalar = typename unpacket_traits<Packet>::type;
+  }
-  enum {
-    value = internal::is_same<Packet, Scalar>::value
-  };
 };
 
-/** \internal \returns static_cast<TgtType>(a) (coeff-wise) */
+template <typename Packet>
-template <typename SrcPacket, typename TgtPacket>
+struct preinterpret_generic<Packet, Packet, true> {
-EIGEN_DEVICE_FUNC inline TgtPacket
+  // the packets are the same type: do nothing
-pcast(const SrcPacket& a) {
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet run(const Packet& a) { return a; }
-  return static_cast<TgtPacket>(a);
+};
-}
-template <typename SrcPacket, typename TgtPacket>
-EIGEN_DEVICE_FUNC inline TgtPacket
-pcast(const SrcPacket& a, const SrcPacket& /*b*/) {
-  return static_cast<TgtPacket>(a);
-}
-template <typename SrcPacket, typename TgtPacket>
-EIGEN_DEVICE_FUNC inline TgtPacket
-pcast(const SrcPacket& a, const SrcPacket& /*b*/, const SrcPacket& /*c*/, const SrcPacket& /*d*/) {
-  return static_cast<TgtPacket>(a);
-}
-template <typename SrcPacket, typename TgtPacket>
-EIGEN_DEVICE_FUNC inline TgtPacket
-pcast(const SrcPacket& a, const SrcPacket& /*b*/, const SrcPacket& /*c*/, const SrcPacket& /*d*/,
-      const SrcPacket& /*e*/, const SrcPacket& /*f*/, const SrcPacket& /*g*/, const SrcPacket& /*h*/) {
-  return static_cast<TgtPacket>(a);
-}
 
 /** \internal \returns reinterpret_cast<Target>(a) */
 template <typename Target, typename Packet>
-EIGEN_DEVICE_FUNC inline Target
+EIGEN_DEVICE_FUNC inline Target preinterpret(const Packet& a) {
-preinterpret(const Packet& a); /* { return reinterpret_cast<const Target&>(a); } */
+  return preinterpret_generic<Target, Packet>::run(a);
+}
+
+template <typename SrcPacket, typename TgtPacket, bool Degenerate = is_degenerate<SrcPacket, TgtPacket>::value, bool TgtIsHalf = is_half<TgtPacket>::value>
+struct pcast_generic;
+
+template <typename SrcPacket, typename TgtPacket>
+struct pcast_generic<SrcPacket, TgtPacket, false, false> {
+  // the packets are not degenerate: attempt scalar static_cast
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TgtPacket run(const SrcPacket& a) {
+    return cast_impl<SrcPacket, TgtPacket>::run(a);
+  }
+};
+
+template <typename Packet>
+struct pcast_generic<Packet, Packet, true, false> {
+  // the packets are the same: do nothing
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet run(const Packet& a) { return a; }
+};
+
+template <typename SrcPacket, typename TgtPacket, bool TgtIsHalf>
+struct pcast_generic<SrcPacket, TgtPacket, true, TgtIsHalf> {
+  // the packets are degenerate: preinterpret is equivalent to pcast
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TgtPacket run(const SrcPacket& a) { return preinterpret<TgtPacket>(a); }
+};
+
+
+
+/** \internal \returns static_cast<TgtType>(a) (coeff-wise) */
+template <typename SrcPacket, typename TgtPacket>
+EIGEN_DEVICE_FUNC inline TgtPacket pcast(const SrcPacket& a) {
+  return pcast_generic<SrcPacket, TgtPacket>::run(a);
+}
+template <typename SrcPacket, typename TgtPacket>
+EIGEN_DEVICE_FUNC inline TgtPacket pcast(const SrcPacket& a, const SrcPacket& b) {
+  return pcast_generic<SrcPacket, TgtPacket>::run(a, b);
+}
+template <typename SrcPacket, typename TgtPacket>
+EIGEN_DEVICE_FUNC inline TgtPacket pcast(const SrcPacket& a, const SrcPacket& b, const SrcPacket& c,
+                                         const SrcPacket& d) {
+  return pcast_generic<SrcPacket, TgtPacket>::run(a, b, c, d);
+}
+template <typename SrcPacket, typename TgtPacket>
+EIGEN_DEVICE_FUNC inline TgtPacket pcast(const SrcPacket& a, const SrcPacket& b, const SrcPacket& c, const SrcPacket& d,
+                                         const SrcPacket& e, const SrcPacket& f, const SrcPacket& g,
+                                         const SrcPacket& h) {
+  return pcast_generic<SrcPacket, TgtPacket>::run(a, b, c, d, e, f, g, h);
+}
+
+template <typename SrcPacket, typename TgtPacket>
+struct pcast_generic<SrcPacket, TgtPacket, false, true> {
+  // TgtPacket is a half packet of some other type
+  // perform cast and truncate result
+  using DefaultTgtPacket = typename is_half<TgtPacket>::DefaultPacket;
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TgtPacket run(const SrcPacket& a) {
+    return preinterpret<TgtPacket>(pcast<SrcPacket, DefaultTgtPacket>(a));
+  }
+};
 
