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lammps/lib/smd/Eigen/src/Core/Redux.h
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Redux.h
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.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_REDUX_H
#define EIGEN_REDUX_H
namespace Eigen {
namespace internal {
// 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 redux_traits
{
public:
enum {
PacketSize = packet_traits<typename Derived::Scalar>::size,
InnerMaxSize = int(Derived::IsRowMajor)
? Derived::MaxColsAtCompileTime
: Derived::MaxRowsAtCompileTime
};
enum {
MightVectorize = (int(Derived::Flags)&ActualPacketAccessBit)
&& (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)
};
public:
enum {
Cost = ( Derived::SizeAtCompileTime == Dynamic
|| Derived::CoeffReadCost == Dynamic
|| (Derived::SizeAtCompileTime!=1 && functor_traits<Func>::Cost == Dynamic)
) ? Dynamic
: Derived::SizeAtCompileTime * Derived::CoeffReadCost
+ (Derived::SizeAtCompileTime-1) * functor_traits<Func>::Cost,
UnrollingLimit = EIGEN_UNROLLING_LIMIT * (int(Traversal) == int(DefaultTraversal) ? 1 : int(PacketSize))
};
public:
enum {
Unrolling = Cost != Dynamic && Cost <= UnrollingLimit
? CompleteUnrolling
: NoUnrolling
};
};
/***************************************************************************
* Part 2 : unrollers
***************************************************************************/
/*** no vectorization ***/
template<typename Func, typename Derived, int Start, int Length>
struct redux_novec_unroller
{
enum {
HalfLength = Length/2
};
typedef typename Derived::Scalar Scalar;
static EIGEN_STRONG_INLINE Scalar run(const Derived &mat, const Func& func)
{
return func(redux_novec_unroller<Func, Derived, Start, HalfLength>::run(mat,func),
redux_novec_unroller<Func, Derived, Start+HalfLength, Length-HalfLength>::run(mat,func));
}
};
template<typename Func, typename Derived, int Start>
struct redux_novec_unroller<Func, Derived, Start, 1>
{
enum {
outer = Start / Derived::InnerSizeAtCompileTime,
inner = Start % Derived::InnerSizeAtCompileTime
};
typedef typename Derived::Scalar Scalar;
static EIGEN_STRONG_INLINE Scalar run(const Derived &mat, const Func&)
{
return mat.coeffByOuterInner(outer, inner);
}
};
// 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 redux_novec_unroller<Func, Derived, Start, 0>
{
typedef typename Derived::Scalar Scalar;
static EIGEN_STRONG_INLINE Scalar run(const Derived&, const Func&) { return Scalar(); }
};
/*** vectorization ***/
template<typename Func, typename Derived, int Start, int Length>
struct redux_vec_unroller
{
enum {
PacketSize = packet_traits<typename Derived::Scalar>::size,
HalfLength = Length/2
};
typedef typename Derived::Scalar Scalar;
typedef typename packet_traits<Scalar>::type PacketScalar;
static EIGEN_STRONG_INLINE PacketScalar run(const Derived &mat, const Func& func)
{
return func.packetOp(
redux_vec_unroller<Func, Derived, Start, HalfLength>::run(mat,func),
redux_vec_unroller<Func, Derived, Start+HalfLength, Length-HalfLength>::run(mat,func) );
}
};
template<typename Func, typename Derived, int Start>
struct redux_vec_unroller<Func, Derived, Start, 1>
{
enum {
index = Start * packet_traits<typename Derived::Scalar>::size,
outer = index / int(Derived::InnerSizeAtCompileTime),
inner = index % int(Derived::InnerSizeAtCompileTime),
alignment = (Derived::Flags & AlignedBit) ? Aligned : Unaligned
};
typedef typename Derived::Scalar Scalar;
typedef typename packet_traits<Scalar>::type PacketScalar;
static EIGEN_STRONG_INLINE PacketScalar run(const Derived &mat, const Func&)
{
return mat.template packetByOuterInner<alignment>(outer, inner);
}
};
/***************************************************************************
* Part 3 : implementation of all cases
***************************************************************************/
template<typename Func, typename Derived,
int Traversal = redux_traits<Func, Derived>::Traversal,
