35#ifndef _BLAZE_MATH_EXPRESSIONS_TSMATTDMATMULTEXPR_H_
36#define _BLAZE_MATH_EXPRESSIONS_TSMATTDMATMULTEXPR_H_
122template<
typename MT1
129 :
public MatMatMultExpr< DenseMatrix< TSMatTDMatMultExpr<MT1,MT2,SF,HF,LF,UF>, true > >
144 static constexpr bool evaluateLeft = ( IsComputation_v<MT1> || RequiresEvaluation_v<MT1> );
149 static constexpr bool evaluateRight = ( IsComputation_v<MT2> || RequiresEvaluation_v<MT2> );
153 static constexpr bool SYM = ( SF && !( HF || LF || UF ) );
154 static constexpr bool HERM = ( HF && !( LF || UF ) );
155 static constexpr bool LOW = ( LF || ( ( SF || HF ) && UF ) );
156 static constexpr bool UPP = ( UF || ( ( SF || HF ) && LF ) );
166 template<
typename T1,
typename T2,
typename T3 >
167 static constexpr bool CanExploitSymmetry_v = ( IsSymmetric_v<T2> || IsSymmetric_v<T3> );
177 template<
typename T1,
typename T2,
typename T3 >
178 static constexpr bool IsEvaluationRequired_v =
188 template<
typename T1,
typename T2,
typename T3 >
189 static constexpr bool UseOptimizedKernel_v =
190 ( useOptimizedKernels &&
192 !IsResizable_v< ElementType_t<T1> > &&
193 !IsResizable_v<ET1> );
202 template<
typename T1,
typename T2,
typename T3 >
203 static constexpr bool UseDefaultKernel_v = !UseOptimizedKernel_v<T1,T2,T3>;
300 if( IsDiagonal_v<MT1> ) {
303 else if( IsDiagonal_v<MT2> ) {
306 else if( IsTriangular_v<MT1> || IsTriangular_v<MT2> ) {
307 const size_t begin( ( IsUpper_v<MT1> )
308 ?( ( IsLower_v<MT2> )
309 ?(
max( ( IsStrictlyUpper_v<MT1> ? i+1UL : i )
310 , ( IsStrictlyLower_v<MT2> ? j+1UL : j ) ) )
311 :( IsStrictlyUpper_v<MT1> ? i+1UL : i ) )
312 :( ( IsLower_v<MT2> )
313 ?( IsStrictlyLower_v<MT2> ? j+1UL : j )
315 const size_t end( ( IsLower_v<MT1> )
316 ?( ( IsUpper_v<MT2> )
317 ?(
min( ( IsStrictlyLower_v<MT1> ? i : i+1UL )
318 , ( IsStrictlyUpper_v<MT2> ? j : j+1UL ) ) )
319 :( IsStrictlyLower_v<MT1> ? i : i+1UL ) )
320 :( ( IsUpper_v<MT2> )
321 ?( IsStrictlyUpper_v<MT2> ? j : j+1UL )
322 :(
lhs_.columns() ) ) );
346 if( i >=
lhs_.rows() ) {
349 if( j >=
rhs_.columns() ) {
361 inline size_t rows() const noexcept {
372 return rhs_.columns();
402 template<
typename T >
403 inline bool canAlias(
const T* alias )
const noexcept {
404 return (
lhs_.isAliased( alias ) ||
rhs_.isAliased( alias ) );
414 template<
typename T >
415 inline bool isAliased(
const T* alias )
const noexcept {
416 return (
lhs_.isAliased( alias ) ||
rhs_.isAliased( alias ) );
426 return rhs_.isAligned();
436 return (
rows() *
columns() >= SMP_TSMATTDMATMULT_THRESHOLD ) && !IsDiagonal_v<MT2>;
459 template<
typename MT
479 TSMatTDMatMultExpr::selectAssignKernel( *lhs, A, B );
495 template<
typename MT3
498 static inline void selectAssignKernel( MT3& C,
const MT4& A,
const MT5& B )
500 const size_t size( C.rows() * C.columns() );
502 if( ( IsRowMajorMatrix_v<MT3> &&
size < TSMATTDMATMULT_THRESHOLD ) ||
503 ( IsColumnMajorMatrix_v<MT3> &&
size < 625UL ) )
504 selectSmallAssignKernel( C, A, B );
506 selectLargeAssignKernel( C, A, B );
526 template<
typename MT3
529 static inline void selectDefaultAssignKernel( MT3& C,
const MT4& A,
const MT5& B )
533 if( IsDiagonal_v<MT5> )
535 for(
size_t i=0UL; i<A.columns(); ++i )
537 const auto end( A.end(i) );
538 auto element( A.begin(i) );
540 for( ; element!=
end; ++element ) {
541 C(element->index(),i) = element->value() * B(i,i);
547 const size_t block( 64UL );
549 for(
size_t jj=0UL; jj<B.columns(); jj+=block )
551 const size_t jpos( ( jj+block > B.columns() )?( B.columns() ):( jj+block ) );
553 for(
size_t i=0UL; i<A.columns(); ++i )
555 const auto end( A.end(i) );
556 auto element( A.begin(i) );
558 for( ; element!=
end; ++element )
560 const size_t i1( element->index() );
562 const size_t jbegin( ( IsUpper_v<MT5> )
564 ?(
max( i1, IsStrictlyUpper_v<MT5> ? i+1UL : i, jj ) )
565 :(
max( IsStrictlyUpper_v<MT5> ? i+1UL : i, jj ) ) )
567 const size_t jend( ( IsLower_v<MT5> )
569 ?(
min( i1+1UL, IsStrictlyLower_v<MT5> ? i : i+1UL, jpos ) )
570 :(
min( IsStrictlyLower_v<MT5> ? i : i+1UL, jpos ) ) )
571 :(
LOW ?
min(i1+1UL,jpos) : jpos ) );
576 for(
size_t j=jbegin; j<jend; ++j ) {
578 C(i1,j) = element->value() * B(i,j);
580 C(i1,j) += element->value() * B(i,j);
588 for(
size_t j=0UL; j<B.columns(); ++j ) {
589 for(
size_t i=j+1UL; i<A.rows(); ++i ) {
590 C(i,j) =
HERM ?
