Use numerically stable tree reduction in TensorReduction.

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

@@ -58,16 +58,15 @@ template<typename Reducer, typename Device>
 struct reducer_traits {
   enum {
     Cost = 1,
-    PacketAccess = false
+    PacketAccess = false,
+    IsStateful = false,
+    IsExactlyAssociative = true
   };
 };
 
 // Standard reduction functors
 template <typename T> struct SumReducer
 {
-  static const bool PacketAccess = packet_traits<T>::HasAdd;
-  static const bool IsStateful = false;
-
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const T t, T* accum) const {
     internal::scalar_sum_op<T> sum_op;
     *accum = sum_op(*accum, t);
@@ -103,16 +102,14 @@ template <typename T, typename Device>
 struct reducer_traits<SumReducer<T>, Device> {
   enum {
     Cost = NumTraits<T>::AddCost,
-    PacketAccess = PacketType<T, Device>::HasAdd
+    PacketAccess = PacketType<T, Device>::HasAdd,
+    IsStateful = false,
+    IsExactlyAssociative = NumTraits<T>::IsInteger
   };
 };
 
-
 template <typename T> struct MeanReducer
 {
-  static const bool PacketAccess = packet_traits<T>::HasAdd && packet_traits<T>::HasDiv && !NumTraits<T>::IsInteger;
-  static const bool IsStateful = true;
-
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
   MeanReducer() : scalarCount_(0), packetCount_(0) { }
 
@@ -161,7 +158,9 @@ template <typename T, typename Device>
 struct reducer_traits<MeanReducer<T>, Device> {
   enum {
     Cost = NumTraits<T>::AddCost,
-    PacketAccess = PacketType<T, Device>::HasAdd
+    PacketAccess = PacketType<T, Device>::HasAdd && !NumTraits<T>::IsInteger,
+    IsStateful = true,
+    IsExactlyAssociative = NumTraits<T>::IsInteger
   };
 };
 
@@ -194,9 +193,6 @@ struct MinMaxBottomValue<T, false, false> {
 
 template <typename T> struct MaxReducer
 {
-  static const bool PacketAccess = packet_traits<T>::HasMax;
-  static const bool IsStateful = false;
-
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const T t, T* accum) const {
     if (t > *accum) { *accum = t; }
   }
@@ -228,16 +224,15 @@ template <typename T, typename Device>
 struct reducer_traits<MaxReducer<T>, Device> {
   enum {
     Cost = NumTraits<T>::AddCost,
-    PacketAccess = PacketType<T, Device>::HasMax
+    PacketAccess = PacketType<T, Device>::HasMax,
+    IsStateful = false,
+    IsExactlyAssociative = true
   };
 };
 
 
 template <typename T> struct MinReducer
 {
-  static const bool PacketAccess = packet_traits<T>::HasMin;
-  static const bool IsStateful = false;
-
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const T t, T* accum) const {
     if (t < *accum) { *accum = t; }
   }
@@ -269,16 +264,15 @@ template <typename T, typename Device>
 struct reducer_traits<MinReducer<T>, Device> {
   enum {
     Cost = NumTraits<T>::AddCost,
-    PacketAccess = PacketType<T, Device>::HasMin
+    PacketAccess = PacketType<T, Device>::HasMin,
+    IsStateful = false,
+    IsExactlyAssociative = true
   };
 };
 
 
 template <typename T> struct ProdReducer
 {
-  static const bool PacketAccess = packet_traits<T>::HasMul;
-  static const bool IsStateful = false;
-
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const T t, T* accum) const {
     internal::scalar_product_op<T> prod_op;
     (*accum) = prod_op(*accum, t);
@@ -314,16 +308,15 @@ template <typename T, typename Device>
 struct reducer_traits<ProdReducer<T>, Device> {
   enum {
     Cost = NumTraits<T>::MulCost,
-    PacketAccess = PacketType<T, Device>::HasMul
+    PacketAccess = PacketType<T, Device>::HasMul,
+    IsStateful = false,
+    IsExactlyAssociative = true
   };
 };
 
