bug #1195: move NumTraits::Div<>::Cost to internal::scalar_div_cost (with some specializations in arch/SSE and arch/AVX)

Eigen/src/Core/NumTraits.h

@@ -97,23 +97,6 @@ template<typename T> struct GenericNumTraits
     MulCost = 1
   };
 
-  // Division is messy but important, because it is expensive and throughput
-  // varies significantly. The following numbers are based on min division
-  // throughput on Haswell.
-  template<bool Vectorized>
-  struct Div {
-    enum {
-#ifdef EIGEN_VECTORIZE_AVX
-      AVX = true,
-#else
-      AVX = false,
-#endif
-      Cost = IsInteger ? (sizeof(T) == 8 ? (IsSigned ? 24 : 21) : (IsSigned ? 8 : 9)):
-          Vectorized ? (sizeof(T) == 8 ? (AVX ? 16 : 8) : (AVX ? 14 : 7)) : 8
-    };
-  };
-
-
   typedef T Real;
   typedef typename internal::conditional<
                      IsInteger,

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

@@ -94,6 +94,9 @@ template<> struct packet_traits<double> : default_packet_traits
   };
 };
 
+template<> struct scalar_div_cost<float,true> { enum { value = 14 }; };
+template<> struct scalar_div_cost<double,true> { enum { value = 16 }; };
+
 /* Proper support for integers is only provided by AVX2. In the meantime, we'll
    use SSE instructions and packets to deal with integers.
 template<> struct packet_traits<int>    : default_packet_traits

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

@@ -162,6 +162,11 @@ template<> struct unpacket_traits<Packet4f> { typedef float  type; enum {size=4,
 template<> struct unpacket_traits<Packet2d> { typedef double type; enum {size=2, alignment=Aligned16}; typedef Packet2d half; };
 template<> struct unpacket_traits<Packet4i> { typedef int    type; enum {size=4, alignment=Aligned16}; typedef Packet4i half; };
 
+#ifndef EIGEN_VECTORIZE_AVX
+template<> struct scalar_div_cost<float,true> { enum { value = 7 }; };
+template<> struct scalar_div_cost<double,true> { enum { value = 8 }; };
+#endif
+
 #if EIGEN_COMP_MSVC==1500
 // Workaround MSVC 9 internal compiler error.
 // TODO: It has been detected with win64 builds (amd64), so let's check whether it also happens in 32bits+SSE mode

Eigen/src/Core/functors/BinaryFunctors.h

@@ -287,7 +287,7 @@ struct functor_traits<scalar_hypot_op<Scalar,Scalar> > {
   {
     Cost = 3 * NumTraits<Scalar>::AddCost +
            2 * NumTraits<Scalar>::MulCost +
-           2 * NumTraits<Scalar>::template Div<false>::Cost,
+           2 * scalar_div_cost<Scalar,false>::value,
     PacketAccess = false
   };
 };
@@ -375,7 +375,7 @@ struct functor_traits<scalar_quotient_op<LhsScalar,RhsScalar> > {
   typedef typename scalar_quotient_op<LhsScalar,RhsScalar>::result_type result_type;
   enum {
     PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasDiv && packet_traits<RhsScalar>::HasDiv,
-    Cost = NumTraits<result_type>::template Div<PacketAccess>::Cost
+    Cost = scalar_div_cost<result_type,PacketAccess>::value
   };
 };
 