 /** \internal \returns a + b (coeff-wise) */
 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet

Eigen/src/Core/MathFunctions.h

@@ -430,6 +430,13 @@ struct cast_impl
   }
 };
 
+template <typename OldType>
+struct cast_impl<OldType, bool> {
+  EIGEN_DEVICE_FUNC
+  static inline bool run(const OldType& x) { return x != OldType(0); }
+};
+
+
 // Casting from S -> Complex<T> leads to an implicit conversion from S to T,
 // generating warnings on clang.  Here we explicitly cast the real component.
 template<typename OldType, typename NewType>

Eigen/src/Core/arch/AVX/TypeCasting.h

@@ -80,6 +80,14 @@ template<> EIGEN_STRONG_INLINE Packet8i pcast<Packet4d, Packet8i>(const Packet4d
   return _mm256_set_m128i(_mm256_cvttpd_epi32(b), _mm256_cvttpd_epi32(a));
 }
 
+template <> EIGEN_STRONG_INLINE Packet4f pcast<Packet4d, Packet4f>(const Packet4d& a) {
+  return _mm256_cvtpd_ps(a);
+}
+
+template <> EIGEN_STRONG_INLINE Packet4i pcast<Packet4d, Packet4i>(const Packet4d& a) {
+  return _mm256_cvttpd_epi32(a);
+}
+
 template <>
 EIGEN_STRONG_INLINE Packet16b pcast<Packet8f, Packet16b>(const Packet8f& a,
                                                          const Packet8f& b) {
@@ -118,6 +126,44 @@ template<> EIGEN_STRONG_INLINE Packet8f preinterpret<Packet8f,Packet8i>(const Pa
   return _mm256_castsi256_ps(a);
 }
 
+template<> EIGEN_STRONG_INLINE Packet8ui preinterpret<Packet8ui, Packet8i>(const Packet8i& a) {
+  return Packet8ui(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8i preinterpret<Packet8i, Packet8ui>(const Packet8ui& a) {
+  return Packet8i(a);
+}
+
+// truncation operations
+
+template<> EIGEN_STRONG_INLINE Packet4f preinterpret<Packet4f, Packet8f>(const Packet8f& a) {
+  return _mm256_castps256_ps128(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d preinterpret<Packet2d, Packet4d>(const Packet4d& a) {
+  return _mm256_castpd256_pd128(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i preinterpret<Packet4i, Packet8i>(const Packet8i& a) {
+  return _mm256_castsi256_si128(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4ui preinterpret<Packet4ui, Packet8ui>(const Packet8ui& a) {
+  return _mm256_castsi256_si128(a);
+}
+
+
+#ifdef EIGEN_VECTORIZE_AVX2
+template<> EIGEN_STRONG_INLINE Packet4ul preinterpret<Packet4ul, Packet4l>(const Packet4l& a) {
+  return Packet4ul(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4l preinterpret<Packet4l, Packet4ul>(const Packet4ul& a) {
+  return Packet4l(a);
+}
+
+#endif
+
 template<> EIGEN_STRONG_INLINE Packet8f pcast<Packet8h, Packet8f>(const Packet8h& a) {
   return half2float(a);
 }