 
 struct AndReducer
 {
-  static const bool PacketAccess = false;
-  static const bool IsStateful = false;
-
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(bool t, bool* accum) const {
     *accum = *accum && t;
   }
@@ -339,15 +332,14 @@ template <typename Device>
 struct reducer_traits<AndReducer, Device> {
   enum {
     Cost = 1,
-    PacketAccess = false
+    PacketAccess = false,
+    IsStateful = false,
+    IsExactlyAssociative = true
   };
 };
 
 
 struct OrReducer {
-  static const bool PacketAccess = false;
-  static const bool IsStateful = false;
-
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(bool t, bool* accum) const {
     *accum = *accum || t;
   }
@@ -363,7 +355,9 @@ template <typename Device>
 struct reducer_traits<OrReducer, Device> {
   enum {
     Cost = 1,
-    PacketAccess = false
+    PacketAccess = false,
+    IsStateful = false,
+    IsExactlyAssociative = true
   };
 };
 
@@ -371,9 +365,6 @@ struct reducer_traits<OrReducer, Device> {
 // Argmin/Argmax reducers
 template <typename T> struct ArgMaxTupleReducer
 {
-  static const bool PacketAccess = false;
-  static const bool IsStateful = false;
-
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const T t, T* accum) const {
     if (t.second > accum->second) { *accum = t; }
   }
@@ -389,16 +380,15 @@ template <typename T, typename Device>
 struct reducer_traits<ArgMaxTupleReducer<T>, Device> {
   enum {
     Cost = NumTraits<T>::AddCost,
-    PacketAccess = false
+    PacketAccess = false,
+    IsStateful = false,
+    IsExactlyAssociative = true
   };
 };
 
 
 template <typename T> struct ArgMinTupleReducer
 {
-  static const bool PacketAccess = false;
-  static const bool IsStateful = false;
-
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const T& t, T* accum) const {
     if (t.second < accum->second) { *accum = t; }
   }
@@ -414,7 +404,9 @@ template <typename T, typename Device>
 struct reducer_traits<ArgMinTupleReducer<T>, Device> {
   enum {
     Cost = NumTraits<T>::AddCost,
-    PacketAccess = false
+    PacketAccess = false,
+    IsStateful = false,
+    IsExactlyAssociative = true
   };
 };
 

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

@@ -165,7 +165,9 @@ struct GenericDimReducer<-1, Self, Op> {
   }
 };
 
-template <typename Self, typename Op, bool Vectorizable = (Self::InputPacketAccess & Op::PacketAccess)>
+template <typename Self, typename Op, bool Vectorizable = (Self::InputPacketAccess && Self::ReducerTraits::PacketAccess),
+          bool UseTreeReduction = (!Self::ReducerTraits::IsStateful &&
+                                   !Self::ReducerTraits::IsExactlyAssociative)>
 struct InnerMostDimReducer {
   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Self::CoeffReturnType reduce(const Self& self, typename Self::Index firstIndex, typename Self::Index numValuesToReduce, Op& reducer) {
     typename Self::CoeffReturnType accum = reducer.initialize();
@@ -177,23 +179,88 @@ struct InnerMostDimReducer {
 };
 
 template <typename Self, typename Op>
-struct InnerMostDimReducer<Self, Op, true> {
+struct InnerMostDimReducer<Self, Op, true, false> {
   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Self::CoeffReturnType reduce(const Self& self, typename Self::Index firstIndex, typename Self::Index numValuesToReduce, Op& reducer) {
-    const int packetSize = internal::unpacket_traits<typename Self::PacketReturnType>::size;
+    const typename Self::Index packetSize = internal::unpacket_traits<typename Self::PacketReturnType>::size;
     const typename Self::Index VectorizedSize = (numValuesToReduce / packetSize) * packetSize;
-    typename Self::PacketReturnType p = reducer.template initializePacket<typename Self::PacketReturnType>();
+    typename Self::PacketReturnType paccum = reducer.template initializePacket<typename Self::PacketReturnType>();
     for (typename Self::Index j = 0; j < VectorizedSize; j += packetSize) {
-      reducer.reducePacket(self.m_impl.template packet<Unaligned>(firstIndex + j), &p);
+      reducer.reducePacket(self.m_impl.template packet<Unaligned>(firstIndex + j), &paccum);
     }
     typename Self::CoeffReturnType accum = reducer.initialize();
     for (typename Self::Index j = VectorizedSize; j < numValuesToReduce; ++j) {
       reducer.reduce(self.m_impl.coeff(firstIndex + j), &accum);
     }
-    return reducer.finalizeBoth(accum, p);
+    return reducer.finalizeBoth(accum, paccum);
   }
 };
 