conj( C(j,i) ) : C(j,i);
612 template<
typename MT3
615 static inline auto selectSmallAssignKernel( MT3& C,
const MT4& A,
const MT5& B )
616 -> EnableIf_t< UseDefaultKernel_v<MT3,MT4,MT5> >
618 selectDefaultAssignKernel( C, A, B );
638 template<
typename MT3
641 static inline auto selectSmallAssignKernel( MT3& C,
const MT4& A,
const MT5& B )
642 -> EnableIf_t< UseOptimizedKernel_v<MT3,MT4,MT5> >
644 const size_t block( IsRowMajorMatrix_v<MT3> ? 128UL : 64UL );
646 for(
size_t jj=0UL; jj<B.columns(); jj+=block )
648 const size_t jpos( ( jj+block > B.columns() )?( B.columns() ):( jj+block ) );
650 for(
size_t i=0UL; i<A.rows(); ++i ) {
651 for(
size_t j=jj; j<jpos; ++j ) {
656 for(
size_t i=0UL; i<A.columns(); ++i )
658 const auto end( A.end(i) );
659 auto element( A.begin(i) );
661 const size_t nonzeros( A.nonZeros(i) );
665 for(
size_t k=0UL; k<kpos; k+=4UL )
667 const size_t i1( element->index() );
668 const ET1 v1( element->value() );
670 const size_t i2( element->index() );
671 const ET1 v2( element->value() );
673 const size_t i3( element->index() );
674 const ET1 v3( element->value() );
676 const size_t i4( element->index() );
677 const ET1 v4( element->value() );
682 const size_t jbegin( ( IsUpper_v<MT5> )
684 ?(
max( i1, IsStrictlyUpper_v<MT5> ? i+1UL : i, jj ) )
685 :(
max( IsStrictlyUpper_v<MT5> ? i+1UL : i, jj ) ) )
687 const size_t jend( ( IsLower_v<MT5> )
689 ?(
min( i4+1UL, IsStrictlyLower_v<MT5> ? i : i+1UL, jpos ) )
690 :(
min( IsStrictlyLower_v<MT5> ? i : i+1UL, jpos ) ) )
691 :(
LOW ?
min(i4+1UL,jpos) : jpos ) );
696 for(
size_t j=jbegin; j<jend; ++j ) {
697 C(i1,j) += v1 * B(i,j);
698 C(i2,j) += v2 * B(i,j);
699 C(i3,j) += v3 * B(i,j);
700 C(i4,j) += v4 * B(i,j);
704 for( ; element!=
end; ++element )
706 const size_t i1( element->index() );
708 const size_t jbegin( ( IsUpper_v<MT5> )
710 ?(
max( i1, IsStrictlyUpper_v<MT5> ? i+1UL : i, jj ) )
711 :(
max( IsStrictlyUpper_v<MT5> ? i+1UL : i, jj ) ) )
713 const size_t jend( ( IsLower_v<MT5> )
715 ?(
min( i1+1UL, IsStrictlyLower_v<MT5> ? i : i+1UL, jpos ) )
716 :(
min( IsStrictlyLower_v<MT5> ? i : i+1UL, jpos ) ) )
717 :(
LOW ?
min(i1+1UL,jpos) : jpos ) );
722 for(
size_t j=jbegin; j<jend; ++j ) {
723 C(i1,j) += element->value() * B(i,j);
730 for(
size_t j=0UL; j<B.columns(); ++j ) {
731 for(
size_t i=j+1UL; i<A.rows(); ++i ) {
732 C(i,j) =
HERM ?
conj( C(j,i) ) : C(j,i);
754 template<
typename MT3
757 static inline auto selectLargeAssignKernel( MT3& C,
const MT4& A,
const MT5& B )
758 -> EnableIf_t< UseDefaultKernel_v<MT3,MT4,MT5> >
760 selectDefaultAssignKernel( C, A, B );
780 template<
typename MT3
783 static inline auto selectLargeAssignKernel( MT3& C,
const MT4& A,
const MT5& B )
784 -> EnableIf_t< UseOptimizedKernel_v<MT3,MT4,MT5> >
788 const ForwardFunctor fwd;
790 const OppositeType_t<MT4> tmp(
serial( A ) );
791 assign( C, fwd( tmp * B ) );
809 template<
typename MT
812 -> DisableIf_t< CanExploitSymmetry_v<MT,MT1,MT2> >
816 using TmpType = If_t< SO, ResultType, OppositeType >;
828 const ForwardFunctor fwd;
830 const TmpType tmp(
serial( rhs ) );
831 assign( *lhs, fwd( tmp ) );
851 template<
typename MT
854 -> EnableIf_t< CanExploitSymmetry_v<MT,MT1,MT2> >
863 const ForwardFunctor fwd;
865 decltype(
auto) A(
transIf< IsSymmetric_v<MT1> >( rhs.lhs_ ) );
866 decltype(
auto) B(
transIf< IsSymmetric_v<MT2> >( rhs.rhs_ ) );
868 assign( *lhs, fwd( A * B ) );
886 template<
typename MT
888 friend inline auto addAssign( DenseMatrix<MT,SO>& lhs,
const TSMatTDMatMultExpr& rhs )
889 -> DisableIf_t< CanExploitSymmetry_v<MT,MT1,MT2> >
906 TSMatTDMatMultExpr::selectAddAssignKernel( *lhs, A, B );
922 template<
typename MT3
925 static inline void selectAddAssignKernel( MT3& C,
const MT4& A,
const MT5& B )
927 const size_t size( C.rows() * C.columns() );
929 if( ( IsRowMajorMatrix_v<MT3> &&
size < TSMATTDMATMULT_THRESHOLD ) ||
930 ( IsColumnMajorMatrix_v<MT3> &&
size < 625UL ) )
931 selectSmallAddAssignKernel( C, A, B );
933 selectLargeAddAssignKernel( C, A, B );
953 template<
typename MT3
956 static inline void selectDefaultAddAssignKernel( MT3& C,
const MT4& A,
const MT5& B )
958 if( IsDiagonal_v<MT5> )
960 for(
size_t i=0UL; i<A.columns(); ++i )
962 const auto end( A.end(i) );
963 auto element( A.begin(i) );
965 for( ; element!=
end; ++element ) {
966 C(element->index(),i) += element->value() * B(i,i);
972 const size_t block( 64UL );
974 for(
size_t jj=0UL; jj<B.columns(); jj+=block )
976 const size_t jpos( ( jj+block > B.columns() )?( B.columns() ):( jj+block ) );
978 for(
size_t i=0UL; i<A.columns(); ++i )
980 const auto end( A.end(i) );
981 auto element( A.begin(i) );
983 for( ; element!=
end; ++element )
985 const size_t i1( element->index() );
987 const size_t jbegin( ( IsUpper_v<MT5> )
989 ?(
max( i1, IsStrictlyUpper_v<MT5> ? i+1UL : i, jj ) )
990 :(
max( IsStrictlyUpper_v<MT5> ? i+1UL : i, jj ) ) )
991 :(
UPP ?