Eigen/src/Core/arch/AVX512/TypeCasting.h

@@ -59,6 +59,13 @@ template<> EIGEN_STRONG_INLINE Packet16i pcast<Packet8d, Packet16i>(const Packet
   return  cat256i(_mm512_cvttpd_epi32(a), _mm512_cvttpd_epi32(b));
 }
 
+template<> EIGEN_STRONG_INLINE Packet8i pcast<Packet8d, Packet8i>(const Packet8d& a) {
+  return _mm512_cvtpd_epi32(a);
+}
+template<> EIGEN_STRONG_INLINE Packet8f pcast<Packet8d, Packet8f>(const Packet8d& a) {
+  return _mm512_cvtpd_ps(a);
+}
+
 template<> EIGEN_STRONG_INLINE Packet16i preinterpret<Packet16i, Packet16f>(const Packet16f& a) {
   return _mm512_castps_si512(a);
 }
@@ -107,12 +114,19 @@ template<> EIGEN_STRONG_INLINE Packet8d preinterpret<Packet8d, Packet2d>(const P
   return _mm512_castpd128_pd512(a);
 }
 
-template<> EIGEN_STRONG_INLINE Packet16f preinterpret<Packet16f, Packet16f>(const Packet16f& a) {
+template<> EIGEN_STRONG_INLINE Packet8i preinterpret<Packet8i, Packet16i>(const Packet16i& a) {
-  return a;
+  return _mm512_castsi512_si256(a);
+}
+template<> EIGEN_STRONG_INLINE Packet4i preinterpret<Packet4i, Packet16i>(const Packet16i& a) {
+  return _mm512_castsi512_si128(a);
 }
 
-template<> EIGEN_STRONG_INLINE Packet8d preinterpret<Packet8d, Packet8d>(const Packet8d& a) {
+template<> EIGEN_STRONG_INLINE Packet8h preinterpret<Packet8h, Packet16h>(const Packet16h& a) {
-  return a;
+  return _mm256_castsi256_si128(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf preinterpret<Packet8bf, Packet16bf>(const Packet16bf& a) {
+  return _mm256_castsi256_si128(a);
 }
 
 #ifndef EIGEN_VECTORIZE_AVX512FP16
@@ -191,6 +205,13 @@ struct type_casting_traits<float, half> {
   };
 };
 
+template<> EIGEN_STRONG_INLINE Packet16h preinterpret<Packet16h, Packet32h>(const Packet32h& a) {
+  return _mm256_castpd_si256(_mm512_extractf64x4_pd(_mm512_castph_pd(a), 0));
+}
+template<> EIGEN_STRONG_INLINE Packet8h preinterpret<Packet8h, Packet32h>(const Packet32h& a) {
+  return _mm256_castsi256_si128(preinterpret<Packet16h>(a));
+}
+
 template <>
 EIGEN_STRONG_INLINE Packet16f pcast<Packet32h, Packet16f>(const Packet32h& a) {
   // Discard second-half of input.

Eigen/src/Core/arch/Default/Half.h

@@ -1014,4 +1014,49 @@ struct hash<Eigen::half> {
 } // end namespace std
 #endif
 
+namespace Eigen {
+namespace internal {
+
+template <>
+struct cast_impl<float, half> {
+  EIGEN_DEVICE_FUNC
+  static inline half run(const float& a) {
+#if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 300) || \
+    (defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
+    return __float2half(a);
+#else
+    return half(a);
+#endif
+  }
+};
+
+template <>
+struct cast_impl<int, half> {
+  EIGEN_DEVICE_FUNC
+  static inline half run(const int& a) {
+#if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 300) || \
+    (defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
+    return __float2half(static_cast<float>(a));
+#else
+    return half(static_cast<float>(a));
+#endif
+  }
+};
+
+template <>
+struct cast_impl<half, float> {
+  EIGEN_DEVICE_FUNC
+  static inline float run(const half& a) {
+#if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 300) || \
+    (defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
+    return __half2float(a);
+#else
+    return static_cast<float>(a);
+#endif
+  }
+};
+
+}  // namespace internal
+}  // namespace Eigen
+
 #endif // EIGEN_HALF_H