int Unrolling = redux_traits<Func, Derived>::Unrolling
>
struct redux_impl;
template<typename Func, typename Derived>
struct redux_impl<Func, Derived, DefaultTraversal, NoUnrolling>
{
typedef typename Derived::Scalar Scalar;
typedef typename Derived::Index Index;
static EIGEN_STRONG_INLINE Scalar run(const Derived& mat, const Func& func)
{
eigen_assert(mat.rows()>0 && mat.cols()>0 && "you are using an empty matrix");
Scalar res;
res = mat.coeffByOuterInner(0, 0);
for(Index i = 1; i < mat.innerSize(); ++i)
res = func(res, mat.coeffByOuterInner(0, i));
for(Index i = 1; i < mat.outerSize(); ++i)
for(Index j = 0; j < mat.innerSize(); ++j)
res = func(res, mat.coeffByOuterInner(i, j));
return res;
}
};
template<typename Func, typename Derived>
struct redux_impl<Func,Derived, DefaultTraversal, CompleteUnrolling>
: public redux_novec_unroller<Func,Derived, 0, Derived::SizeAtCompileTime>
{};
template<typename Func, typename Derived>
struct redux_impl<Func, Derived, LinearVectorizedTraversal, NoUnrolling>
{
typedef typename Derived::Scalar Scalar;
typedef typename packet_traits<Scalar>::type PacketScalar;
typedef typename Derived::Index Index;
static Scalar run(const Derived& mat, const Func& func)
{
const Index size = mat.size();
eigen_assert(size && "you are using an empty matrix");
const Index packetSize = packet_traits<Scalar>::size;
const Index alignedStart = internal::first_aligned(mat);
enum {
alignment = bool(Derived::Flags & DirectAccessBit) || bool(Derived::Flags & AlignedBit)
? Aligned : Unaligned
};
const Index alignedSize2 = ((size-alignedStart)/(2*packetSize))*(2*packetSize);
const Index alignedSize = ((size-alignedStart)/(packetSize))*(packetSize);
const Index alignedEnd2 = alignedStart + alignedSize2;
const Index alignedEnd = alignedStart + alignedSize;
Scalar res;
if(alignedSize)
{
PacketScalar packet_res0 = mat.template packet<alignment>(alignedStart);
if(alignedSize>packetSize) // we have at least two packets to partly unroll the loop
{
PacketScalar packet_res1 = mat.template packet<alignment>(alignedStart+packetSize);
for(Index index = alignedStart + 2*packetSize; index < alignedEnd2; index += 2*packetSize)
{
packet_res0 = func.packetOp(packet_res0, mat.template packet<alignment>(index));
packet_res1 = func.packetOp(packet_res1, mat.template packet<alignment>(index+packetSize));
}
packet_res0 = func.packetOp(packet_res0,packet_res1);
if(alignedEnd>alignedEnd2)
packet_res0 = func.packetOp(packet_res0, mat.template packet<alignment>(alignedEnd2));
}
res = func.predux(packet_res0);
for(Index index = 0; index < alignedStart; ++index)
res = func(res,mat.coeff(index));
for(Index 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(Index index = 1; index < size; ++index)
res = func(res,mat.coeff(index));
}
return res;
}
};
// NOTE: for SliceVectorizedTraversal we simply bypass unrolling
template<typename Func, typename Derived, int Unrolling>
struct redux_impl<Func, Derived, SliceVectorizedTraversal, Unrolling>
{
typedef typename Derived::Scalar Scalar;
typedef typename packet_traits<Scalar>::type PacketScalar;
typedef typename Derived::Index Index;
static Scalar run(const Derived& mat, const Func& func)
{
eigen_assert(mat.rows()>0 && mat.cols()>0 && "you are using an empty matrix");
const Index innerSize = mat.innerSize();
const Index outerSize = mat.outerSize();
enum {
packetSize = packet_traits<Scalar>::size
};
const Index packetedInnerSize = ((innerSize)/packetSize)*packetSize;
Scalar res;
if(packetedInnerSize)
{
PacketScalar packet_res = mat.template packet<Unaligned>(0,0);
for(Index j=0; j<outerSize; ++j)
for(Index i=(j==0?packetSize:0); i<packetedInnerSize; i+=Index(packetSize))
packet_res = func.packetOp(packet_res, mat.template packetByOuterInner<Unaligned>(j,i));
res = func.predux(packet_res);
for(Index j=0; j<outerSize; ++j)
for(Index i=packetedInnerSize; i<innerSize; ++i)
res = func(res, mat.coeffByOuterInner(j,i));
}
else // too small to vectorize anything.
