Namespaces
namespace	_ftranspose_impl

namespace	BLAS3

namespace	csr_hyb_details

namespace	CuttingStrategy

namespace	details

namespace	details_spmv

namespace	ElementCategories

namespace	ell_r_details

namespace	FieldCategories
	Traits and categories will need to be placed in a proper file later.

namespace	MMHelperAlgo

namespace	ModeCategories
	Specifies the mode of action for an algorithm w.r.t.

namespace	ParSeqHelper
	ParSeqHelper for both fgemm and ftrsm.

namespace	Protected

namespace	sell_details

namespace	sparse_details

namespace	sparse_details_impl

namespace	StrategyParameter

namespace	StructureHelper
	StructureHelper for ftrsm.

namespace	vectorised

Data Structures
struct	AlgoChooser

struct	AlgoChooser< ModeCategories::ConvertTo< ElementCategories::RNSElementTag >, ParSeq >

struct	associatedDelayedField

struct	associatedDelayedField< const FFPACK::RNSIntegerMod< RNS > >

struct	associatedDelayedField< const Givaro::Modular< T, X > >

struct	associatedDelayedField< const Givaro::ModularBalanced< T > >

struct	associatedDelayedField< const Givaro::ZRing< T > >

struct	BlockTransposeSIMD

struct	Checker_Empty

class	CheckerImplem_fgemm

class	CheckerImplem_ftrsm

struct	CooMat

struct	CsrMat

struct	ElementTraits
	ElementTraits. More...

struct	ElementTraits< double >

struct	ElementTraits< FFPACK::rns_double_elt >

struct	ElementTraits< float >

struct	ElementTraits< Givaro::Integer >

struct	ElementTraits< int16_t >

struct	ElementTraits< int32_t >

struct	ElementTraits< int64_t >

struct	ElementTraits< int8_t >

struct	ElementTraits< RecInt::rint< K > >

struct	ElementTraits< RecInt::rmint< K, MG > >

struct	ElementTraits< RecInt::ruint< K > >

struct	ElementTraits< uint16_t >

struct	ElementTraits< uint32_t >

struct	ElementTraits< uint64_t >

struct	ElementTraits< uint8_t >

struct	EllMat

struct	FieldTraits
	FieldTrait. More...

struct	FieldTraits< FFPACK::RNSInteger< T > >

struct	FieldTraits< FFPACK::RNSIntegerMod< T > >

struct	FieldTraits< Givaro::Modular< Element > >

struct	FieldTraits< Givaro::ModularBalanced< Element > >

struct	FieldTraits< Givaro::ZRing< double > >

struct	FieldTraits< Givaro::ZRing< float > >

struct	FieldTraits< Givaro::ZRing< Givaro::Integer > >

struct	FieldTraits< Givaro::ZRing< int16_t > >

struct	FieldTraits< Givaro::ZRing< int32_t > >

struct	FieldTraits< Givaro::ZRing< int64_t > >

struct	FieldTraits< Givaro::ZRing< RecInt::ruint< K > > >

struct	FieldTraits< Givaro::ZRing< uint16_t > >

struct	FieldTraits< Givaro::ZRing< uint32_t > >

struct	FieldTraits< Givaro::ZRing< uint64_t > >

struct	ForStrategy1D

struct	ForStrategy2D

struct	has_minus_eq_impl

struct	has_minus_impl

struct	has_mul_eq_impl

struct	has_mul_impl

struct	has_operation

struct	has_plus_eq_impl

struct	has_plus_impl

struct	HelperFlag

struct	isSparseMatrix

struct	isSparseMatrix< Field, Sparse< Field, SparseMatrix_t::COO > >

struct	isSparseMatrix< Field, Sparse< Field, SparseMatrix_t::COO_ZO > >

struct	isSparseMatrix< Field, Sparse< Field, SparseMatrix_t::CSR > >

struct	isSparseMatrix< Field, Sparse< Field, SparseMatrix_t::CSR_HYB > >

struct	isSparseMatrix< Field, Sparse< Field, SparseMatrix_t::CSR_ZO > >

struct	isSparseMatrix< Field, Sparse< Field, SparseMatrix_t::ELL > >

struct	isSparseMatrix< Field, Sparse< Field, SparseMatrix_t::ELL_simd > >

struct	isSparseMatrix< Field, Sparse< Field, SparseMatrix_t::ELL_simd_ZO > >

struct	isSparseMatrix< Field, Sparse< Field, SparseMatrix_t::ELL_ZO > >

struct	isSparseMatrix< Field, Sparse< Field, SparseMatrix_t::HYB_ZO > >

struct	isSparseMatrix< Field, Sparse< Field, SparseMatrix_t::SELL > >

struct	isSparseMatrix< Field, Sparse< Field, SparseMatrix_t::SELL_ZO > >

struct	isSparseMatrixMKLFormat

struct	isSparseMatrixSimdFormat

struct	isZOSparseMatrix

struct	isZOSparseMatrix< Field, Sparse< Field, SparseMatrix_t::COO_ZO > >

struct	isZOSparseMatrix< Field, Sparse< Field, SparseMatrix_t::CSR_ZO > >

struct	isZOSparseMatrix< Field, Sparse< Field, SparseMatrix_t::ELL_simd_ZO > >

struct	isZOSparseMatrix< Field, Sparse< Field, SparseMatrix_t::ELL_ZO > >

struct	isZOSparseMatrix< Field, Sparse< Field, SparseMatrix_t::SELL_ZO > >

struct	MMHelper

struct	MMHelper< FFPACK::RNSInteger< E >, AlgoTrait, ModeCategories::DefaultTag, ParSeqTrait >

struct	MMHelper< FFPACK::RNSIntegerMod< E >, AlgoTrait, ModeCategories::DefaultTag, ParSeqTrait >

struct	MMHelper< Field, AlgoTrait, ModeCategories::ConvertTo< Dest >, ParSeqTrait >

struct	MMHelper< Field, AlgoTrait, ModeCategories::ConvertTo< ElementCategories::RNSElementTag >, ParSeqTrait >

struct	MMHelper< Field, AlgoTrait, ModeCategories::DefaultTag, ParSeqTrait >
	FGEMM Helper for Default and ConvertTo modes of operation. More...

struct	ModeTraits
	ModeTraits. More...

struct	ModeTraits< Givaro::Modular< Element, Compute > >

struct	ModeTraits< Givaro::Modular< Givaro::Integer, Compute > >

struct	ModeTraits< Givaro::Modular< int16_t, Compute > >

struct	ModeTraits< Givaro::Modular< int32_t, Compute > >

struct	ModeTraits< Givaro::Modular< int64_t, uint64_t > >

struct	ModeTraits< Givaro::Modular< int8_t, Compute > >

struct	ModeTraits< Givaro::Modular< RecInt::ruint< K >, Compute > >

struct	ModeTraits< Givaro::Modular< uint16_t, Compute > >

struct	ModeTraits< Givaro::Modular< uint32_t, Compute > >

struct	ModeTraits< Givaro::Modular< uint8_t, Compute > >

struct	ModeTraits< Givaro::ModularBalanced< Element > >

struct	ModeTraits< Givaro::ModularBalanced< Givaro::Integer > >

struct	ModeTraits< Givaro::ModularBalanced< int16_t > >

struct	ModeTraits< Givaro::ModularBalanced< int32_t > >

struct	ModeTraits< Givaro::ModularBalanced< int8_t > >

struct	ModeTraits< Givaro::Montgomery< T > >

struct	ModeTraits< Givaro::ZRing< double > >

struct	ModeTraits< Givaro::ZRing< float > >

struct	ModeTraits< Givaro::ZRing< Givaro::Integer > >

struct	Packer

struct	Packer< double, 2 >

struct	readMyMachineType

struct	readMyMachineType< Field, mpz_t >

struct	Sparse

struct	Sparse< _Field, SparseMatrix_t::COO >

struct	Sparse< _Field, SparseMatrix_t::COO_ZO >

struct	Sparse< _Field, SparseMatrix_t::CSR >

struct	Sparse< _Field, SparseMatrix_t::CSR_HYB >

struct	Sparse< _Field, SparseMatrix_t::CSR_ZO >

struct	Sparse< _Field, SparseMatrix_t::ELL >

struct	Sparse< _Field, SparseMatrix_t::ELL_R >

struct	Sparse< _Field, SparseMatrix_t::ELL_R_ZO >

struct	Sparse< _Field, SparseMatrix_t::ELL_simd >

struct	Sparse< _Field, SparseMatrix_t::ELL_simd_ZO >

struct	Sparse< _Field, SparseMatrix_t::ELL_ZO >

struct	Sparse< _Field, SparseMatrix_t::HYB_ZO >

struct	Sparse< _Field, SparseMatrix_t::SELL >

struct	Sparse< _Field, SparseMatrix_t::SELL_ZO >

struct	SpMat

struct	StatsMatrix

struct	support_fast_mod

struct	support_fast_mod< double >

struct	support_fast_mod< float >

struct	support_fast_mod< int64_t >

struct	support_simd

struct	support_simd_add

struct	support_simd_mod

struct	tfn_minus

struct	tfn_minus_eq

struct	tfn_mul

struct	tfn_mul_eq

struct	tfn_plus

struct	tfn_plus_eq

struct	TRSMHelper
	TRSM Helper. More...

Typedefs
template<class Field >
using	Checker_fgemm = FFLAS::Checker_Empty< Field >

template<class Field >
using	Checker_ftrsm = FFLAS::Checker_Empty< Field >

template<class Field >
using	ForceCheck_fgemm = CheckerImplem_fgemm< Field >

template<class Field >
using	ForceCheck_ftrsm = CheckerImplem_ftrsm< Field >

using	ZOSparseMatrix = std::true_type

using	NotZOSparseMatrix = std::false_type

using	SimdSparseMatrix = std::true_type

using	NoSimdSparseMatrix = std::false_type

using	MKLSparseMatrixFormat = std::true_type

using	NotMKLSparseMatrixFormat = std::false_type

template<class T >
using	has_plus = typename std::conditional< std::is_arithmetic< T >::value, std::true_type, has_plus_impl< T > >::type

template<class T >
using	has_minus = typename std::conditional< std::is_arithmetic< T >::value, std::true_type, has_minus_impl< T > >::type

template<class T >
using	has_equal = typename std::conditional< std::is_arithmetic< T >::value, std::true_type, std::is_copy_assignable< T > >::type

template<class T >
using	has_plus_eq = typename std::conditional< std::is_arithmetic< T >::value, std::true_type, has_plus_eq_impl< T > >::type

template<class T >
using	has_minus_eq = typename std::conditional< std::is_arithmetic< T >::value, std::true_type, has_minus_eq_impl< T > >::type

template<class T >
using	has_mul = typename std::conditional< std::is_arithmetic< T >::value, std::true_type, has_mul_impl< T > >::type

template<class T >
using	has_mul_eq = typename std::conditional< std::is_arithmetic< T >::value, std::true_type, has_mul_eq_impl< T > >::type

typedef Givaro::Timer	Timer

typedef Givaro::BaseTimer	BaseTimer

typedef Givaro::UserTimer	UserTimer

typedef Givaro::SysTimer	SysTimer

Enumerations
enum	FFLAS_ORDER { FflasRowMajor =101 , FflasColMajor =102 }
	Storage by row or col ? More...

enum	FFLAS_TRANSPOSE { FflasNoTrans = 111 , FflasTrans = 112 }
	Is matrix transposed ? More...

enum	FFLAS_UPLO { FflasUpper = 121 , FflasLower = 122 , FflasLeftTri = 123 , FflasRightTri = 124 }
	Is triangular matrix's shape upper ? More...

enum	FFLAS_DIAG { FflasNonUnit = 131 , FflasUnit = 132 }
	Is the triangular matrix implicitly unit diagonal ? More...

enum	FFLAS_SIDE { FflasLeft = 141 , FflasRight = 142 }
	On what side ? More...

enum	FFLAS_BASE { FflasDouble = 151 , FflasFloat = 152 , FflasGeneric = 153 }
	`FFLAS_BASE` determines the type of the element representation for Matrix Mult kernel. More...

enum	number_kind { zero =0 , one =1 , mone =-1 , other =2 }

enum class	SparseMatrix_t { CSR , CSR_ZO , CSC , CSC_ZO , COO , COO_ZO , ELL , ELL_ZO , SELL , SELL_ZO , ELL_simd , ELL_simd_ZO , CSR_HYB , HYB_ZO }

enum	FFLAS_FORMAT { FflasAuto = 0 , FflasDense = 1 , FflasSMS = 2 , FflasBinary = 3 , FflasMath = 4 , FflasMaple = 5 , FflasSageMath = 6 }

Functions
Givaro::Integer	InfNorm (const size_t M, const size_t N, const Givaro::Integer *A, const size_t lda)

template<class T >
const T &	min3 (const T &m, const T &n, const T &k)

template<class T >
const T &	max3 (const T &m, const T &n, const T &k)

template<class T >
const T &	min4 (const T &m, const T &n, const T &k, const T &l)

template<class T >
const T &	max4 (const T &m, const T &n, const T &k, const T &l)

template<class Field >
void	fadd (const Field &F, const size_t N, typename Field::ConstElement_ptr A, const size_t inca, typename Field::ConstElement_ptr B, const size_t incb, typename Field::Element_ptr C, const size_t incc)

template<class Field >
void	faddin (const Field &F, const size_t N, typename Field::ConstElement_ptr B, const size_t incb, typename Field::Element_ptr C, const size_t incc)

template<class Field >
void	fsub (const Field &F, const size_t N, typename Field::ConstElement_ptr A, const size_t inca, typename Field::ConstElement_ptr B, const size_t incb, typename Field::Element_ptr C, const size_t incc)

template<class Field >
void	fsubin (const Field &F, const size_t N, typename Field::ConstElement_ptr B, const size_t incb, typename Field::Element_ptr C, const size_t incc)

template<class Field >
void	fadd (const Field &F, const size_t N, typename Field::ConstElement_ptr A, const size_t inca, const typename Field::Element alpha, typename Field::ConstElement_ptr B, const size_t incb, typename Field::Element_ptr C, const size_t incc)

template<class Field >
void	pfadd (const Field &F, const size_t M, const size_t N, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr B, const size_t ldb, typename Field::Element_ptr C, const size_t ldc, const size_t numths)

template<class Field >
void	pfsub (const Field &F, const size_t M, const size_t N, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr B, const size_t ldb, typename Field::Element_ptr C, const size_t ldc, const size_t numths)

template<class Field >
void	pfaddin (const Field &F, const size_t M, const size_t N, typename Field::ConstElement_ptr B, const size_t ldb, typename Field::Element_ptr C, const size_t ldc, size_t numths)

template<class Field >
void	pfsubin (const Field &F, const size_t M, const size_t N, typename Field::ConstElement_ptr B, const size_t ldb, typename Field::Element_ptr C, const size_t ldc, size_t numths)

template<class Field >
void	fadd (const Field &F, const size_t M, const size_t N, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr B, const size_t ldb, typename Field::Element_ptr C, const size_t ldc)
	fadd : matrix addition. More...

template<class Field >
void	fsub (const Field &F, const size_t M, const size_t N, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr B, const size_t ldb, typename Field::Element_ptr C, const size_t ldc)
	fsub : matrix subtraction. More...

template<class Field >
void	faddin (const Field &F, const size_t M, const size_t N, typename Field::ConstElement_ptr B, const size_t ldb, typename Field::Element_ptr C, const size_t ldc)
	faddin More...

template<class Field >
void	faddin (const Field &F, const FFLAS_UPLO uplo, const size_t N, typename Field::ConstElement_ptr B, const size_t ldb, typename Field::Element_ptr C, const size_t ldc)
	fadding for symmetric matrices More...

template<class Field >
void	fsubin (const Field &F, const size_t M, const size_t N, typename Field::ConstElement_ptr B, const size_t ldb, typename Field::Element_ptr C, const size_t ldc)
	fsubin C = C - B More...

template<class Field >
void	fadd (const Field &F, const size_t M, const size_t N, typename Field::ConstElement_ptr A, const size_t lda, const typename Field::Element alpha, typename Field::ConstElement_ptr B, const size_t ldb, typename Field::Element_ptr C, const size_t ldc)
	fadd : matrix addition with scaling. More...

template<class Field >
void	fassign (const Field &F, const size_t N, typename Field::ConstElement_ptr Y, const size_t incY, typename Field::Element_ptr X, const size_t incX)
	fassign : $x \gets y$ . More...

template<>
void	fassign (const Givaro::Modular< float > &F, const size_t N, const float Y, const size_t incY, float X, const size_t incX)

template<>
void	fassign (const Givaro::ModularBalanced< float > &F, const size_t N, const float Y, const size_t incY, float X, const size_t incX)

template<>
void	fassign (const Givaro::ZRing< float > &F, const size_t N, const float Y, const size_t incY, float X, const size_t incX)

template<>
void	fassign (const Givaro::Modular< double > &F, const size_t N, const double Y, const size_t incY, double X, const size_t incX)

template<>
void	fassign (const Givaro::ModularBalanced< double > &F, const size_t N, const double Y, const size_t incY, double X, const size_t incX)

template<>
void	fassign (const Givaro::ZRing< double > &F, const size_t N, const double Y, const size_t incY, double X, const size_t incX)

template<class Field >
void	fassign (const Field &F, const size_t m, const size_t n, typename Field::ConstElement_ptr B, const size_t ldb, typename Field::Element_ptr A, const size_t lda)
	fassign : $A \gets B$ . More...

template<class Field >
void	faxpy (const Field &F, const size_t N, const typename Field::Element alpha, typename Field::ConstElement_ptr X, const size_t incX, typename Field::Element_ptr Y, const size_t incY)
	faxpy : $y \gets \alpha \cdot x + y$ . More...

template<>
void	faxpy (const Givaro::DoubleDomain &, const size_t N, const Givaro::DoubleDomain::Element a, Givaro::DoubleDomain::ConstElement_ptr x, const size_t incx, Givaro::DoubleDomain::Element_ptr y, const size_t incy)

template<>
void	faxpy (const Givaro::FloatDomain &, const size_t N, const Givaro::FloatDomain::Element a, Givaro::FloatDomain::ConstElement_ptr x, const size_t incx, Givaro::FloatDomain::Element_ptr y, const size_t incy)

template<class Field >
void	faxpy (const Field &F, const size_t m, const size_t n, const typename Field::Element alpha, typename Field::ConstElement_ptr X, const size_t ldx, typename Field::Element_ptr Y, const size_t ldy)
	faxpy : $y \gets \alpha \cdot x + y$ . More...

template<class Field >
Field::Element	fdot (const Field &F, const size_t N, typename Field::ConstElement_ptr x, const size_t incx, typename Field::ConstElement_ptr y, const size_t incy, ModeCategories::DefaultTag &MT)

template<class Field >
Field::Element	fdot (const Field &F, const size_t N, typename Field::ConstElement_ptr x, const size_t incx, typename Field::ConstElement_ptr y, const size_t incy, ModeCategories::DelayedTag &MT)

template<>
Givaro::DoubleDomain::Element	fdot (const Givaro::DoubleDomain &, const size_t N, Givaro::DoubleDomain::ConstElement_ptr x, const size_t incx, Givaro::DoubleDomain::ConstElement_ptr y, const size_t incy, ModeCategories::DefaultTag &MT)

template<>
Givaro::FloatDomain::Element	fdot (const Givaro::FloatDomain &, const size_t N, Givaro::FloatDomain::ConstElement_ptr x, const size_t incx, Givaro::FloatDomain::ConstElement_ptr y, const size_t incy, ModeCategories::DefaultTag &MT)

template<class Field , class T >
Field::Element	fdot (const Field &F, const size_t N, typename Field::ConstElement_ptr x, const size_t incx, typename Field::ConstElement_ptr y, const size_t incy, ModeCategories::ConvertTo< T > &MT)

template<class Field >
Field::Element	fdot (const Field &F, const size_t N, typename Field::ConstElement_ptr x, const size_t incx, typename Field::ConstElement_ptr y, const size_t incy, ModeCategories::DefaultBoundedTag &dbt)

template<class Field >
Field::Element	fdot (const Field &F, const size_t N, typename Field::ConstElement_ptr x, const size_t incx, typename Field::ConstElement_ptr y, const size_t incy, const ParSeqHelper::Sequential seq)

template<class Field >
Field::Element	fdot (const Field &F, const size_t N, typename Field::ConstElement_ptr X, const size_t incX, typename Field::ConstElement_ptr Y, const size_t incY)
	fdot: dot product . More...

template<class Field >
Field::Element_ptr	fgemm (const Field &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr B, const size_t ldb, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, MMHelper< Field, MMHelperAlgo::Winograd, ModeCategories::ConvertTo< ElementCategories::MachineFloatTag >, ParSeqHelper::Sequential > &H)

template<typename Field >
Field::Element_ptr	fgemm (const Field &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr B, const size_t ldb, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, const ParSeqHelper::Sequential seq)

template<typename Field , class Cut , class Param >
Field::Element_ptr	fgemm (const Field &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr B, const size_t ldb, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, const ParSeqHelper::Parallel< Cut, Param > par)

template<typename Field >
Field::Element_ptr	fgemm (const Field &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr B, const size_t ldb, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc)
	fgemm: Field GEneral Matrix Multiply. More...

template<typename Field , class ModeT , class ParSeq >
Field::Element_ptr	fgemm (const Field &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr B, const size_t ldb, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, MMHelper< Field, MMHelperAlgo::Auto, ModeT, ParSeq > &H)

template<class Field >
Field::Element_ptr	fgemm (const Field &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr B, const size_t ldb, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, MMHelper< Field, MMHelperAlgo::Winograd, ModeCategories::DelayedTag, ParSeqHelper::Sequential > &H)

template<class Field >
Field::Element_ptr	fsquare (const Field &F, const FFLAS_TRANSPOSE ta, const size_t n, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc)
	fsquare: Squares a matrix. More...