max(i1,jj) : jj ) );
992 const size_t jend( ( IsLower_v<MT5> )
994 ?(
min( i1+1UL, IsStrictlyLower_v<MT5> ? i : i+1UL, jpos ) )
995 :(
min( IsStrictlyLower_v<MT5> ? i : i+1UL, jpos ) ) )
996 :(
LOW ?
min(i1+1UL,jpos) : jpos ) );
1001 for(
size_t j=jbegin; j<jend; ++j ) {
1002 C(i1,j) += element->value() * B(i,j);
1026 template<
typename MT3
1029 static inline auto selectSmallAddAssignKernel( MT3& C,
const MT4& A,
const MT5& B )
1030 -> EnableIf_t< UseDefaultKernel_v<MT3,MT4,MT5> >
1032 selectDefaultAddAssignKernel( C, A, B );
1052 template<
typename MT3
1055 static inline auto selectSmallAddAssignKernel( MT3& C,
const MT4& A,
const MT5& B )
1056 -> EnableIf_t< UseOptimizedKernel_v<MT3,MT4,MT5> >
1058 const size_t block( IsRowMajorMatrix_v<MT3> ? 128UL : 64UL );
1060 for(
size_t jj=0UL; jj<B.columns(); jj+=block )
1062 const size_t jpos( ( jj+block > B.columns() )?( B.columns() ):( jj+block ) );
1064 for(
size_t i=0UL; i<A.columns(); ++i )
1066 const auto end( A.end(i) );
1067 auto element( A.begin(i) );
1069 const size_t nonzeros( A.nonZeros(i) );
1073 for(
size_t k=0UL; k<kpos; k+=4UL )
1075 const size_t i1( element->index() );
1076 const ET1 v1( element->value() );
1078 const size_t i2( element->index() );
1079 const ET1 v2( element->value() );
1081 const size_t i3( element->index() );
1082 const ET1 v3( element->value() );
1084 const size_t i4( element->index() );
1085 const ET1 v4( element->value() );
1090 const size_t jbegin( ( IsUpper_v<MT5> )
1092 ?(
max( i1, IsStrictlyUpper_v<MT5> ? i+1UL : i, jj ) )
1093 :(
max( IsStrictlyUpper_v<MT5> ? i+1UL : i, jj ) ) )
1094 :(
UPP ?
max(i1,jj) : jj ) );
1095 const size_t jend( ( IsLower_v<MT5> )
1097 ?(
min( i4+1UL, IsStrictlyLower_v<MT5> ? i : i+1UL, jpos ) )
1098 :(
min( IsStrictlyLower_v<MT5> ? i : i+1UL, jpos ) ) )
1099 :(
LOW ?
min(i4+1UL,jpos) : jpos ) );
1101 if( jbegin >= jend )
1104 for(
size_t j=jbegin; j<jend; ++j ) {
1105 C(i1,j) += v1 * B(i,j);
1106 C(i2,j) += v2 * B(i,j);
1107 C(i3,j) += v3 * B(i,j);
1108 C(i4,j) += v4 * B(i,j);
1112 for( ; element!=
end; ++element )
1114 const size_t i1( element->index() );
1116 const size_t jbegin( ( IsUpper_v<MT5> )
1118 ?(
max( i1, IsStrictlyUpper_v<MT5> ? i+1UL : i, jj ) )
1119 :(
max( IsStrictlyUpper_v<MT5> ? i+1UL : i, jj ) ) )
1120 :(
UPP ?
max(i1,jj) : jj ) );
1121 const size_t jend( ( IsLower_v<MT5> )
1123 ?(
min( i1+1UL, IsStrictlyLower_v<MT5> ? i : i+1UL, jpos ) )
1124 :(
min( IsStrictlyLower_v<MT5> ? i : i+1UL, jpos ) ) )
1125 :(
LOW ?
min(i1+1UL,jpos) : jpos ) );
1127 if( jbegin >= jend )
1130 for(
size_t j=jbegin; j<jend; ++j ) {
1131 C(i1,j) += element->value() * B(i,j);
1154 template<
typename MT3
1157 static inline auto selectLargeAddAssignKernel( MT3& C,
const MT4& A,
const MT5& B )
1158 -> EnableIf_t< UseDefaultKernel_v<MT3,MT4,MT5> >
1160 selectDefaultAddAssignKernel( C, A, B );
1180 template<
typename MT3
1183 static inline auto selectLargeAddAssignKernel( MT3& C,
const MT4& A,
const MT5& B )
1184 -> EnableIf_t< UseOptimizedKernel_v<MT3,MT4,MT5> >
1188 const ForwardFunctor fwd;
1190 const OppositeType_t<MT4> tmp(
serial( A ) );
1191 addAssign( C, fwd( tmp * B ) );
1211 template<
typename MT
1214 -> EnableIf_t< CanExploitSymmetry_v<MT,MT1,MT2> >
1223 const ForwardFunctor fwd;
1225 decltype(
auto) A(
transIf< IsSymmetric_v<MT1> >( rhs.lhs_ ) );
1226 decltype(
auto) B(
transIf< IsSymmetric_v<MT2> >( rhs.rhs_ ) );
1228 addAssign( *lhs, fwd( A * B ) );
1250 template<
typename MT
1252 friend inline auto subAssign( DenseMatrix<MT,SO>& lhs,
const TSMatTDMatMultExpr& rhs )
1253 -> DisableIf_t< CanExploitSymmetry_v<MT,MT1,MT2> >
1270 TSMatTDMatMultExpr::selectSubAssignKernel( *lhs, A, B );
1286 template<
typename MT3
1289 static inline void selectSubAssignKernel( MT3& C,
const MT4& A,
const MT5& B )
1291 const size_t size( C.rows() * C.columns() );
1293 if( ( IsRowMajorMatrix_v<MT3> &&
size < TSMATTDMATMULT_THRESHOLD ) ||
1294 ( IsColumnMajorMatrix_v<MT3> &&
size < 625UL ) )
1295 selectSmallSubAssignKernel( C, A, B );
1297 selectLargeSubAssignKernel( C, A, B );
1317 template<
typename MT3
1320 static inline void selectDefaultSubAssignKernel( MT3& C,
const MT4& A,
const MT5& B )
1322 if( IsDiagonal_v<MT5> )
1324 for(
size_t i=0UL; i<A.columns(); ++i )
1326 const auto end( A.end(i) );
1327 auto element( A.begin(i) );
1329 for( ; element!=
end; ++element ) {
1330 C(element->index(),i) -= element->value() * B(i,i);
1336 const size_t block( 64UL );
1338 for(
size_t jj=0UL; jj<B.columns(); jj+=block )
1340 const size_t jpos( ( jj+block > B.columns() )?( B.columns() ):( jj+block ) );
1342 for(
size_t i=0UL; i<A.columns(); ++i )
1344 const auto end( A.end(i) );
1345 auto element( A.begin(i) );
1347 for( ; element!=
end; ++element )
1349 const size_t i1( element->index() );
1351 const size_t jbegin( ( IsUpper_v<MT5> )
1353 ?(
max( i1, IsStrictlyUpper_v<MT5> ? i+1UL : i, jj ) )
1354 :(
max( IsStrictlyUpper_v<MT5> ? i+1UL : i, jj ) ) )
1355 :(
UPP ?
