* add ei_predux_mul internal function

* apply Ricard Marxer's prod() patch with fixes for the vectorized path

Eigen/Core

@@ -139,6 +139,7 @@ namespace Eigen {
 #include "src/Core/DiagonalMatrix.h"
 #include "src/Core/DiagonalCoeffs.h"
 #include "src/Core/Sum.h"
+#include "src/Core/Prod.h"
 #include "src/Core/Redux.h"
 #include "src/Core/Visitor.h"
 #include "src/Core/Fuzzy.h"

Eigen/src/Array/PartialRedux.h

@@ -115,6 +115,8 @@ EIGEN_MEMBER_FUNCTOR(maxCoeff, (Size-1)*NumTraits<Scalar>::AddCost);
 EIGEN_MEMBER_FUNCTOR(all, (Size-1)*NumTraits<Scalar>::AddCost);
 EIGEN_MEMBER_FUNCTOR(any, (Size-1)*NumTraits<Scalar>::AddCost);
 EIGEN_MEMBER_FUNCTOR(count, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(prod, (Size-1)*NumTraits<Scalar>::MulCost);
+
 
 /** \internal */
 template <typename BinaryOp, typename Scalar>
@@ -257,6 +259,16 @@ template<typename ExpressionType, int Direction> class PartialRedux
       * \sa MatrixBase::count() */
     const PartialReduxExpr<ExpressionType, ei_member_count<int>, Direction> count() const
     { return _expression(); }
+
+    /** \returns a row (or column) vector expression of the product
+      * of each column (or row) of the referenced expression.
+      *
+      * Example: \include PartialRedux_prod.cpp
+      * Output: \verbinclude PartialRedux_prod.out
+      *
+      * \sa MatrixBase::prod() */
+    const typename ReturnType<ei_member_prod>::Type prod() const
+    { return _expression(); }
     
     
     /** \returns a matrix expression

Eigen/src/Core/GenericPacketMath.h

@@ -96,6 +96,10 @@ ei_preduxp(const Packet* vecs) { return vecs[0]; }
 template<typename Packet> inline typename ei_unpacket_traits<Packet>::type ei_predux(const Packet& a)
 { return a; }
 
+/** \internal \returns the product of the elements of \a a*/
+template<typename Packet> inline typename ei_unpacket_traits<Packet>::type ei_predux_mul(const Packet& a)
+{ return a; }
+
 /** \internal \returns the reversed elements of \a a*/
 template<typename Packet> inline Packet ei_preverse(const Packet& a)
 { return a; }

Eigen/src/Core/MatrixBase.h

@@ -535,6 +535,8 @@ template<typename Derived> class MatrixBase
     Scalar sum() const;
     Scalar trace() const;
 
+    Scalar prod() const;
+
     typename ei_traits<Derived>::Scalar minCoeff() const;
     typename ei_traits<Derived>::Scalar maxCoeff() const;
 