// since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.
{
res = redux_impl<Func, Derived, DefaultTraversal, NoUnrolling>::run(mat, func);
}
return res;
}
};
template<typename Func, typename Derived>
struct redux_impl<Func, Derived, LinearVectorizedTraversal, CompleteUnrolling>
{
typedef typename Derived::Scalar Scalar;
typedef typename packet_traits<Scalar>::type PacketScalar;
enum {
PacketSize = packet_traits<Scalar>::size,
Size = Derived::SizeAtCompileTime,
VectorizedSize = (Size / PacketSize) * PacketSize
};
static EIGEN_STRONG_INLINE Scalar run(const Derived& mat, const Func& func)
{
eigen_assert(mat.rows()>0 && mat.cols()>0 && "you are using an empty matrix");
Scalar res = func.predux(redux_vec_unroller<Func, Derived, 0, Size / PacketSize>::run(mat,func));
if (VectorizedSize != Size)
res = func(res,redux_novec_unroller<Func, Derived, VectorizedSize, Size-VectorizedSize>::run(mat,func));
return res;
}
};
} // end namespace internal
/***************************************************************************
* Part 4 : public API
***************************************************************************/
/** \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 DenseBase::sum(), DenseBase::minCoeff(), DenseBase::maxCoeff(), MatrixBase::colwise(), MatrixBase::rowwise()
*/
template<typename Derived>
template<typename Func>
EIGEN_STRONG_INLINE typename internal::result_of<Func(typename internal::traits<Derived>::Scalar)>::type
DenseBase<Derived>::redux(const Func& func) const
{
typedef typename internal::remove_all<typename Derived::Nested>::type ThisNested;
return internal::redux_impl<Func, ThisNested>
::run(derived(), func);
}
/** \returns the minimum of all coefficients of \c *this.
* \warning the result is undefined if \c *this contains NaN.
*/
template<typename Derived>
EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
DenseBase<Derived>::minCoeff() const
{
return this->redux(Eigen::internal::scalar_min_op<Scalar>());
}
/** \returns the maximum of all coefficients of \c *this.
* \warning the result is undefined if \c *this contains NaN.
*/
template<typename Derived>
EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
DenseBase<Derived>::maxCoeff() const
{
return this->redux(Eigen::internal::scalar_max_op<Scalar>());
}
/** \returns the sum of all coefficients of *this
*
* \sa trace(), prod(), mean()
*/
template<typename Derived>
EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
DenseBase<Derived>::sum() const
{
if(SizeAtCompileTime==0 || (SizeAtCompileTime==Dynamic && size()==0))
return Scalar(0);
return this->redux(Eigen::internal::scalar_sum_op<Scalar>());
}
/** \returns the mean of all coefficients of *this
*
* \sa trace(), prod(), sum()
*/
template<typename Derived>
EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
DenseBase<Derived>::mean() const
{
return Scalar(this->redux(Eigen::internal::scalar_sum_op<Scalar>())) / 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 internal::traits<Derived>::Scalar
DenseBase<Derived>::prod() const
{
if(SizeAtCompileTime==0 || (SizeAtCompileTime==Dynamic && size()==0))
return Scalar(1);
return this->redux(Eigen::internal::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 internal::traits<Derived>::Scalar
MatrixBase<Derived>::trace() const
{
return derived().diagonal().sum();
}
} // end namespace Eigen
#endif // EIGEN_REDUX_H
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