max(i1,jj) : jj ) );
1356 const size_t jend( ( IsLower_v<MT5> )
1358 ?(
min( i1+1UL, IsStrictlyLower_v<MT5> ? i : i+1UL, jpos ) )
1359 :(
min( IsStrictlyLower_v<MT5> ? i : i+1UL, jpos ) ) )
1360 :(
LOW ?
min(i1+1UL,jpos) : jpos ) );
1362 if( jbegin >= jend )
1365 for(
size_t j=jbegin; j<jend; ++j ) {
1366 C(i1,j) -= element->value() * B(i,j);
1390 template<
typename MT3
1393 static inline auto selectSmallSubAssignKernel( MT3& C,
const MT4& A,
const MT5& B )
1394 -> EnableIf_t< UseDefaultKernel_v<MT3,MT4,MT5> >
1396 selectDefaultSubAssignKernel( C, A, B );
1416 template<
typename MT3
1419 static inline auto selectSmallSubAssignKernel( MT3& C,
const MT4& A,
const MT5& B )
1420 -> EnableIf_t< UseOptimizedKernel_v<MT3,MT4,MT5> >
1422 const size_t block( IsRowMajorMatrix_v<MT3> ? 128UL : 64UL );
1424 for(
size_t jj=0UL; jj<B.columns(); jj+=block )
1426 const size_t jpos( ( jj+block > B.columns() )?( B.columns() ):( jj+block ) );
1428 for(
size_t i=0UL; i<A.columns(); ++i )
1430 const auto end( A.end(i) );
1431 auto element( A.begin(i) );
1433 const size_t nonzeros( A.nonZeros(i) );
1437 for(
size_t k=0UL; k<kpos; k+=4UL )
1439 const size_t i1( element->index() );
1440 const ET1 v1( element->value() );
1442 const size_t i2( element->index() );
1443 const ET1 v2( element->value() );
1445 const size_t i3( element->index() );
1446 const ET1 v3( element->value() );
1448 const size_t i4( element->index() );
1449 const ET1 v4( element->value() );
1454 const size_t jbegin( ( IsUpper_v<MT5> )
1456 ?(
max( i1, IsStrictlyUpper_v<MT5> ? i+1UL : i, jj ) )
1457 :(
max( IsStrictlyUpper_v<MT5> ? i+1UL : i, jj ) ) )
1458 :(
UPP ?
max(i1,jj) : jj ) );
1459 const size_t jend( ( IsLower_v<MT5> )
1461 ?(
min( i4+1UL, IsStrictlyLower_v<MT5> ? i : i+1UL, jpos ) )
1462 :(
min( IsStrictlyLower_v<MT5> ? i : i+1UL, jpos ) ) )
1463 :(
LOW ?
min(i4+1UL,jpos) : jpos ) );
1465 if( jbegin >= jend )
1468 for(
size_t j=jbegin; j<jend; ++j ) {
1469 C(i1,j) -= v1 * B(i,j);
1470 C(i2,j) -= v2 * B(i,j);
1471 C(i3,j) -= v3 * B(i,j);
1472 C(i4,j) -= v4 * B(i,j);
1476 for( ; element!=
end; ++element )
1478 const size_t i1( element->index() );
1480 const size_t jbegin( ( IsUpper_v<MT5> )
1482 ?(
max( i1, IsStrictlyUpper_v<MT5> ? i+1UL : i, jj ) )
1483 :(
max( IsStrictlyUpper_v<MT5> ? i+1UL : i, jj ) ) )
1484 :(
UPP ?
max(i1,jj) : jj ) );
1485 const size_t jend( ( IsLower_v<MT5> )
1487 ?(
min( i1+1UL, IsStrictlyLower_v<MT5> ? i : i+1UL, jpos ) )
1488 :(
min( IsStrictlyLower_v<MT5> ? i : i+1UL, jpos ) ) )
1489 :(
LOW ?