template<>
double *	fsquare (const Givaro::ModularBalanced< double > &F, const FFLAS_TRANSPOSE ta, const size_t n, const double alpha, const double A, const size_t lda, const double beta, double C, const size_t ldc)

template<>
float *	fsquare (const Givaro::ModularBalanced< float > &F, const FFLAS_TRANSPOSE ta, const size_t n, const float alpha, const float A, const size_t lda, const float beta, float C, const size_t ldc)

template<>
double *	fsquare (const Givaro::Modular< double > &F, const FFLAS_TRANSPOSE ta, const size_t n, const double alpha, const double A, const size_t lda, const double beta, double C, const size_t ldc)

template<>
float *	fsquare (const Givaro::Modular< float > &F, const FFLAS_TRANSPOSE ta, const size_t n, const float alpha, const float A, const size_t lda, const float beta, float C, const size_t ldc)

template<typename RNS , typename ParSeqTrait >
FFPACK::RNSInteger< RNS >::Element_ptr	fgemm (const FFPACK::RNSInteger< RNS > &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename FFPACK::RNSInteger< RNS >::Element alpha, typename FFPACK::RNSInteger< RNS >::ConstElement_ptr Ad, const size_t lda, typename FFPACK::RNSInteger< RNS >::ConstElement_ptr Bd, const size_t ldb, const typename FFPACK::RNSInteger< RNS >::Element beta, typename FFPACK::RNSInteger< RNS >::Element_ptr Cd, const size_t ldc, MMHelper< FFPACK::RNSInteger< RNS >, MMHelperAlgo::Classic, ModeCategories::DefaultTag, ParSeqHelper::Compose< ParSeqHelper::Sequential, ParSeqTrait > > &H)

template<typename RNS >
FFPACK::RNSInteger< RNS >::Element_ptr	fgemm (const FFPACK::RNSInteger< RNS > &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename FFPACK::RNSInteger< RNS >::Element alpha, typename FFPACK::RNSInteger< RNS >::ConstElement_ptr Ad, const size_t lda, typename FFPACK::RNSInteger< RNS >::ConstElement_ptr Bd, const size_t ldb, const typename FFPACK::RNSInteger< RNS >::Element beta, typename FFPACK::RNSInteger< RNS >::Element_ptr Cd, const size_t ldc, MMHelper< FFPACK::RNSInteger< RNS >, MMHelperAlgo::Classic, ModeCategories::DefaultTag, ParSeqHelper::Sequential > &H)

template<typename RNS , typename ParSeqTrait >
FFPACK::RNSInteger< RNS >::Element_ptr	fgemm (const FFPACK::RNSInteger< RNS > &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename FFPACK::RNSInteger< RNS >::Element alpha, typename FFPACK::RNSInteger< RNS >::ConstElement_ptr Ad, const size_t lda, typename FFPACK::RNSInteger< RNS >::ConstElement_ptr Bd, const size_t ldb, const typename FFPACK::RNSInteger< RNS >::Element beta, typename FFPACK::RNSInteger< RNS >::Element_ptr Cd, const size_t ldc, MMHelper< FFPACK::RNSInteger< RNS >, MMHelperAlgo::Classic, ModeCategories::DefaultTag, ParSeqHelper::Compose< ParSeqHelper::Parallel< CuttingStrategy::RNSModulus, StrategyParameter::Threads >, ParSeqTrait > > &H)

template<typename RNS , typename Cut , typename Param >
FFPACK::RNSInteger< RNS >::Element_ptr	fgemm (const FFPACK::RNSInteger< RNS > &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename FFPACK::RNSInteger< RNS >::Element alpha, typename FFPACK::RNSInteger< RNS >::ConstElement_ptr Ad, const size_t lda, typename FFPACK::RNSInteger< RNS >::ConstElement_ptr Bd, const size_t ldb, const typename FFPACK::RNSInteger< RNS >::Element beta, typename FFPACK::RNSInteger< RNS >::Element_ptr Cd, const size_t ldc, MMHelper< FFPACK::RNSInteger< RNS >, MMHelperAlgo::Classic, ModeCategories::DefaultTag, ParSeqHelper::Parallel< Cut, Param > > &H)

template<class ParSeq >
Givaro::Integer *	fgemm (const Givaro::ZRing< Givaro::Integer > &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const Givaro::Integer alpha, const Givaro::Integer A, const size_t lda, const Givaro::Integer B, const size_t ldb, Givaro::Integer beta, Givaro::Integer *C, const size_t ldc, MMHelper< Givaro::ZRing< Givaro::Integer >, MMHelperAlgo::Classic, ModeCategories::ConvertTo< ElementCategories::RNSElementTag >, ParSeq > &H)

template<typename RNS , class ModeT >
RNS::Element_ptr	fgemm (const FFPACK::RNSInteger< RNS > &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename RNS::Element alpha, typename RNS::ConstElement_ptr Ad, const size_t lda, typename RNS::ConstElement_ptr Bd, const size_t ldb, const typename RNS::Element beta, typename RNS::Element_ptr Cd, const size_t ldc, MMHelper< FFPACK::RNSInteger< RNS >, MMHelperAlgo::Winograd, ModeT, ParSeqHelper::Sequential > &H)

template<typename RNS >
RNS::Element_ptr	fgemm (const FFPACK::RNSIntegerMod< RNS > &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename RNS::Element alpha, typename RNS::ConstElement_ptr Ad, const size_t lda, typename RNS::ConstElement_ptr Bd, const size_t ldb, const typename RNS::Element beta, typename RNS::Element_ptr Cd, const size_t ldc, MMHelper< FFPACK::RNSIntegerMod< RNS >, MMHelperAlgo::Winograd > &H)

Givaro::Integer *	fgemm (const Givaro::Modular< Givaro::Integer > &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const Givaro::Integer alpha, const Givaro::Integer A, const size_t lda, const Givaro::Integer B, const size_t ldb, const Givaro::Integer beta, Givaro::Integer *C, const size_t ldc, MMHelper< Givaro::Modular< Givaro::Integer >, MMHelperAlgo::Classic, ModeCategories::ConvertTo< ElementCategories::RNSElementTag > > &H)

template<class ParSeq >
Givaro::Integer *	fgemm (const Givaro::Modular< Givaro::Integer > &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const Givaro::Integer alpha, const Givaro::Integer A, const size_t lda, const Givaro::Integer B, const size_t ldb, const Givaro::Integer beta, Givaro::Integer *C, const size_t ldc, MMHelper< Givaro::Modular< Givaro::Integer >, MMHelperAlgo::Auto, ModeCategories::ConvertTo< ElementCategories::RNSElementTag >, ParSeq > &H)

template<size_t K1, size_t K2, class ParSeq >
RecInt::ruint< K1 > *	fgemm (const Givaro::Modular< RecInt::ruint< K1 >, RecInt::ruint< K2 > > &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const RecInt::ruint< K1 > alpha, const RecInt::ruint< K1 > A, const size_t lda, const RecInt::ruint< K1 > B, const size_t ldb, RecInt::ruint< K1 > beta, RecInt::ruint< K1 > *C, const size_t ldc, MMHelper< Givaro::Modular< RecInt::ruint< K1 >, RecInt::ruint< K2 > >, MMHelperAlgo::Classic, ModeCategories::ConvertTo< ElementCategories::RNSElementTag >, ParSeq > &H)

template<class Field , class ModeT >
Field::Element_ptr	fgemm (const Field &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr B, const size_t ldb, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, MMHelper< Field, MMHelperAlgo::Winograd, ModeT > &H)

template<class Field , class ModeT , class Cut , class Param >
Field::Element_ptr	fgemm (const Field &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr B, const size_t ldb, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, MMHelper< Field, MMHelperAlgo::WinogradPar, ModeT, ParSeqHelper::Parallel< Cut, Param > > &H)

template<class Field >
Field::Element_ptr	fgemv (const Field &F, const FFLAS_TRANSPOSE ta, const size_t M, const size_t N, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr X, const size_t incX, const typename Field::Element beta, typename Field::Element_ptr Y, const size_t incY, MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::ConvertTo< ElementCategories::MachineFloatTag > > &H)

template<class Field >
Field::Element_ptr	fgemv (const Field &F, const FFLAS_TRANSPOSE ta, const size_t M, const size_t N, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr X, const size_t incX, const typename Field::Element beta, typename Field::Element_ptr Y, const size_t incY, MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::DelayedTag > &H)

template<class Field >
Field::Element_ptr	fgemv (const Field &F, const FFLAS_TRANSPOSE ta, const size_t M, const size_t N, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr X, const size_t incX, const typename Field::Element beta, typename Field::Element_ptr Y, const size_t incY, MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &H)

template<class Field >
Field::Element_ptr	fgemv (const Field &F, const FFLAS_TRANSPOSE ta, const size_t M, const size_t N, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr X, const size_t incX, const typename Field::Element beta, typename Field::Element_ptr Y, const size_t incY, MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::LazyTag > &H)

template<class Field >
Field::Element_ptr	fgemv (const Field &F, const FFLAS_TRANSPOSE TransA, const size_t M, const size_t N, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr X, const size_t incX, const typename Field::Element beta, typename Field::Element_ptr Y, const size_t incY)
	finite prime Field GEneral Matrix Vector multiplication. More...

Givaro::ZRing< int64_t >::Element_ptr	fgemv (const Givaro::ZRing< int64_t > &F, const FFLAS_TRANSPOSE ta, const size_t M, const size_t N, const int64_t alpha, const int64_t A, const size_t lda, const int64_t X, const size_t incX, const int64_t beta, int64_t *Y, const size_t incY, MMHelper< Givaro::ZRing< int64_t >, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &H)

Givaro::DoubleDomain::Element_ptr	fgemv (const Givaro::DoubleDomain &F, const FFLAS_TRANSPOSE ta, const size_t M, const size_t N, const Givaro::DoubleDomain::Element alpha, const Givaro::DoubleDomain::ConstElement_ptr A, const size_t lda, const Givaro::DoubleDomain::ConstElement_ptr X, const size_t incX, const Givaro::DoubleDomain::Element beta, Givaro::DoubleDomain::Element_ptr Y, const size_t incY, MMHelper< Givaro::DoubleDomain, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &H)

template<class Field >
Field::Element_ptr	fgemv (const Field &F, const FFLAS_TRANSPOSE ta, const size_t M, const size_t N, const typename Field::Element alpha, const typename Field::ConstElement_ptr A, const size_t lda, const typename Field::ConstElement_ptr X, const size_t incX, const typename Field::Element beta, typename Field::Element_ptr Y, const size_t incY, MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::DefaultBoundedTag > &H)

Givaro::FloatDomain::Element_ptr	fgemv (const Givaro::FloatDomain &F, const FFLAS_TRANSPOSE ta, const size_t M, const size_t N, const Givaro::FloatDomain::Element alpha, const Givaro::FloatDomain::ConstElement_ptr A, const size_t lda, const Givaro::FloatDomain::ConstElement_ptr X, const size_t incX, const Givaro::FloatDomain::Element beta, Givaro::FloatDomain::Element_ptr Y, const size_t incY, MMHelper< Givaro::FloatDomain, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &H)

template<class Field , class Cut , class Param >
Field::Element_ptr	fgemv (const Field &F, const FFLAS_TRANSPOSE ta, const size_t m, const size_t n, const typename Field::Element alpha, const typename Field::ConstElement_ptr A, const size_t lda, const typename Field::ConstElement_ptr X, const size_t incX, const typename Field::Element beta, typename Field::Element_ptr Y, const size_t incY, ParSeqHelper::Parallel< Cut, Param > &parH)

template<class Field >
Field::Element_ptr	fgemv (const Field &F, const FFLAS_TRANSPOSE ta, const size_t m, const size_t n, const typename Field::Element alpha, const typename Field::ConstElement_ptr A, const size_t lda, const typename Field::ConstElement_ptr X, const size_t incX, const typename Field::Element beta, typename Field::Element_ptr Y, const size_t incY, ParSeqHelper::Sequential &seqH)

FFPACK::rns_double::Element_ptr	fgemv (const FFPACK::RNSInteger< FFPACK::rns_double > &F, const FFLAS_TRANSPOSE ta, const size_t M, const size_t N, const FFPACK::rns_double::Element alpha, FFPACK::rns_double::ConstElement_ptr A, const size_t lda, FFPACK::rns_double::ConstElement_ptr X, const size_t incX, const FFPACK::rns_double::Element beta, FFPACK::rns_double::Element_ptr Y, const size_t incY, MMHelper< FFPACK::RNSInteger< FFPACK::rns_double >, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &H)

FFPACK::rns_double::Element_ptr	fgemv (const FFPACK::RNSIntegerMod< FFPACK::rns_double > &F, const FFLAS_TRANSPOSE ta, const size_t M, const size_t N, const FFPACK::rns_double::Element alpha, FFPACK::rns_double::ConstElement_ptr A, const size_t lda, FFPACK::rns_double::ConstElement_ptr X, const size_t incX, const FFPACK::rns_double::Element beta, FFPACK::rns_double::Element_ptr Y, const size_t incY, MMHelper< FFPACK::RNSIntegerMod< FFPACK::rns_double >, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &H)

Givaro::Integer *	fgemv (const Givaro::ZRing< Givaro::Integer > &F, const FFLAS_TRANSPOSE ta, const size_t m, const size_t n, const Givaro::Integer alpha, Givaro::Integer A, const size_t lda, Givaro::Integer X, const size_t ldx, Givaro::Integer beta, Givaro::Integer *Y, const size_t ldy, MMHelper< Givaro::ZRing< Givaro::Integer >, MMHelperAlgo::Classic, ModeCategories::ConvertTo< ElementCategories::RNSElementTag > > &H)

Givaro::Integer *	fgemv (const Givaro::Modular< Givaro::Integer > &F, const FFLAS_TRANSPOSE ta, const size_t m, const size_t n, const Givaro::Integer alpha, Givaro::Integer A, const size_t lda, Givaro::Integer X, const size_t ldx, Givaro::Integer beta, Givaro::Integer *Y, const size_t ldy, MMHelper< Givaro::Modular< Givaro::Integer >, MMHelperAlgo::Classic, ModeCategories::ConvertTo< ElementCategories::RNSElementTag > > &H)

template<size_t K1, size_t K2, class ParSeq >
RecInt::ruint< K1 > *	fgemv (const Givaro::Modular< RecInt::ruint< K1 >, RecInt::ruint< K2 > > &F, const FFLAS_TRANSPOSE ta, const size_t m, const size_t n, const RecInt::ruint< K1 > alpha, const RecInt::ruint< K1 > A, const size_t lda, const RecInt::ruint< K1 > X, const size_t incx, RecInt::ruint< K1 > beta, RecInt::ruint< K1 > *Y, const size_t incy, MMHelper< Givaro::Modular< RecInt::ruint< K1 >, RecInt::ruint< K2 > >, MMHelperAlgo::Classic, ModeCategories::ConvertTo< ElementCategories::RNSElementTag >, ParSeq > &H)

template<class Field >
void	fger (const Field &F, const size_t M, const size_t N, const typename Field::Element alpha, typename Field::ConstElement_ptr x, const size_t incx, typename Field::ConstElement_ptr y, const size_t incy, typename Field::Element_ptr A, const size_t lda)
	fger: rank one update of a general matrix More...

template<class Field >
void	fger (const Field &F, const size_t M, const size_t N, const typename Field::Element alpha, typename Field::ConstElement_ptr x, const size_t incx, typename Field::ConstElement_ptr y, const size_t incy, typename Field::Element_ptr A, const size_t lda, MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::ConvertTo< ElementCategories::MachineFloatTag > > &H)

template<class Field , class AnyTag >
void	fger (const Field &F, const size_t M, const size_t N, const typename Field::Element alpha, typename Field::ConstElement_ptr x, const size_t incx, typename Field::ConstElement_ptr y, const size_t incy, typename Field::Element_ptr A, const size_t lda, MMHelper< Field, MMHelperAlgo::Classic, AnyTag > &H)

void	fger (const Givaro::DoubleDomain &F, const size_t M, const size_t N, const Givaro::DoubleDomain::Element alpha, const Givaro::DoubleDomain::ConstElement_ptr x, const size_t incx, const Givaro::DoubleDomain::ConstElement_ptr y, const size_t incy, Givaro::DoubleDomain::Element_ptr A, const size_t lda, MMHelper< Givaro::DoubleDomain, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &H)

template<class Field >
void	fger (const Field &F, const size_t M, const size_t N, const typename Field::Element alpha, const typename Field::ConstElement_ptr x, const size_t incx, const typename Field::ConstElement_ptr y, const size_t incy, typename Field::Element_ptr A, const size_t lda, MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::DefaultBoundedTag > &H)

void	fger (const Givaro::FloatDomain &F, const size_t M, const size_t N, const Givaro::FloatDomain::Element alpha, const Givaro::FloatDomain::ConstElement_ptr x, const size_t incx, const Givaro::FloatDomain::ConstElement_ptr y, const size_t incy, Givaro::FloatDomain::Element_ptr A, const size_t lda, MMHelper< Givaro::FloatDomain, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &H)

template<class Field >
void	fger (const Field &F, const size_t M, const size_t N, const typename Field::Element alpha, typename Field::ConstElement_ptr x, const size_t incx, typename Field::ConstElement_ptr y, const size_t incy, typename Field::Element_ptr A, const size_t lda, MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::LazyTag > &H)

template<class Field >
void	fger (const Field &F, const size_t M, const size_t N, const typename Field::Element alpha, typename Field::ConstElement_ptr x, const size_t incx, typename Field::ConstElement_ptr y, const size_t incy, typename Field::Element_ptr A, const size_t lda, MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::DelayedTag > &H)

void	fger (const Givaro::Modular< Givaro::Integer > &F, const size_t M, const size_t N, const typename Givaro::Integer alpha, typename Givaro::Integer x, const size_t incx, typename Givaro::Integer y, const size_t incy, typename Givaro::Integer *A, const size_t lda, MMHelper< Givaro::Modular< Givaro::Integer >, MMHelperAlgo::Classic, ModeCategories::ConvertTo< ElementCategories::RNSElementTag > > &H)

template<typename RNS >
void	fger (const FFPACK::RNSInteger< RNS > &F, const size_t M, const size_t N, const typename FFPACK::RNSInteger< RNS >::Element alpha, typename FFPACK::RNSInteger< RNS >::Element_ptr x, const size_t incx, typename FFPACK::RNSInteger< RNS >::Element_ptr y, const size_t incy, typename FFPACK::RNSInteger< RNS >::Element_ptr A, const size_t lda, MMHelper< FFPACK::RNSInteger< RNS >, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &H)

template<typename RNS >
void	fger (const FFPACK::RNSIntegerMod< RNS > &F, const size_t M, const size_t N, const typename FFPACK::RNSIntegerMod< RNS >::Element alpha, typename FFPACK::RNSIntegerMod< RNS >::Element_ptr x, const size_t incx, typename FFPACK::RNSIntegerMod< RNS >::Element_ptr y, const size_t incy, typename FFPACK::RNSIntegerMod< RNS >::Element_ptr A, const size_t lda, MMHelper< FFPACK::RNSIntegerMod< RNS >, MMHelperAlgo::Classic > &H)

template<class Field >
void	freduce (const Field &F, const size_t n, typename Field::ConstElement_ptr Y, const size_t incY, typename Field::Element_ptr X, const size_t incX)
	freduce $x \gets y mod F$ . More...

template<class Field >
void	freduce (const Field &F, const size_t n, typename Field::Element_ptr X, const size_t incX)
	freduce $x \gets x mod F$ . More...

template<class Field >
void	freduce_constoverride (const Field &F, const size_t m, typename Field::ConstElement_ptr A, const size_t incX)

template<class Field , class ConstOtherElement_ptr >
void	finit (const Field &F, const size_t n, ConstOtherElement_ptr Y, const size_t incY, typename Field::Element_ptr X, const size_t incX)

template<class Field >
void	finit (const Field &F, const size_t n, typename Field::Element_ptr X, const size_t incX)
	finit Initializes `X` in `F$`. More...

template<class Field >
void	freduce (const Field &F, const size_t m, const size_t n, typename Field::Element_ptr A, const size_t lda)
	freduce $A \gets A mod F$ . More...

template<class Field >
void	freduce (const Field &F, const FFLAS_UPLO uplo, const size_t N, typename Field::Element_ptr A, const size_t lda)
	freduce for square symmetric matrices More...

template<class Field >
void	pfreduce (const Field &F, const size_t m, const size_t n, typename Field::Element_ptr A, const size_t lda, const size_t numths)

template<class Field >
void	freduce (const Field &F, const size_t m, const size_t n, typename Field::ConstElement_ptr B, const size_t ldb, typename Field::Element_ptr A, const size_t lda)
	freduce $A \gets B mod F$ . More...

template<class Field >
void	freduce_constoverride (const Field &F, const size_t m, const size_t n, typename Field::ConstElement_ptr A, const size_t lda)

template<class Field , class OtherElement_ptr >
void	finit (const Field &F, const size_t m, const size_t n, const OtherElement_ptr B, const size_t ldb, typename Field::Element_ptr A, const size_t lda)
	finit $A \gets B mod F$ . More...

template<class Field >
void	finit (const Field &F, const size_t m, const size_t n, typename Field::Element_ptr A, const size_t lda)

template<>
void	freduce (const FFPACK::RNSIntegerMod< FFPACK::rns_double > &F, const size_t n, FFPACK::RNSIntegerMod< FFPACK::rns_double >::Element_ptr A, size_t inc)

template<>
void	freduce (const FFPACK::RNSIntegerMod< FFPACK::rns_double > &F, const size_t m, const size_t n, FFPACK::rns_double::Element_ptr A, size_t lda)

template<class Field >
bool	freivalds (const Field &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr B, const size_t ldb, typename Field::ConstElement_ptr C, const size_t ldc)
	freivalds: Freivalds GEneral Matrix Multiply Random Check. More...

template<class Field >
void	fscalin (const Field &F, const size_t n, const typename Field::Element alpha, typename Field::Element_ptr X, const size_t incX)
	fscalin $x \gets \alpha \cdot x$ . More...

template<class Field >
void	fscal (const Field &F, const size_t n, const typename Field::Element alpha, typename Field::ConstElement_ptr X, const size_t incX, typename Field::Element_ptr Y, const size_t incY)
	fscal $y \gets \alpha \cdot x$ . More...

template<>
void	fscal (const Givaro::DoubleDomain &, const size_t N, const Givaro::DoubleDomain::Element a, Givaro::DoubleDomain::ConstElement_ptr x, const size_t incx, Givaro::DoubleDomain::Element_ptr y, const size_t incy)

template<>
void	fscal (const Givaro::FloatDomain &, const size_t N, const Givaro::FloatDomain::Element a, Givaro::FloatDomain::ConstElement_ptr x, const size_t incx, Givaro::FloatDomain::Element_ptr y, const size_t incy)

template<>
void	fscalin (const Givaro::DoubleDomain &, const size_t N, const Givaro::DoubleDomain::Element a, Givaro::DoubleDomain::Element_ptr y, const size_t incy)

template<>
void	fscalin (const Givaro::FloatDomain &, const size_t N, const Givaro::FloatDomain::Element a, Givaro::FloatDomain::Element_ptr y, const size_t incy)

template<class Field >
void	fscalin (const Field &F, const size_t m, const size_t n, const typename Field::Element alpha, typename Field::Element_ptr A, const size_t lda)
	fscalin $A \gets a \cdot A$ . More...

template<class Field >
void	fscal (const Field &F, const size_t m, const size_t n, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr B, const size_t ldb)
	fscal $B \gets a \cdot A$ . More...

template<>
void	fscalin (const FFPACK::RNSInteger< FFPACK::rns_double > &F, const size_t n, const FFPACK::rns_double::Element alpha, FFPACK::rns_double::Element_ptr A, const size_t inc)

template<>
void	fscal (const FFPACK::RNSInteger< FFPACK::rns_double > &F, const size_t n, const FFPACK::rns_double::Element alpha, FFPACK::rns_double::ConstElement_ptr A, const size_t Ainc, FFPACK::rns_double::Element_ptr B, const size_t Binc)

template<>
void	fscalin (const FFPACK::RNSInteger< FFPACK::rns_double > &F, const size_t m, const size_t n, const FFPACK::rns_double::Element alpha, FFPACK::rns_double::Element_ptr A, const size_t lda)

template<>
void	fscal (const FFPACK::RNSInteger< FFPACK::rns_double > &F, const size_t m, const size_t n, const FFPACK::rns_double::Element alpha, FFPACK::rns_double::ConstElement_ptr A, const size_t lda, FFPACK::rns_double::Element_ptr B, const size_t ldb)

template<>
void	fscalin (const FFPACK::RNSIntegerMod< FFPACK::rns_double > &F, const size_t n, const typename FFPACK::RNSIntegerMod< FFPACK::rns_double >::Element alpha, typename FFPACK::RNSIntegerMod< FFPACK::rns_double >::Element_ptr A, const size_t inc)

template<>
void	fscal (const FFPACK::RNSIntegerMod< FFPACK::rns_double > &F, const size_t n, const FFPACK::rns_double::Element alpha, FFPACK::rns_double::ConstElement_ptr A, const size_t Ainc, FFPACK::rns_double::Element_ptr B, const size_t Binc)

template<>
void	fscalin (const FFPACK::RNSIntegerMod< FFPACK::rns_double > &F, const size_t m, const size_t n, const FFPACK::rns_double::Element alpha, FFPACK::rns_double::Element_ptr A, const size_t lda)

template<>
void	fscal (const FFPACK::RNSIntegerMod< FFPACK::rns_double > &F, const size_t m, const size_t n, const FFPACK::rns_double::Element alpha, FFPACK::rns_double::ConstElement_ptr A, const size_t lda, FFPACK::rns_double::Element_ptr B, const size_t ldb)

template<class Field >
Field::Element_ptr	fsyr2k (const Field &F, const FFLAS_UPLO UpLo, const FFLAS_TRANSPOSE trans, const size_t n, const size_t k, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr B, const size_t ldb, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc)
	fsyr2k: Symmetric Rank 2K update More...

template<class Field >
Field::Element_ptr	fsyrk (const Field &F, const FFLAS_UPLO UpLo, const FFLAS_TRANSPOSE trans, const size_t n, const size_t k, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc)
	fsyrk: Symmetric Rank K update More...

template<class Field >
Field::Element_ptr	fsyrk (const Field &F, const FFLAS_UPLO UpLo, const FFLAS_TRANSPOSE trans, const size_t N, const size_t K, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, const ParSeqHelper::Sequential seq)

template<class Field >
Field::Element_ptr	fsyrk (const Field &F, const FFLAS_UPLO UpLo, const FFLAS_TRANSPOSE trans, const size_t N, const size_t K, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &H)

template<class Field >
Field::Element_ptr	fsyrk (const Field &F, const FFLAS_UPLO UpLo, const FFLAS_TRANSPOSE trans, const size_t N, const size_t K, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::ConvertTo< ElementCategories::MachineFloatTag >, ParSeqHelper::Sequential > &H)

template<class Field >
Field::Element_ptr	fsyrk (const Field &F, const FFLAS_UPLO UpLo, const FFLAS_TRANSPOSE trans, const size_t N, const size_t K, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::DelayedTag > &H)

template<class Field >
Field::Element_ptr	fsyrk (const Field &F, const FFLAS_UPLO UpLo, const FFLAS_TRANSPOSE trans, const size_t N, const size_t K, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::LazyTag > &H)

template<class Field , typename Mode >
Field::Element_ptr	fsyrk (const Field &F, const FFLAS_UPLO UpLo, const FFLAS_TRANSPOSE trans, const size_t N, const size_t K, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, MMHelper< Field, MMHelperAlgo::DivideAndConquer, Mode > &H)

template<class Field >
Field::Element_ptr	fsyrk (const Field &F, const FFLAS_UPLO UpLo, const FFLAS_TRANSPOSE trans, const size_t N, const size_t K, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::DefaultBoundedTag > &H)

