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GEMM: catch all scalar-multiple variants when falling-back to a coeff-based product.

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Before only s*A*B was caught which was both inconsistent with GEMM, sub-optimal,
and could even lead to compilation-errors (https://stackoverflow.com/questions/54738495).
This commit is contained in:
Gael Guennebaud 2019-02-18 11:47:54 +01:00
parent ec032ac03b
commit 512b74aaa1
3 changed files with 92 additions and 23 deletions
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63
Eigen/src/Core/ProductEvaluators.h
View File

@ -411,35 +411,56 @@ struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,CoeffBasedProductMode>
call_assignment_no_alias(dst, lhs.lazyProduct(rhs), internal::sub_assign_op<typename Dst::Scalar,Scalar>());
}
// Catch "dst {,+,-}= (s*A)*B" and evaluate it lazily by moving out the scalar factor:
// dst {,+,-}= s * (A.lazyProduct(B))
// This is a huge benefit for heap-allocated matrix types as it save one costly allocation.
// For them, this strategy is also faster than simply by-passing the heap allocation through
// stack allocation.
// For fixed sizes matrices, this is less obvious, it is sometimes x2 faster, but sometimes x3 slower,
// and the behavior depends also a lot on the compiler... so let's be conservative and enable them for dynamic-size only,
// that is when coming from generic_product_impl<...,GemmProduct> in file GeneralMatrixMatrix.h
template<typename Dst, typename Scalar1, typename Scalar2, typename Plain1, typename Xpr2, typename Func>
// This is a special evaluation path called from generic_product_impl<...,GemmProduct> in file GeneralMatrixMatrix.h
// This variant tries to extract scalar multiples from both the LHS and RHS and factor them out. For instance:
// dst {,+,-}= (s1*A)*(B*s2)
// will be rewritten as:
// dst {,+,-}= (s1*s2) * (A.lazyProduct(B))
// There are at least four benefits of doing so:
// 1 - huge performance gain for heap-allocated matrix types as it save costly allocations.
// 2 - it is faster than simply by-passing the heap allocation through stack allocation.
// 3 - it makes this fallback consistent with the heavy GEMM routine.
// 4 - it fully by-passes huge stack allocation attempts when multiplying huge fixed-size matrices.
// (see https://stackoverflow.com/questions/54738495)
// For small fixed sizes matrices, howver, the gains are less obvious, it is sometimes x2 faster, but sometimes x3 slower,
// and the behavior depends also a lot on the compiler... This is why this re-writting strategy is currently
// enabled only when falling back from the main GEMM.
template<typename Dst, typename Func>
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
void eval_dynamic(Dst& dst, const CwiseBinaryOp<internal::scalar_product_op<Scalar1,Scalar2>,
const CwiseNullaryOp<internal::scalar_constant_op<Scalar1>, Plain1>, Xpr2>& lhs, const Rhs& rhs, const Func &func)
void eval_dynamic(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Func &func)
{
call_restricted_packet_assignment_no_alias(dst, lhs.lhs().functor().m_other * lhs.rhs().lazyProduct(rhs), func);
enum {
HasScalarFactor = blas_traits<Lhs>::HasScalarFactor || blas_traits<Rhs>::HasScalarFactor
};
// FIXME: in c++11 this should be auto, and extractScalarFactor should also return auto
// this is important for real*complex_mat
Scalar actualAlpha = blas_traits<Lhs>::extractScalarFactor(lhs)
* blas_traits<Rhs>::extractScalarFactor(rhs);
eval_dynamic_impl(dst,
blas_traits<Lhs>::extract(lhs),
blas_traits<Rhs>::extract(rhs),
func,
actualAlpha,
typename conditional<HasScalarFactor,true_type,false_type>::type());
}
// Here, we we always have LhsT==Lhs, but we need to make it a template type to make the above
// overload more specialized.
template<typename Dst, typename LhsT, typename Func>
protected:
template<typename Dst, typename LhsT, typename RhsT, typename Func, typename Scalar>
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
void eval_dynamic(Dst& dst, const LhsT& lhs, const Rhs& rhs, const Func &func)
void eval_dynamic_impl(Dst& dst, const LhsT& lhs, const RhsT& rhs, const Func &func, const Scalar& /* s == 1 */, false_type)
{
call_restricted_packet_assignment_no_alias(dst, lhs.lazyProduct(rhs), func);
}
// template<typename Dst>
// static inline void scaleAndAddTo(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
// { dst.noalias() += alpha * lhs.lazyProduct(rhs); }
template<typename Dst, typename LhsT, typename RhsT, typename Func, typename Scalar>
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
void eval_dynamic_impl(Dst& dst, const LhsT& lhs, const RhsT& rhs, const Func &func, const Scalar& s, true_type)
{
call_restricted_packet_assignment_no_alias(dst, s * lhs.lazyProduct(rhs), func);
}
};
// This specialization enforces the use of a coefficient-based evaluation strategy