min(i1+1UL,jpos) : jpos ) );
1491 if( jbegin >= jend )
1494 for(
size_t j=jbegin; j<jend; ++j ) {
1495 C(i1,j) -= element->value() * B(i,j);
1518 template<
typename MT3
1521 static inline auto selectLargeSubAssignKernel( MT3& C,
const MT4& A,
const MT5& B )
1522 -> EnableIf_t< UseDefaultKernel_v<MT3,MT4,MT5> >
1524 selectDefaultSubAssignKernel( C, A, B );
1544 template<
typename MT3
1547 static inline auto selectLargeSubAssignKernel( MT3& C,
const MT4& A,
const MT5& B )
1548 -> EnableIf_t< UseOptimizedKernel_v<MT3,MT4,MT5> >
1552 const ForwardFunctor fwd;
1554 const OppositeType_t<MT4> tmp(
serial( A ) );
1555 subAssign( C, fwd( tmp * B ) );
1575 template<
typename MT
1578 -> EnableIf_t< CanExploitSymmetry_v<MT,MT1,MT2> >
1587 const ForwardFunctor fwd;
1589 decltype(
auto) A(
transIf< IsSymmetric_v<MT1> >( rhs.lhs_ ) );
1590 decltype(
auto) B(
transIf< IsSymmetric_v<MT2> >( rhs.rhs_ ) );
1592 subAssign( *lhs, fwd( A * B ) );
1614 template<
typename MT
1616 friend inline void schurAssign( DenseMatrix<MT,SO>& lhs,
const TSMatTDMatMultExpr& rhs )
1628 schurAssign( *lhs, tmp );
1661 template<
typename MT
1664 -> EnableIf_t< IsEvaluationRequired_v<MT,MT1,MT2> >
1702 template<
typename MT
1705 -> EnableIf_t< IsEvaluationRequired_v<MT,MT1,MT2> >
1709 using TmpType = If_t< SO, ResultType, OppositeType >;
1721 const ForwardFunctor fwd;
1723 const TmpType tmp( rhs );
1744 template<
typename MT
1747 -> EnableIf_t< CanExploitSymmetry_v<MT,MT1,MT2> >
1756 const ForwardFunctor fwd;
1758 decltype(
auto) A(
transIf< IsSymmetric_v<MT1> >( rhs.lhs_ ) );
1759 decltype(
auto) B(
transIf< IsSymmetric_v<MT2> >( rhs.rhs_ ) );
1782 template<
typename MT
1785 -> EnableIf_t< IsEvaluationRequired_v<MT,MT1,MT2> >
1822 template<
typename MT
1825 -> EnableIf_t< CanExploitSymmetry_v<MT,MT1,MT2> >
1834 const ForwardFunctor fwd;
1836 decltype(
auto) A(
transIf< IsSymmetric_v<MT1> >( rhs.lhs_ ) );
1837 decltype(
auto) B(
transIf< IsSymmetric_v<MT2> >( rhs.rhs_ ) );
1864 template<
typename MT
1867 -> EnableIf_t< IsEvaluationRequired_v<MT,MT1,MT2> >
1904 template<
typename MT
1907 -> EnableIf_t< CanExploitSymmetry_v<MT,MT1,MT2> >
1916 const ForwardFunctor fwd;
1918 decltype(
auto) A(
transIf< IsSymmetric_v<MT1> >( rhs.lhs_ ) );
1919 decltype(
auto) B(
transIf< IsSymmetric_v<MT2> >( rhs.rhs_ ) );
1943 template<
typename MT
2009template<
typename MT1
2012 IsSame_v< ElementType_t<MT1>, ElementType_t<MT2> > ) ||
2013 IsZero_v<MT1> >* =
nullptr >
2014inline const TSMatTDMatMultExpr<MT1,MT2,false,false,false,false>
2015 tsmattdmatmult(
const SparseMatrix<MT1,true>& lhs,
const DenseMatrix<MT2,true>& rhs )
2021 return TSMatTDMatMultExpr<MT1,MT2,false,false,false,false>( *lhs, *rhs );
2041template<
typename MT1
2043 , EnableIf_t< IsIdentity_v<MT1> &&
2044 IsSame_v< ElementType_t<MT1>, ElementType_t<MT2> > >* =
nullptr >
2046 tsmattdmatmult(
const SparseMatrix<MT1,true>& lhs,
const DenseMatrix<MT2,true>& rhs )
2073template<
typename MT1
2075 , EnableIf_t< IsZero_v<MT1> >* =
nullptr >
2076inline decltype(
auto)
2077 tsmattdmatmult(
const SparseMatrix<MT1,true>& lhs,
const DenseMatrix<MT2,true>& rhs )
2083 using ReturnType =
const MultTrait_t< ResultType_t<MT1>, ResultType_t<MT2> >;
2088 return ReturnType( (*lhs).rows(), (*rhs).columns() );
2123template<
typename MT1
2125inline decltype(
auto)
2130 if( (*lhs).columns() != (*rhs).rows() ) {
2134 return tsmattdmatmult( *lhs, *rhs );
2171template<
typename MT1
2177inline decltype(
auto)
declsym(
const TSMatTDMatMultExpr<MT1,MT2,SF,HF,LF,UF>& dm )
2185 using ReturnType =
const TSMatTDMatMultExpr<MT1,MT2,true,HF,LF,UF>;
2186 return ReturnType( dm.leftOperand(), dm.rightOperand() );
2216template<
typename MT1
2222inline decltype(
auto)
declherm(
const TSMatTDMatMultExpr<MT1,MT2,SF,HF,LF,UF>& dm )
2230 using ReturnType =
const TSMatTDMatMultExpr<MT1,MT2,SF,true,LF,UF>;
2231 return ReturnType( dm.leftOperand(), dm.rightOperand() );
2261template<
typename MT1
2267inline decltype(
auto)
decllow(
const TSMatTDMatMultExpr<MT1,MT2,SF,HF,LF,UF>& dm )
2275 using ReturnType =
const TSMatTDMatMultExpr<MT1,MT2,SF,HF,true,UF>;
2276 return ReturnType( dm.leftOperand(), dm.rightOperand() );
2306template<
typename MT1
2311inline decltype(
auto)
declunilow(
const TSMatTDMatMultExpr<MT1,MT2,SF,HF,false,UF>& dm )
2349template<
typename MT1
2354inline decltype(
auto)
declstrlow(
const TSMatTDMatMultExpr<MT1,MT2,SF,HF,false,UF>& dm )
2392template<
typename MT1
2398inline decltype(
auto)
declupp(
const TSMatTDMatMultExpr<MT1,MT2,SF,HF,LF,UF>& dm )
2406 using ReturnType =
const TSMatTDMatMultExpr<MT1,MT2,SF,HF,LF,true>;
2407 return ReturnType( dm.leftOperand(), dm.rightOperand() );
2437template<
typename MT1
2442inline decltype(
auto)
decluniupp(
const TSMatTDMatMultExpr<MT1,MT2,SF,HF,LF,false>& dm )
2480template<
typename MT1
2485inline decltype(
auto)
declstrupp(
const TSMatTDMatMultExpr<MT1,MT2,SF,HF,LF,false>& dm )
2523template<
typename MT1
2529inline decltype(
auto)
decldiag(
const TSMatTDMatMultExpr<MT1,MT2,SF,HF,LF,UF>& dm )
2537 using ReturnType =
const TSMatTDMatMultExpr<MT1,MT2,SF,HF,true,true>;
2538 return ReturnType( dm.leftOperand(), dm.rightOperand() );
2554template<
typename MT1,
typename MT2,
bool SF,
bool HF,
bool LF,
bool UF >
2555struct Size< TSMatTDMatMultExpr<MT1,MT2,SF,HF,LF,UF>, 0UL >
2556 :
public Size<MT1,0UL>
2559template<
typename MT1,
typename MT2,
bool SF,
bool HF,
bool LF,
bool UF >
2560struct Size< TSMatTDMatMultExpr<MT1,MT2,SF,HF,LF,UF>, 1UL >
2561 :
public Size<MT2,1UL>
2577template<
typename MT1,
typename MT2,
bool SF,
bool HF,
bool LF,
bool UF >
2578struct IsAligned< TSMatTDMatMultExpr<MT1,MT2,SF,HF,LF,UF> >
2579 :
public IsAligned<MT2>
Header file for auxiliary alias declarations.
typename T::CompositeType CompositeType_t
Alias declaration for nested CompositeType type definitions.