Givaro::FloatDomain::Element_ptr	fsyrk (const Givaro::FloatDomain &F, const FFLAS_UPLO UpLo, const FFLAS_TRANSPOSE trans, const size_t N, const size_t K, const Givaro::FloatDomain::Element alpha, Givaro::FloatDomain::ConstElement_ptr A, const size_t lda, const Givaro::FloatDomain::Element beta, Givaro::FloatDomain::Element_ptr C, const size_t ldc, MMHelper< Givaro::FloatDomain, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &H)

Givaro::DoubleDomain::Element_ptr	fsyrk (const Givaro::DoubleDomain &F, const FFLAS_UPLO UpLo, const FFLAS_TRANSPOSE trans, const size_t N, const size_t K, const Givaro::DoubleDomain::Element alpha, Givaro::DoubleDomain::ConstElement_ptr A, const size_t lda, const Givaro::DoubleDomain::Element beta, Givaro::DoubleDomain::Element_ptr C, const size_t ldc, MMHelper< Givaro::DoubleDomain, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &H)

template<class Field >
Field::Element_ptr	fsyrk (const Field &F, const FFLAS_UPLO UpLo, const FFLAS_TRANSPOSE trans, const size_t n, const size_t k, const typename Field::Element alpha, typename Field::Element_ptr A, const size_t lda, typename Field::ConstElement_ptr D, const size_t incD, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, const size_t threshold=__FFLASFFPACK_FSYRK_THRESHOLD)
	fsyrk: Symmetric Rank K update with diagonal scaling More...

template<class Field >
Field::Element_ptr	fsyrk (const Field &F, const FFLAS_UPLO UpLo, const FFLAS_TRANSPOSE trans, const size_t N, const size_t K, const typename Field::Element alpha, typename Field::Element_ptr A, const size_t lda, typename Field::ConstElement_ptr D, const size_t incD, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, const ParSeqHelper::Sequential seq, const size_t threshold)

template<class Field , class Cut , class Param >
Field::Element_ptr	fsyrk (const Field &F, const FFLAS_UPLO UpLo, const FFLAS_TRANSPOSE trans, const size_t N, const size_t K, const typename Field::Element alpha, typename Field::Element_ptr A, const size_t lda, typename Field::ConstElement_ptr D, const size_t incD, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, const ParSeqHelper::Parallel< Cut, Param > par, const size_t threshold)

template<class Field >
Field::Element_ptr	fsyrk (const Field &F, const FFLAS_UPLO UpLo, const FFLAS_TRANSPOSE trans, const size_t n, const size_t k, const typename Field::Element alpha, typename Field::Element_ptr A, const size_t lda, typename Field::ConstElement_ptr D, const size_t incD, const std::vector< bool > &twoBlock, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, const size_t threshold=__FFLASFFPACK_FSYRK_THRESHOLD)
	fsyrk: Symmetric Rank K update with diagonal scaling More...

template<class Field , class FieldTrait >
void	computeS1S2 (const Field &F, const FFLAS_TRANSPOSE trans, const size_t N, const size_t K, const typename Field::Element x, const typename Field::Element y, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr S, const size_t lds, typename Field::Element_ptr T, const size_t ldt, MMHelper< Field, MMHelperAlgo::Winograd, FieldTrait > &WH)

template<class Field >
Field::Element_ptr	fsyrk (const Field &F, const FFLAS_UPLO UpLo, const FFLAS_TRANSPOSE trans, const size_t N, const size_t K, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, MMHelper< Field, MMHelperAlgo::Winograd, ModeCategories::DelayedTag, ParSeqHelper::Sequential > &H)

template<class Field , class Mode >
Field::Element_ptr	fsyrk (const Field &F, const FFLAS_UPLO UpLo, const FFLAS_TRANSPOSE trans, const size_t N, const size_t K, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, MMHelper< Field, MMHelperAlgo::Winograd, Mode > &H)

template<class Field , class FieldTrait >
Field::Element_ptr	fsyrk_strassen (const Field &F, const FFLAS_UPLO uplo, const FFLAS_TRANSPOSE trans, const size_t N, const size_t K, const typename Field::Element y1, const typename Field::Element y2, const typename Field::Element alpha, typename Field::Element_ptr A, const size_t lda, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, MMHelper< Field, MMHelperAlgo::Winograd, FieldTrait > &WH)

template<class Field >
void	ftrmm (const Field &F, const FFLAS_SIDE Side, const FFLAS_UPLO Uplo, const FFLAS_TRANSPOSE TransA, const FFLAS_DIAG Diag, const size_t M, const size_t N, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr B, const size_t ldb)
	ftrmm: TRiangular Matrix Multiply. More...

template<class Field >
void	ftrmm (const Field &F, const FFLAS_SIDE Side, const FFLAS_UPLO Uplo, const FFLAS_TRANSPOSE TransA, const FFLAS_DIAG Diag, const size_t M, const size_t N, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr B, const size_t ldb, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc)
	ftrmm: TRiangular Matrix Multiply with 3 operands Computes $C \gets \alpha \mathrm{op}(A) B + beta C$ or $C \gets \alpha B \mathrm{op}(A) + beta C$ . More...

template<class Field >
void	ftrsm (const Field &F, const FFLAS_SIDE Side, const FFLAS_UPLO Uplo, const FFLAS_TRANSPOSE TransA, const FFLAS_DIAG Diag, const size_t M, const size_t N, const typename Field::Element alpha, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr B, const size_t ldb)

template<class Field >
void	ftrsm (const Field &F, const FFLAS_SIDE Side, const FFLAS_UPLO Uplo, const FFLAS_TRANSPOSE TransA, const FFLAS_DIAG Diag, const size_t M, const size_t N, const typename Field::Element alpha, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr B, const size_t ldb, const ParSeqHelper::Sequential &PSH)

template<class Field , class Cut , class Param >
void	ftrsm (const Field &F, const FFLAS_SIDE Side, const FFLAS_UPLO Uplo, const FFLAS_TRANSPOSE TransA, const FFLAS_DIAG Diag, const size_t M, const size_t N, const typename Field::Element alpha, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr B, const size_t ldb, const ParSeqHelper::Parallel< Cut, Param > &PSH)

template<class Field , class ParSeqTrait = ParSeqHelper::Sequential>
void	ftrsm (const Field &F, const FFLAS_SIDE Side, const FFLAS_UPLO Uplo, const FFLAS_TRANSPOSE TransA, const FFLAS_DIAG Diag, const size_t M, const size_t N, const typename Field::Element alpha, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr B, const size_t ldb, TRSMHelper< StructureHelper::Recursive, ParSeqTrait > &H)

void	ftrsm (const Givaro::Modular< Givaro::Integer > &F, const FFLAS_SIDE Side, const FFLAS_UPLO Uplo, const FFLAS_TRANSPOSE TransA, const FFLAS_DIAG Diag, const size_t M, const size_t N, const Givaro::Integer alpha, const Givaro::Integer A, const size_t lda, Givaro::Integer B, const size_t ldb)

void	cblas_imptrsm (const enum FFLAS_ORDER Order, const enum FFLAS_SIDE Side, const enum FFLAS_UPLO Uplo, const enum FFLAS_TRANSPOSE TransA, const enum FFLAS_DIAG Diag, const int M, const int N, const FFPACK::rns_double_elt alpha, FFPACK::rns_double_elt_cstptr A, const int lda, FFPACK::rns_double_elt_ptr B, const int ldb)

template<class Field >
void	ftrsv (const Field &F, const FFLAS_UPLO Uplo, const FFLAS_TRANSPOSE TransA, const FFLAS_DIAG Diag, const size_t N, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr X, int incX)
	ftrsv: TRiangular System solve with Vector Computes $X \gets \mathrm{op}(A^{-1}) X$ More...

void	igemm_ (const enum FFLAS_ORDER Order, const enum FFLAS_TRANSPOSE TransA, const enum FFLAS_TRANSPOSE TransB, const size_t M, const size_t N, const size_t K, const int64_t alpha, const int64_t A, const size_t lda, const int64_t B, const size_t ldb, const int64_t beta, int64_t *C, const size_t ldc)

template<class Field , class OtherElement_ptr >
void	finit (const Field &F, const size_t n, const OtherElement_ptr Y, const size_t incY, typename Field::Element_ptr X, const size_t incX)
	finit $x \gets y mod F$ . More...

template<class Field , class OtherElement_ptr >
void	fconvert (const Field &F, const size_t n, OtherElement_ptr X, const size_t incX, typename Field::ConstElement_ptr Y, const size_t incY)
	fconvert $x \gets y mod F$ . More...

template<class Field >
void	fnegin (const Field &F, const size_t n, typename Field::Element_ptr X, const size_t incX)
	fnegin $x \gets - x$ . More...

template<class Field >
void	fneg (const Field &F, const size_t n, typename Field::ConstElement_ptr Y, const size_t incY, typename Field::Element_ptr X, const size_t incX)
	fneg $x \gets - y$ . More...

template<class Field >
void	fzero (const Field &F, const size_t n, typename Field::Element_ptr X, const size_t incX)
	fzero : $A \gets 0$ . More...

template<class Field , class RandIter >
void	frand (const Field &F, RandIter &G, const size_t n, typename Field::Element_ptr X, const size_t incX)
	frand : $A \gets random$ . More...

template<class Field >
bool	fiszero (const Field &F, const size_t n, typename Field::ConstElement_ptr X, const size_t incX)
	fiszero : test . More...

template<class Field >
bool	fequal (const Field &F, const size_t n, typename Field::ConstElement_ptr X, const size_t incX, typename Field::ConstElement_ptr Y, const size_t incY)
	fequal : test . More...

template<class Field >
void	faxpby (const Field &F, const size_t N, const typename Field::Element alpha, typename Field::ConstElement_ptr X, const size_t incX, const typename Field::Element beta, typename Field::Element_ptr Y, const size_t incY)
	faxpby : $y \gets \alpha \cdot x + \beta \cdot y$ . More...

template<typename Field , class Cut , class Param >
Field::Element	fdot (const Field &F, const size_t N, typename Field::ConstElement_ptr X, const size_t incX, typename Field::ConstElement_ptr Y, const size_t incY, const ParSeqHelper::Parallel< Cut, Param > par)

template<class Field >
void	fswap (const Field &F, const size_t N, typename Field::Element_ptr X, const size_t incX, typename Field::Element_ptr Y, const size_t incY)
	fswap: $X \leftrightarrow Y$ . More...

template<class Field >
void	fzero (const Field &F, const size_t m, const size_t n, typename Field::Element_ptr A, const size_t lda)
	fzero : $A \gets 0$ . More...

template<class Field >
void	fzero (const Field &F, const FFLAS_UPLO shape, const FFLAS_DIAG diag, const size_t n, typename Field::Element_ptr A, const size_t lda)
	fzero : $A \gets 0$ for a triangular matrix. More...

template<class Field , class RandIter >
void	frand (const Field &F, RandIter &G, const size_t m, const size_t n, typename Field::Element_ptr A, const size_t lda)
	frand : $A \gets random$ . More...

template<class Field >
bool	fequal (const Field &F, const size_t m, const size_t n, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr B, const size_t ldb)
	fequal : test . More...

template<class Field >
bool	fiszero (const Field &F, const size_t m, const size_t n, typename Field::ConstElement_ptr A, const size_t lda)
	fiszero : test . More...

template<class Field >
void	fidentity (const Field &F, const size_t m, const size_t n, typename Field::Element_ptr A, const size_t lda, const typename Field::Element &d)
	creates a diagonal matrix More...

template<class Field >
void	fidentity (const Field &F, const size_t m, const size_t n, typename Field::Element_ptr A, const size_t lda)
	creates a diagonal matrix More...

template<class Field , class OtherElement_ptr >
void	finit (const Field &F, const size_t m, const size_t n, typename Field::Element_ptr A, const size_t lda)
	finit Initializes `A` in `F$`. More...

template<class Field , class OtherElement_ptr >
void	fconvert (const Field &F, const size_t m, const size_t n, OtherElement_ptr A, const size_t lda, typename Field::ConstElement_ptr B, const size_t ldb)
	fconvert $A \gets B mod F$ . More...

template<class Field >
void	fnegin (const Field &F, const size_t m, const size_t n, typename Field::Element_ptr A, const size_t lda)
	fnegin $A \gets - A$ . More...

template<class Field >
void	fneg (const Field &F, const size_t m, const size_t n, typename Field::ConstElement_ptr B, const size_t ldb, typename Field::Element_ptr A, const size_t lda)
	fneg $A \gets - B$ . More...

template<class Field >
void	faxpby (const Field &F, const size_t m, const size_t n, const typename Field::Element alpha, typename Field::ConstElement_ptr X, const size_t ldx, const typename Field::Element beta, typename Field::Element_ptr Y, const size_t ldy)
	faxpby : $y \gets \alpha \cdot x + \beta \cdot y$ . More...

template<class Field >
void	fmove (const Field &F, const size_t m, const size_t n, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr B, const size_t ldb)
	fmove : $A \gets B$ and $B \gets 0$ . More...

template<class Field >
size_t	bitsize (const Field &F, size_t M, size_t N, const typename Field::ConstElement_ptr A, size_t lda)
	bitsize: Computes the largest bitsize of the matrix' coefficients. More...

template<>
size_t	bitsize< Givaro::ZRing< Givaro::Integer > > (const Givaro::ZRing< Givaro::Integer > &F, size_t M, size_t N, const Givaro::Integer *A, size_t lda)

template<class Field >
void	ftrmv (const Field &F, const FFLAS_UPLO Uplo, const FFLAS_TRANSPOSE TransA, const FFLAS_DIAG Diag, const size_t N, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr X, int incX)
	ftrsm: TRiangular Matrix Vector prodcut Computes $X \gets \mathrm{op}(A) X$ More...

template<class Field >
void	ftrsm (const Field &F, const FFLAS_SIDE Side, const FFLAS_UPLO Uplo, const FFLAS_TRANSPOSE TransA, const FFLAS_DIAG Diag, const size_t M, const size_t N, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr B, const size_t ldb)
	ftrsm: TRiangular System solve with Matrix. More...

template<class Field , typename FieldTrait >
Field::Element_ptr	fsyrk_strassen (const Field &F, const FFLAS_UPLO UpLo, const FFLAS_TRANSPOSE trans, const size_t N, const size_t K, const typename Field::Element y1, const typename Field::Element y2, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, MMHelper< Field, MMHelperAlgo::Winograd, FieldTrait > &H)

template<typename Field >
Field::Element_ptr	pfgemm (const Field &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr B, const size_t ldb, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, size_t numthreads=0)

template<class Field >
Field::Element *	pfgemm_1D_rec (const Field &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename Field::Element alpha, const typename Field::Element_ptr A, const size_t lda, const typename Field::Element_ptr B, const size_t ldb, const typename Field::Element beta, typename Field::Element *C, const size_t ldc, size_t seuil)

template<class Field >
Field::Element *	pfgemm_2D_rec (const Field &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename Field::Element alpha, const typename Field::Element_ptr A, const size_t lda, const typename Field::Element_ptr B, const size_t ldb, const typename Field::Element beta, typename Field::Element *C, const size_t ldc, size_t seuil)

template<class Field >
Field::Element *	pfgemm_3D_rec (const Field &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename Field::Element alpha, const typename Field::Element_ptr A, const size_t lda, const typename Field::Element_ptr B, const size_t ldb, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, size_t seuil, size_t *x)

template<class Field >
Field::Element_ptr	pfgemm_3D_rec2 (const Field &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename Field::Element alpha, const typename Field::Element_ptr A, const size_t lda, const typename Field::Element_ptr B, const size_t ldb, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, size_t seuil, size_t *x)

template<class Field , class ModeTrait , class Strat , class Param >
std::enable_if<!std::is_same< ModeTrait, ModeCategories::ConvertTo< ElementCategories::RNSElementTag > >::value, typenameField::Element_ptr >::type	fgemm (const Field &F, const FFLAS::FFLAS_TRANSPOSE ta, const FFLAS::FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename Field::Element alpha, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr B, const size_t ldb, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, MMHelper< Field, MMHelperAlgo::Winograd, ModeTrait, ParSeqHelper::Parallel< Strat, Param > > &H)

template<class Field , class Cut , class Param >
Field::Element_ptr	ftrsm (const Field &F, const FFLAS::FFLAS_SIDE Side, const FFLAS::FFLAS_UPLO UpLo, const FFLAS::FFLAS_TRANSPOSE TA, const FFLAS::FFLAS_DIAG Diag, const size_t m, const size_t n, const typename Field::Element alpha, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr B, const size_t ldb, TRSMHelper< StructureHelper::Iterative, ParSeqHelper::Parallel< Cut, Param > > &H)

template<class Field , class Cut , class Param >
Field::Element_ptr	ftrsm (const Field &F, const FFLAS::FFLAS_SIDE Side, const FFLAS::FFLAS_UPLO UpLo, const FFLAS::FFLAS_TRANSPOSE TA, const FFLAS::FFLAS_DIAG Diag, const size_t m, const size_t n, const typename Field::Element alpha, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr B, const size_t ldb, TRSMHelper< StructureHelper::Hybrid, ParSeqHelper::Parallel< Cut, Param > > &H)

template<class Field , class SM >
void	fspmv (const Field &F, const SM &A, typename Field::ConstElement_ptr x, const typename Field::Element &beta, typename Field::Element_ptr y)

template<class Field , class SM >
void	fspmm (const Field &F, const SM &A, size_t blockSize, typename Field::ConstElement_ptr x, int ldx, const typename Field::Element &beta, typename Field::Element_ptr y, int ldy)

template<class Field , class IndexT >
void	sparse_init (const Field &F, Sparse< Field, SparseMatrix_t::COO > &A, const IndexT row, const IndexT col, typename Field::ConstElement_ptr dat, uint64_t rowdim, uint64_t coldim, uint64_t nnz)

template<class Field , class IndexT >
void	sparse_init (const Field &F, Sparse< Field, SparseMatrix_t::COO_ZO > &A, const IndexT row, const IndexT col, typename Field::ConstElement_ptr dat, uint64_t rowdim, uint64_t coldim, uint64_t nnz)

template<class Field >
void	sparse_delete (const Sparse< Field, SparseMatrix_t::COO > &A)

template<class Field >
void	sparse_delete (const Sparse< Field, SparseMatrix_t::COO_ZO > &A)

template<class Field , class IndexT >
void	sparse_init (const Field &F, Sparse< Field, SparseMatrix_t::CSR > &A, const IndexT row, const IndexT col, typename Field::ConstElement_ptr dat, uint64_t rowdim, uint64_t coldim, uint64_t nnz)

template<class Field , class IndexT >
void	sparse_init (const Field &F, Sparse< Field, SparseMatrix_t::CSR_ZO > &A, const IndexT row, const IndexT col, typename Field::ConstElement_ptr dat, uint64_t rowdim, uint64_t coldim, uint64_t nnz)

template<class Field >
void	sparse_delete (const Sparse< Field, SparseMatrix_t::CSR > &A)

template<class Field >
void	sparse_delete (const Sparse< Field, SparseMatrix_t::CSR_ZO > &A)

template<class Field >
std::ostream &	sparse_print (std::ostream &os, const Sparse< Field, SparseMatrix_t::CSR > &A)

template<class IndexT >
void	sparse_init (const Givaro::Modular< Givaro::Integer > &F, Sparse< Givaro::Modular< Givaro::Integer >, SparseMatrix_t::CSR > &A, const IndexT row, const IndexT col, Givaro::Integer *dat, uint64_t rowdim, uint64_t coldim, uint64_t nnz)

template<class IndexT >
void	sparse_init (const Givaro::ZRing< Givaro::Integer > &F, Sparse< Givaro::ZRing< Givaro::Integer >, SparseMatrix_t::CSR_ZO > &A, const IndexT row, const IndexT col, Givaro::Integer *dat, uint64_t rowdim, uint64_t coldim, uint64_t nnz)

template<class IndexT , size_t RECINT_SIZE>
void	sparse_init (const Givaro::ZRing< RecInt::rmint< RECINT_SIZE > > &F, Sparse< Givaro::ZRing< RecInt::rmint< RECINT_SIZE > >, SparseMatrix_t::CSR_ZO > &A, const IndexT row, const IndexT col, typename Givaro::ZRing< RecInt::rmint< RECINT_SIZE > >::Element_ptr dat, uint64_t rowdim, uint64_t coldim, uint64_t nnz)

template<class IndexT , size_t RECINT_SIZE>
void	sparse_init (const Givaro::ZRing< RecInt::rmint< RECINT_SIZE > > &F, Sparse< Givaro::ZRing< RecInt::rmint< RECINT_SIZE > >, SparseMatrix_t::CSR > &A, const IndexT row, const IndexT col, typename Givaro::ZRing< RecInt::rmint< RECINT_SIZE > >::Element_ptr dat, uint64_t rowdim, uint64_t coldim, uint64_t nnz)

template<class Field >
void	sparse_delete (const Sparse< Field, SparseMatrix_t::CSR_HYB > &A)

template<class Field , class IndexT >
void	sparse_init (const Field &F, Sparse< Field, SparseMatrix_t::CSR_HYB > &A, const IndexT row, const IndexT col, typename Field::ConstElement_ptr dat, uint64_t rowdim, uint64_t coldim, uint64_t nnz)

template<class Field , class IndexT >
void	sparse_init (const Field &F, Sparse< Field, SparseMatrix_t::ELL > &A, const IndexT row, const IndexT col, typename Field::ConstElement_ptr dat, uint64_t rowdim, uint64_t coldim, uint64_t nnz)

template<class Field , class IndexT >
void	sparse_init (const Field &F, Sparse< Field, SparseMatrix_t::ELL_ZO > &A, const IndexT row, const IndexT col, typename Field::ConstElement_ptr dat, uint64_t rowdim, uint64_t coldim, uint64_t nnz)

template<class Field >
void	sparse_delete (const Sparse< Field, SparseMatrix_t::ELL > &A)

template<class Field >
void	sparse_delete (const Sparse< Field, SparseMatrix_t::ELL_ZO > &A)

template<class Field >
void	fspmv (const Field &F, const Sparse< Field, SparseMatrix_t::ELL_R > &A, typename Field::ConstElement_ptr x, const typename Field::Element &beta, typename Field::Element_ptr y)

template<class Field >
void	fspmv (const Field &F, const Sparse< Field, SparseMatrix_t::ELL_R_ZO > &A, typename Field::ConstElement_ptr x, const typename Field::Element &beta, typename Field::Element_ptr y)

template<class Field >
void	fspmm (const Field &F, const Sparse< Field, SparseMatrix_t::ELL_R > &A, const size_t blockSize, const typename Field::Element_ptr &x, const int ldx, const typename Field::Element &beta, typename Field::Element_ptr &y, const int ldy)

template<class Field >
void	fspmm (const Field &F, const Sparse< Field, SparseMatrix_t::ELL_R_ZO > &A, const size_t blockSize, const typename Field::Element_ptr &x, const int ldx, const typename Field::Element &beta, typename Field::Element_ptr &y, const int ldy)

template<class Field >
void	fspmv (const Field &F, const Sparse< Field, SparseMatrix_t::ELL_R > &A, typename Field::ConstElement_ptr x, typename Field::Element_ptr y, FieldCategories::GenericTag)

template<class Field >
void	fspmv (const Field &F, const Sparse< Field, SparseMatrix_t::ELL_R > &A, typename Field::ConstElement_ptr x, typename Field::Element_ptr y, FieldCategories::UnparametricTag)

template<class Field >
void	fspmv (const Field &F, const Sparse< Field, SparseMatrix_t::ELL_R > &A, typename Field::ConstElement_ptr x, typename Field::Element_ptr y, FieldCategories::ModularTag)