14
Eigen/src/Core/util/BlasUtil.h
View File

@ -274,7 +274,8 @@ template<typename XprType> struct blas_traits
HasUsableDirectAccess = ( (int(XprType::Flags)&DirectAccessBit)
&& ( bool(XprType::IsVectorAtCompileTime)
|| int(inner_stride_at_compile_time<XprType>::ret) == 1)
) ? 1 : 0
) ? 1 : 0,
HasScalarFactor = false
};
typedef typename conditional<bool(HasUsableDirectAccess),
ExtractType,
@ -306,6 +307,9 @@ template<typename Scalar, typename NestedXpr, typename Plain>
struct blas_traits<CwiseBinaryOp<scalar_product_op<Scalar>, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain>, NestedXpr> >
: blas_traits<NestedXpr>
{
enum {
HasScalarFactor = true
};
typedef blas_traits<NestedXpr> Base;
typedef CwiseBinaryOp<scalar_product_op<Scalar>, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain>, NestedXpr> XprType;
typedef typename Base::ExtractType ExtractType;
@ -317,6 +321,9 @@ template<typename Scalar, typename NestedXpr, typename Plain>
struct blas_traits<CwiseBinaryOp<scalar_product_op<Scalar>, NestedXpr, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain> > >
: blas_traits<NestedXpr>
{
enum {
HasScalarFactor = true
};
typedef blas_traits<NestedXpr> Base;
typedef CwiseBinaryOp<scalar_product_op<Scalar>, NestedXpr, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain> > XprType;
typedef typename Base::ExtractType ExtractType;
@ -335,6 +342,9 @@ template<typename Scalar, typename NestedXpr>
struct blas_traits<CwiseUnaryOp<scalar_opposite_op<Scalar>, NestedXpr> >
: blas_traits<NestedXpr>
{
enum {
HasScalarFactor = true
};
typedef blas_traits<NestedXpr> Base;
typedef CwiseUnaryOp<scalar_opposite_op<Scalar>, NestedXpr> XprType;
typedef typename Base::ExtractType ExtractType;
@ -358,7 +368,7 @@ struct blas_traits<Transpose<NestedXpr> >
typename ExtractType::PlainObject
>::type DirectLinearAccessType;
enum {
IsTransposed = Base::IsTransposed ? 0 : 1
IsTransposed = Base::IsTransposed ? 0 : 1,
};
static inline ExtractType extract(const XprType& x) { return ExtractType(Base::extract(x.nestedExpression())); }
static inline Scalar extractScalarFactor(const XprType& x) { return Base::extractScalarFactor(x.nestedExpression()); }

38
test/product_notemporary.cpp
View File

@ -11,6 +11,35 @@
#include "main.h"
template<typename Dst, typename Lhs, typename Rhs>
void check_scalar_multiple3(Dst &dst, const Lhs& A, const Rhs& B)
{
VERIFY_EVALUATION_COUNT( (dst.noalias() = A * B), 0);
VERIFY_IS_APPROX( dst, (A.eval() * B.eval()).eval() );
VERIFY_EVALUATION_COUNT( (dst.noalias() += A * B), 0);
VERIFY_IS_APPROX( dst, 2*(A.eval() * B.eval()).eval() );
VERIFY_EVALUATION_COUNT( (dst.noalias() -= A * B), 0);
VERIFY_IS_APPROX( dst, (A.eval() * B.eval()).eval() );
}
template<typename Dst, typename Lhs, typename Rhs, typename S2>
void check_scalar_multiple2(Dst &dst, const Lhs& A, const Rhs& B, S2 s2)
{
CALL_SUBTEST( check_scalar_multiple3(dst, A, B) );
CALL_SUBTEST( check_scalar_multiple3(dst, A, -B) );
CALL_SUBTEST( check_scalar_multiple3(dst, A, s2*B) );
CALL_SUBTEST( check_scalar_multiple3(dst, A, B*s2) );
}
template<typename Dst, typename Lhs, typename Rhs, typename S1, typename S2>
void check_scalar_multiple1(Dst &dst, const Lhs& A, const Rhs& B, S1 s1, S2 s2)
{
CALL_SUBTEST( check_scalar_multiple2(dst, A, B, s2) );
CALL_SUBTEST( check_scalar_multiple2(dst, -A, B, s2) );
CALL_SUBTEST( check_scalar_multiple2(dst, s1*A, B, s2) );
CALL_SUBTEST( check_scalar_multiple2(dst, A*s1, B, s2) );
}
template<typename MatrixType> void product_notemporary(const MatrixType& m)
{
/* This test checks the number of temporaries created
@ -148,6 +177,15 @@ template<typename MatrixType> void product_notemporary(const MatrixType& m)
// Check nested products
VERIFY_EVALUATION_COUNT( cvres.noalias() = m1.adjoint() * m1 * cv1, 1 );
VERIFY_EVALUATION_COUNT( rvres.noalias() = rv1 * (m1 * m2.adjoint()), 1 );
// exhaustively check all scalar multiple combinations:
{
// Generic path:
check_scalar_multiple1(m3, m1, m2, s1, s2);
// Force fall back to coeff-based:
typename ColMajorMatrixType::BlockXpr m3_blck = m3.block(r0,r0,1,1);
check_scalar_multiple1(m3_blck, m1.block(r0,c0,1,1), m2.block(c0,r0,1,1), s1, s2);
}
}
EIGEN_DECLARE_TEST(product_notemporary)