Eigen/src/Core/arch/Default/TypeCasting.h

@@ -1,116 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
-// Copyright (C) 2019 Rasmus Munk Larsen <rmlarsen@google.com>
-//
-// This Source Code Form is subject to the terms of the Mozilla
-// Public License v. 2.0. If a copy of the MPL was not distributed
-// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
-
-#ifndef EIGEN_GENERIC_TYPE_CASTING_H
-#define EIGEN_GENERIC_TYPE_CASTING_H
-
-#include "../../InternalHeaderCheck.h"
-
-namespace Eigen {
-
-namespace internal {
-
-template<>
-struct scalar_cast_op<float, Eigen::half> {
-  typedef Eigen::half result_type;
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half operator() (const float& a) const {
-    #if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 300) || \
-      (defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
-      return __float2half(a);
-    #else
-      return Eigen::half(a);
-    #endif
-  }
-};
-
-template<>
-struct functor_traits<scalar_cast_op<float, Eigen::half> >
-{ enum { Cost = NumTraits<float>::AddCost, PacketAccess = false }; };
-
-
-template<>
-struct scalar_cast_op<int, Eigen::half> {
-  typedef Eigen::half result_type;
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half operator() (const int& a) const {
-    #if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 300) || \
-      (defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
-      return __float2half(static_cast<float>(a));
-    #else
-      return Eigen::half(static_cast<float>(a));
-    #endif
-  }
-};
-
-template<>
-struct functor_traits<scalar_cast_op<int, Eigen::half> >
-{ enum { Cost = NumTraits<float>::AddCost, PacketAccess = false }; };
-
-
-template<>
-struct scalar_cast_op<Eigen::half, float> {
-  typedef float result_type;
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float operator() (const Eigen::half& a) const {
-    #if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 300) || \
-      (defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
-      return __half2float(a);
-    #else
-      return static_cast<float>(a);
-    #endif
-  }
-};
-
-template<>
-struct functor_traits<scalar_cast_op<Eigen::half, float> >
-{ enum { Cost = NumTraits<float>::AddCost, PacketAccess = false }; };
-
-
-template<>
-struct scalar_cast_op<float, Eigen::bfloat16> {
-  typedef Eigen::bfloat16 result_type;
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::bfloat16 operator() (const float& a) const {
-    return Eigen::bfloat16(a);
-  }
-};
-
-template<>
-struct functor_traits<scalar_cast_op<float, Eigen::bfloat16> >
-{ enum { Cost = NumTraits<float>::AddCost, PacketAccess = false }; };
-
-
-template<>
-struct scalar_cast_op<int, Eigen::bfloat16> {
-  typedef Eigen::bfloat16 result_type;
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::bfloat16 operator() (const int& a) const {
-    return Eigen::bfloat16(static_cast<float>(a));
-  }
-};
-
-template<>
-struct functor_traits<scalar_cast_op<int, Eigen::bfloat16> >
-{ enum { Cost = NumTraits<float>::AddCost, PacketAccess = false }; };
-
-
-template<>
-struct scalar_cast_op<Eigen::bfloat16, float> {
-  typedef float result_type;
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float operator() (const Eigen::bfloat16& a) const {
-    return static_cast<float>(a);
-  }
-};
-
-template<>
-struct functor_traits<scalar_cast_op<Eigen::bfloat16, float> >
-{ enum { Cost = NumTraits<float>::AddCost, PacketAccess = false }; };
-
-
-}
-}
-
-#endif  // EIGEN_GENERIC_TYPE_CASTING_H

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

@@ -135,6 +135,13 @@ template<> EIGEN_STRONG_INLINE Packet4i preinterpret<Packet4i,Packet2d>(const Pa
   return _mm_castpd_si128(a);
 }
 