Definition: Aliases.h:110
typename T::ResultType ResultType_t
Alias declaration for nested ResultType type definitions.
Definition: Aliases.h:450
typename T::ElementType ElementType_t
Alias declaration for nested ElementType type definitions.
Definition: Aliases.h:190
typename T::OppositeType OppositeType_t
Alias declaration for nested OppositeType type definitions.
Definition: Aliases.h:310
typename T::TransposeType TransposeType_t
Alias declaration for nested TransposeType type definitions.
Definition: Aliases.h:550
Header file for run time assertion macros.
Header file for the blaze::checked and blaze::unchecked instances.
Constraints on the storage order of matrix types.
Header file for the conjugate shim.
Header file for the decldiag trait.
Header file for the DeclDiag functor.
Header file for the declherm trait.
Header file for the DeclHerm functor.
Header file for the decllow trait.
Header file for the DeclLow functor.
Header file for the declsym trait.
Header file for the DeclSym functor.
Header file for the declupp trait.
Header file for the DeclUpp functor.
Header file for the EnableIf class template.
Header file for the function trace functionality.
Header file for the If class template.
Header file for the IntegralConstant class template.
Header file for the IsAligned type trait.
Header file for the IsBuiltin type trait.
Header file for the IsColumnMajorMatrix type trait.
Header file for the IsComputation type trait class.
Header file for the isDefault shim.
Header file for the IsDiagonal type trait.
Header file for the IsExpression type trait class.
Header file for the IsIdentity type trait.
Header file for the IsLower type trait.
Header file for the IsResizable type trait.
Header file for the IsRowMajorMatrix type trait.
Header file for the IsStrictlyLower type trait.
Header file for the IsStrictlyUpper type trait.
Header file for the IsSymmetric type trait.
Header file for the IsTriangular type trait.
Header file for the IsUpper type trait.
Header file for the MAYBE_UNUSED function template.
Header file for the multiplication trait.
Header file for the Noop functor.
Header file for the prevMultiple shim.
Constraints on the storage order of matrix types.
Constraint on the data type.
Constraint on the data type.
Base class for dense matrices.
Definition: DenseMatrix.h:82
Base class for sparse matrices.
Definition: SparseMatrix.h:77
Expression object for transpose sparse matrix-transpose dense matrix multiplications.
Definition: TSMatTDMatMultExpr.h:131
RightOperand rightOperand() const noexcept
Returns the right-hand side transpose dense matrix operand.
Definition: TSMatTDMatMultExpr.h:391
static constexpr bool evaluateRight
Compilation switch for the composite type of the right-hand side dense matrix expression.
Definition: TSMatTDMatMultExpr.h:149
ElementType_t< RT1 > ET1
Element type of the left-hand side dense matrix expression.
Definition: TSMatTDMatMultExpr.h:136
bool isAligned() const noexcept
Returns whether the operands of the expression are properly aligned in memory.
Definition: TSMatTDMatMultExpr.h:425
If_t< IsExpression_v< MT2 >, const MT2, const MT2 & > RightOperand
Composite type of the right-hand side dense matrix expression.
Definition: TSMatTDMatMultExpr.h:257
static constexpr bool SYM
Flag for symmetric matrices.
Definition: TSMatTDMatMultExpr.h:153
static constexpr bool simdEnabled
Compilation switch for the expression template evaluation strategy.
Definition: TSMatTDMatMultExpr.h:268
OppositeType_t< ResultType > OppositeType
Result type with opposite storage order for expression template evaluations.
Definition: TSMatTDMatMultExpr.h:247
size_t rows() const noexcept
Returns the current number of rows of the matrix.
Definition: TSMatTDMatMultExpr.h:361
CompositeType_t< MT1 > CT1
Composite type of the left-hand side sparse matrix expression.
Definition: TSMatTDMatMultExpr.h:138
static constexpr bool LOW
Flag for lower matrices.
Definition: TSMatTDMatMultExpr.h:155
ElementType_t< ResultType > ElementType
Resulting element type.
Definition: TSMatTDMatMultExpr.h:249
static constexpr bool evaluateLeft
Compilation switch for the composite type of the left-hand side sparse matrix expression.
Definition: TSMatTDMatMultExpr.h:144
CompositeType_t< MT2 > CT2
Composite type of the right-hand side dense matrix expression.
Definition: TSMatTDMatMultExpr.h:139
ResultType_t< MT1 > RT1
Result type of the left-hand side sparse matrix expression.
Definition: TSMatTDMatMultExpr.h:134
size_t columns() const noexcept
Returns the current number of columns of the matrix.
Definition: TSMatTDMatMultExpr.h:371
const ResultType CompositeType
Data type for composite expression templates.
Definition: TSMatTDMatMultExpr.h:251
static constexpr bool UPP
Flag for upper matrices.
Definition: TSMatTDMatMultExpr.h:156
typename If_t< HERM, DeclHermTrait< MultTrait_t< RT1, RT2 > >, If_t< SYM, DeclSymTrait< MultTrait_t< RT1, RT2 > >, If_t< LOW, If_t< UPP, DeclDiagTrait< MultTrait_t< RT1, RT2 > >, DeclLowTrait< MultTrait_t< RT1, RT2 > > >, If_t< UPP, DeclUppTrait< MultTrait_t< RT1, RT2 > >, MultTrait< RT1, RT2 > > > > >::Type ResultType
Result type for expression template evaluations.