template<class Field >
void	fspmv (const Field &F, const Sparse< Field, SparseMatrix_t::ELL_R_ZO > &A, typename Field::ConstElement_ptr x, typename Field::Element_ptr y, FieldCategories::GenericTag)

template<class Field >
void	fspmv (const Field &F, const Sparse< Field, SparseMatrix_t::ELL_R_ZO > &A, typename Field::ConstElement_ptr x, typename Field::Element_ptr y, FieldCategories::UnparametricTag)

template<class Field >
void	fspmv (const Field &F, const Sparse< Field, SparseMatrix_t::ELL_R_ZO > &A, typename Field::ConstElement_ptr x, typename Field::Element_ptr y, FieldCategories::ModularTag)

template<class Field >
void	sparse_delete (const Sparse< Field, SparseMatrix_t::ELL_R > &A)

template<class Field >
void	sparse_delete (const Sparse< Field, SparseMatrix_t::ELL_R_ZO > &A)

template<class Field , class IndexT >
void	sparse_init (const Field &F, Sparse< Field, SparseMatrix_t::ELL_R > &A, const IndexT row, const IndexT col, typename Field::ConstElement_ptr dat, uint64_t rowdim, uint64_t coldim, uint64_t nnz)

template<class Field , class IndexT >
void	sparse_init (const Field &F, Sparse< Field, SparseMatrix_t::ELL_R_ZO > &A, const IndexT row, const IndexT col, typename Field::ConstElement_ptr dat, uint64_t rowdim, uint64_t coldim, uint64_t nnz)

template<class Field , class IndexT >
void	sparse_init (const Field &F, Sparse< Field, SparseMatrix_t::ELL_simd > &A, const IndexT row, const IndexT col, typename Field::ConstElement_ptr dat, uint64_t rowdim, uint64_t coldim, uint64_t nnz)

template<class Field , class IndexT >
void	sparse_init (const Field &F, Sparse< Field, SparseMatrix_t::ELL_simd_ZO > &A, const IndexT row, const IndexT col, typename Field::ConstElement_ptr dat, uint64_t rowdim, uint64_t coldim, uint64_t nnz)

template<class Field >
void	sparse_delete (const Sparse< Field, SparseMatrix_t::ELL_simd > &A)

template<class Field >
void	sparse_delete (const Sparse< Field, SparseMatrix_t::ELL_simd_ZO > &A)

template<class Field >
void	sparse_print (const Sparse< Field, SparseMatrix_t::ELL_simd > &A)

template<class Field >
void	sparse_delete (const Sparse< Field, SparseMatrix_t::HYB_ZO > &A)

template<class Field , class IndexT >
void	sparse_init (const Field &F, Sparse< Field, SparseMatrix_t::HYB_ZO > &A, const IndexT row, const IndexT col, typename Field::ConstElement_ptr dat, uint64_t rowdim, uint64_t coldim, uint64_t nnz)

template<typename _Field >
std::ostream &	operator<< (std::ostream &os, const Sparse< _Field, SparseMatrix_t::HYB_ZO > &A)

template<class Field , bool sorted = true, bool read_integer = false>
void	readSmsFormat (const std::string &path, const Field &f, index_t &row, index_t &col, typename Field::Element_ptr &val, index_t &rowdim, index_t &coldim, uint64_t &nnz)

template<class Field >
void	readSprFormat (const std::string &path, const Field &f, index_t &row, index_t &col, typename Field::Element_ptr &val, index_t &rowdim, index_t &coldim, uint64_t &nnz)

template<class T >
std::enable_if< std::is_integral< T >::value, int >	getDataType ()

template<class T >
std::enable_if< std::is_floating_point< T >::value, int >	getDataType ()

template<class T >
std::enable_if< std::is_same< T, mpz_t >::value, int >	getDataType ()

template<class T >
int	getDataType ()

template<class Field >
void	readMachineType (const Field &F, typename Field::Element &modulo, typename Field::Element_ptr val, std::ifstream &file, const uint64_t dims, const mask_t data_type, const mask_t field_desc)

template<class Field >
void	readDnsFormat (const std::string &path, const Field &F, index_t &rowdim, index_t &coldim, typename Field::Element_ptr &val)

template<class Field >
void	writeDnsFormat (const std::string &path, const Field &F, const index_t &rowdim, const index_t &coldim, typename Field::Element_ptr A, index_t ldA)

template<class Field >
void	fspmv (const Field &F, const Sparse< Field, SparseMatrix_t::SELL_ZO > &A, typename Field::ConstElement_ptr x, typename Field::Element_ptr y, FieldCategories::ModularTag)

template<class Field >
void	sparse_delete (const Sparse< Field, SparseMatrix_t::SELL > &A)

template<class Field >
void	sparse_delete (const Sparse< Field, SparseMatrix_t::SELL_ZO > &A)

template<class Field >
void	sparse_print (const Sparse< Field, SparseMatrix_t::SELL > &A)

template<class Field , class IndexT >
void	sparse_init (const Field &F, Sparse< Field, SparseMatrix_t::SELL > &A, const IndexT row, const IndexT col, typename Field::ConstElement_ptr dat, uint64_t rowdim, uint64_t coldim, uint64_t nnz, uint64_t sigma=0)

template<class Field , class IndexT >
void	sparse_init (const Field &F, Sparse< Field, SparseMatrix_t::SELL_ZO > &A, const IndexT row, const IndexT col, typename Field::ConstElement_ptr dat, uint64_t rowdim, uint64_t coldim, uint64_t nnz)

template<class It >
double	computeDeviation (It begin, It end)

template<class Field >
StatsMatrix	getStat (const Field &F, const index_t row, const index_t col, typename Field::ConstElement_ptr val, uint64_t rowdim, uint64_t coldim, uint64_t nnz)

template<class Field , class enable = void>
Field::Residu_t	maxCardinality ()

template<>
uint64_t	maxCardinality< Givaro::Modular< int64_t > > ()

template<>
uint32_t	maxCardinality< Givaro::Modular< int32_t > > ()

template<class Field >
Field::Residu_t	minCardinality ()

template<>
void	fflas_delete (FFPACK::rns_double_elt_ptr A)

template<>
void	fflas_delete (FFPACK::rns_double_elt_cstptr A)

template<>
FFPACK::rns_double_elt_ptr	fflas_new (const FFPACK::RNSIntegerMod< FFPACK::rns_double > &F, const size_t m, const Alignment align)

template<>
FFPACK::rns_double_elt_ptr	fflas_new (const FFPACK::RNSIntegerMod< FFPACK::rns_double > &F, const size_t m, const size_t n, const Alignment align)

template<typename RNS >
void	finit_rns (const FFPACK::RNSIntegerMod< RNS > &F, const size_t m, const size_t n, size_t k, const Givaro::Integer *B, const size_t ldb, typename RNS::Element_ptr A)

template<typename RNS >
void	finit_trans_rns (const FFPACK::RNSIntegerMod< RNS > &F, const size_t m, const size_t n, size_t k, const Givaro::Integer *B, const size_t ldb, typename RNS::Element_ptr A)

template<typename RNS >
void	fconvert_rns (const FFPACK::RNSIntegerMod< RNS > &F, const size_t m, const size_t n, Givaro::Integer alpha, Givaro::Integer *B, const size_t ldb, typename RNS::ConstElement_ptr A)

template<typename RNS >
void	fconvert_trans_rns (const FFPACK::RNSIntegerMod< RNS > &F, const size_t m, const size_t n, Givaro::Integer alpha, Givaro::Integer *B, const size_t ldb, typename RNS::ConstElement_ptr A)

template<>
FFPACK::rns_double_elt_ptr	fflas_new (const FFPACK::RNSInteger< FFPACK::rns_double > &F, const size_t m, const Alignment align)

template<>
FFPACK::rns_double_elt_ptr	fflas_new (const FFPACK::RNSInteger< FFPACK::rns_double > &F, const size_t m, const size_t n, const Alignment align)

template<typename RNS >
void	finit_rns (const FFPACK::RNSInteger< RNS > &F, const size_t m, const size_t n, size_t k, const Givaro::Integer *B, const size_t ldb, typename FFPACK::RNSInteger< RNS >::Element_ptr A)

template<typename RNS >
void	fconvert_rns (const FFPACK::RNSInteger< RNS > &F, const size_t m, const size_t n, Givaro::Integer alpha, Givaro::Integer *B, const size_t ldb, typename FFPACK::RNSInteger< RNS >::ConstElement_ptr A)

template INST_OR_DECL void	freduce (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t n, FFLAS_ELT *X, const size_t incX)
	freduce $x \gets x mod F$ . More...

template INST_OR_DECL void	freduce (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t n, const FFLAS_ELT Y, const size_t incY, FFLAS_ELT X, const size_t incX)
	freduce $x \gets y mod F$ . More...

template INST_OR_DECL void	finit (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t n, const FFLAS_ELT Y, const size_t incY, FFLAS_ELT X, const size_t incX)
	finit $x \gets y mod F$ . More...

template INST_OR_DECL void	fconvert (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t n, FFLAS_ELT X, const size_t incX, const FFLAS_ELT Y, const size_t incY)
	fconvert $x \gets y mod F$ . More...

template INST_OR_DECL void	fnegin (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t n, FFLAS_ELT *X, const size_t incX)
	fnegin $x \gets - x$ . More...

template INST_OR_DECL void	fneg (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t n, const FFLAS_ELT Y, const size_t incY, FFLAS_ELT X, const size_t incX)
	fneg $x \gets - y$ . More...

template INST_OR_DECL void	fzero (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t n, FFLAS_ELT *X, const size_t incX)
	fzero : $A \gets 0$ . More...

template INST_OR_DECL bool	fiszero (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t n, const FFLAS_ELT *X, const size_t incX)
	fiszero : test . More...

template INST_OR_DECL bool	fequal (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t n, const FFLAS_ELT X, const size_t incX, const FFLAS_ELT Y, const size_t incY)
	fequal : test . More...

template INST_OR_DECL void	fassign (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t N, const FFLAS_ELT Y, const size_t incY, FFLAS_ELT X, const size_t incX)
	fassign : $x \gets y$ . More...

template INST_OR_DECL void	fscalin (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t n, const FFLAS_ELT alpha, FFLAS_ELT *X, const size_t incX)
	fscalin $x \gets \alpha \cdot x$ . More...

template INST_OR_DECL void	fscal (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t n, const FFLAS_ELT alpha, const FFLAS_ELT X, const size_t incX, FFLAS_ELT Y, const size_t incY)
	fscal $y \gets \alpha \cdot x$ . More...

template INST_OR_DECL void	faxpy (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t N, const FFLAS_ELT alpha, const FFLAS_ELT X, const size_t incX, FFLAS_ELT Y, const size_t incY)
	faxpy : $y \gets \alpha \cdot x + y$ . More...

template INST_OR_DECL FFLAS_ELT	fdot (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t N, const FFLAS_ELT X, const size_t incX, const FFLAS_ELT Y, const size_t incY)
	faxpby : $y \gets \alpha \cdot x + \beta \cdot y$ . More...

template INST_OR_DECL void	fswap (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t N, FFLAS_ELT X, const size_t incX, FFLAS_ELT Y, const size_t incY)
	fswap: $X \leftrightarrow Y$ . More...

template INST_OR_DECL void	fadd (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t N, const FFLAS_ELT A, const size_t inca, const FFLAS_ELT B, const size_t incb, FFLAS_ELT *C, const size_t incc)

template INST_OR_DECL void	fsub (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t N, const FFLAS_ELT A, const size_t inca, const FFLAS_ELT B, const size_t incb, FFLAS_ELT *C, const size_t incc)

template INST_OR_DECL void	faddin (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t N, const FFLAS_ELT B, const size_t incb, FFLAS_ELT C, const size_t incc)

template INST_OR_DECL void	fadd (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t N, const FFLAS_ELT A, const size_t inca, const FFLAS_ELT alpha, const FFLAS_ELT B, const size_t incb, FFLAS_ELT *C, const size_t incc)

template INST_OR_DECL void	fassign (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t m, const size_t n, const FFLAS_ELT B, const size_t ldb, FFLAS_ELT A, const size_t lda)
	fassign : $A \gets B$ . More...

template INST_OR_DECL void	fzero (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t m, const size_t n, FFLAS_ELT *A, const size_t lda)
	fzero : $A \gets 0$ . More...

template INST_OR_DECL bool	fequal (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t m, const size_t n, const FFLAS_ELT A, const size_t lda, const FFLAS_ELT B, const size_t ldb)
	fequal : test . More...

template INST_OR_DECL bool	fiszero (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t m, const size_t n, const FFLAS_ELT *A, const size_t lda)
	fiszero : test . More...

template INST_OR_DECL void	fidentity (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t m, const size_t n, FFLAS_ELT *A, const size_t lda, const FFLAS_ELT &d)
	creates a diagonal matrix More...

template INST_OR_DECL void	fidentity (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t m, const size_t n, FFLAS_ELT *A, const size_t lda)
	creates a diagonal matrix More...

template INST_OR_DECL void	freduce (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t m, const size_t n, FFLAS_ELT *A, const size_t lda)
	freduce $A \gets A mod F$ . More...

template INST_OR_DECL void	freduce (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t m, const size_t n, const FFLAS_ELT B, const size_t ldb, FFLAS_ELT A, const size_t lda)
	freduce $A \gets B mod F$ . More...

template INST_OR_DECL void	finit (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t m, const size_t n, const FFLAS_ELT B, const size_t ldb, FFLAS_ELT A, const size_t lda)
	finit $A \gets B mod F$ . More...

template INST_OR_DECL void	fnegin (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t m, const size_t n, FFLAS_ELT *A, const size_t lda)
	fnegin $A \gets - A$ . More...

template INST_OR_DECL void	fneg (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t m, const size_t n, const FFLAS_ELT B, const size_t ldb, FFLAS_ELT A, const size_t lda)
	fneg $A \gets - B$ . More...

template INST_OR_DECL void	fscalin (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t m, const size_t n, const FFLAS_ELT alpha, FFLAS_ELT *A, const size_t lda)
	fscalin $A \gets a \cdot A$ . More...

template INST_OR_DECL void	fscal (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t m, const size_t n, const FFLAS_ELT alpha, const FFLAS_ELT A, const size_t lda, FFLAS_ELT B, const size_t ldb)
	fscal $B \gets a \cdot A$ . More...

template INST_OR_DECL void	faxpy (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t m, const size_t n, const FFLAS_ELT alpha, const FFLAS_ELT X, const size_t ldx, FFLAS_ELT Y, const size_t ldy)
	faxpy : $y \gets \alpha \cdot x + y$ . More...

template INST_OR_DECL void	fmove (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t m, const size_t n, FFLAS_ELT A, const size_t lda, FFLAS_ELT B, const size_t ldb)
	faxpby : $y \gets \alpha \cdot x + \beta \cdot y$ . More...

template INST_OR_DECL void	fadd (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t M, const size_t N, const FFLAS_ELT A, const size_t lda, const FFLAS_ELT B, const size_t ldb, FFLAS_ELT *C, const size_t ldc)
	fadd : matrix addition. More...

template INST_OR_DECL void	fsub (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t M, const size_t N, const FFLAS_ELT A, const size_t lda, const FFLAS_ELT B, const size_t ldb, FFLAS_ELT *C, const size_t ldc)
	fsub : matrix subtraction. More...

template INST_OR_DECL void	fsubin (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t M, const size_t N, const FFLAS_ELT B, const size_t ldb, FFLAS_ELT C, const size_t ldc)
	fsubin C = C - B More...

template INST_OR_DECL void	fadd (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t M, const size_t N, const FFLAS_ELT A, const size_t lda, const FFLAS_ELT alpha, const FFLAS_ELT B, const size_t ldb, FFLAS_ELT *C, const size_t ldc)
	fadd : matrix addition with scaling. More...

template INST_OR_DECL void	faddin (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t M, const size_t N, const FFLAS_ELT B, const size_t ldb, FFLAS_ELT C, const size_t ldc)
	faddin More...

template INST_OR_DECL FFLAS_ELT *	fgemv (const FFLAS_FIELD< FFLAS_ELT > &F, const FFLAS_TRANSPOSE TransA, const size_t M, const size_t N, const FFLAS_ELT alpha, const FFLAS_ELT A, const size_t lda, const FFLAS_ELT X, const size_t incX, const FFLAS_ELT beta, FFLAS_ELT *Y, const size_t incY)
	finite prime FFLAS_FIELD<FFLAS_ELT> GEneral Matrix Vector multiplication. More...

template INST_OR_DECL void	fger (const FFLAS_FIELD< FFLAS_ELT > &F, const size_t M, const size_t N, const FFLAS_ELT alpha, const FFLAS_ELT x, const size_t incx, const FFLAS_ELT y, const size_t incy, FFLAS_ELT *A, const size_t lda)
	fger: rank one update of a general matrix More...

template INST_OR_DECL void	ftrsv (const FFLAS_FIELD< FFLAS_ELT > &F, const FFLAS_UPLO Uplo, const FFLAS_TRANSPOSE TransA, const FFLAS_DIAG Diag, const size_t N, const FFLAS_ELT A, const size_t lda, FFLAS_ELT X, int incX)
	ftrsv: TRiangular System solve with Vector Computes $X \gets \mathrm{op}(A^{-1}) X$ More...

template INST_OR_DECL void	ftrsm (const FFLAS_FIELD< FFLAS_ELT > &F, const FFLAS_SIDE Side, const FFLAS_UPLO Uplo, const FFLAS_TRANSPOSE TransA, const FFLAS_DIAG Diag, const size_t M, const size_t N, const FFLAS_ELT alpha, const FFLAS_ELT A, const size_t lda, FFLAS_ELT B, const size_t ldb)
	ftrsm: TRiangular System solve with Matrix. More...

template INST_OR_DECL void	ftrmm (const FFLAS_FIELD< FFLAS_ELT > &F, const FFLAS_SIDE Side, const FFLAS_UPLO Uplo, const FFLAS_TRANSPOSE TransA, const FFLAS_DIAG Diag, const size_t M, const size_t N, const FFLAS_ELT alpha, const FFLAS_ELT A, const size_t lda, FFLAS_ELT B, const size_t ldb)
	ftrmm: TRiangular Matrix Multiply. More...

template INST_OR_DECL FFLAS_ELT *	fgemm (const FFLAS_FIELD< FFLAS_ELT > &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const FFLAS_ELT alpha, const FFLAS_ELT A, const size_t lda, const FFLAS_ELT B, const size_t ldb, const FFLAS_ELT beta, FFLAS_ELT *C, const size_t ldc)
	fgemm: Field GEneral Matrix Multiply. More...

template INST_OR_DECL FFLAS_ELT *	fgemm (const FFLAS_FIELD< FFLAS_ELT > &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const FFLAS_ELT alpha, const FFLAS_ELT A, const size_t lda, const FFLAS_ELT B, const size_t ldb, const FFLAS_ELT beta, FFLAS_ELT *C, const size_t ldc, const ParSeqHelper::Sequential seq)

template INST_OR_DECL FFLAS_ELT *	fgemm (const FFLAS_FIELD< FFLAS_ELT > &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const FFLAS_ELT alpha, const FFLAS_ELT A, const size_t lda, const FFLAS_ELT B, const size_t ldb, const FFLAS_ELT beta, FFLAS_ELT *C, const size_t ldc, const ParSeqHelper::Parallel< CuttingStrategy::Recursive, StrategyParameter::TwoDAdaptive > par)

template INST_OR_DECL FFLAS_ELT *	fgemm (const FFLAS_FIELD< FFLAS_ELT > &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const FFLAS_ELT alpha, const FFLAS_ELT A, const size_t lda, const FFLAS_ELT B, const size_t ldb, const FFLAS_ELT beta, FFLAS_ELT *C, const size_t ldc, const ParSeqHelper::Parallel< CuttingStrategy::Block, StrategyParameter::Threads > par)

template INST_OR_DECL FFLAS_ELT *	fsquare (const FFLAS_FIELD< FFLAS_ELT > &F, const FFLAS_TRANSPOSE ta, const size_t n, const FFLAS_ELT alpha, const FFLAS_ELT A, const size_t lda, const FFLAS_ELT beta, FFLAS_ELT C, const size_t ldc)
	fsquare: Squares a matrix. More...

template<class Cut = CuttingStrategy::Block, class Strat = StrategyParameter::Threads>
void	BlockCuts (size_t &RBLOCKSIZE, size_t &CBLOCKSIZE, const size_t m, const size_t n, const size_t numthreads)

template<>
void	BlockCuts< CuttingStrategy::Single, StrategyParameter::Threads > (size_t &RBLOCKSIZE, size_t &CBLOCKSIZE, const size_t m, const size_t n, const size_t numthreads)

template<>
void	BlockCuts< CuttingStrategy::Row, StrategyParameter::Fixed > (size_t &RBLOCKSIZE, size_t &CBLOCKSIZE, const size_t m, const size_t n, const size_t numthreads)

template<>
void	BlockCuts< CuttingStrategy::Row, StrategyParameter::Grain > (size_t &RBLOCKSIZE, size_t &CBLOCKSIZE, const size_t m, const size_t n, const size_t grainsize)

template<>
void	BlockCuts< CuttingStrategy::Block, StrategyParameter::Grain > (size_t &RBLOCKSIZE, size_t &CBLOCKSIZE, const size_t m, const size_t n, const size_t grainsize)

template<>
void	BlockCuts< CuttingStrategy::Column, StrategyParameter::Fixed > (size_t &RBLOCKSIZE, size_t &CBLOCKSIZE, const size_t m, const size_t n, const size_t numthreads)

template<>
void	BlockCuts< CuttingStrategy::Column, StrategyParameter::Grain > (size_t &RBLOCKSIZE, size_t &CBLOCKSIZE, const size_t m, const size_t n, const size_t grainsize)

template<>
void	BlockCuts< CuttingStrategy::Block, StrategyParameter::Fixed > (size_t &RBLOCKSIZE, size_t &CBLOCKSIZE, const size_t m, const size_t n, const size_t numthreads)

template<>
void	BlockCuts< CuttingStrategy::Row, StrategyParameter::Threads > (size_t &RBLOCKSIZE, size_t &CBLOCKSIZE, const size_t m, const size_t n, const size_t numthreads)

template<>
void	BlockCuts< CuttingStrategy::Column, StrategyParameter::Threads > (size_t &RBLOCKSIZE, size_t &CBLOCKSIZE, const size_t m, const size_t n, const size_t numthreads)

template<>
void	BlockCuts< CuttingStrategy::Block, StrategyParameter::Threads > (size_t &RBLOCKSIZE, size_t &CBLOCKSIZE, const size_t m, const size_t n, const size_t numthreads)

template<class Cut = CuttingStrategy::Block, class Param = StrategyParameter::Threads>
void	BlockCuts (size_t &rowBlockSize, size_t &colBlockSize, size_t &lastRBS, size_t &lastCBS, size_t &changeRBS, size_t &changeCBS, size_t &numRowBlock, size_t &numColBlock, size_t m, size_t n, const size_t numthreads)

template<class Field >
void	pfzero (const Field &F, size_t m, size_t n, typename Field::Element_ptr C, size_t BS=0)

template<class Field , class RandIter >
void	pfrand (const Field &F, RandIter &G, size_t m, size_t n, typename Field::Element_ptr C, size_t BS=0)

template<class Field , class Cut , class Param >
Field::Element &	fdot (const Field &F, const size_t N, typename Field::ConstElement_ptr x, const size_t incx, typename Field::ConstElement_ptr y, const size_t incy, typename Field::Element &d, const ParSeqHelper::Parallel< Cut, Param > par)

template<class Field , class AlgoT , class FieldTrait >
Field::Element *	pfgemm (const Field &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename Field::Element alpha, const typename Field::ConstElement_ptr A, const size_t lda, const typename Field::ConstElement_ptr B, const size_t ldb, const typename Field::Element beta, typename Field::Element *C, const size_t ldc, MMHelper< Field, AlgoT, FieldTrait, ParSeqHelper::Parallel< CuttingStrategy::Block, StrategyParameter::Threads > > &H)

template<class Field , class AlgoT , class FieldTrait >
Field::Element *	pfgemm (const Field &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename Field::Element alpha, const typename Field::ConstElement_ptr AA, const size_t lda, const typename Field::ConstElement_ptr BB, const size_t ldb, const typename Field::Element beta, typename Field::Element *C, const size_t ldc, MMHelper< Field, AlgoT, FieldTrait, ParSeqHelper::Parallel< CuttingStrategy::Recursive, StrategyParameter::ThreeDAdaptive > > &H)

template<class Field , class AlgoT , class FieldTrait >
Field::Element *	pfgemm (const Field &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename Field::Element alpha, const typename Field::ConstElement_ptr AA, const size_t lda, const typename Field::ConstElement_ptr BB, const size_t ldb, const typename Field::Element beta, typename Field::Element *C, const size_t ldc, MMHelper< Field, AlgoT, FieldTrait, ParSeqHelper::Parallel< CuttingStrategy::Recursive, StrategyParameter::TwoDAdaptive > > &H)

template<class Field , class AlgoT , class FieldTrait >
Field::Element *	pfgemm (const Field &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename Field::Element alpha, const typename Field::ConstElement_ptr AA, const size_t lda, const typename Field::ConstElement_ptr BB, const size_t ldb, const typename Field::Element beta, typename Field::Element *C, const size_t ldc, MMHelper< Field, AlgoT, FieldTrait, ParSeqHelper::Parallel< CuttingStrategy::Recursive, StrategyParameter::TwoD > > &H)

template<class Field , class AlgoT , class FieldTrait >
Field::Element_ptr	pfgemm (const Field &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename Field::Element alpha, const typename Field::ConstElement_ptr A, const size_t lda, const typename Field::ConstElement_ptr B, const size_t ldb, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, MMHelper< Field, AlgoT, FieldTrait, ParSeqHelper::Parallel< CuttingStrategy::Recursive, StrategyParameter::ThreeD > > &H)

template<class Field , class AlgoT , class FieldTrait >
Field::Element *	pfgemm (const Field &F, const FFLAS_TRANSPOSE ta, const FFLAS_TRANSPOSE tb, const size_t m, const size_t n, const size_t k, const typename Field::Element alpha, const typename Field::ConstElement_ptr A, const size_t lda, const typename Field::ConstElement_ptr B, const size_t ldb, const typename Field::Element beta, typename Field::Element_ptr C, const size_t ldc, MMHelper< Field, AlgoT, FieldTrait, ParSeqHelper::Parallel< CuttingStrategy::Recursive, StrategyParameter::ThreeDInPlace > > &H)

template<class Field , class AlgoT , class FieldTrait >
Field::Element_ptr	fgemv (const Field &F, const FFLAS_TRANSPOSE ta, const size_t m, const size_t n, const typename Field::Element alpha, const typename Field::ConstElement_ptr A, const size_t lda, const typename Field::ConstElement_ptr X, const size_t incX, const typename Field::Element beta, typename Field::Element_ptr Y, const size_t incY, MMHelper< Field, AlgoT, FieldTrait, ParSeqHelper::Parallel< CuttingStrategy::Recursive, StrategyParameter::Threads > > &H)

template<class Field , class AlgoT , class FieldTrait , class Cut >
Field::Element_ptr	fgemv (const Field &F, const FFLAS_TRANSPOSE ta, const size_t m, const size_t n, const typename Field::Element alpha, const typename Field::ConstElement_ptr A, const size_t lda, const typename Field::ConstElement_ptr X, const size_t incX, const typename Field::Element beta, typename Field::Element_ptr Y, const size_t incY, MMHelper< Field, AlgoT, FieldTrait, ParSeqHelper::Parallel< CuttingStrategy::Row, Cut > > &H)

void	parseArguments (int argc, char *argv, Argument args, bool printDefaults=true)

char *	getArgumentValue (int argc, char **argv, int i)
	Get the value of an argument and avoid core dump when no value was given after an argument. More...