+template<> EIGEN_STRONG_INLINE Packet4ui preinterpret<Packet4ui, Packet4i>(const Packet4i& a) {
+  return Packet4ui(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i preinterpret<Packet4i, Packet4ui>(const Packet4ui& a) {
+  return Packet4i(a);
+}
 // Disable the following code since it's broken on too many platforms / compilers.
 //#elif defined(EIGEN_VECTORIZE_SSE) && (!EIGEN_ARCH_x86_64) && (!EIGEN_COMP_MSVC)
 #if 0

Eigen/src/Core/functors/UnaryFunctors.h

@@ -179,16 +179,28 @@ struct scalar_cast_op {
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const NewType operator() (const Scalar& a) const { return cast<Scalar, NewType>(a); }
 };
 
-template <typename Scalar>
-struct scalar_cast_op<Scalar, bool> {
-  typedef bool result_type;
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const Scalar& a) const { return a != Scalar(0); }
-};
-
 template<typename Scalar, typename NewType>
 struct functor_traits<scalar_cast_op<Scalar,NewType> >
 { enum { Cost = is_same<Scalar, NewType>::value ? 0 : NumTraits<NewType>::AddCost, PacketAccess = false }; };
 
+/** \internal
+ * `core_cast_op` serves to distinguish the vectorized implementation from that of the legacy `scalar_cast_op` for backwards
+ * compatibility. The manner in which packet ops are handled is defined by the specialized unary_evaluator:
+ * `unary_evaluator<CwiseUnaryOp<core_cast_op<SrcType, DstType>, ArgType>, IndexBased>` in CoreEvaluators.h
+ * Otherwise, the non-vectorized behavior is identical to that of `scalar_cast_op`
+ */
+template <typename SrcType, typename DstType>
+struct core_cast_op : scalar_cast_op<SrcType, DstType> {};
+
+template <typename SrcType, typename DstType>
+struct functor_traits<core_cast_op<SrcType, DstType>> {
+  using CastingTraits = type_casting_traits<SrcType, DstType>;
+  enum {
+    Cost = is_same<SrcType, DstType>::value ? 0 : NumTraits<DstType>::AddCost,
+    PacketAccess = CastingTraits::VectorizedCast && (CastingTraits::SrcCoeffRatio <= 8)
+  };
+};
+
 /** \internal
   * \brief Template functor to arithmetically shift a scalar right by a number of bits
   *

Eigen/src/Core/util/XprHelper.h

@@ -190,6 +190,30 @@ struct find_best_packet
   typedef typename find_best_packet_helper<Size,typename packet_traits<T>::type>::type type;
 };
 
+template <int Size, typename PacketType,
+          bool Stop = (Size == unpacket_traits<PacketType>::size) ||
+                      is_same<PacketType, typename unpacket_traits<PacketType>::half>::value>
+struct find_packet_by_size_helper;
+template <int Size, typename PacketType>
+struct find_packet_by_size_helper<Size, PacketType, true> {
+  using type = PacketType;
+};
+template <int Size, typename PacketType>
+struct find_packet_by_size_helper<Size, PacketType, false> {
+  using type = typename find_packet_by_size_helper<Size, typename unpacket_traits<PacketType>::half>::type;
+};
+
+template <typename T, int Size>
+struct find_packet_by_size {
+  using type = typename find_packet_by_size_helper<Size, typename packet_traits<T>::type>::type;
+  static constexpr bool value = (Size == unpacket_traits<type>::size);
+};
+template <typename T>
+struct find_packet_by_size<T, 1> {
+  using type = typename unpacket_traits<T>::type;
+  static constexpr bool value = (unpacket_traits<type>::size == 1);
+};
+
 #if EIGEN_MAX_STATIC_ALIGN_BYTES>0
 constexpr inline int compute_default_alignment_helper(int ArrayBytes, int AlignmentBytes) {
   if((ArrayBytes % AlignmentBytes) == 0) {