Definition: TSMatTDMatMultExpr.h:245
TSMatTDMatMultExpr(const MT1 &lhs, const MT2 &rhs) noexcept
Constructor for the TSMatTDMatMultExpr class.
Definition: TSMatTDMatMultExpr.h:281
LeftOperand leftOperand() const noexcept
Returns the left-hand side transpose sparse matrix operand.
Definition: TSMatTDMatMultExpr.h:381
RightOperand rhs_
Right-hand side dense matrix of the multiplication expression.
Definition: TSMatTDMatMultExpr.h:443
bool isAliased(const T *alias) const noexcept
Returns whether the expression is aliased with the given address alias.
Definition: TSMatTDMatMultExpr.h:415
ResultType_t< MT2 > RT2
Result type of the right-hand side dense matrix expression.
Definition: TSMatTDMatMultExpr.h:135
bool canSMPAssign() const noexcept
Returns whether the expression can be used in SMP assignments.
Definition: TSMatTDMatMultExpr.h:435
ElementType_t< RT2 > ET2
Element type of the right-hand side sparse matrix expression.
Definition: TSMatTDMatMultExpr.h:137
If_t< evaluateRight, const RT2, CT2 > RT
Type for the assignment of the right-hand side dense matrix operand.
Definition: TSMatTDMatMultExpr.h:263
ReturnType at(size_t i, size_t j) const
Checked access to the matrix elements.
Definition: TSMatTDMatMultExpr.h:345
const ElementType ReturnType
Return type for expression template evaluations.
Definition: TSMatTDMatMultExpr.h:250
If_t< evaluateLeft, const RT1, CT1 > LT
Type for the assignment of the left-hand side sparse matrix operand.
Definition: TSMatTDMatMultExpr.h:260
LeftOperand lhs_
Left-hand side sparse matrix of the multiplication expression.
Definition: TSMatTDMatMultExpr.h:442
ReturnType operator()(size_t i, size_t j) const
2D-access to the matrix elements.
Definition: TSMatTDMatMultExpr.h:296
bool canAlias(const T *alias) const noexcept
Returns whether the expression can alias with the given address alias.
Definition: TSMatTDMatMultExpr.h:403
TransposeType_t< ResultType > TransposeType
Transpose type for expression template evaluations.
Definition: TSMatTDMatMultExpr.h:248
static constexpr bool HERM
Flag for Hermitian matrices.
Definition: TSMatTDMatMultExpr.h:154
If_t< IsExpression_v< MT1 >, const MT1, const MT1 & > LeftOperand
Composite type of the left-hand side sparse matrix expression.
Definition: TSMatTDMatMultExpr.h:254
static constexpr bool smpAssignable
Compilation switch for the expression template assignment strategy.
Definition: TSMatTDMatMultExpr.h:271
Constraint on the data type.
Constraint on the data type.
Constraint on the data type.
Constraint on the data type.
Header file for the Computation base class.
Header file for the DenseMatrix base class.
Header file for the MatMatMultExpr base class.
decltype(auto) column(Matrix< MT, SO > &matrix, RCAs... args)
Creating a view on a specific column of the given matrix.
Definition: Column.h:137
decltype(auto) transIf(const DenseMatrix< MT, SO > &dm)
Conditional calculation of the transpose of the given dense matrix.
Definition: DMatTransExpr.h:832
decltype(auto) min(const DenseMatrix< MT1, SO1 > &lhs, const DenseMatrix< MT2, SO2 > &rhs)
Computes the componentwise minimum of the dense matrices lhs and rhs.
Definition: DMatDMatMapExpr.h:1339
decltype(auto) max(const DenseMatrix< MT1, SO1 > &lhs, const DenseMatrix< MT2, SO2 > &rhs)
Computes the componentwise maximum of the dense matrices lhs and rhs.
Definition: DMatDMatMapExpr.h:1375
decltype(auto) declstrupp(const DenseMatrix< MT, SO > &dm)
Declares the given dense matrix expression dm as strictly upper.
Definition: DMatDeclStrUppExpr.h:1003
decltype(auto) conj(const DenseMatrix< MT, SO > &dm)
Returns a matrix containing the complex conjugate of each single element of dm.
Definition: DMatMapExpr.h:1464
decltype(auto) decldiag(const DenseMatrix< MT, SO > &dm)
Declares the given dense matrix expression dm as diagonal.
Definition: DMatDeclDiagExpr.h:978
decltype(auto) declstrlow(const DenseMatrix< MT, SO > &dm)
Declares the given dense matrix expression dm as strictly lower.
Definition: DMatDeclStrLowExpr.h:1003
decltype(auto) serial(const DenseMatrix< MT, SO > &dm)
Forces the serial evaluation of the given dense matrix expression dm.
Definition: DMatSerialExpr.h:812
decltype(auto) declupp(const DenseMatrix< MT, SO > &dm)
Declares the given dense matrix expression dm as upper.
Definition: DMatDeclUppExpr.h:1004
decltype(auto) decllow(const DenseMatrix< MT, SO > &dm)
Declares the given dense matrix expression dm as lower.
Definition: DMatDeclLowExpr.h:1004
decltype(auto) decluniupp(const DenseMatrix< MT, SO > &dm)
Declares the given dense matrix expression dm as uniupper.
Definition: DMatDeclUniUppExpr.h:1005
decltype(auto) declherm(const DenseMatrix< MT, SO > &dm)
Declares the given dense matrix expression dm as Hermitian.
Definition: DMatDeclHermExpr.h:1005
decltype(auto) declsym(const DenseMatrix< MT, SO > &dm)
Declares the given dense matrix expression dm as symmetric.
Definition: DMatDeclSymExpr.h:1005
decltype(auto) declunilow(const DenseMatrix< MT, SO > &dm)
Declares the given dense matrix expression dm as unilower.
Definition: DMatDeclUniLowExpr.h:1004
bool isDefault(const DiagonalMatrix< MT, SO, DF > &m)
Returns whether the given diagonal matrix is in default state.
Definition: DiagonalMatrix.h:169
#define BLAZE_CONSTRAINT_MUST_NOT_BE_SYMMETRIC_MATRIX_TYPE(T)
Constraint on the data type.
Definition: Symmetric.h:79
#define BLAZE_CONSTRAINT_MUST_BE_ROW_MAJOR_MATRIX_TYPE(T)
Constraint on the data type.
Definition: RowMajorMatrix.h:61
#define BLAZE_CONSTRAINT_MATRICES_MUST_HAVE_SAME_STORAGE_ORDER(T1, T2)
Constraint on the data type.