std::ostream &	writeCommandString (std::ostream &os, Argument args, const char programName=nullptr)
	writes the values of all arguments, preceded by the programName More...

template<class Field >
std::ostream &	WriteMatrix (std::ostream &c, const Field &F, size_t m, size_t n, typename Field::ConstElement_ptr A, size_t lda, FFLAS_FORMAT format, bool column_major)
	WriteMatrix: write a matrix to an output stream. More...

void	preamble (std::ifstream &ifs, FFLAS_FORMAT &format)

template<class Field >
Field::Element_ptr	ReadMatrix (std::ifstream &ifs, Field &F, size_t &m, size_t &n, typename Field::Element_ptr &A, FFLAS_FORMAT format=FflasAuto)
	ReadMatrix: read a matrix from an input stream. More...

template<class Field >
Field::Element_ptr	ReadMatrix (const std::string &matrix_file, Field &F, size_t &m, size_t &n, typename Field::Element_ptr &A, FFLAS_FORMAT format=FflasAuto)
	ReadMatrix: read a matrix from a file. More...

template<class Field >
void	WriteMatrix (std::string &matrix_file, const Field &F, int m, int n, typename Field::ConstElement_ptr A, size_t lda, FFLAS_FORMAT format=FflasDense, bool column_major=false)
	WriteMatrix: write a matrix to a file. More...

std::ostream &	WritePermutation (std::ostream &c, const size_t *P, size_t N)
	WritePermutation: write a permutation matrix to an output stream. More...

template<class Element >
bool	alignable ()

template<>
bool	alignable< Givaro::Integer * > ()

template<class Field >
Field::Element_ptr	fflas_new (const Field &F, const size_t m, const Alignment align=Alignment::DEFAULT)

template<class Field >
Field::Element_ptr	fflas_new (const Field &F, const size_t m, const size_t n, const Alignment align=Alignment::DEFAULT)

template<class Element >
Element *	fflas_new (const size_t m, const Alignment align=Alignment::DEFAULT)

template<class Element_ptr >
void	fflas_delete (Element_ptr A)

template<class Ptr , class ... Args>
void	fflas_delete (Ptr p, Args ... args)

void	prefetch (const int64_t *)

void	getTLBSize (int &tlb)

void	queryCacheSizes (int &l1, int &l2, int &l3)

int	queryL1CacheSize ()

int	queryTopLevelCacheSize ()

uint64_t	getSeed ()

template<class wide_T , class pack_T , int Nb>
void	pack_word (pack_T packed, const wide_T words, int32_t stride, Packer< pack_T, Nb > &packer)

template<class wide_T >
void	pack_word (double packed, const wide_T words, int32_t stride, Packer< double, 2 > &packer)

template<class wide_T , class pack_T , int Nb>
void	pack_word_part (pack_T packed, int32_t nb, const wide_T words, int32_t stride, Packer< pack_T, Nb > &packer)

template<class wide_T >
void	pack_word_part (double packed, int32_t nb, const wide_T words, int32_t stride, Packer< double, 2 > &packer)

template<class wide_T , class pack_T , int Nb>
void	unpack_word (wide_T words, int32_t stride, const pack_T packed, Packer< pack_T, Nb > &packer)

template<class wide_T >
void	unpack_word (wide_T words, int32_t stride, const double packed, Packer< double, 2 > &packer)

template<class wide_T , class pack_T , int Nb>
void	unpack_word_part (wide_T words, int32_t stride, const pack_T packed, int32_t nb, Packer< pack_T, Nb > &packer)

template<class wide_T >
void	unpack_word_part (wide_T words, int32_t stride, const double packed, int32_t nb, Packer< double, 2 > &packer)

template<class wide_T , class pack_T , int Nb, bool row_packed>
void	pack_matrix (pack_T packed, int32_t row_p, int32_t col_p, int32_t ldm_p, const wide_T elemts, int32_t row_e, int32_t col_e, int32_t ldm_e, Packer< pack_T, Nb > &packer)

template<class wide_T , class pack_T , int Nb, bool row_packed>
void	unpack_matrix (wide_T elemts, int32_t row_e, int32_t col_e, int32_t ldm_e, const pack_T packed, int32_t row_p, int32_t col_p, int32_t ldm_p, Packer< pack_T, Nb > &packer)

template<class Field , bool left_compress>
void	fgemm_compressed (const Field &F, int m, int n, int k, const typename Field::Element A, int lda, const typename Field::Element B, int ldb, typename Field::Element *C, int ldc)

template<class Field >
void	finit_fuzzy (Field &F, size_t m, size_t n, double *C, size_t ldc)

void	add (const size_t m, const size_t n, double a, const double A, const size_t lda, const double B, const size_t ldb, double *C, const size_t ldc)

void	subadd (const size_t m, const size_t n, const double A, const size_t lda, const double B, const size_t ldb, double *C, const size_t ldc)

void	negadd (const size_t m, const size_t n, const double A, const size_t lda, const double B, const size_t ldb, double *C, const size_t ldc)

void	addsub (const size_t m, const size_t n, const double A, const size_t lda, const double B, const size_t ldb, double *C, const size_t ldc)

template<class Field >
void	addscalinf (const Field &F, const size_t m, const size_t n, const double B, const size_t ldb, double e, double C, const size_t ldc)

template<class Field >
void	subscalinf (const Field &F, const size_t m, const size_t n, const double B, const size_t ldb, double e, double C, const size_t ldc)

template<class Field >
void	subscal (const Field &F, const size_t m, const size_t n, const double D, const size_t ldd, const double B, const size_t ldb, double e, double *C, const size_t ldc)

template<class Field >
void	addscal (const Field &F, const size_t m, const size_t n, const double D, const size_t ldd, const double B, const size_t ldb, double e, double *C, const size_t ldc)

template<class Field >
void	subscalacc (const Field &F, const size_t m, const size_t n, const double D, const size_t ldd, const double B, const size_t ldb, double e, double *C, const size_t ldc)

template<class Field >
double *	gemm_fflas (const Field &F, const size_t m, const size_t n, const size_t k, const double A, size_t lda, const double B, size_t ldb, double *C, size_t ldc, int rec=0)

Typedef Documentation

◆ Checker_fgemm

using Checker_fgemm = FFLAS::Checker_Empty<Field>

◆ Checker_ftrsm

using Checker_ftrsm = FFLAS::Checker_Empty<Field>

◆ ForceCheck_fgemm

using ForceCheck_fgemm = CheckerImplem_fgemm<Field>

◆ ForceCheck_ftrsm

using ForceCheck_ftrsm = CheckerImplem_ftrsm<Field>

◆ ZOSparseMatrix

using ZOSparseMatrix = std::true_type

◆ NotZOSparseMatrix

using NotZOSparseMatrix = std::false_type

◆ SimdSparseMatrix

using SimdSparseMatrix = std::true_type

◆ NoSimdSparseMatrix

using NoSimdSparseMatrix = std::false_type

◆ MKLSparseMatrixFormat

using MKLSparseMatrixFormat = std::true_type

◆ NotMKLSparseMatrixFormat

using NotMKLSparseMatrixFormat = std::false_type

◆ has_plus

using has_plus = typename std::conditional<std::is_arithmetic<T>::value, std::true_type, has_plus_impl<T> >::type

◆ has_minus

using has_minus = typename std::conditional<std::is_arithmetic<T>::value, std::true_type, has_minus_impl<T> >::type

◆ has_equal

using has_equal = typename std::conditional<std::is_arithmetic<T>::value, std::true_type, std::is_copy_assignable<T> >::type

◆ has_plus_eq

using has_plus_eq = typename std::conditional<std::is_arithmetic<T>::value, std::true_type, has_plus_eq_impl<T> >::type

◆ has_minus_eq

using has_minus_eq = typename std::conditional<std::is_arithmetic<T>::value, std::true_type, has_minus_eq_impl<T> >::type

◆ has_mul

using has_mul = typename std::conditional<std::is_arithmetic<T>::value, std::true_type, has_mul_impl<T> >::type

◆ has_mul_eq

using has_mul_eq = typename std::conditional<std::is_arithmetic<T>::value, std::true_type, has_mul_eq_impl<T> >::type

◆ Timer

typedef Givaro::Timer Timer

◆ BaseTimer

typedef Givaro::BaseTimer BaseTimer

◆ UserTimer

typedef Givaro::UserTimer UserTimer

◆ SysTimer

typedef Givaro::SysTimer SysTimer

Enumeration Type Documentation

◆ FFLAS_ORDER

enum FFLAS_ORDER

Storage by row or col ?

Enumerator
FflasRowMajor	row major
FflasColMajor	col major

◆ FFLAS_TRANSPOSE

enum FFLAS_TRANSPOSE

Is matrix transposed ?

Enumerator
FflasNoTrans	Matrix is not transposed.
FflasTrans	Matrix is transposed.

◆ FFLAS_UPLO

enum FFLAS_UPLO

Is triangular matrix's shape upper ?

Enumerator
FflasUpper	Triangular matrix is Upper triangular (if then $T_{i,j} = 0$ )
FflasLower	Triangular matrix is Lower triangular (if then $T_{i,j} = 0$ )
FflasLeftTri	Triangular matrix is Left triangular (if then $T_{i,j} = 0$ )
FflasRightTri	Triangular matrix is Right triangular (if then $T_{i,j} = 0$ )

◆ FFLAS_DIAG

enum FFLAS_DIAG

Is the triangular matrix implicitly unit diagonal ?

Enumerator
FflasNonUnit	Triangular matrix has an explicit arbitrary diagonal.
FflasUnit	Triangular matrix has an implicit unit diagonal ( $T_{i,i} = 1$ )

◆ FFLAS_SIDE

enum FFLAS_SIDE

On what side ?

Enumerator
FflasLeft	Operator applied on the left.
FflasRight	Operator applied on the rigth.

◆ FFLAS_BASE

enum FFLAS_BASE

FFLAS_BASE determines the type of the element representation for Matrix Mult kernel.

(deprecated, should not be used)

Enumerator
FflasDouble	to use the double precision BLAS
FflasFloat	to use the single precison BLAS
FflasGeneric	for any other domain, that can not be converted to floating point integers

◆ number_kind

enum number_kind

Enumerator
zero
one
mone
other

◆ SparseMatrix_t

enum class SparseMatrix_t

strong

Enumerator
CSR
CSR_ZO
CSC
CSC_ZO
COO
COO_ZO
ELL
ELL_ZO
SELL
SELL_ZO
ELL_simd
ELL_simd_ZO
CSR_HYB
HYB_ZO

◆ FFLAS_FORMAT

enum FFLAS_FORMAT

Enumerator
FflasAuto
FflasDense
FflasSMS
FflasBinary
FflasMath
FflasMaple
FflasSageMath

Function Documentation

◆ InfNorm()

Givaro::Integer InfNorm	(	const size_t	M,
		const size_t	N,
		const Givaro::Integer *	A,
		const size_t	lda
	)

inline

◆ min3()

const T & min3	(	const T &	m,
		const T &	n,
		const T &	k
	)

◆ max3()

const T & max3	(	const T &	m,
		const T &	n,
		const T &	k
	)

◆ min4()

const T & min4	(	const T &	m,
		const T &	n,
		const T &	k,
		const T &	l
	)

◆ max4()

const T & max4	(	const T &	m,
		const T &	n,
		const T &	k,
		const T &	l
	)

◆ fadd() [1/8]

void fadd	(	const Field &	F,
		const size_t	N,
		typename Field::ConstElement_ptr	A,
		const size_t	inca,
		typename Field::ConstElement_ptr	B,
		const size_t	incb,
		typename Field::Element_ptr	C,
		const size_t	incc
	)

◆ faddin() [1/5]

void faddin	(	const Field &	F,
		const size_t	N,
		typename Field::ConstElement_ptr	B,
		const size_t	incb,
		typename Field::Element_ptr	C,
		const size_t	incc
	)

◆ fsub() [1/4]

void fsub	(	const Field &	F,
		const size_t	N,
		typename Field::ConstElement_ptr	A,
		const size_t	inca,
		typename Field::ConstElement_ptr	B,
		const size_t	incb,
		typename Field::Element_ptr	C,
		const size_t	incc
	)

◆ fsubin() [1/3]

void fsubin	(	const Field &	F,
		const size_t	N,
		typename Field::ConstElement_ptr	B,
		const size_t	incb,
		typename Field::Element_ptr	C,
		const size_t	incc
	)

◆ fadd() [2/8]

void fadd	(	const Field &	F,
		const size_t	N,
		typename Field::ConstElement_ptr	A,
		const size_t	inca,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	B,
		const size_t	incb,
		typename Field::Element_ptr	C,
		const size_t	incc
	)

Todo:: optimise here

◆ pfadd()

void pfadd	(	const Field &	F,
		const size_t	M,
		const size_t	N,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		const size_t	numths
	)

◆ pfsub()

void pfsub	(	const Field &	F,
		const size_t	M,
		const size_t	N,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		const size_t	numths
	)

◆ pfaddin()

void pfaddin	(	const Field &	F,
		const size_t	M,
		const size_t	N,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		size_t	numths
	)

◆ pfsubin()

void pfsubin	(	const Field &	F,
		const size_t	M,
		const size_t	N,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		size_t	numths
	)

◆ fadd() [3/8]

void fadd	(	const Field &	F,
		const size_t	M,
		const size_t	N,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		typename Field::Element_ptr	C,
		const size_t	ldc
	)

fadd : matrix addition.

Computes C = A + B.

Parameters

F	field
M	rows
N	cols
A	dense matrix of size `MxN`
lda	leading dimension of `A`
B	dense matrix of size `MxN`
ldb	leading dimension of `B`
C	dense matrix of size `MxN`
ldc	leading dimension of `C`

◆ fsub() [2/4]

void fsub	(	const Field &	F,
		const size_t	M,
		const size_t	N,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		typename Field::Element_ptr	C,
		const size_t	ldc
	)

fsub : matrix subtraction.

Computes C = A - B.

Parameters

F	field
M	rows
N	cols
A	dense matrix of size `MxN`
lda	leading dimension of `A`
B	dense matrix of size `MxN`
ldb	leading dimension of `B`
C	dense matrix of size `MxN`
ldc	leading dimension of `C`

◆ faddin() [2/5]

void faddin	(	const Field &	F,
		const size_t	M,
		const size_t	N,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		typename Field::Element_ptr	C,
		const size_t	ldc
	)

faddin

◆ faddin() [3/5]

void faddin	(	const Field &	F,
		const FFLAS_UPLO	uplo,
		const size_t	N,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		typename Field::Element_ptr	C,
		const size_t	ldc
	)

fadding for symmetric matrices

◆ fsubin() [2/3]

void fsubin	(	const Field &	F,
		const size_t	M,
		const size_t	N,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		typename Field::Element_ptr	C,
		const size_t	ldc
	)

fsubin C = C - B

◆ fadd() [4/8]

void fadd	(	const Field &	F,
		const size_t	M,
		const size_t	N,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		typename Field::Element_ptr	C,
		const size_t	ldc
	)

fadd : matrix addition with scaling.

Computes C = A + alpha B.

Parameters

F	field
M	rows
N	cols
A	dense matrix of size `MxN`
lda	leading dimension of `A`
alpha	some scalar
B	dense matrix of size `MxN`
ldb	leading dimension of `B`
C	dense matrix of size `MxN`
ldc	leading dimension of `C`

◆ fassign() [1/10]

void fassign	(	const Field &	F,
		const size_t	N,
		typename Field::ConstElement_ptr	Y,
		const size_t	incY,
		typename Field::Element_ptr	X,
		const size_t	incX
	)

inline

fassign : $x \gets y$ .

X is preallocated

Todo:: variant for triagular matrix

Parameters

	F	field
	N	size of the vectors
[out]	X	vector in `F`
	incX	stride of `X`
[in]	Y	vector in `F`
	incY	stride of `Y`

◆ fassign() [2/10]

void fassign	(	const Givaro::Modular< float > &	F,
		const size_t	N,
		const float *	Y,
		const size_t	incY,
		float *	X,
		const size_t	incX
	)

inline

◆ fassign() [3/10]

void fassign	(	const Givaro::ModularBalanced< float > &	F,
		const size_t	N,
		const float *	Y,
		const size_t	incY,
		float *	X,
		const size_t	incX
	)

inline

◆ fassign() [4/10]

void fassign	(	const Givaro::ZRing< float > &	F,
		const size_t	N,
		const float *	Y,
		const size_t	incY,
		float *	X,
		const size_t	incX
	)

inline

◆ fassign() [5/10]

void fassign	(	const Givaro::Modular< double > &	F,
		const size_t	N,
		const double *	Y,
		const size_t	incY,
		double *	X,
		const size_t	incX
	)

inline

◆ fassign() [6/10]

void fassign	(	const Givaro::ModularBalanced< double > &	F,
		const size_t	N,
		const double *	Y,
		const size_t	incY,
		double *	X,
		const size_t	incX
	)

inline

◆ fassign() [7/10]

void fassign	(	const Givaro::ZRing< double > &	F,
		const size_t	N,
		const double *	Y,
		const size_t	incY,
		double *	X,
		const size_t	incX
	)

inline

◆ fassign() [8/10]

void fassign	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		typename Field::Element_ptr	A,
		const size_t	lda
	)

fassign : $A \gets B$ .

Parameters

F	field
m	number of rows to copy
n	number of cols to copy
A	matrix in `F`
lda	stride of `A`
B	vector in `F`
ldb	stride of `B`

◆ faxpy() [1/6]

void faxpy	(	const Field &	F,
		const size_t	N,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	X,
		const size_t	incX,
		typename Field::Element_ptr	Y,
		const size_t	incY
	)

inline

faxpy : $y \gets \alpha \cdot x + y$ .

Parameters

	F	field
	N	size of the vectors
	alpha	scalar
[in]	X	vector in `F`
	incX	stride of `X`
[in,out]	Y	vector in `F`
	incY	stride of `Y`

◆ faxpy() [2/6]

void faxpy	(	const Givaro::DoubleDomain &	,
		const size_t	N,
		const Givaro::DoubleDomain::Element	a,
		Givaro::DoubleDomain::ConstElement_ptr	x,
		const size_t	incx,
		Givaro::DoubleDomain::Element_ptr	y,
		const size_t	incy
	)

inline

◆ faxpy() [3/6]

void faxpy	(	const Givaro::FloatDomain &	,
		const size_t	N,
		const Givaro::FloatDomain::Element	a,
		Givaro::FloatDomain::ConstElement_ptr	x,
		const size_t	incx,
		Givaro::FloatDomain::Element_ptr	y,
		const size_t	incy
	)

inline

◆ faxpy() [4/6]

void faxpy	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	X,
		const size_t	ldx,
		typename Field::Element_ptr	Y,
		const size_t	ldy
	)

inline

faxpy : $y \gets \alpha \cdot x + y$ .

Parameters

	F	field
	m	row dimension
	n	column dimension
	alpha	scalar
[in]	X	vector in `F`
	ldx	leading dimension of `X`
[in,out]	Y	vector in `F`
	ldy	leading dimension of `Y`

◆ fdot() [1/11]

Field::Element fdot	(	const Field &	F,
		const size_t	N,
		typename Field::ConstElement_ptr	x,
		const size_t	incx,
		typename Field::ConstElement_ptr	y,
		const size_t	incy,
		ModeCategories::DefaultTag &	MT
	)

inline

◆ fdot() [2/11]

Field::Element fdot	(	const Field &	F,
		const size_t	N,
		typename Field::ConstElement_ptr	x,
		const size_t	incx,
		typename Field::ConstElement_ptr	y,
		const size_t	incy,
		ModeCategories::DelayedTag &	MT
	)

inline

◆ fdot() [3/11]

Givaro::DoubleDomain::Element fdot	(	const Givaro::DoubleDomain &	,
		const size_t	N,
		Givaro::DoubleDomain::ConstElement_ptr	x,
		const size_t	incx,
		Givaro::DoubleDomain::ConstElement_ptr	y,
		const size_t	incy,
		ModeCategories::DefaultTag &	MT
	)

inline

◆ fdot() [4/11]

Givaro::FloatDomain::Element fdot	(	const Givaro::FloatDomain &	,
		const size_t	N,
		Givaro::FloatDomain::ConstElement_ptr	x,
		const size_t	incx,
		Givaro::FloatDomain::ConstElement_ptr	y,
		const size_t	incy,
		ModeCategories::DefaultTag &	MT
	)

inline

◆ fdot() [5/11]

Field::Element fdot	(	const Field &	F,
		const size_t	N,
		typename Field::ConstElement_ptr	x,
		const size_t	incx,
		typename Field::ConstElement_ptr	y,
		const size_t	incy,
		ModeCategories::ConvertTo< T > &	MT
	)

inline

◆ fdot() [6/11]

Field::Element fdot	(	const Field &	F,
		const size_t	N,
		typename Field::ConstElement_ptr	x,
		const size_t	incx,
		typename Field::ConstElement_ptr	y,
		const size_t	incy,
		ModeCategories::DefaultBoundedTag &	dbt
	)

inline

◆ fdot() [7/11]

Field::Element fdot	(	const Field &	F,
		const size_t	N,
		typename Field::ConstElement_ptr	x,
		const size_t	incx,
		typename Field::ConstElement_ptr	y,
		const size_t	incy,
		const ParSeqHelper::Sequential	seq
	)

inline

◆ fdot() [8/11]

Field::Element fdot	(	const Field &	F,
		const size_t	N,
		typename Field::ConstElement_ptr	X,
		const size_t	incX,
		typename Field::ConstElement_ptr	Y,
		const size_t	incY
	)

inline

fdot: dot product .