-template <int DimIndex, typename Self, typename Op, bool vectorizable = (Self::InputPacketAccess & Op::PacketAccess)>
+static const int kLeafSize = 1024;
+
+template <typename Self, typename Op>
+struct InnerMostDimReducer<Self, Op, false, true> {
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Self::CoeffReturnType
+  reduce(const Self& self, typename Self::Index firstIndex,
+         typename Self::Index numValuesToReduce, Op& reducer) {
+    typename Self::CoeffReturnType accum = reducer.initialize();
+    if (numValuesToReduce > kLeafSize) {
+      const typename Self::Index half = numValuesToReduce / 2;
+      reducer.reduce(reduce(self, firstIndex, half, reducer), &accum);
+      reducer.reduce(
+          reduce(self, firstIndex + half, numValuesToReduce - half, reducer),
+          &accum);
+    } else {
+      for (typename Self::Index j = 0; j < numValuesToReduce; ++j) {
+        reducer.reduce(self.m_impl.coeff(firstIndex + j), &accum);
+      }
+    }
+    return reducer.finalize(accum);
+  }
+};
+
+#if !defined(EIGEN_USE_GPU) || !defined(__CUDACC__)
+template <typename Self, typename Op>
+struct InnerMostDimReducer<Self, Op, true, true> {
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Self::CoeffReturnType
+  reduce(const Self& self, typename Self::Index firstIndex,
+         typename Self::Index numValuesToReduce, Op& reducer) {
+    const typename Self::Index packetSize =
+        internal::unpacket_traits<typename Self::PacketReturnType>::size;
+    typename Self::CoeffReturnType accum = reducer.initialize();
+    if (numValuesToReduce > packetSize * kLeafSize) {
+      // Make sure the split point is aligned on a packet boundary.
+      const typename Self::Index split =
+          packetSize *
+          divup(firstIndex + divup(numValuesToReduce, typename Self::Index(2)),
+                packetSize);
+      const typename Self::Index num_left =
+          numext::mini(split - firstIndex, numValuesToReduce);
+      reducer.reduce(reduce(self, firstIndex, num_left, reducer), &accum);
+      if (num_left < numValuesToReduce) {
+        reducer.reduce(
+            reduce(self, split, numValuesToReduce - num_left, reducer), &accum);
+      }
+      return reducer.finalize(accum);
+    } else {
+      const typename Self::Index VectorizedSize =
+          (numValuesToReduce / packetSize) * packetSize;
+      typename Self::PacketReturnType paccum =
+          reducer.template initializePacket<typename Self::PacketReturnType>();
+      for (typename Self::Index j = 0; j < VectorizedSize; j += packetSize) {
+        reducer.reducePacket(
+            self.m_impl.template packet<Unaligned>(firstIndex + j), &paccum);
+      }
+      for (typename Self::Index j = VectorizedSize; j < numValuesToReduce;
+           ++j) {
+        reducer.reduce(self.m_impl.coeff(firstIndex + j), &accum);
+      }
+      return reducer.finalizeBoth(accum, paccum);
+    }
+  }
+};
+#endif
+
+template <int DimIndex, typename Self, typename Op, bool vectorizable = (Self::InputPacketAccess && Self::ReducerTraits::PacketAccess)>
 struct InnerMostDimPreserver {
   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const Self&, typename Self::Index, Op&, typename Self::PacketReturnType*) {
     eigen_assert(false && "should never be called");
@@ -228,7 +295,7 @@ struct InnerMostDimPreserver<-1, Self, Op, true> {
 };
 
 // Default full reducer
-template <typename Self, typename Op, typename Device, bool Vectorizable = (Self::InputPacketAccess & Op::PacketAccess)>
+template <typename Self, typename Op, typename Device, bool Vectorizable = (Self::InputPacketAccess && Self::ReducerTraits::PacketAccess)>
 struct FullReducer {
   static const bool HasOptimizedImplementation = false;
 