Eigen/src/Core/functors/UnaryFunctors.h

@@ -248,7 +248,7 @@ struct functor_traits<scalar_exp_op<Scalar> > {
      // double: 7 pmadd, 5 pmul, 3 padd/psub, 1 div,  13 other
      : (14 * NumTraits<Scalar>::AddCost +
         6 * NumTraits<Scalar>::MulCost +
-        NumTraits<Scalar>::template Div<packet_traits<Scalar>::HasDiv>::Cost))
+        scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value))
 #else
     Cost =
     (sizeof(Scalar) == 4
@@ -257,7 +257,7 @@ struct functor_traits<scalar_exp_op<Scalar> > {
      // double: 7 pmadd, 5 pmul, 3 padd/psub, 1 div,  13 other
      : (23 * NumTraits<Scalar>::AddCost +
         12 * NumTraits<Scalar>::MulCost +
-        NumTraits<Scalar>::template Div<packet_traits<Scalar>::HasDiv>::Cost))
+        scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value))
 #endif
   };
 };
@@ -514,17 +514,16 @@ struct functor_traits<scalar_tanh_op<Scalar> > {
                 // 9 pmadd, 2 pmul, 1 div, 2 other
                 ? (2 * NumTraits<Scalar>::AddCost +
                    6 * NumTraits<Scalar>::MulCost +
-                   NumTraits<Scalar>::template Div<packet_traits<Scalar>::HasDiv>::Cost)
+                   scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value)
 #else
                 ? (11 * NumTraits<Scalar>::AddCost +
                    11 * NumTraits<Scalar>::MulCost +
-                   NumTraits<Scalar>::template Div<packet_traits<Scalar>::HasDiv>::Cost)
+                   scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value)
 #endif
                 // This number assumes a naive implementation of tanh
                 : (6 * NumTraits<Scalar>::AddCost +
                    3 * NumTraits<Scalar>::MulCost +
-                   2 * NumTraits<Scalar>::template Div<
-                           packet_traits<Scalar>::HasDiv>::Cost +
+                   2 * scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value +
                    functor_traits<scalar_exp_op<Scalar> >::Cost))
   };
 };

Eigen/src/Core/util/XprHelper.h

@@ -664,6 +664,20 @@ bool is_same_dense(const T1 &, const T2 &, typename enable_if<!(has_direct_acces
   return false;
 }
 
+// Internal helper defining the cost of a scalar division for the type T.
+// The default heuristic can be specialized for each scalar type and architecture.
+template<typename T,bool Vectorized=false,typename EnaleIf = void>
+struct scalar_div_cost {
+  enum { value = 8*NumTraits<T>::MulCost };
+};
+
+
+template<bool Vectorized>
+struct scalar_div_cost<signed long,Vectorized,typename enable_if<sizeof(long)==8>::type> { enum { value = 24 }; };
+template<bool Vectorized>
+struct scalar_div_cost<unsigned long,Vectorized,typename enable_if<sizeof(long)==8>::type> { enum { value = 21 }; };
+
+
 #ifdef EIGEN_DEBUG_ASSIGN
 std::string demangle_traversal(int t)
 {

test/integer_types.cpp

@@ -158,4 +158,12 @@ void test_integer_types()
 
     CALL_SUBTEST_8( integer_type_tests(Matrix<unsigned long long, Dynamic, 5>(1, 5)) );
   }
+#ifdef EIGEN_TEST_PART_9
+  VERIFY_IS_EQUAL(internal::scalar_div_cost<int>::value, 8);
+  VERIFY_IS_EQUAL(internal::scalar_div_cost<unsigned int>::value, 8);
+  if(sizeof(long)>sizeof(int)) {
+    VERIFY(internal::scalar_div_cost<long>::value > internal::scalar_div_cost<int>::value);
+    VERIFY(internal::scalar_div_cost<unsigned long>::value > internal::scalar_div_cost<int>::value);
+  }
+#endif
 }

unsupported/Eigen/CXX11/src/Tensor/TensorFunctors.h

@@ -25,7 +25,7 @@ struct scalar_mod_op {
 };
 template <typename Scalar>
 struct functor_traits<scalar_mod_op<Scalar> >
-{ enum { Cost = NumTraits<Scalar>::template Div<false>::Cost, PacketAccess = false }; };
+{ enum { Cost = scalar_div_cost<Scalar,false>::value, PacketAccess = false }; };
 
 
 /** \internal
@@ -38,7 +38,7 @@ struct scalar_mod2_op {
 };
 template <typename Scalar>
 struct functor_traits<scalar_mod2_op<Scalar> >
-{ enum { Cost = NumTraits<Scalar>::template Div<false>::Cost, PacketAccess = false }; };
+{ enum { Cost = scalar_div_cost<Scalar,false>::value, PacketAccess = false }; };
 
 template <typename Scalar>
 struct scalar_fmod_op {