Parameters

F	field
N	size of the vectors
X	vector in `F`
incX	stride of `X`
Y	vector in `F`
incY	stride of `Y`

◆ fgemm() [1/23]

Field::Element_ptr fgemm	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		MMHelper< Field, MMHelperAlgo::Winograd, ModeCategories::ConvertTo< ElementCategories::MachineFloatTag >, ParSeqHelper::Sequential > &	H
	)

inline

◆ fgemm() [2/23]

Field::Element_ptr fgemm	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		const ParSeqHelper::Sequential	seq
	)

inline

◆ fgemm() [3/23]

Field::Element_ptr fgemm	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		const ParSeqHelper::Parallel< Cut, Param >	par
	)

inline

◆ fgemm() [4/23]

Field::Element_ptr fgemm	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc
	)

inline

fgemm: Field GEneral Matrix Multiply.

Computes $C = \alpha \mathrm{op}(A) \times \mathrm{op}(B) + \beta C$ Automatically set Winograd recursion level

Parameters

F	field.
ta	if `ta==FflasTrans` then $\mathrm{op}(A)=A^t$ , else $\mathrm{op}(A)=A$ ,
tb	same for matrix `B`
m	see `A`
n	see `B`
k	see `A`
alpha	scalar
beta	scalar
A	$\mathrm{op}(A)$ is $m \times k$
B	$\mathrm{op}(B)$ is $k \times n$
C	is $m \times n$
lda	leading dimension of `A`
ldb	leading dimension of `B`
ldc	leading dimension of `C`
w	recursive levels of Winograd's algorithm are used. No argument (or -1) does auto computation of `w`.

Warning: $\alpha$ must be invertible

◆ fgemm() [5/23]

Field::Element_ptr fgemm	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		MMHelper< Field, MMHelperAlgo::Auto, ModeT, ParSeq > &	H
	)

inline

◆ fgemm() [6/23]

Field::Element_ptr fgemm	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		MMHelper< Field, MMHelperAlgo::Winograd, ModeCategories::DelayedTag, ParSeqHelper::Sequential > &	H
	)

inline

◆ fsquare() [1/6]

Field::Element_ptr fsquare	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	n,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc
	)

inline

fsquare: Squares a matrix.

compute $C \gets \alpha \mathrm{op}(A) \mathrm{op}(A) + \beta C$ over a Field F Avoid the conversion of B

Parameters

ta	if `ta==FflasTrans`, $\mathrm{op}(A)=A^T$ .
F	field
n	size of `A`
alpha	scalar
beta	scalar
A	dense matrix of size `nxn`
lda	leading dimension of `A`
C	dense matrix of size `nxn`
ldc	leading dimension of `C`

Bug:: why double ?

◆ fsquare() [2/6]

double * fsquare	(	const Givaro::ModularBalanced< double > &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	n,
		const double	alpha,
		const double *	A,
		const size_t	lda,
		const double	beta,
		double *	C,
		const size_t	ldc
	)

inline

◆ fsquare() [3/6]

float * fsquare	(	const Givaro::ModularBalanced< float > &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	n,
		const float	alpha,
		const float *	A,
		const size_t	lda,
		const float	beta,
		float *	C,
		const size_t	ldc
	)

inline

◆ fsquare() [4/6]

double * fsquare	(	const Givaro::Modular< double > &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	n,
		const double	alpha,
		const double *	A,
		const size_t	lda,
		const double	beta,
		double *	C,
		const size_t	ldc
	)

inline

◆ fsquare() [5/6]

float * fsquare	(	const Givaro::Modular< float > &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	n,
		const float	alpha,
		const float *	A,
		const size_t	lda,
		const float	beta,
		float *	C,
		const size_t	ldc
	)

inline

◆ fgemm() [7/23]

FFPACK::RNSInteger< RNS >::Element_ptr fgemm	(	const FFPACK::RNSInteger< RNS > &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename FFPACK::RNSInteger< RNS >::Element	alpha,
		typename FFPACK::RNSInteger< RNS >::ConstElement_ptr	Ad,
		const size_t	lda,
		typename FFPACK::RNSInteger< RNS >::ConstElement_ptr	Bd,
		const size_t	ldb,
		const typename FFPACK::RNSInteger< RNS >::Element	beta,
		typename FFPACK::RNSInteger< RNS >::Element_ptr	Cd,
		const size_t	ldc,
		MMHelper< FFPACK::RNSInteger< RNS >, MMHelperAlgo::Classic, ModeCategories::DefaultTag, ParSeqHelper::Compose< ParSeqHelper::Sequential, ParSeqTrait > > &	H
	)

inline

◆ fgemm() [8/23]

FFPACK::RNSInteger< RNS >::Element_ptr fgemm	(	const FFPACK::RNSInteger< RNS > &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename FFPACK::RNSInteger< RNS >::Element	alpha,
		typename FFPACK::RNSInteger< RNS >::ConstElement_ptr	Ad,
		const size_t	lda,
		typename FFPACK::RNSInteger< RNS >::ConstElement_ptr	Bd,
		const size_t	ldb,
		const typename FFPACK::RNSInteger< RNS >::Element	beta,
		typename FFPACK::RNSInteger< RNS >::Element_ptr	Cd,
		const size_t	ldc,
		MMHelper< FFPACK::RNSInteger< RNS >, MMHelperAlgo::Classic, ModeCategories::DefaultTag, ParSeqHelper::Sequential > &	H
	)

inline

◆ fgemm() [9/23]

FFPACK::RNSInteger< RNS >::Element_ptr fgemm	(	const FFPACK::RNSInteger< RNS > &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename FFPACK::RNSInteger< RNS >::Element	alpha,
		typename FFPACK::RNSInteger< RNS >::ConstElement_ptr	Ad,
		const size_t	lda,
		typename FFPACK::RNSInteger< RNS >::ConstElement_ptr	Bd,
		const size_t	ldb,
		const typename FFPACK::RNSInteger< RNS >::Element	beta,
		typename FFPACK::RNSInteger< RNS >::Element_ptr	Cd,
		const size_t	ldc,
		MMHelper< FFPACK::RNSInteger< RNS >, MMHelperAlgo::Classic, ModeCategories::DefaultTag, ParSeqHelper::Compose< ParSeqHelper::Parallel< CuttingStrategy::RNSModulus, StrategyParameter::Threads >, ParSeqTrait > > &	H
	)

inline

◆ fgemm() [10/23]

FFPACK::RNSInteger< RNS >::Element_ptr fgemm	(	const FFPACK::RNSInteger< RNS > &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename FFPACK::RNSInteger< RNS >::Element	alpha,
		typename FFPACK::RNSInteger< RNS >::ConstElement_ptr	Ad,
		const size_t	lda,
		typename FFPACK::RNSInteger< RNS >::ConstElement_ptr	Bd,
		const size_t	ldb,
		const typename FFPACK::RNSInteger< RNS >::Element	beta,
		typename FFPACK::RNSInteger< RNS >::Element_ptr	Cd,
		const size_t	ldc,
		MMHelper< FFPACK::RNSInteger< RNS >, MMHelperAlgo::Classic, ModeCategories::DefaultTag, ParSeqHelper::Parallel< Cut, Param > > &	H
	)

inline

◆ fgemm() [11/23]

Givaro::Integer * fgemm	(	const Givaro::ZRing< Givaro::Integer > &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const Givaro::Integer	alpha,
		const Givaro::Integer *	A,
		const size_t	lda,
		const Givaro::Integer *	B,
		const size_t	ldb,
		Givaro::Integer	beta,
		Givaro::Integer *	C,
		const size_t	ldc,
		MMHelper< Givaro::ZRing< Givaro::Integer >, MMHelperAlgo::Classic, ModeCategories::ConvertTo< ElementCategories::RNSElementTag >, ParSeq > &	H
	)

inline

◆ fgemm() [12/23]

RNS::Element_ptr fgemm	(	const FFPACK::RNSInteger< RNS > &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename RNS::Element	alpha,
		typename RNS::ConstElement_ptr	Ad,
		const size_t	lda,
		typename RNS::ConstElement_ptr	Bd,
		const size_t	ldb,
		const typename RNS::Element	beta,
		typename RNS::Element_ptr	Cd,
		const size_t	ldc,
		MMHelper< FFPACK::RNSInteger< RNS >, MMHelperAlgo::Winograd, ModeT, ParSeqHelper::Sequential > &	H
	)

inline

◆ fgemm() [13/23]

RNS::Element_ptr fgemm	(	const FFPACK::RNSIntegerMod< RNS > &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename RNS::Element	alpha,
		typename RNS::ConstElement_ptr	Ad,
		const size_t	lda,
		typename RNS::ConstElement_ptr	Bd,
		const size_t	ldb,
		const typename RNS::Element	beta,
		typename RNS::Element_ptr	Cd,
		const size_t	ldc,
		MMHelper< FFPACK::RNSIntegerMod< RNS >, MMHelperAlgo::Winograd > &	H
	)

inline

◆ fgemm() [14/23]

Givaro::Integer * fgemm	(	const Givaro::Modular< Givaro::Integer > &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const Givaro::Integer	alpha,
		const Givaro::Integer *	A,
		const size_t	lda,
		const Givaro::Integer *	B,
		const size_t	ldb,
		const Givaro::Integer	beta,
		Givaro::Integer *	C,
		const size_t	ldc,
		MMHelper< Givaro::Modular< Givaro::Integer >, MMHelperAlgo::Classic, ModeCategories::ConvertTo< ElementCategories::RNSElementTag > > &	H
	)

inline

◆ fgemm() [15/23]

Givaro::Integer * fgemm	(	const Givaro::Modular< Givaro::Integer > &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const Givaro::Integer	alpha,
		const Givaro::Integer *	A,
		const size_t	lda,
		const Givaro::Integer *	B,
		const size_t	ldb,
		const Givaro::Integer	beta,
		Givaro::Integer *	C,
		const size_t	ldc,
		MMHelper< Givaro::Modular< Givaro::Integer >, MMHelperAlgo::Auto, ModeCategories::ConvertTo< ElementCategories::RNSElementTag >, ParSeq > &	H
	)

inline

◆ fgemm() [16/23]

RecInt::ruint< K1 > * fgemm	(	const Givaro::Modular< RecInt::ruint< K1 >, RecInt::ruint< K2 > > &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const RecInt::ruint< K1 >	alpha,
		const RecInt::ruint< K1 > *	A,
		const size_t	lda,
		const RecInt::ruint< K1 > *	B,
		const size_t	ldb,
		RecInt::ruint< K1 >	beta,
		RecInt::ruint< K1 > *	C,
		const size_t	ldc,
		MMHelper< Givaro::Modular< RecInt::ruint< K1 >, RecInt::ruint< K2 > >, MMHelperAlgo::Classic, ModeCategories::ConvertTo< ElementCategories::RNSElementTag >, ParSeq > &	H
	)

inline

◆ fgemm() [17/23]

Field::Element_ptr fgemm	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		MMHelper< Field, MMHelperAlgo::Winograd, ModeT > &	H
	)

inline

◆ fgemm() [18/23]

Field::Element_ptr fgemm	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		MMHelper< Field, MMHelperAlgo::WinogradPar, ModeT, ParSeqHelper::Parallel< Cut, Param > > &	H
	)

inline

◆ fgemv() [1/19]

Field::Element_ptr fgemv	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	M,
		const size_t	N,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	X,
		const size_t	incX,
		const typename Field::Element	beta,
		typename Field::Element_ptr	Y,
		const size_t	incY,
		MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::ConvertTo< ElementCategories::MachineFloatTag > > &	H
	)

inline

◆ fgemv() [2/19]

Field::Element_ptr fgemv	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	M,
		const size_t	N,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	X,
		const size_t	incX,
		const typename Field::Element	beta,
		typename Field::Element_ptr	Y,
		const size_t	incY,
		MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::DelayedTag > &	H
	)

inline

◆ fgemv() [3/19]

Field::Element_ptr fgemv	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	M,
		const size_t	N,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	X,
		const size_t	incX,
		const typename Field::Element	beta,
		typename Field::Element_ptr	Y,
		const size_t	incY,
		MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &	H
	)

inline

◆ fgemv() [4/19]

Field::Element_ptr fgemv	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	M,
		const size_t	N,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	X,
		const size_t	incX,
		const typename Field::Element	beta,
		typename Field::Element_ptr	Y,
		const size_t	incY,
		MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::LazyTag > &	H
	)

inline

◆ fgemv() [5/19]

Field::Element_ptr fgemv	(	const Field &	F,
		const FFLAS_TRANSPOSE	TransA,
		const size_t	M,
		const size_t	N,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	X,
		const size_t	incX,
		const typename Field::Element	beta,
		typename Field::Element_ptr	Y,
		const size_t	incY
	)

inline

finite prime Field GEneral Matrix Vector multiplication.

Computes $Y \gets \alpha \mathrm{op}(A) X + \beta Y$ .

Parameters

	F	field
	TransA	if `TransA==FflasTrans` then $\mathrm{op}(A)=A^t$ .
	M	rows
	N	cols
	alpha	scalar
	A	dense matrix of size `MxN`
	lda	leading dimension of `A`
	X	dense vector of size `N`
	incX	stride of `X`
	beta	scalar
[out]	Y	dense vector of size `M`
	incY	stride of `Y`

◆ fgemv() [6/19]

Givaro::ZRing< int64_t >::Element_ptr fgemv	(	const Givaro::ZRing< int64_t > &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	M,
		const size_t	N,
		const int64_t	alpha,
		const int64_t *	A,
		const size_t	lda,
		const int64_t *	X,
		const size_t	incX,
		const int64_t	beta,
		int64_t *	Y,
		const size_t	incY,
		MMHelper< Givaro::ZRing< int64_t >, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &	H
	)

inline

◆ fgemv() [7/19]

Givaro::DoubleDomain::Element_ptr fgemv	(	const Givaro::DoubleDomain &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	M,
		const size_t	N,
		const Givaro::DoubleDomain::Element	alpha,
		const Givaro::DoubleDomain::ConstElement_ptr	A,
		const size_t	lda,
		const Givaro::DoubleDomain::ConstElement_ptr	X,
		const size_t	incX,
		const Givaro::DoubleDomain::Element	beta,
		Givaro::DoubleDomain::Element_ptr	Y,
		const size_t	incY,
		MMHelper< Givaro::DoubleDomain, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &	H
	)

inline

◆ fgemv() [8/19]

Field::Element_ptr fgemv	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	M,
		const size_t	N,
		const typename Field::Element	alpha,
		const typename Field::ConstElement_ptr	A,
		const size_t	lda,
		const typename Field::ConstElement_ptr	X,
		const size_t	incX,
		const typename Field::Element	beta,
		typename Field::Element_ptr	Y,
		const size_t	incY,
		MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::DefaultBoundedTag > &	H
	)

inline

◆ fgemv() [9/19]

Givaro::FloatDomain::Element_ptr fgemv	(	const Givaro::FloatDomain &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	M,
		const size_t	N,
		const Givaro::FloatDomain::Element	alpha,
		const Givaro::FloatDomain::ConstElement_ptr	A,
		const size_t	lda,
		const Givaro::FloatDomain::ConstElement_ptr	X,
		const size_t	incX,
		const Givaro::FloatDomain::Element	beta,
		Givaro::FloatDomain::Element_ptr	Y,
		const size_t	incY,
		MMHelper< Givaro::FloatDomain, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &	H
	)

inline

◆ fgemv() [10/19]

Field::Element_ptr fgemv	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	m,
		const size_t	n,
		const typename Field::Element	alpha,
		const typename Field::ConstElement_ptr	A,
		const size_t	lda,
		const typename Field::ConstElement_ptr	X,
		const size_t	incX,
		const typename Field::Element	beta,
		typename Field::Element_ptr	Y,
		const size_t	incY,
		ParSeqHelper::Parallel< Cut, Param > &	parH
	)

◆ fgemv() [11/19]

Field::Element_ptr fgemv	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	m,
		const size_t	n,
		const typename Field::Element	alpha,
		const typename Field::ConstElement_ptr	A,
		const size_t	lda,
		const typename Field::ConstElement_ptr	X,
		const size_t	incX,
		const typename Field::Element	beta,
		typename Field::Element_ptr	Y,
		const size_t	incY,
		ParSeqHelper::Sequential &	seqH
	)

◆ fgemv() [12/19]

FFPACK::rns_double::Element_ptr fgemv	(	const FFPACK::RNSInteger< FFPACK::rns_double > &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	M,
		const size_t	N,
		const FFPACK::rns_double::Element	alpha,
		FFPACK::rns_double::ConstElement_ptr	A,
		const size_t	lda,
		FFPACK::rns_double::ConstElement_ptr	X,
		const size_t	incX,
		const FFPACK::rns_double::Element	beta,
		FFPACK::rns_double::Element_ptr	Y,
		const size_t	incY,
		MMHelper< FFPACK::RNSInteger< FFPACK::rns_double >, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &	H
	)

inline

◆ fgemv() [13/19]

FFPACK::rns_double::Element_ptr fgemv	(	const FFPACK::RNSIntegerMod< FFPACK::rns_double > &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	M,
		const size_t	N,
		const FFPACK::rns_double::Element	alpha,
		FFPACK::rns_double::ConstElement_ptr	A,
		const size_t	lda,
		FFPACK::rns_double::ConstElement_ptr	X,
		const size_t	incX,
		const FFPACK::rns_double::Element	beta,
		FFPACK::rns_double::Element_ptr	Y,
		const size_t	incY,
		MMHelper< FFPACK::RNSIntegerMod< FFPACK::rns_double >, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &	H
	)

inline

◆ fgemv() [14/19]

Givaro::Integer * fgemv	(	const Givaro::ZRing< Givaro::Integer > &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	m,
		const size_t	n,
		const Givaro::Integer	alpha,
		Givaro::Integer *	A,
		const size_t	lda,
		Givaro::Integer *	X,
		const size_t	ldx,
		Givaro::Integer	beta,
		Givaro::Integer *	Y,
		const size_t	ldy,
		MMHelper< Givaro::ZRing< Givaro::Integer >, MMHelperAlgo::Classic, ModeCategories::ConvertTo< ElementCategories::RNSElementTag > > &	H
	)

inline

◆ fgemv() [15/19]

Givaro::Integer * fgemv	(	const Givaro::Modular< Givaro::Integer > &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	m,
		const size_t	n,
		const Givaro::Integer	alpha,
		Givaro::Integer *	A,
		const size_t	lda,
		Givaro::Integer *	X,
		const size_t	ldx,
		Givaro::Integer	beta,
		Givaro::Integer *	Y,
		const size_t	ldy,
		MMHelper< Givaro::Modular< Givaro::Integer >, MMHelperAlgo::Classic, ModeCategories::ConvertTo< ElementCategories::RNSElementTag > > &	H
	)

inline

◆ fgemv() [16/19]

RecInt::ruint< K1 > * fgemv	(	const Givaro::Modular< RecInt::ruint< K1 >, RecInt::ruint< K2 > > &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	m,
		const size_t	n,
		const RecInt::ruint< K1 >	alpha,
		const RecInt::ruint< K1 > *	A,
		const size_t	lda,
		const RecInt::ruint< K1 > *	X,
		const size_t	incx,
		RecInt::ruint< K1 >	beta,
		RecInt::ruint< K1 > *	Y,
		const size_t	incy,
		MMHelper< Givaro::Modular< RecInt::ruint< K1 >, RecInt::ruint< K2 > >, MMHelperAlgo::Classic, ModeCategories::ConvertTo< ElementCategories::RNSElementTag >, ParSeq > &	H
	)

inline

◆ fger() [1/12]

void fger	(	const Field &	F,
		const size_t	M,
		const size_t	N,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	x,
		const size_t	incx,
		typename Field::ConstElement_ptr	y,
		const size_t	incy,
		typename Field::Element_ptr	A,
		const size_t	lda
	)

inline

fger: rank one update of a general matrix

Computes $A \gets \alpha x . y^T + A$

Parameters

	F	field
	M	rows
	N	cols
	alpha	scalar
[in,out]	A	dense matrix of size `MxN` and leading dimension `lda`
	lda	leading dimension of `A`
	x	dense vector of size `M`
	incx	stride of `X`
	y	dense vector of size `N`
	incy	stride of `Y`

◆ fger() [2/12]

void fger	(	const Field &	F,
		const size_t	M,
		const size_t	N,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	x,
		const size_t	incx,
		typename Field::ConstElement_ptr	y,
		const size_t	incy,
		typename Field::Element_ptr	A,
		const size_t	lda,
		MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::ConvertTo< ElementCategories::MachineFloatTag > > &	H
	)

inline

◆ fger() [3/12]

void fger	(	const Field &	F,
		const size_t	M,
		const size_t	N,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	x,
		const size_t	incx,
		typename Field::ConstElement_ptr	y,
		const size_t	incy,
		typename Field::Element_ptr	A,
		const size_t	lda,
		MMHelper< Field, MMHelperAlgo::Classic, AnyTag > &	H
	)

inline

◆ fger() [4/12]

void fger	(	const Givaro::DoubleDomain &	F,
		const size_t	M,
		const size_t	N,
		const Givaro::DoubleDomain::Element	alpha,
		const Givaro::DoubleDomain::ConstElement_ptr	x,
		const size_t	incx,
		const Givaro::DoubleDomain::ConstElement_ptr	y,
		const size_t	incy,
		Givaro::DoubleDomain::Element_ptr	A,
		const size_t	lda,
		MMHelper< Givaro::DoubleDomain, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &	H
	)

inline

◆ fger() [5/12]

void fger	(	const Field &	F,
		const size_t	M,
		const size_t	N,
		const typename Field::Element	alpha,
		const typename Field::ConstElement_ptr	x,
		const size_t	incx,
		const typename Field::ConstElement_ptr	y,
		const size_t	incy,
		typename Field::Element_ptr	A,
		const size_t	lda,
		MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::DefaultBoundedTag > &	H
	)

inline

◆ fger() [6/12]

void fger	(	const Givaro::FloatDomain &	F,
		const size_t	M,
		const size_t	N,
		const Givaro::FloatDomain::Element	alpha,
		const Givaro::FloatDomain::ConstElement_ptr	x,
		const size_t	incx,
		const Givaro::FloatDomain::ConstElement_ptr	y,
		const size_t	incy,
		Givaro::FloatDomain::Element_ptr	A,
		const size_t	lda,
		MMHelper< Givaro::FloatDomain, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &	H
	)

inline

◆ fger() [7/12]

void fger	(	const Field &	F,
		const size_t	M,
		const size_t	N,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	x,
		const size_t	incx,
		typename Field::ConstElement_ptr	y,
		const size_t	incy,
		typename Field::Element_ptr	A,
		const size_t	lda,
		MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::LazyTag > &	H
	)

inline

◆ fger() [8/12]

void fger	(	const Field &	F,
		const size_t	M,
		const size_t	N,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	x,
		const size_t	incx,
		typename Field::ConstElement_ptr	y,
		const size_t	incy,
		typename Field::Element_ptr	A,
		const size_t	lda,
		MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::DelayedTag > &	H
	)

inline

◆ fger() [9/12]

void fger	(	const Givaro::Modular< Givaro::Integer > &	F,
		const size_t	M,
		const size_t	N,
		const typename Givaro::Integer	alpha,
		typename Givaro::Integer *	x,
		const size_t	incx,
		typename Givaro::Integer *	y,
		const size_t	incy,
		typename Givaro::Integer *	A,
		const size_t	lda,
		MMHelper< Givaro::Modular< Givaro::Integer >, MMHelperAlgo::Classic, ModeCategories::ConvertTo< ElementCategories::RNSElementTag > > &	H
	)

inline

◆ fger() [10/12]

void fger	(	const FFPACK::RNSInteger< RNS > &	F,
		const size_t	M,
		const size_t	N,
		const typename FFPACK::RNSInteger< RNS >::Element	alpha,
		typename FFPACK::RNSInteger< RNS >::Element_ptr	x,
		const size_t	incx,
		typename FFPACK::RNSInteger< RNS >::Element_ptr	y,
		const size_t	incy,
		typename FFPACK::RNSInteger< RNS >::Element_ptr	A,
		const size_t	lda,
		MMHelper< FFPACK::RNSInteger< RNS >, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &	H
	)

inline

◆ fger() [11/12]

void fger	(	const FFPACK::RNSIntegerMod< RNS > &	F,
		const size_t	M,
		const size_t	N,
		const typename FFPACK::RNSIntegerMod< RNS >::Element	alpha,
		typename FFPACK::RNSIntegerMod< RNS >::Element_ptr	x,
		const size_t	incx,
		typename FFPACK::RNSIntegerMod< RNS >::Element_ptr	y,
		const size_t	incy,
		typename FFPACK::RNSIntegerMod< RNS >::Element_ptr	A,
		const size_t	lda,
		MMHelper< FFPACK::RNSIntegerMod< RNS >, MMHelperAlgo::Classic > &	H
	)

inline

◆ freduce() [1/11]

void freduce	(	const Field &	F,
		const size_t	n,
		typename Field::ConstElement_ptr	Y,
		const size_t	incY,
		typename Field::Element_ptr	X,
		const size_t	incX
	)

freduce $x \gets y mod F$ .