@@ -242,7 +309,7 @@ struct FullReducer {
 #ifdef EIGEN_USE_THREADS
 // Multithreaded full reducers
 template <typename Self, typename Op,
-          bool Vectorizable = (Self::InputPacketAccess & Op::PacketAccess)>
+          bool Vectorizable = (Self::InputPacketAccess && Self::ReducerTraits::PacketAccess)>
 struct FullReducerShard {
   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Self& self, typename Self::Index firstIndex,
                   typename Self::Index numValuesToReduce, Op& reducer,
@@ -255,8 +322,8 @@ struct FullReducerShard {
 // Multithreaded full reducer
 template <typename Self, typename Op, bool Vectorizable>
 struct FullReducer<Self, Op, ThreadPoolDevice, Vectorizable> {
-  static const bool HasOptimizedImplementation = !Op::IsStateful;
+  static const bool HasOptimizedImplementation = !Self::ReducerTraits::IsStateful;
-  static const int PacketSize =
+  static const Index PacketSize =
       unpacket_traits<typename Self::PacketReturnType>::size;
 
   // launch one reducer per thread and accumulate the result.
@@ -394,6 +461,7 @@ class TensorReductionOp : public TensorBase<TensorReductionOp<Op, Dims, XprType,
 template<typename Op, typename Dims, typename ArgType, template <class> class MakePointer_, typename Device>
 struct TensorEvaluator<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Device>
 {
+  typedef internal::reducer_traits<Op, Device> ReducerTraits;
   typedef TensorReductionOp<Op, Dims, ArgType, MakePointer_> XprType;
   typedef typename XprType::Index Index;
   typedef ArgType ChildType;
@@ -407,11 +475,11 @@ struct TensorEvaluator<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>,
   static const bool InputPacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess;
   typedef typename internal::remove_const<typename XprType::CoeffReturnType>::type CoeffReturnType;
   typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
-  static const int PacketSize = PacketType<CoeffReturnType, Device>::size;
+  static const Index PacketSize = PacketType<CoeffReturnType, Device>::size;
 
   enum {
     IsAligned = false,
-    PacketAccess = Self::InputPacketAccess && Op::PacketAccess,
+    PacketAccess = Self::InputPacketAccess && ReducerTraits::PacketAccess,
     BlockAccess = false,
     Layout = TensorEvaluator<ArgType, Device>::Layout,
     CoordAccess = false,  // to be implemented
@@ -696,7 +764,7 @@ struct TensorEvaluator<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>,
 
   private:
   template <int, typename, typename> friend struct internal::GenericDimReducer;
-  template <typename, typename, bool> friend struct internal::InnerMostDimReducer;
+  template <typename, typename, bool, bool> friend struct internal::InnerMostDimReducer;
   template <int, typename, typename, bool> friend struct internal::InnerMostDimPreserver;
   template <typename S, typename O, typename D, bool V> friend struct internal::FullReducer;
 #ifdef EIGEN_USE_THREADS