Eigen/src/Core/Prod.h

@@ -0,0 +1,262 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_PROD_H
+#define EIGEN_PROD_H
+
+/***************************************************************************
+* Part 1 : the logic deciding a strategy for vectorization and unrolling
+***************************************************************************/
+
+template<typename Derived>
+struct ei_prod_traits
+{
+private:
+  enum {
+    PacketSize = ei_packet_traits<typename Derived::Scalar>::size
+  };
+
+public:
+  enum {
+    Vectorization = (int(Derived::Flags)&ActualPacketAccessBit)
+                 && (int(Derived::Flags)&LinearAccessBit)
+                  ? LinearVectorization
+                  : NoVectorization
+  };
+
+private:
+  enum {
+    Cost = Derived::SizeAtCompileTime * Derived::CoeffReadCost
+           + (Derived::SizeAtCompileTime-1) * NumTraits<typename Derived::Scalar>::MulCost,
+    UnrollingLimit = EIGEN_UNROLLING_LIMIT * (int(Vectorization) == int(NoVectorization) ? 1 : int(PacketSize))
+  };
+
+public:
+  enum {
+    Unrolling = Cost <= UnrollingLimit
+              ? CompleteUnrolling
+              : NoUnrolling
+  };
+};
+
+/***************************************************************************
+* Part 2 : unrollers
+***************************************************************************/
+
+/*** no vectorization ***/
+
+template<typename Derived, int Start, int Length>
+struct ei_prod_novec_unroller
+{
+  enum {
+    HalfLength = Length/2
+  };
+
+  typedef typename Derived::Scalar Scalar;
+
+  inline static Scalar run(const Derived &mat)
+  {
+    return ei_prod_novec_unroller<Derived, Start, HalfLength>::run(mat)
+         * ei_prod_novec_unroller<Derived, Start+HalfLength, Length-HalfLength>::run(mat);
+  }
+};
+
+template<typename Derived, int Start>
+struct ei_prod_novec_unroller<Derived, Start, 1>
+{
+  enum {
+    col = Start / Derived::RowsAtCompileTime,
+    row = Start % Derived::RowsAtCompileTime
+  };
+
+  typedef typename Derived::Scalar Scalar;
+
+  inline static Scalar run(const Derived &mat)
+  {
+    return mat.coeff(row, col);
+  }
+};
+
+/*** vectorization ***/
+  
+template<typename Derived, int Start, int Length>
+struct ei_prod_vec_unroller
+{
+  enum {
+    PacketSize = ei_packet_traits<typename Derived::Scalar>::size,
+    HalfLength = Length/2
+  };
+
+  typedef typename Derived::Scalar Scalar;
+  typedef typename ei_packet_traits<Scalar>::type PacketScalar;
+
+  inline static PacketScalar run(const Derived &mat)
+  {
+    return ei_pmul(
+            ei_prod_vec_unroller<Derived, Start, HalfLength>::run(mat),
+            ei_prod_vec_unroller<Derived, Start+HalfLength, Length-HalfLength>::run(mat) );
+  }
+};
+
+template<typename Derived, int Start>
+struct ei_prod_vec_unroller<Derived, Start, 1>
+{
+  enum {
+    index = Start * ei_packet_traits<typename Derived::Scalar>::size,
+    row = int(Derived::Flags)&RowMajorBit
+        ? index / int(Derived::ColsAtCompileTime)
+        : index % Derived::RowsAtCompileTime,
+    col = int(Derived::Flags)&RowMajorBit
+        ? index % int(Derived::ColsAtCompileTime)
+        : index / Derived::RowsAtCompileTime,
+    alignment = (Derived::Flags & AlignedBit) ? Aligned : Unaligned
+  };
+
+  typedef typename Derived::Scalar Scalar;
+  typedef typename ei_packet_traits<Scalar>::type PacketScalar;
+
+  inline static PacketScalar run(const Derived &mat)
+  {
+    return mat.template packet<alignment>(row, col);
+  }
+};
+
+/***************************************************************************
+* Part 3 : implementation of all cases
+***************************************************************************/
+
+template<typename Derived,
+         int Vectorization = ei_prod_traits<Derived>::Vectorization,
+         int Unrolling = ei_prod_traits<Derived>::Unrolling
+>
+struct ei_prod_impl;
+
+template<typename Derived>
+struct ei_prod_impl<Derived, NoVectorization, NoUnrolling>
+{
+  typedef typename Derived::Scalar Scalar;
+  static Scalar run(const Derived& mat)
+  {
+    ei_assert(mat.rows()>0 && mat.cols()>0 && "you are using a non initialized matrix");
+    Scalar res;
+    res = mat.coeff(0, 0);
+    for(int i = 1; i < mat.rows(); ++i)
+      res *= mat.coeff(i, 0);
+    for(int j = 1; j < mat.cols(); ++j)
+      for(int i = 0; i < mat.rows(); ++i)
+        res *= mat.coeff(i, j);
+    return res;
+  }
+};
+
+template<typename Derived>
+struct ei_prod_impl<Derived, NoVectorization, CompleteUnrolling>
+  : public ei_prod_novec_unroller<Derived, 0, Derived::SizeAtCompileTime>
+{};
+
+template<typename Derived>
+struct ei_prod_impl<Derived, LinearVectorization, NoUnrolling>
+{
+  typedef typename Derived::Scalar Scalar;
+  typedef typename ei_packet_traits<Scalar>::type PacketScalar;
+
+  static Scalar run(const Derived& mat)
+  {
+    const int size = mat.size();
+    const int packetSize = ei_packet_traits<Scalar>::size;
+    const int alignedStart =  (Derived::Flags & AlignedBit)
+                           || !(Derived::Flags & DirectAccessBit)
+                           ? 0
+                           : ei_alignmentOffset(&mat.const_cast_derived().coeffRef(0), size);
+    enum {
+      alignment = (Derived::Flags & DirectAccessBit) || (Derived::Flags & AlignedBit)
+                ? Aligned : Unaligned
+    };
+    const int alignedSize = ((size-alignedStart)/packetSize)*packetSize;
+    const int alignedEnd = alignedStart + alignedSize;
+    Scalar res;
+
+    if(alignedSize)
+    {
+      PacketScalar packet_res = mat.template packet<alignment>(alignedStart);
+      for(int index = alignedStart + packetSize; index < alignedEnd; index += packetSize)
+        packet_res = ei_pmul(packet_res, mat.template packet<alignment>(index));
+      res = ei_predux_mul(packet_res);
+    }
+    else // too small to vectorize anything.
+         // since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.
+    {
+      res = Scalar(1);
+    }
+
+    for(int index = 0; index < alignedStart; ++index)
+      res *= mat.coeff(index);
+
+    for(int index = alignedEnd; index < size; ++index)
+      res *= mat.coeff(index);
+
+    return res;
+  }
+};
+
+template<typename Derived>
+struct ei_prod_impl<Derived, LinearVectorization, CompleteUnrolling>
+{
+  typedef typename Derived::Scalar Scalar;
+  typedef typename ei_packet_traits<Scalar>::type PacketScalar;
+  enum {
+    PacketSize = ei_packet_traits<Scalar>::size,
+    Size = Derived::SizeAtCompileTime,
+    VectorizationSize = (Size / PacketSize) * PacketSize
+  };
+  static Scalar run(const Derived& mat)
+  {
+    Scalar res = ei_predux_mul(ei_prod_vec_unroller<Derived, 0, Size / PacketSize>::run(mat));
+    if (VectorizationSize != Size)
+      res *= ei_prod_novec_unroller<Derived, VectorizationSize, Size-VectorizationSize>::run(mat);
+    return res;
+  }
+};
+
+/***************************************************************************
+* Part 4 : implementation of MatrixBase methods
+***************************************************************************/
+
+/** \returns the product of all coefficients of *this
+  *
+  * Example: \include MatrixBase_prod.cpp
+  * Output: \verbinclude MatrixBase_prod.out
+  *
+  * \sa sum()
+  */
+template<typename Derived>
+inline typename ei_traits<Derived>::Scalar
+MatrixBase<Derived>::prod() const
+{
+  typedef typename ei_cleantype<typename Derived::Nested>::type ThisNested;
+  return ei_prod_impl<ThisNested>::run(derived());
+}
+
+#endif // EIGEN_PROD_H