Parameters

F	field
n	size of the vectors
Y	vector of `Element`
incY	stride of `Y`
X	vector in `F`
incX	stride of `X`

Bug:: use cblas_(d)scal when possible

◆ freduce() [2/11]

void freduce	(	const Field &	F,
		const size_t	n,
		typename Field::Element_ptr	X,
		const size_t	incX
	)

freduce $x \gets x mod F$ .

Parameters

F	field
n	size of the vectors
X	vector in `F`
incX	stride of `X`

Bug:: use cblas_(d)scal when possible

◆ freduce_constoverride() [1/2]

void freduce_constoverride	(	const Field &	F,
		const size_t	m,
		typename Field::ConstElement_ptr	A,
		const size_t	incX
	)

◆ finit() [1/8]

void finit	(	const Field &	F,
		const size_t	n,
		ConstOtherElement_ptr	Y,
		const size_t	incY,
		typename Field::Element_ptr	X,
		const size_t	incX
	)

◆ finit() [2/8]

void finit	(	const Field &	F,
		const size_t	n,
		typename Field::Element_ptr	X,
		const size_t	incX
	)

finit Initializes X in F$.

Parameters

F	field
n	size of the vectors
X	vector in `F`
incX	stride of `X`

◆ freduce() [3/11]

void freduce	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		typename Field::Element_ptr	A,
		const size_t	lda
	)

freduce $A \gets A mod F$ .

Parameters

F	field
m	number of rows
n	number of cols
A	matrix in `F`
lda	stride of `A`

◆ freduce() [4/11]

void freduce	(	const Field &	F,
		const FFLAS_UPLO	UpLo,
		const size_t	N,
		typename Field::Element_ptr	A,
		const size_t	lda
	)

freduce for square symmetric matrices

◆ pfreduce()

void pfreduce	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		typename Field::Element_ptr	A,
		const size_t	lda,
		const size_t	numths
	)

◆ freduce() [5/11]

void freduce	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		typename Field::Element_ptr	A,
		const size_t	lda
	)

freduce $A \gets B mod F$ .

Parameters

F	field
m	number of rows
n	number of cols
A	matrix in `F`
lda	stride of `A`
B	matrix in `Element`
ldb	stride of `B`

◆ freduce_constoverride() [2/2]

void freduce_constoverride	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		typename Field::ConstElement_ptr	A,
		const size_t	lda
	)

◆ finit() [3/8]

void finit	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		const OtherElement_ptr	B,
		const size_t	ldb,
		typename Field::Element_ptr	A,
		const size_t	lda
	)

finit $A \gets B mod F$ .

Parameters

F	field
m	number of rows
n	number of cols
A	matrix in `F`
lda	stride of `A`
B	matrix in `OtherElement`
ldb	stride of `B`

◆ finit() [4/8]

void finit	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		typename Field::Element_ptr	A,
		const size_t	lda
	)

◆ freduce() [6/11]

void freduce	(	const FFPACK::RNSIntegerMod< FFPACK::rns_double > &	F,
		const size_t	n,
		FFPACK::RNSIntegerMod< FFPACK::rns_double >::Element_ptr	A,
		size_t	inc
	)

inline

◆ freduce() [7/11]

void freduce	(	const FFPACK::RNSIntegerMod< FFPACK::rns_double > &	F,
		const size_t	m,
		const size_t	n,
		FFPACK::rns_double::Element_ptr	A,
		size_t	lda
	)

inline

◆ freivalds()

bool freivalds	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		typename Field::ConstElement_ptr	C,
		const size_t	ldc
	)

inline

freivalds: Freivalds GEneral Matrix Multiply Random Check.

Randomly Checks $C = \alpha \mathrm{op}(A) \times \mathrm{op}(B)$

Parameters

F	field.
ta	if `ta==FflasTrans` then $\mathrm{op}(A)=A^t$ , else $\mathrm{op}(A)=A$ ,
tb	same for matrix `B`
m	see `A`
n	see `B`
k	see `A`
alpha	scalar
A	$\mathrm{op}(A)$ is $m \times k$
B	$\mathrm{op}(B)$ is $k \times n$
C	is $m \times n$
lda	leading dimension of `A`
ldb	leading dimension of `B`
ldc	leading dimension of `C`

◆ fscalin() [1/10]

void fscalin	(	const Field &	F,
		const size_t	n,
		const typename Field::Element	alpha,
		typename Field::Element_ptr	X,
		const size_t	incX
	)

inline

fscalin $x \gets \alpha \cdot x$ .

Parameters

F	field
n	size of the vectors
alpha	scalar
X	vector in `F`
incX	stride of `X`

Bug:: use cblas_(d)scal when possible

Todo:: check if comparison with +/-1,0 is necessary.

◆ fscal() [1/10]

void fscal	(	const Field &	F,
		const size_t	n,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	X,
		const size_t	incX,
		typename Field::Element_ptr	Y,
		const size_t	incY
	)

inline

fscal $y \gets \alpha \cdot x$ .

Parameters

	F	field
	n	size of the vectors
	alpha	scalar
[in]	X	vector in `F`
	incX	stride of `X`
[out]	Y	vector in `F`
	incY	stride of `Y`

Bug:: use cblas_(d)scal when possible

Todo:: check if comparison with +/-1,0 is necessary.

◆ fscal() [2/10]

void fscal	(	const Givaro::DoubleDomain &	,
		const size_t	N,
		const Givaro::DoubleDomain::Element	a,
		Givaro::DoubleDomain::ConstElement_ptr	x,
		const size_t	incx,
		Givaro::DoubleDomain::Element_ptr	y,
		const size_t	incy
	)

inline

◆ fscal() [3/10]

void fscal	(	const Givaro::FloatDomain &	,
		const size_t	N,
		const Givaro::FloatDomain::Element	a,
		Givaro::FloatDomain::ConstElement_ptr	x,
		const size_t	incx,
		Givaro::FloatDomain::Element_ptr	y,
		const size_t	incy
	)

inline

◆ fscalin() [2/10]

void fscalin	(	const Givaro::DoubleDomain &	,
		const size_t	N,
		const Givaro::DoubleDomain::Element	a,
		Givaro::DoubleDomain::Element_ptr	y,
		const size_t	incy
	)

inline

◆ fscalin() [3/10]

void fscalin	(	const Givaro::FloatDomain &	,
		const size_t	N,
		const Givaro::FloatDomain::Element	a,
		Givaro::FloatDomain::Element_ptr	y,
		const size_t	incy
	)

inline

◆ fscalin() [4/10]

void fscalin	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		const typename Field::Element	alpha,
		typename Field::Element_ptr	A,
		const size_t	lda
	)

inline

fscalin $A \gets a \cdot A$ .

Parameters

F	field
m	number of rows
n	number of cols
alpha	homotecie scalar
A	matrix in `F`
lda	stride of `A`

◆ fscal() [4/10]

void fscal	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::Element_ptr	B,
		const size_t	ldb
	)

inline

fscal $B \gets a \cdot A$ .

Parameters

	F	field
	m	number of rows
	n	number of cols
	alpha	homotecie scalar
[in]	A	matrix in `F`
	lda	stride of `A`
[out]	B	matrix in `F`
	ldb	stride of `B`

◆ fscalin() [5/10]

void fscalin	(	const FFPACK::RNSInteger< FFPACK::rns_double > &	F,
		const size_t	n,
		const FFPACK::rns_double::Element	alpha,
		FFPACK::rns_double::Element_ptr	A,
		const size_t	inc
	)

inline

◆ fscal() [5/10]

void fscal	(	const FFPACK::RNSInteger< FFPACK::rns_double > &	F,
		const size_t	n,
		const FFPACK::rns_double::Element	alpha,
		FFPACK::rns_double::ConstElement_ptr	A,
		const size_t	Ainc,
		FFPACK::rns_double::Element_ptr	B,
		const size_t	Binc
	)

inline

◆ fscalin() [6/10]

void fscalin	(	const FFPACK::RNSInteger< FFPACK::rns_double > &	F,
		const size_t	m,
		const size_t	n,
		const FFPACK::rns_double::Element	alpha,
		FFPACK::rns_double::Element_ptr	A,
		const size_t	lda
	)

inline

◆ fscal() [6/10]

void fscal	(	const FFPACK::RNSInteger< FFPACK::rns_double > &	F,
		const size_t	m,
		const size_t	n,
		const FFPACK::rns_double::Element	alpha,
		FFPACK::rns_double::ConstElement_ptr	A,
		const size_t	lda,
		FFPACK::rns_double::Element_ptr	B,
		const size_t	ldb
	)

inline

◆ fscalin() [7/10]

void fscalin	(	const FFPACK::RNSIntegerMod< FFPACK::rns_double > &	F,
		const size_t	n,
		const typename FFPACK::RNSIntegerMod< FFPACK::rns_double >::Element	alpha,
		typename FFPACK::RNSIntegerMod< FFPACK::rns_double >::Element_ptr	A,
		const size_t	inc
	)

inline

◆ fscal() [7/10]

void fscal	(	const FFPACK::RNSIntegerMod< FFPACK::rns_double > &	F,
		const size_t	n,
		const FFPACK::rns_double::Element	alpha,
		FFPACK::rns_double::ConstElement_ptr	A,
		const size_t	Ainc,
		FFPACK::rns_double::Element_ptr	B,
		const size_t	Binc
	)

inline

◆ fscalin() [8/10]

void fscalin	(	const FFPACK::RNSIntegerMod< FFPACK::rns_double > &	F,
		const size_t	m,
		const size_t	n,
		const FFPACK::rns_double::Element	alpha,
		FFPACK::rns_double::Element_ptr	A,
		const size_t	lda
	)

inline

◆ fscal() [8/10]

void fscal	(	const FFPACK::RNSIntegerMod< FFPACK::rns_double > &	F,
		const size_t	m,
		const size_t	n,
		const FFPACK::rns_double::Element	alpha,
		FFPACK::rns_double::ConstElement_ptr	A,
		const size_t	lda,
		FFPACK::rns_double::Element_ptr	B,
		const size_t	ldb
	)

inline

◆ fsyr2k()

Field::Element_ptr fsyr2k	(	const Field &	F,
		const FFLAS_UPLO	UpLo,
		const FFLAS_TRANSPOSE	trans,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc
	)

inline

fsyr2k: Symmetric Rank 2K update

Computes the Lower or Upper triangular part of $C = \alpha ( A \times B^T + B \times A^T) + \beta C$ or $C = \alpha ( A^T \times B + B^T \times A ) + \beta C$

Parameters

F	field.
UpLo	whether to compute the upper or the lower triangular part of the symmetric matrix `C`
trans	if `ta==FflasNoTrans` then compute $C = \alpha ( A \times B^T + B \times A^T ) + \beta C$ , else $C = \alpha ( A^T \times B + B^T \times A) + \beta C$
n	order of matrix `C`
k	see `A`
alpha	scalar
A	is $n \times k$ (FflasNoTrans) or is $k \times n$ (FflasTrans)
lda	leading dimension of `A`
beta	scalar
C	is $n \times n$
ldc	leading dimension of `C`

Warning: $\alpha$ must be invertible

◆ fsyrk() [1/16]

Field::Element_ptr fsyrk	(	const Field &	F,
		const FFLAS_UPLO	UpLo,
		const FFLAS_TRANSPOSE	trans,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc
	)

inline

fsyrk: Symmetric Rank K update

Computes the Lower or Upper triangular part of $C = \alpha A \times A^T + \beta C$ or $C = \alpha A^T \times A + \beta C$

Parameters

F	field.
UpLo	whether to compute the upper or the lower triangular part of the symmetric matrix `C`
trans	if `ta==FflasNoTrans` then comput $C = \alpha A \times A^T + \beta C$ , else $C = \alpha A^T \times A + \beta C$
n	order of matrix `C`
k	see `A`
alpha	scalar
A	is $n \times k$ or is $k \times n$
lda	leading dimension of `A`
beta	scalar
C	is $n \times n$
ldc	leading dimension of `C`

Warning: $\alpha$ must be invertible

◆ fsyrk() [2/16]

Field::Element_ptr fsyrk	(	const Field &	F,
		const FFLAS_UPLO	UpLo,
		const FFLAS_TRANSPOSE	trans,
		const size_t	N,
		const size_t	K,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		const ParSeqHelper::Sequential	seq
	)

inline

◆ fsyrk() [3/16]

Field::Element_ptr fsyrk	(	const Field &	F,
		const FFLAS_UPLO	UpLo,
		const FFLAS_TRANSPOSE	trans,
		const size_t	N,
		const size_t	K,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &	H
	)

inline

◆ fsyrk() [4/16]

Field::Element_ptr fsyrk	(	const Field &	F,
		const FFLAS_UPLO	UpLo,
		const FFLAS_TRANSPOSE	trans,
		const size_t	N,
		const size_t	K,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::ConvertTo< ElementCategories::MachineFloatTag >, ParSeqHelper::Sequential > &	H
	)

inline

◆ fsyrk() [5/16]

Field::Element_ptr fsyrk	(	const Field &	F,
		const FFLAS_UPLO	UpLo,
		const FFLAS_TRANSPOSE	trans,
		const size_t	N,
		const size_t	K,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::DelayedTag > &	H
	)

inline

◆ fsyrk() [6/16]

Field::Element_ptr fsyrk	(	const Field &	F,
		const FFLAS_UPLO	UpLo,
		const FFLAS_TRANSPOSE	trans,
		const size_t	N,
		const size_t	K,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::LazyTag > &	H
	)

inline

◆ fsyrk() [7/16]

Field::Element_ptr fsyrk	(	const Field &	F,
		const FFLAS_UPLO	UpLo,
		const FFLAS_TRANSPOSE	trans,
		const size_t	N,
		const size_t	K,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		MMHelper< Field, MMHelperAlgo::DivideAndConquer, Mode > &	H
	)

inline

◆ fsyrk() [8/16]

Field::Element_ptr fsyrk	(	const Field &	F,
		const FFLAS_UPLO	UpLo,
		const FFLAS_TRANSPOSE	trans,
		const size_t	N,
		const size_t	K,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		MMHelper< Field, MMHelperAlgo::Classic, ModeCategories::DefaultBoundedTag > &	H
	)

inline

◆ fsyrk() [9/16]

Givaro::FloatDomain::Element_ptr fsyrk	(	const Givaro::FloatDomain &	F,
		const FFLAS_UPLO	UpLo,
		const FFLAS_TRANSPOSE	trans,
		const size_t	N,
		const size_t	K,
		const Givaro::FloatDomain::Element	alpha,
		Givaro::FloatDomain::ConstElement_ptr	A,
		const size_t	lda,
		const Givaro::FloatDomain::Element	beta,
		Givaro::FloatDomain::Element_ptr	C,
		const size_t	ldc,
		MMHelper< Givaro::FloatDomain, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &	H
	)

inline

◆ fsyrk() [10/16]

Givaro::DoubleDomain::Element_ptr fsyrk	(	const Givaro::DoubleDomain &	F,
		const FFLAS_UPLO	UpLo,
		const FFLAS_TRANSPOSE	trans,
		const size_t	N,
		const size_t	K,
		const Givaro::DoubleDomain::Element	alpha,
		Givaro::DoubleDomain::ConstElement_ptr	A,
		const size_t	lda,
		const Givaro::DoubleDomain::Element	beta,
		Givaro::DoubleDomain::Element_ptr	C,
		const size_t	ldc,
		MMHelper< Givaro::DoubleDomain, MMHelperAlgo::Classic, ModeCategories::DefaultTag > &	H
	)

inline

◆ fsyrk() [11/16]

Field::Element_ptr fsyrk	(	const Field &	F,
		const FFLAS_UPLO	UpLo,
		const FFLAS_TRANSPOSE	trans,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		typename Field::Element_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	D,
		const size_t	incD,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		const size_t	threshold = `__FFLASFFPACK_FSYRK_THRESHOLD`
	)

inline

fsyrk: Symmetric Rank K update with diagonal scaling

Computes the Lower or Upper triangular part of $C = \alpha A \times D \times A^T + \beta C$ or $C = \alpha A^T \times D \times A + \beta C$ where D is a diagonal matrix. Matrix A is updated into $D\times A$ (if trans = FflasTrans) or $A\times D$ (if trans = FflasNoTrans).

Parameters

F	field.
UpLo	whether to compute the upper or the lower triangular part of the symmetric matrix `C`
trans	if `ta==FflasNoTrans` then compute $C = \alpha A \times A^T + \beta C$ , else $C = \alpha A^T \times A + \beta C$
n	order of matrix `C`
k	see `A`
alpha	scalar
A	is $n \times k$ or is $k \times n$
lda	leading dimension of `A`
D	is $k \times k$ diagonal matrix, stored as a vector of k coefficients
lda	leading dimension of `A`
beta	scalar
C	is $n \times n$
ldc	leading dimension of `C`

Warning: $\alpha$ must be invertible

◆ fsyrk() [12/16]

Field::Element_ptr fsyrk	(	const Field &	F,
		const FFLAS_UPLO	UpLo,
		const FFLAS_TRANSPOSE	trans,
		const size_t	N,
		const size_t	K,
		const typename Field::Element	alpha,
		typename Field::Element_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	D,
		const size_t	incD,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		const ParSeqHelper::Sequential	seq,
		const size_t	threshold
	)

inline

◆ fsyrk() [13/16]

Field::Element_ptr fsyrk	(	const Field &	F,
		const FFLAS_UPLO	UpLo,
		const FFLAS_TRANSPOSE	trans,
		const size_t	N,
		const size_t	K,
		const typename Field::Element	alpha,
		typename Field::Element_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	D,
		const size_t	incD,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		const ParSeqHelper::Parallel< Cut, Param >	par,
		const size_t	threshold
	)

inline

◆ fsyrk() [14/16]

Field::Element_ptr fsyrk	(	const Field &	F,
		const FFLAS_UPLO	UpLo,
		const FFLAS_TRANSPOSE	trans,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		typename Field::Element_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	D,
		const size_t	incD,
		const std::vector< bool > &	twoBlock,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		const size_t	threshold = `__FFLASFFPACK_FSYRK_THRESHOLD`
	)

inline

fsyrk: Symmetric Rank K update with diagonal scaling

Computes the Lower or Upper triangular part of $C = \alpha A \times Delta D \times A^T + \beta C$ or $C = \alpha A^T \times Delta D \times A + \beta C$ where D is a diagonal matrix and Delta is a block diagonal with either 1 on the diagonal or 2x2 swap blocks Matrix A is updated into $D\times A$ (if trans = FflasTrans) or $A\times D$ (if trans = FflasNoTrans).

Parameters

F	field.
UpLo	whether to compute the upper or the lower triangular part of the symmetric matrix `C`
trans	if `ta==FflasNoTrans` then compute $C = \alpha A Delta D \times A^T + \beta C$ , else $C = \alpha A^T Delta D \times A + \beta C$
n	see `B`
k	see `A`
alpha	scalar
A	is $n \times k$ or is $k \times n$
lda	leading dimension of `A`
D	is $k \times k$ diagonal matrix, stored as a vector of k coefficients
twoBlocks	a vector boolean indicating the beginning of each 2x2 blocs in Delta
lda	leading dimension of `A`
beta	scalar
C	is $n \times n$
ldc	leading dimension of `C`

Warning: $\alpha$ must be invertible

◆ computeS1S2()

void computeS1S2	(	const Field &	F,
		const FFLAS_TRANSPOSE	trans,
		const size_t	N,
		const size_t	K,
		const typename Field::Element	x,
		const typename Field::Element	y,
		typename Field::Element_ptr	A,
		const size_t	lda,
		typename Field::Element_ptr	S,
		const size_t	lds,
		typename Field::Element_ptr	T,
		const size_t	ldt,
		MMHelper< Field, MMHelperAlgo::Winograd, FieldTrait > &	WH
	)

inline

◆ fsyrk() [15/16]

Field::Element_ptr fsyrk	(	const Field &	F,
		const FFLAS_UPLO	UpLo,
		const FFLAS_TRANSPOSE	trans,
		const size_t	N,
		const size_t	K,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		MMHelper< Field, MMHelperAlgo::Winograd, ModeCategories::DelayedTag, ParSeqHelper::Sequential > &	H
	)

inline

◆ fsyrk() [16/16]

Field::Element_ptr fsyrk	(	const Field &	F,
		const FFLAS_UPLO	UpLo,
		const FFLAS_TRANSPOSE	trans,
		const size_t	N,
		const size_t	K,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		MMHelper< Field, MMHelperAlgo::Winograd, Mode > &	H
	)

inline

◆ fsyrk_strassen() [1/2]

Field::Element_ptr fsyrk_strassen	(	const Field &	F,
		const FFLAS_UPLO	uplo,
		const FFLAS_TRANSPOSE	trans,
		const size_t	N,
		const size_t	K,
		const typename Field::Element	y1,
		const typename Field::Element	y2,
		const typename Field::Element	alpha,
		typename Field::Element_ptr	A,
		const size_t	lda,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		MMHelper< Field, MMHelperAlgo::Winograd, FieldTrait > &	WH
	)

inline

◆ ftrmm() [1/3]

void ftrmm	(	const Field &	F,
		const FFLAS_SIDE	Side,
		const FFLAS_UPLO	Uplo,
		const FFLAS_TRANSPOSE	TransA,
		const FFLAS_DIAG	Diag,
		const size_t	M,
		const size_t	N,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::Element_ptr	B,
		const size_t	ldb
	)

inline

ftrmm: TRiangular Matrix Multiply.

Computes $B \gets \alpha \mathrm{op}(A) B$ or $B \gets \alpha B \mathrm{op}(A)$ .

Parameters

F	field
Side	if `Side==FflasLeft` then $B \gets \alpha \mathrm{op}(A) B$ is computed.
Uplo	if `Uplo==FflasUpper` then `A` is upper triangular
TransA	if `TransA==FflasTrans` then $\mathrm{op}(A)=A^t$ .
Diag	if `Diag==FflasUnit` then `A` is implicitly unit.
M	rows of `B`
N	cols of `B`
alpha	scalar
A	triangular matrix. If `Side==FflasLeft` then `A` is $N\times N$ , otherwise `A` is $M\times M$
lda	leading dim of `A`
B	matrix of size `MxN`
ldb	leading dim of `B`

◆ ftrmm() [2/3]

void ftrmm	(	const Field &	F,
		const FFLAS_SIDE	Side,
		const FFLAS_UPLO	Uplo,
		const FFLAS_TRANSPOSE	TransA,
		const FFLAS_DIAG	Diag,
		const size_t	M,
		const size_t	N,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc
	)

inline

ftrmm: TRiangular Matrix Multiply with 3 operands Computes $C \gets \alpha \mathrm{op}(A) B + beta C$ or $C \gets \alpha B \mathrm{op}(A) + beta C$ .