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

@@ -376,12 +376,12 @@ struct FullReducer<Self, Op, GpuDevice, Vectorizable> {
   // so reduce the scope of the optimized version of the code to the simple cases
   // of doubles, floats and half floats
 #ifdef EIGEN_HAS_GPU_FP16
-  static const bool HasOptimizedImplementation = !Op::IsStateful &&
+  static const bool HasOptimizedImplementation = !Self::ReducerTraits::IsStateful &&
       (internal::is_same<typename Self::CoeffReturnType, float>::value ||
        internal::is_same<typename Self::CoeffReturnType, double>::value ||
        (internal::is_same<typename Self::CoeffReturnType, Eigen::half>::value && reducer_traits<Op, GpuDevice>::PacketAccess));
 #else // EIGEN_HAS_GPU_FP16
-  static const bool HasOptimizedImplementation = !Op::IsStateful &&
+  static const bool HasOptimizedImplementation = !Self::ReducerTraits::IsStateful &&
                                                 (internal::is_same<typename Self::CoeffReturnType, float>::value ||
                                                  internal::is_same<typename Self::CoeffReturnType, double>::value);
 #endif // EIGEN_HAS_GPU_FP16
@@ -697,12 +697,12 @@ struct InnerReducer<Self, Op, GpuDevice> {
   // so reduce the scope of the optimized version of the code to the simple case
   // of floats and half floats.
 #ifdef EIGEN_HAS_GPU_FP16
-  static const bool HasOptimizedImplementation = !Op::IsStateful &&
+  static const bool HasOptimizedImplementation = !Self::ReducerTraits::IsStateful &&
       (internal::is_same<typename Self::CoeffReturnType, float>::value ||
        internal::is_same<typename Self::CoeffReturnType, double>::value ||
        (internal::is_same<typename Self::CoeffReturnType, Eigen::half>::value && reducer_traits<Op, GpuDevice>::PacketAccess));
 #else // EIGEN_HAS_GPU_FP16
-  static const bool HasOptimizedImplementation = !Op::IsStateful &&
+  static const bool HasOptimizedImplementation = !Self::ReducerTraits::IsStateful &&
                                                  (internal::is_same<typename Self::CoeffReturnType, float>::value ||
                                                   internal::is_same<typename Self::CoeffReturnType, double>::value);
 #endif // EIGEN_HAS_GPU_FP16
@@ -759,7 +759,7 @@ struct OuterReducer<Self, Op, GpuDevice> {
   // Unfortunately nvidia doesn't support well exotic types such as complex,
   // so reduce the scope of the optimized version of the code to the simple case
   // of floats.
-  static const bool HasOptimizedImplementation = !Op::IsStateful &&
+  static const bool HasOptimizedImplementation = !Self::ReducerTraits::IsStateful &&
                                                  (internal::is_same<typename Self::CoeffReturnType, float>::value ||
                                                   internal::is_same<typename Self::CoeffReturnType, double>::value);
   template <typename Device, typename OutputType>

unsupported/test/cxx11_tensor_reduction.cpp

@@ -386,7 +386,7 @@ static void test_static_dims() {
           expected = (std::max)(expected, in(i, k, j, l));
         }
       }
-      VERIFY_IS_APPROX(out(i, j), expected);
+      VERIFY_IS_EQUAL(out(i, j), expected);
     }
   }
 }
@@ -417,7 +417,7 @@ static void test_innermost_last_dims() {
           expected = (std::max)(expected, in(l, k, i, j));
         }
       }
-      VERIFY_IS_APPROX(out(i, j), expected);
+      VERIFY_IS_EQUAL(out(i, j), expected);
     }
   }
 }
@@ -448,7 +448,7 @@ static void test_innermost_first_dims() {
           expected = (std::max)(expected, in(i, j, k, l));
         }
       }
-      VERIFY_IS_APPROX(out(i, j), expected);
+      VERIFY_IS_EQUAL(out(i, j), expected);
     }
   }
 }
@@ -479,11 +479,30 @@ static void test_reduce_middle_dims() {
           expected = (std::max)(expected, in(i, k, l, j));
         }
       }
-      VERIFY_IS_APPROX(out(i, j), expected);
+      VERIFY_IS_EQUAL(out(i, j), expected);
     }
   }
 }
 
+static void test_sum_accuracy() {
+  Tensor<float, 3> tensor(101, 101, 101);
+  for (float prescribed_mean : {1.0f, 10.0f, 100.0f, 1000.0f, 10000.0f}) {
+    tensor.setRandom();
+    tensor += tensor.constant(prescribed_mean);
+
+    Tensor<float, 0> sum = tensor.sum();
+    double expected_sum = 0.0;
+    for (int i = 0; i < 101; ++i) {
+      for (int j = 0; j < 101; ++j) {
+        for (int k = 0; k < 101; ++k) {
+          expected_sum += static_cast<double>(tensor(i, j, k));
+        }
+      }
+    }
+    VERIFY_IS_APPROX(sum(), static_cast<float>(expected_sum));
+  }
+}
+
 EIGEN_DECLARE_TEST(cxx11_tensor_reduction) {
   CALL_SUBTEST(test_trivial_reductions<ColMajor>());
   CALL_SUBTEST(test_trivial_reductions<RowMajor>());
@@ -506,4 +525,5 @@ EIGEN_DECLARE_TEST(cxx11_tensor_reduction) {
   CALL_SUBTEST(test_innermost_first_dims<RowMajor>());
   CALL_SUBTEST(test_reduce_middle_dims<ColMajor>());
   CALL_SUBTEST(test_reduce_middle_dims<RowMajor>());
+  CALL_SUBTEST(test_sum_accuracy());
 }