Eigen/src/plugins/CommonCwiseUnaryOps.h

@@ -45,7 +45,7 @@ inline const NegativeReturnType
 operator-() const { return NegativeReturnType(derived()); }
 
 
-template<class NewType> struct CastXpr { typedef typename internal::cast_return_type<Derived,const CwiseUnaryOp<internal::scalar_cast_op<Scalar, NewType>, const Derived> >::type Type; };
+template<class NewType> struct CastXpr { typedef typename internal::cast_return_type<Derived,const CwiseUnaryOp<internal::core_cast_op<Scalar, NewType>, const Derived> >::type Type; };
 
 /// \returns an expression of \c *this with the \a Scalar type casted to
 /// \a NewScalar.

test/array_cwise.cpp

@@ -9,6 +9,7 @@
 
 #include <vector>
 #include "main.h"
+#include "random_without_cast_overflow.h"
 
 // suppress annoying unsigned integer warnings
 template <typename Scalar, bool IsSigned = NumTraits<Scalar>::IsSigned>
@@ -1213,6 +1214,109 @@ void typed_logicals_test(const ArrayType& m) {
     typed_logicals_test_impl<ArrayType>::run(m);
 }
 
+template <typename SrcType, typename DstType, int RowsAtCompileTime, int ColsAtCompileTime>
+struct cast_test_impl {
+  using SrcArray = Array<SrcType, RowsAtCompileTime, ColsAtCompileTime>;
+  using DstArray = Array<DstType, RowsAtCompileTime, ColsAtCompileTime>;
+  struct RandomOp {
+    inline SrcType operator()(const SrcType&) const {
+      return internal::random_without_cast_overflow<SrcType, DstType>::value();
+    }
+  };
+
+  static constexpr int SrcPacketSize = internal::packet_traits<SrcType>::size;
+  static constexpr int DstPacketSize = internal::packet_traits<DstType>::size;
+  static constexpr int MaxPacketSize = internal::plain_enum_max(SrcPacketSize, DstPacketSize);
+
+  // print non-mangled typenames
+  template <typename T>
+  static std::string printTypeInfo(const T&) {
+    if (internal::is_same<bool, T>::value)
+      return "bool";
+    else if (internal::is_same<int8_t, T>::value)
+      return "int8_t";
+    else if (internal::is_same<int16_t, T>::value)
+      return "int16_t";
+    else if (internal::is_same<int32_t, T>::value)
+      return "int32_t";
+    else if (internal::is_same<int64_t, T>::value)
+      return "int64_t";
+    else if (internal::is_same<uint8_t, T>::value)
+      return "uint8_t";
+    else if (internal::is_same<uint16_t, T>::value)
+      return "uint16_t";
+    else if (internal::is_same<uint32_t, T>::value)
+      return "uint32_t";
+    else if (internal::is_same<uint64_t, T>::value)
+      return "uint64_t";
+    else if (internal::is_same<float, T>::value)
+      return "float";
+    else if (internal::is_same<double, T>::value)
+      return "double";
+    //else if (internal::is_same<long double, T>::value)
+    //  return "long double";
+    else if (internal::is_same<half, T>::value)
+      return "half";
+    else if (internal::is_same<bfloat16, T>::value)
+      return "bfloat16";
+    else
+      return typeid(T).name();
+  }
+
+  static void run() {
+    const Index testRows = RowsAtCompileTime == Dynamic ? ((10 * MaxPacketSize) + 1) : RowsAtCompileTime;
+    const Index testCols = ColsAtCompileTime == Dynamic ? ((10 * MaxPacketSize) + 1) : ColsAtCompileTime;
+    const Index testSize = testRows * testCols;
+    const Index minTestSize = 100;
+    const Index repeats = numext::div_ceil(minTestSize, testSize);
+    SrcArray src(testRows, testCols);
+    DstArray dst(testRows, testCols);