Eigen/src/Core/Sum.h

@@ -246,7 +246,7 @@ struct ei_sum_impl<Derived, LinearVectorization, CompleteUnrolling>
 
 /** \returns the sum of all coefficients of *this
   *
-  * \sa trace()
+  * \sa trace(), prod()
   */
 template<typename Derived>
 inline typename ei_traits<Derived>::Scalar

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

@@ -214,6 +214,23 @@ template<> EIGEN_STRONG_INLINE __m128i ei_preduxp<__m128i>(const __m128i* vecs)
   return _mm_add_epi32(tmp0, tmp2);
 }
 
+// Other reduction functions:
+
+template<> EIGEN_STRONG_INLINE float ei_predux_mul<__m128>(const __m128& a)
+{
+  __m128 tmp = _mm_mul_ps(a, _mm_movehl_ps(a,a));
+  return ei_pfirst(_mm_mul_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
+}
+template<> EIGEN_STRONG_INLINE double ei_predux_mul<__m128d>(const __m128d& a)
+{
+  return ei_pfirst(_mm_mul_sd(a, _mm_unpackhi_pd(a,a)));
+}
+template<> EIGEN_STRONG_INLINE int ei_predux_mul<__m128i>(const __m128i& a)
+{
+  __m128i tmp = ei_pmul(a, _mm_unpackhi_epi64(a,a));
+  return ei_pfirst(tmp) * ei_pfirst(_mm_shuffle_epi32(tmp, 1));
+}
+
 #if (defined __GNUC__)
 // template <> EIGEN_STRONG_INLINE __m128 ei_pmadd(const __m128&  a, const __m128&  b, const __m128&  c)
 // {