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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
// Copyright (C) 2006-2008 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_REDUX_H
#define EIGEN_REDUX_H
// TODO
// * implement other kind of vectorization
// * factorize code
/***************************************************************************
* Part 1 : the logic deciding a strategy for vectorization and unrolling
***************************************************************************/
template<typename Func, typename Derived>
struct ei_redux_traits
{
private:
enum {
PacketSize = ei_packet_traits<typename Derived::Scalar>::size,
InnerMaxSize = int(Derived::Flags)&RowMajorBit
? Derived::MaxColsAtCompileTime
: Derived::MaxRowsAtCompileTime
};
enum {
MightVectorize = (int(Derived::Flags)&ActualPacketAccessBit)
&& (ei_functor_traits<Func>::PacketAccess),
MayLinearVectorize = MightVectorize && (int(Derived::Flags)&LinearAccessBit),
MaySliceVectorize = MightVectorize && int(InnerMaxSize)>=3*PacketSize
};
public:
enum {
Traversal = int(MayLinearVectorize) ? int(LinearVectorizedTraversal)
: int(MaySliceVectorize) ? int(SliceVectorizedTraversal)
: int(DefaultTraversal)
};
private:
enum {
Cost = Derived::SizeAtCompileTime * Derived::CoeffReadCost
+ (Derived::SizeAtCompileTime-1) * NumTraits<typename Derived::Scalar>::AddCost,
UnrollingLimit = EIGEN_UNROLLING_LIMIT * (int(Traversal) == int(DefaultTraversal) ? 1 : int(PacketSize))
};
public:
enum {
Unrolling = Cost <= UnrollingLimit
? CompleteUnrolling
: NoUnrolling
};
};
/***************************************************************************
* Part 2 : unrollers
***************************************************************************/
/*** no vectorization ***/
template<typename Func, typename Derived, int Start, int Length>
struct ei_redux_novec_unroller
{
enum {
HalfLength = Length/2
};
typedef typename Derived::Scalar Scalar;
EIGEN_STRONG_INLINE static Scalar run(const Derived &mat, const Func& func)
{
return func(ei_redux_novec_unroller<Func, Derived, Start, HalfLength>::run(mat,func),
ei_redux_novec_unroller<Func, Derived, Start+HalfLength, Length-HalfLength>::run(mat,func));
}
};
template<typename Func, typename Derived, int Start>
struct ei_redux_novec_unroller<Func, Derived, Start, 1>
{
enum {
col = Start / Derived::RowsAtCompileTime,
row = Start % Derived::RowsAtCompileTime
};
typedef typename Derived::Scalar Scalar;
EIGEN_STRONG_INLINE static Scalar run(const Derived &mat, const Func&)
{
return mat.coeff(row, col);
}
};
// This is actually dead code and will never be called. It is required
// to prevent false warnings regarding failed inlining though
// for 0 length run() will never be called at all.
template<typename Func, typename Derived, int Start>
struct ei_redux_novec_unroller<Func, Derived, Start, 0>
{
typedef typename Derived::Scalar Scalar;
EIGEN_STRONG_INLINE static Scalar run(const Derived&, const Func&) { return Scalar(); }
};
/*** vectorization ***/
template<typename Func, typename Derived, int Start, int Length>
struct ei_redux_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;
EIGEN_STRONG_INLINE static PacketScalar run(const Derived &mat, const Func& func)
{
return func.packetOp(
ei_redux_vec_unroller<Func, Derived, Start, HalfLength>::run(mat,func),
ei_redux_vec_unroller<Func, Derived, Start+HalfLength, Length-HalfLength>::run(mat,func) );
}
};
template<typename Func, typename Derived, int Start>
struct ei_redux_vec_unroller<Func, 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;
EIGEN_STRONG_INLINE static PacketScalar run(const Derived &mat, const Func&)
{
return mat.template packet<alignment>(row, col);
}
};
/***************************************************************************
* Part 3 : implementation of all cases
***************************************************************************/
template<typename Func, typename Derived,
int Traversal = ei_redux_traits<Func, Derived>::Traversal,
int Unrolling = ei_redux_traits<Func, Derived>::Unrolling
>
struct ei_redux_impl;
template<typename Func, typename Derived>
struct ei_redux_impl<Func, Derived, DefaultTraversal, NoUnrolling>
{
typedef typename Derived::Scalar Scalar;
static Scalar run(const Derived& mat, const Func& func)
{
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 = func(res, mat.coeff(i, 0));
for(int j = 1; j < mat.cols(); ++j)
for(int i = 0; i < mat.rows(); ++i)
res = func(res, mat.coeff(i, j));
return res;
}
};
template<typename Func, typename Derived>
struct ei_redux_impl<Func,Derived, DefaultTraversal, CompleteUnrolling>
: public ei_redux_novec_unroller<Func,Derived, 0, Derived::SizeAtCompileTime>
{};
template<typename Func, typename Derived>
struct ei_redux_impl<Func, Derived, LinearVectorizedTraversal, NoUnrolling>
{
typedef typename Derived::Scalar Scalar;
typedef typename ei_packet_traits<Scalar>::type PacketScalar;
static Scalar run(const Derived& mat, const Func& func)
{
const int size = mat.size();
const int packetSize = ei_packet_traits<Scalar>::size;
const int alignedStart = ei_alignmentOffset(mat,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 = func.packetOp(packet_res, mat.template packet<alignment>(index));
res = func.predux(packet_res);
for(int index = 0; index < alignedStart; ++index)
res = func(res,mat.coeff(index));
for(int index = alignedEnd; index < size; ++index)
res = func(res,mat.coeff(index));
}
else // too small to vectorize anything.