+    for (Index repeat = 0; repeat < repeats; repeat++) {
+      src = src.unaryExpr(RandomOp());
+      dst = src.template cast<DstType>();
+      for (Index i = 0; i < testRows; i++)
+        for (Index j = 0; j < testCols; j++) {
+          DstType ref = internal::cast_impl<SrcType, DstType>::run(src(i, j));
+          bool all_nan = ((numext::isnan)(src(i, j)) && (numext::isnan)(ref) && (numext::isnan)(dst(i, j)));
+          bool is_equal = ref == dst(i, j);
+          bool pass = all_nan || is_equal;
+          if (!pass) {
+            std::cout << printTypeInfo(SrcType()) << ": [" << +src(i, j) << "] to " << printTypeInfo(DstType()) << ": ["
+                      << +dst(i, j) << "] != [" << +ref << "]\n";
+          }
+          VERIFY(pass);
+        }
+    }
+  }
+};
+
+template <int RowsAtCompileTime, int ColsAtCompileTime, typename... ScalarTypes>
+struct cast_tests_impl {
+  using ScalarTuple = std::tuple<ScalarTypes...>;
+  static constexpr size_t ScalarTupleSize = std::tuple_size<ScalarTuple>::value;
+
+  template <size_t i = 0, size_t j = i + 1, bool Done = (i >= ScalarTupleSize - 1) || (j >= ScalarTupleSize)>
+  static std::enable_if_t<Done> run() {}
+
+  template <size_t i = 0, size_t j = i + 1, bool Done = (i >= ScalarTupleSize - 1) || (j >= ScalarTupleSize)>
+  static std::enable_if_t<!Done> run() {
+    using Type1 = typename std::tuple_element<i, ScalarTuple>::type;
+    using Type2 = typename std::tuple_element<j, ScalarTuple>::type;
+    cast_test_impl<Type1, Type2, RowsAtCompileTime, ColsAtCompileTime>::run();
+    cast_test_impl<Type2, Type1, RowsAtCompileTime, ColsAtCompileTime>::run();
+    static constexpr size_t next_i = (j == ScalarTupleSize - 1) ? (i + 1) : (i + 0);
+    static constexpr size_t next_j = (j == ScalarTupleSize - 1) ? (i + 2) : (j + 1);
+    run<next_i, next_j>();
+  }
+};
+
+// for now, remove all references to 'long double' until test passes on all platforms
+template <int RowsAtCompileTime, int ColsAtCompileTime>
+void cast_test() {
+  cast_tests_impl<RowsAtCompileTime, ColsAtCompileTime, bool, int8_t, int16_t, int32_t, int64_t, uint8_t, uint16_t,
+                  uint32_t, uint64_t, float, double, /*long double, */half, bfloat16>::run();
+}
+
 EIGEN_DECLARE_TEST(array_cwise)
 {
   for(int i = 0; i < g_repeat; i++) {
@@ -1269,6 +1373,20 @@ EIGEN_DECLARE_TEST(array_cwise)
     CALL_SUBTEST_3( typed_logicals_test(ArrayX<std::complex<double>>(internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
   }
 
+  for (int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST_1((cast_test<1, 1>()));
+    CALL_SUBTEST_2((cast_test<3, 1>()));
+    CALL_SUBTEST_2((cast_test<3, 3>()));
+    CALL_SUBTEST_3((cast_test<5, 1>()));
+    CALL_SUBTEST_3((cast_test<5, 5>()));
+    CALL_SUBTEST_4((cast_test<9, 1>()));
+    CALL_SUBTEST_4((cast_test<9, 9>()));
+    CALL_SUBTEST_5((cast_test<17, 1>()));
+    CALL_SUBTEST_5((cast_test<17, 17>()));
+    CALL_SUBTEST_6((cast_test<Dynamic, 1>()));
+    CALL_SUBTEST_6((cast_test<Dynamic, Dynamic>()));
+  }
+
   VERIFY((internal::is_same< internal::global_math_functions_filtering_base<int>::type, int >::value));
   VERIFY((internal::is_same< internal::global_math_functions_filtering_base<float>::type, float >::value));
   VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Array2i>::type, ArrayBase<Array2i> >::value));