Definition: StorageOrder.h:84
#define BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION(T)
Constraint on the data type.
Definition: RequiresEvaluation.h:81
#define BLAZE_CONSTRAINT_MUST_FORM_VALID_MATMATMULTEXPR(T1, T2)
Constraint on the data type.
Definition: MatMatMultExpr.h:103
#define BLAZE_CONSTRAINT_MUST_NOT_BE_ZERO_TYPE(T)
Constraint on the data type.
Definition: Zero.h:81
#define BLAZE_CONSTRAINT_MUST_BE_DENSE_MATRIX_TYPE(T)
Constraint on the data type.
Definition: DenseMatrix.h:61
#define BLAZE_CONSTRAINT_MUST_BE_SPARSE_MATRIX_TYPE(T)
Constraint on the data type.
Definition: SparseMatrix.h:61
#define BLAZE_CONSTRAINT_MUST_BE_COLUMN_MAJOR_MATRIX_TYPE(T)
Constraint on the data type.
Definition: ColumnMajorMatrix.h:61
#define BLAZE_CONSTRAINT_MUST_BE_ZERO_TYPE(T)
Constraint on the data type.
Definition: Zero.h:61
BLAZE_ALWAYS_INLINE constexpr auto prevMultiple(T1 value, T2 factor) noexcept
Rounds down an integral value to the previous multiple of a given factor.
Definition: PrevMultiple.h:68
constexpr void reset(Matrix< MT, SO > &matrix)
Resetting the given matrix.
Definition: Matrix.h:806
MT::Iterator end(Matrix< MT, SO > &matrix, size_t i)
Returns an iterator just past the last element of row/column i.
Definition: Matrix.h:584
MT::Iterator begin(Matrix< MT, SO > &matrix, size_t i)
Returns an iterator to the first element of row/column i.
Definition: Matrix.h:518
constexpr size_t size(const Matrix< MT, SO > &matrix) noexcept
Returns the total number of elements of the matrix.
Definition: Matrix.h:676
bool isSquare(const Matrix< MT, SO > &matrix) noexcept
Checks if the given matrix is a square matrix.
Definition: Matrix.h:1383
decltype(auto) row(Matrix< MT, SO > &, RRAs...)
Creating a view on a specific row of the given matrix.
Definition: Row.h:137
#define BLAZE_INTERNAL_ASSERT(expr, msg)
Run time assertion macro for internal checks.
Definition: Assert.h:101
auto smpSubAssign(Matrix< MT1, SO1 > &lhs, const Matrix< MT2, SO2 > &rhs) -> EnableIf_t< IsDenseMatrix_v< MT1 > >
Default implementation of the SMP subtraction assignment of a matrix to dense matrix.
Definition: DenseMatrix.h:162
auto smpAssign(Matrix< MT1, SO1 > &lhs, const Matrix< MT2, SO2 > &rhs) -> EnableIf_t< IsDenseMatrix_v< MT1 > >
Default implementation of the SMP assignment of a matrix to a dense matrix.
Definition: DenseMatrix.h:100
auto smpSchurAssign(Matrix< MT1, SO1 > &lhs, const Matrix< MT2, SO2 > &rhs) -> EnableIf_t< IsDenseMatrix_v< MT1 > >
Default implementation of the SMP Schur product assignment of a matrix to dense matrix.
Definition: DenseMatrix.h:194
auto smpAddAssign(Matrix< MT1, SO1 > &lhs, const Matrix< MT2, SO2 > &rhs) -> EnableIf_t< IsDenseMatrix_v< MT1 > >
Default implementation of the SMP addition assignment of a matrix to a dense matrix.
Definition: DenseMatrix.h:131
decltype(auto) subvector(Vector< VT, TF > &, RSAs...)
Creating a view on a specific subvector of the given vector.
Definition: Subvector.h:158
constexpr void MAYBE_UNUSED(const Args &...)
Suppression of unused parameter warnings.
Definition: MaybeUnused.h:81
typename If< Condition >::template Type< T1, T2 > If_t
Auxiliary alias template for the If class template.
Definition: If.h:108
#define BLAZE_THROW_OUT_OF_RANGE(MESSAGE)
Macro for the emission of a std::out_of_range exception.
Definition: Exception.h:331
#define BLAZE_THROW_INVALID_ARGUMENT(MESSAGE)
Macro for the emission of a std::invalid_argument exception.
Definition: Exception.h:235
typename EnableIf<!Condition, T >::Type DisableIf_t
Auxiliary type for the EnableIf class template.
Definition: EnableIf.h:175
#define BLAZE_FUNCTION_TRACE
Function trace macro.
Definition: FunctionTrace.h:94
constexpr Unchecked unchecked
Global Unchecked instance.
Definition: Check.h:146
Header file for the exception macros of the math module.
Constraints on the storage order of matrix types.
Header file for all forward declarations for expression class templates.
Header file for the Size type trait.
Header file for the reset shim.
Header file for the serial shim.
Base class for all compute expression templates.
Definition: Computation.h:68
Base template for the DeclDiagTrait class.
Definition: DeclDiagTrait.h:127
Generic wrapper for the decldiag() function.
Definition: DeclDiag.h:61
Base template for the DeclHermTrait class.
Definition: DeclHermTrait.h:126
Generic wrapper for the declherm() function.
Definition: DeclHerm.h:61
Base template for the DeclLowTrait class.
Definition: DeclLowTrait.h:126
Generic wrapper for the decllow() function.
Definition: DeclLow.h:61
Base template for the DeclSymTrait class.
Definition: DeclSymTrait.h:126
Generic wrapper for the declsym() function.
Definition: DeclSym.h:61
Base template for the DeclUppTrait class.
Definition: DeclUppTrait.h:126
Generic wrapper for the declupp() function.
Definition: DeclUpp.h:61
Base class for all matrix/matrix multiplication expression templates.
Definition: MatMatMultExpr.h:71
Base template for the MultTrait class.
Definition: MultTrait.h:130
Generic wrapper for the null function.
Definition: Noop.h:62
System settings for performance optimizations.
Header file for the thresholds for matrix/vector and matrix/matrix multiplications.
Header file for the IsZero type trait.
Header file for the RequiresEvaluation type trait.
Header file for basic type definitions.
Header file for the generic max algorithm.
Header file for the generic min algorithm.