// since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.
{
res = mat.coeff(0);
for(int index = 1; index < size; ++index)
res = func(res,mat.coeff(index));
}
return res;
}
};
template<typename Func, typename Derived>
struct ei_redux_impl<Func, Derived, SliceVectorizedTraversal, NoUnrolling>
{
typedef typename Derived::Scalar Scalar;
typedef typename ei_packet_traits<Scalar>::type PacketScalar;
static Scalar run(const Derived& mat, const Func& func)
{
const int innerSize = mat.innerSize();
const int outerSize = mat.outerSize();
enum {
packetSize = ei_packet_traits<Scalar>::size,
isRowMajor = Derived::Flags&RowMajorBit?1:0
};
const int packetedInnerSize = ((innerSize)/packetSize)*packetSize;
Scalar res;
if(packetedInnerSize)
{
PacketScalar packet_res = mat.template packet<Unaligned>(0,0);
for(int j=0; j<outerSize; ++j)
for(int i=0; i<packetedInnerSize; i+=int(packetSize))
packet_res = func.packetOp(packet_res, mat.template packet<Unaligned>
(isRowMajor?j:i, isRowMajor?i:j));
res = func.predux(packet_res);
for(int j=0; j<outerSize; ++j)
for(int i=packetedInnerSize; i<innerSize; ++i)
res = func(res, mat.coeff(isRowMajor?j:i, isRowMajor?i:j));
}
else // too small to vectorize anything.
// since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.
{
res = ei_redux_impl<Func, Derived, DefaultTraversal, NoUnrolling>::run(mat, func);
}
return res;
}
};
template<typename Func, typename Derived>
struct ei_redux_impl<Func, Derived, LinearVectorizedTraversal, CompleteUnrolling>
{
typedef typename Derived::Scalar Scalar;
typedef typename ei_packet_traits<Scalar>::type PacketScalar;
enum {
PacketSize = ei_packet_traits<Scalar>::size,
Size = Derived::SizeAtCompileTime,
VectorizedSize = (Size / PacketSize) * PacketSize
};
EIGEN_STRONG_INLINE static Scalar run(const Derived& mat, const Func& func)
{
Scalar res = func.predux(ei_redux_vec_unroller<Func, Derived, 0, Size / PacketSize>::run(mat,func));
if (VectorizedSize != Size)
res = func(res,ei_redux_novec_unroller<Func, Derived, VectorizedSize, Size-VectorizedSize>::run(mat,func));
return res;
}
};
/** \returns the result of a full redux operation on the whole matrix or vector using \a func
*
* The template parameter \a BinaryOp is the type of the functor \a func which must be
* an associative operator. Both current STL and TR1 functor styles are handled.
*
* \sa MatrixBase::sum(), MatrixBase::minCoeff(), MatrixBase::maxCoeff(), MatrixBase::colwise(), MatrixBase::rowwise()
*/
template<typename Derived>
template<typename Func>
inline typename ei_result_of<Func(typename ei_traits<Derived>::Scalar)>::type
MatrixBase<Derived>::redux(const Func& func) const
{
typename Derived::Nested nested(derived());
typedef typename ei_cleantype<typename Derived::Nested>::type ThisNested;
return ei_redux_impl<Func, ThisNested>
::run(nested, func);
}
/** \returns the minimum of all coefficients of *this
*/
template<typename Derived>
EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar
MatrixBase<Derived>::minCoeff() const
{
return this->redux(Eigen::ei_scalar_min_op<Scalar>());
}
/** \returns the maximum of all coefficients of *this
*/
template<typename Derived>
EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar
MatrixBase<Derived>::maxCoeff() const
{
return this->redux(Eigen::ei_scalar_max_op<Scalar>());
}
/** \returns the sum of all coefficients of *this
*
* \sa trace(), prod(), mean()
*/
template<typename Derived>
EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar
MatrixBase<Derived>::sum() const
{
return this->redux(Eigen::ei_scalar_sum_op<Scalar>());
}
/** \returns the mean of all coefficients of *this
*
* \sa trace(), prod(), sum()
*/
template<typename Derived>
EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar
MatrixBase<Derived>::mean() const
{
return this->redux(Eigen::ei_scalar_sum_op<Scalar>()) / this->size();
}
/** \returns the product of all coefficients of *this
*
* Example: \include MatrixBase_prod.cpp
* Output: \verbinclude MatrixBase_prod.out
*
* \sa sum(), mean(), trace()
*/
template<typename Derived>
EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar
MatrixBase<Derived>::prod() const
{
return this->redux(Eigen::ei_scalar_product_op<Scalar>());
}
/** \returns the trace of \c *this, i.e. the sum of the coefficients on the main diagonal.
*
* \c *this can be any matrix, not necessarily square.
*
* \sa diagonal(), sum()
*/
template<typename Derived>
EIGEN_STRONG_INLINE typename ei_traits<Derived>::Scalar
MatrixBase<Derived>::trace() const
{
return diagonal().sum();
}
#endif // EIGEN_REDUX_H
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