Parameters

F	field
Side	if `Side==FflasLeft` then $B \gets \alpha \mathrm{op}(A) B$ is computed.
Uplo	if `Uplo==FflasUpper` then `A` is upper triangular
TransA	if `TransA==FflasTrans` then $\mathrm{op}(A)=A^t$ .
Diag	if `Diag==FflasUnit` then `A` is implicitly unit.
M	rows of `B`
N	cols of `B`
alpha	scalar
A	triangular matrix. If `Side==FflasLeft` then `A` is $N\times N$ , otherwise `A` is $M\times M$
lda	leading dim of `A`
B	matrix of size `MxN`
ldb	leading dim of `B`
beta	scalar
C	matrix of size `MxN`
ldc	leading dim of `C`

◆ ftrsm() [1/9]

void ftrsm	(	const Field &	F,
		const FFLAS_SIDE	Side,
		const FFLAS_UPLO	Uplo,
		const FFLAS_TRANSPOSE	TransA,
		const FFLAS_DIAG	Diag,
		const size_t	M,
		const size_t	N,
		const typename Field::Element	alpha,
		typename Field::Element_ptr	A,
		const size_t	lda,
		typename Field::Element_ptr	B,
		const size_t	ldb
	)

inline

◆ ftrsm() [2/9]

void ftrsm	(	const Field &	F,
		const FFLAS_SIDE	Side,
		const FFLAS_UPLO	Uplo,
		const FFLAS_TRANSPOSE	TransA,
		const FFLAS_DIAG	Diag,
		const size_t	M,
		const size_t	N,
		const typename Field::Element	alpha,
		typename Field::Element_ptr	A,
		const size_t	lda,
		typename Field::Element_ptr	B,
		const size_t	ldb,
		const ParSeqHelper::Sequential &	PSH
	)

inline

◆ ftrsm() [3/9]

void ftrsm	(	const Field &	F,
		const FFLAS_SIDE	Side,
		const FFLAS_UPLO	Uplo,
		const FFLAS_TRANSPOSE	TransA,
		const FFLAS_DIAG	Diag,
		const size_t	M,
		const size_t	N,
		const typename Field::Element	alpha,
		typename Field::Element_ptr	A,
		const size_t	lda,
		typename Field::Element_ptr	B,
		const size_t	ldb,
		const ParSeqHelper::Parallel< Cut, Param > &	PSH
	)

inline

◆ ftrsm() [4/9]

void ftrsm	(	const Field &	F,
		const FFLAS_SIDE	Side,
		const FFLAS_UPLO	Uplo,
		const FFLAS_TRANSPOSE	TransA,
		const FFLAS_DIAG	Diag,
		const size_t	M,
		const size_t	N,
		const typename Field::Element	alpha,
		typename Field::Element_ptr	A,
		const size_t	lda,
		typename Field::Element_ptr	B,
		const size_t	ldb,
		TRSMHelper< StructureHelper::Recursive, ParSeqTrait > &	H
	)

inline

◆ ftrsm() [5/9]

void ftrsm	(	const Givaro::Modular< Givaro::Integer > &	F,
		const FFLAS_SIDE	Side,
		const FFLAS_UPLO	Uplo,
		const FFLAS_TRANSPOSE	TransA,
		const FFLAS_DIAG	Diag,
		const size_t	M,
		const size_t	N,
		const Givaro::Integer	alpha,
		const Givaro::Integer *	A,
		const size_t	lda,
		Givaro::Integer *	B,
		const size_t	ldb
	)

inline

◆ cblas_imptrsm()

void cblas_imptrsm	(	const enum FFLAS_ORDER	Order,
		const enum FFLAS_SIDE	Side,
		const enum FFLAS_UPLO	Uplo,
		const enum FFLAS_TRANSPOSE	TransA,
		const enum FFLAS_DIAG	Diag,
		const int	M,
		const int	N,
		const FFPACK::rns_double_elt	alpha,
		FFPACK::rns_double_elt_cstptr	A,
		const int	lda,
		FFPACK::rns_double_elt_ptr	B,
		const int	ldb
	)

inline

◆ ftrsv() [1/2]

void ftrsv	(	const Field &	F,
		const FFLAS_UPLO	Uplo,
		const FFLAS_TRANSPOSE	TransA,
		const FFLAS_DIAG	Diag,
		const size_t	N,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::Element_ptr	X,
		int	incX
	)

inline

ftrsv: TRiangular System solve with Vector Computes $X \gets \mathrm{op}(A^{-1}) X$

Parameters

F	field
X	vector of size `N` on a field `F`
incX	stride of `X`
A	a matrix of leading dimension `lda` and size `N`
lda	leading dimension of `A`
N	number of rows or columns of `A` according to `TransA`
TransA	if `TransA==FflasTrans` then $\mathrm{op}(A)=A^t$ .
Diag	if `Diag==FflasUnit` then `A` is unit.
Uplo	if `Uplo==FflasUpper` then `A` is upper triangular

◆ igemm_()

void igemm_	(	const enum FFLAS_ORDER	Order,
		const enum FFLAS_TRANSPOSE	TransA,
		const enum FFLAS_TRANSPOSE	TransB,
		const size_t	M,
		const size_t	N,
		const size_t	K,
		const int64_t	alpha,
		const int64_t *	A,
		const size_t	lda,
		const int64_t *	B,
		const size_t	ldb,
		const int64_t	beta,
		int64_t *	C,
		const size_t	ldc
	)

inline

◆ finit() [5/8]

void finit	(	const Field &	F,
		const size_t	n,
		const OtherElement_ptr	Y,
		const size_t	incY,
		typename Field::Element_ptr	X,
		const size_t	incX
	)

finit $x \gets y mod F$ .

Parameters

F	field
n	size of the vectors
Y	vector of `OtherElement`
incY	stride of `Y`
X	vector in `F`
incX	stride of `X`

Bug:: use cblas_(d)scal when possible

◆ fconvert() [1/3]

void fconvert	(	const Field &	F,
		const size_t	n,
		OtherElement_ptr	X,
		const size_t	incX,
		typename Field::ConstElement_ptr	Y,
		const size_t	incY
	)

fconvert $x \gets y mod F$ .

Parameters

F	field
n	size of the vectors
Y	vector of `F`
incY	stride of `Y`
X	vector in `OtherElement`
incX	stride of `X`

Bug:: use cblas_(d)scal when possible

◆ fnegin() [1/4]

void fnegin	(	const Field &	F,
		const size_t	n,
		typename Field::Element_ptr	X,
		const size_t	incX
	)

fnegin $x \gets - x$ .

Parameters

F	field
n	size of the vectors
X	vector in `F`
incX	stride of `X`

Bug:: use cblas_(d)scal when possible

◆ fneg() [1/4]

void fneg	(	const Field &	F,
		const size_t	n,
		typename Field::ConstElement_ptr	Y,
		const size_t	incY,
		typename Field::Element_ptr	X,
		const size_t	incX
	)

fneg $x \gets - y$ .

Parameters

F	field
n	size of the vectors
X	vector in `F`
incX	stride of `X`
Y	vector in `F`
incY	stride of `Y`

Bug:: use cblas_(d)scal when possible

◆ fzero() [1/5]

void fzero	(	const Field &	F,
		const size_t	n,
		typename Field::Element_ptr	X,
		const size_t	incX
	)

fzero : $A \gets 0$ .

Parameters

F	field
n	number of elements to zero
X	vector in `F`
incX	stride of `X`

◆ frand() [1/2]

void frand	(	const Field &	F,
		RandIter &	G,
		const size_t	n,
		typename Field::Element_ptr	X,
		const size_t	incX
	)

frand : $A \gets random$ .

Parameters

F	field
G	randomiterator
n	number of elements to randomize
X	vector in `F`
incX	stride of `X`

◆ fiszero() [1/4]

bool fiszero	(	const Field &	F,
		const size_t	n,
		typename Field::ConstElement_ptr	X,
		const size_t	incX
	)

fiszero : test .

Parameters

F	field
n	vector dimension
X	vector in `F`
incX	increment of `X`

◆ fequal() [1/4]

bool fequal	(	const Field &	F,
		const size_t	n,
		typename Field::ConstElement_ptr	X,
		const size_t	incX,
		typename Field::ConstElement_ptr	Y,
		const size_t	incY
	)

fequal : test .

Parameters

F	field
n	vector dimension
X	vector in `F`
incX	increment of `X`
Y	vector in `F`
incY	increment of `Y`

◆ faxpby() [1/2]

void faxpby	(	const Field &	F,
		const size_t	N,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	X,
		const size_t	incX,
		const typename Field::Element	beta,
		typename Field::Element_ptr	Y,
		const size_t	incY
	)

faxpby : $y \gets \alpha \cdot x + \beta \cdot y$ .

Parameters

	F	field
	N	size of the vectors
	alpha	scalar
[in]	X	vector in `F`
	incX	stride of `X`
	beta	scalar
[in,out]	Y	vector in `F`
	incY	stride of `Y`

Note: this is a catlas function

◆ fdot() [9/11]

Field::Element fdot	(	const Field &	F,
		const size_t	N,
		typename Field::ConstElement_ptr	X,
		const size_t	incX,
		typename Field::ConstElement_ptr	Y,
		const size_t	incY,
		const ParSeqHelper::Parallel< Cut, Param >	par
	)

inline

◆ fswap() [1/2]

void fswap	(	const Field &	F,
		const size_t	N,
		typename Field::Element_ptr	X,
		const size_t	incX,
		typename Field::Element_ptr	Y,
		const size_t	incY
	)

fswap: $X \leftrightarrow Y$ .

Bug:: use cblas_dswap when double

Parameters

F	field
N	size of the vectors
X	vector in `F`
incX	stride of `X`
Y	vector in `F`
incY	stride of `Y`

◆ fzero() [2/5]

void fzero	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		typename Field::Element_ptr	A,
		const size_t	lda
	)

fzero : $A \gets 0$ .

Parameters

F	field
m	number of rows to zero
n	number of cols to zero
A	matrix in `F`
lda	stride of `A`

Warning: may be buggy if Element is larger than int

◆ fzero() [3/5]

void fzero	(	const Field &	F,
		const FFLAS_UPLO	shape,
		const FFLAS_DIAG	diag,
		const size_t	n,
		typename Field::Element_ptr	A,
		const size_t	lda
	)

fzero : $A \gets 0$ for a triangular matrix.

Parameters

F	field
shape	shape of the triangular matrix
m	number of rows to zero
n	number of cols to zero
A	matrix in `F`
lda	stride of `A`

Warning: may be buggy if Element is larger than int

◆ frand() [2/2]

void frand	(	const Field &	F,
		RandIter &	G,
		const size_t	m,
		const size_t	n,
		typename Field::Element_ptr	A,
		const size_t	lda
	)

frand : $A \gets random$ .

Parameters

F	field
G	randomiterator
m	number of rows to randomize
n	number of cols to randomize
A	matrix in `F`
lda	stride of `A`

◆ fequal() [2/4]

bool fequal	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb
	)

fequal : test .

Parameters

F	field
m	row dimension
n	column dimension
A	m x n matrix in `F`
lda	leading dimension of A
B	m x n matrix in `F`
ldb	leading dimension of B

◆ fiszero() [2/4]

bool fiszero	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		typename Field::ConstElement_ptr	A,
		const size_t	lda
	)

fiszero : test .

Parameters

F	field
m	row dimension
n	column dimension
A	m x n matrix in `F`
lda	leading dimension of A

◆ fidentity() [1/4]

void fidentity	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		typename Field::Element_ptr	A,
		const size_t	lda,
		const typename Field::Element &	d
	)

creates a diagonal matrix

◆ fidentity() [2/4]

void fidentity	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		typename Field::Element_ptr	A,
		const size_t	lda
	)

creates a diagonal matrix

◆ finit() [6/8]

void finit	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		typename Field::Element_ptr	A,
		const size_t	lda
	)

finit Initializes A in F$.

Parameters

F	field
m	number of rows
n	number of cols
A	matrix in `F`
lda	stride of `A`

◆ fconvert() [2/3]

void fconvert	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		OtherElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb
	)

fconvert $A \gets B mod F$ .

Parameters

F	field
m	number of rows
n	number of cols
A	matrix in `OtherElement`
lda	stride of `A`
B	matrix in `F`
ldb	stride of `B`

Todo:: check if n == lda

◆ fnegin() [2/4]

void fnegin	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		typename Field::Element_ptr	A,
		const size_t	lda
	)

fnegin $A \gets - A$ .

Parameters

F	field
m	number of rows
n	number of cols
A	matrix in `F`
lda	stride of `A`

Todo:: check if n == lda

◆ fneg() [2/4]

void fneg	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		typename Field::Element_ptr	A,
		const size_t	lda
	)

fneg $A \gets - B$ .

Parameters

F	field
m	number of rows
n	number of cols
A	matrix in `F`
lda	stride of `A`

Todo:: check if n == lda

◆ faxpby() [2/2]

void faxpby	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	X,
		const size_t	ldx,
		const typename Field::Element	beta,
		typename Field::Element_ptr	Y,
		const size_t	ldy
	)

faxpby : $y \gets \alpha \cdot x + \beta \cdot y$ .

Parameters

	F	field
	m	row dimension
	n	column dimension
	alpha	scalar
[in]	X	vector in `F`
	ldx	leading dimension of `X`
	beta	scalar
[in,out]	Y	vector in `F`
	ldy	leading dimension of `Y`

Note: this is a catlas function

◆ fmove() [1/2]

void fmove	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		typename Field::Element_ptr	A,
		const size_t	lda,
		typename Field::Element_ptr	B,
		const size_t	ldb
	)

fmove : $A \gets B$ and $B \gets 0$ .

Parameters

F	field
m	number of rows to copy
n	number of cols to copy
A	matrix in `F`
lda	stride of `A`
B	matrix in `F`
ldb	stride of `B`

◆ bitsize()

size_t bitsize	(	const Field &	F,
		size_t	M,
		size_t	N,
		const typename Field::ConstElement_ptr	A,
		size_t	lda
	)

inline

bitsize: Computes the largest bitsize of the matrix' coefficients.

If the matrix is over a modular prime field, it returns the bitsize of the largest element (in a bsolute value)

Parameters

F	field
M	rows
N	cols
incX	stride of `X`
A	a matrix of leading dimension `lda` and size `MxN`
lda	leading dimension of `A`

◆ bitsize< Givaro::ZRing< Givaro::Integer > >()

size_t bitsize< Givaro::ZRing< Givaro::Integer > >	(	const Givaro::ZRing< Givaro::Integer > &	F,
		size_t	M,
		size_t	N,
		const Givaro::Integer *	A,
		size_t	lda
	)

inline

◆ ftrmv()

void ftrmv	(	const Field &	F,
		const FFLAS_UPLO	Uplo,
		const FFLAS_TRANSPOSE	TransA,
		const FFLAS_DIAG	Diag,
		const size_t	N,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::Element_ptr	X,
		int	incX
	)

ftrsm: TRiangular Matrix Vector prodcut Computes $X \gets \mathrm{op}(A) X$

Parameters

F	field
X	vector of size `N` on a field `F`
incX	stride of `X`
A	a matrix of leading dimension `lda` and size `N`
lda	leading dimension of `A`
N	number of rows and columns of `A`
TransA	if `TransA==FflasTrans` then $\mathrm{op}(A)=A^T$ .
Diag	if `Diag==FflasUnit` then `A` is unit diagonal.
Uplo	if `Uplo==FflasUpper` then `A` is upper triangular

◆ ftrsm() [6/9]

void ftrsm	(	const Field &	F,
		const FFLAS_SIDE	Side,
		const FFLAS_UPLO	Uplo,
		const FFLAS_TRANSPOSE	TransA,
		const FFLAS_DIAG	Diag,
		const size_t	M,
		const size_t	N,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::Element_ptr	B,
		const size_t	ldb
	)

ftrsm: TRiangular System solve with Matrix.

Computes $B \gets \alpha \mathrm{op}(A^{-1}) B$ or $B \gets \alpha B \mathrm{op}(A^{-1})$ .

Parameters

F	field
Side	if `Side==FflasLeft` then $B \gets \alpha \mathrm{op}(A^{-1}) B$ is computed.
Uplo	if `Uplo==FflasUpper` then `A` is upper triangular
TransA	if `TransA==FflasTrans` then $\mathrm{op}(A)=A^t$ .
Diag	if `Diag==FflasUnit` then `A` is unit.
M	rows of `B`
N	cols of `B`
alpha	scalar
A	triangular invertible matrix. If `Side==FflasLeft` then `A` is $N\times N$ , otherwise `A` is $M\times M$
lda	leading dim of `A`
B	matrix of size `MxN`
ldb	leading dim of `B`

Bug:: $\alpha$ must be non zero.

◆ fsyrk_strassen() [2/2]

Field::Element_ptr fsyrk_strassen	(	const Field &	F,
		const FFLAS_UPLO	UpLo,
		const FFLAS_TRANSPOSE	trans,
		const size_t	N,
		const size_t	K,
		const typename Field::Element	y1,
		const typename Field::Element	y2,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		MMHelper< Field, MMHelperAlgo::Winograd, FieldTrait > &	H
	)

inline

◆ pfgemm() [1/7]

Field::Element_ptr pfgemm	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		size_t	numthreads = `0`
	)

◆ pfgemm_1D_rec()

Field::Element * pfgemm_1D_rec	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		const typename Field::Element_ptr	A,
		const size_t	lda,
		const typename Field::Element_ptr	B,
		const size_t	ldb,
		const typename Field::Element	beta,
		typename Field::Element *	C,
		const size_t	ldc,
		size_t	seuil
	)

◆ pfgemm_2D_rec()

Field::Element * pfgemm_2D_rec	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		const typename Field::Element_ptr	A,
		const size_t	lda,
		const typename Field::Element_ptr	B,
		const size_t	ldb,
		const typename Field::Element	beta,
		typename Field::Element *	C,
		const size_t	ldc,
		size_t	seuil
	)

◆ pfgemm_3D_rec()

Field::Element * pfgemm_3D_rec	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		const typename Field::Element_ptr	A,
		const size_t	lda,
		const typename Field::Element_ptr	B,
		const size_t	ldb,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		size_t	seuil,
		size_t *	x
	)

◆ pfgemm_3D_rec2()

Field::Element_ptr pfgemm_3D_rec2	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		const typename Field::Element_ptr	A,
		const size_t	lda,
		const typename Field::Element_ptr	B,
		const size_t	ldb,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		size_t	seuil,
		size_t *	x
	)

◆ fgemm() [19/23]

std::enable_if<!std::is_same< ModeTrait, ModeCategories::ConvertTo< ElementCategories::RNSElementTag > >::value, typenameField::Element_ptr >::type fgemm	(	const Field &	F,
		const FFLAS::FFLAS_TRANSPOSE	ta,
		const FFLAS::FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		typename Field::ConstElement_ptr	A,
		const size_t	lda,
		typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		MMHelper< Field, MMHelperAlgo::Winograd, ModeTrait, ParSeqHelper::Parallel< Strat, Param > > &	H
	)

inline

◆ ftrsm() [7/9]

Field::Element_ptr ftrsm	(	const Field &	F,
		const FFLAS::FFLAS_SIDE	Side,
		const FFLAS::FFLAS_UPLO	UpLo,
		const FFLAS::FFLAS_TRANSPOSE	TA,
		const FFLAS::FFLAS_DIAG	Diag,
		const size_t	m,
		const size_t	n,
		const typename Field::Element	alpha,
		typename Field::Element_ptr	A,
		const size_t	lda,
		typename Field::Element_ptr	B,
		const size_t	ldb,
		TRSMHelper< StructureHelper::Iterative, ParSeqHelper::Parallel< Cut, Param > > &	H
	)

inline

◆ ftrsm() [8/9]

Field::Element_ptr ftrsm	(	const Field &	F,
		const FFLAS::FFLAS_SIDE	Side,
		const FFLAS::FFLAS_UPLO	UpLo,
		const FFLAS::FFLAS_TRANSPOSE	TA,
		const FFLAS::FFLAS_DIAG	Diag,
		const size_t	m,
		const size_t	n,
		const typename Field::Element	alpha,
		typename Field::Element_ptr	A,
		const size_t	lda,
		typename Field::Element_ptr	B,
		const size_t	ldb,
		TRSMHelper< StructureHelper::Hybrid, ParSeqHelper::Parallel< Cut, Param > > &	H
	)

inline

◆ fspmv() [1/10]

void fspmv	(	const Field &	F,
		const SM &	A,
		typename Field::ConstElement_ptr	x,
		const typename Field::Element &	beta,
		typename Field::Element_ptr	y
	)

inline

◆ fspmm() [1/3]

void fspmm	(	const Field &	F,
		const SM &	A,
		size_t	blockSize,
		typename Field::ConstElement_ptr	x,
		int	ldx,
		const typename Field::Element &	beta,
		typename Field::Element_ptr	y,
		int	ldy
	)

inline

◆ sparse_init() [1/18]

void sparse_init	(	const Field &	F,
		Sparse< Field, SparseMatrix_t::COO > &	A,
		const IndexT *	row,
		const IndexT *	col,
		typename Field::ConstElement_ptr	dat,
		uint64_t	rowdim,
		uint64_t	coldim,
		uint64_t	nnz
	)

inline

◆ sparse_init() [2/18]

void sparse_init	(	const Field &	F,
		Sparse< Field, SparseMatrix_t::COO_ZO > &	A,
		const IndexT *	row,
		const IndexT *	col,
		typename Field::ConstElement_ptr	dat,
		uint64_t	rowdim,
		uint64_t	coldim,
		uint64_t	nnz
	)

inline

◆ sparse_delete() [1/14]

void sparse_delete ( const Sparse< Field, SparseMatrix_t::COO > & A )

inline

◆ sparse_delete() [2/14]

void sparse_delete ( const Sparse< Field, SparseMatrix_t::COO_ZO > & A )

inline

◆ sparse_init() [3/18]

void sparse_init	(	const Field &	F,
		Sparse< Field, SparseMatrix_t::CSR > &	A,
		const IndexT *	row,
		const IndexT *	col,
		typename Field::ConstElement_ptr	dat,
		uint64_t	rowdim,
		uint64_t	coldim,
		uint64_t	nnz
	)

inline

◆ sparse_init() [4/18]

void sparse_init	(	const Field &	F,
		Sparse< Field, SparseMatrix_t::CSR_ZO > &	A,
		const IndexT *	row,
		const IndexT *	col,
		typename Field::ConstElement_ptr	dat,
		uint64_t	rowdim,
		uint64_t	coldim,
		uint64_t	nnz
	)

inline

◆ sparse_delete() [3/14]

void sparse_delete ( const Sparse< Field, SparseMatrix_t::CSR > & A )

inline

◆ sparse_delete() [4/14]

void sparse_delete ( const Sparse< Field, SparseMatrix_t::CSR_ZO > & A )

inline

◆ sparse_print() [1/3]

std::ostream & sparse_print	(	std::ostream &	os,
		const Sparse< Field, SparseMatrix_t::CSR > &	A
	)

inline

◆ sparse_init() [5/18]

void sparse_init	(	const Givaro::Modular< Givaro::Integer > &	F,
		Sparse< Givaro::Modular< Givaro::Integer >, SparseMatrix_t::CSR > &	A,
		const IndexT *	row,
		const IndexT *	col,
		Givaro::Integer *	dat,
		uint64_t	rowdim,
		uint64_t	coldim,
		uint64_t	nnz
	)

inline

◆ sparse_init() [6/18]

void sparse_init	(	const Givaro::ZRing< Givaro::Integer > &	F,
		Sparse< Givaro::ZRing< Givaro::Integer >, SparseMatrix_t::CSR_ZO > &	A,
		const IndexT *	row,
		const IndexT *	col,
		Givaro::Integer *	dat,
		uint64_t	rowdim,
		uint64_t	coldim,
		uint64_t	nnz
	)

inline

◆ sparse_init() [7/18]

void sparse_init	(	const Givaro::ZRing< RecInt::rmint< RECINT_SIZE > > &	F,
		Sparse< Givaro::ZRing< RecInt::rmint< RECINT_SIZE > >, SparseMatrix_t::CSR_ZO > &	A,
		const IndexT *	row,
		const IndexT *	col,
		typename Givaro::ZRing< RecInt::rmint< RECINT_SIZE > >::Element_ptr	dat,
		uint64_t	rowdim,
		uint64_t	coldim,
		uint64_t	nnz
	)

inline

◆ sparse_init() [8/18]

void sparse_init	(	const Givaro::ZRing< RecInt::rmint< RECINT_SIZE > > &	F,
		Sparse< Givaro::ZRing< RecInt::rmint< RECINT_SIZE > >, SparseMatrix_t::CSR > &	A,
		const IndexT *	row,
		const IndexT *	col,
		typename Givaro::ZRing< RecInt::rmint< RECINT_SIZE > >::Element_ptr	dat,
		uint64_t	rowdim,
		uint64_t	coldim,
		uint64_t	nnz
	)

inline

◆ sparse_delete() [5/14]

void sparse_delete ( const Sparse< Field, SparseMatrix_t::CSR_HYB > & A )

inline

◆ sparse_init() [9/18]

void sparse_init	(	const Field &	F,
		Sparse< Field, SparseMatrix_t::CSR_HYB > &	A,
		const IndexT *	row,
		const IndexT *	col,
		typename Field::ConstElement_ptr	dat,
		uint64_t	rowdim,
		uint64_t	coldim,
		uint64_t	nnz
	)

inline

◆ sparse_init() [10/18]

void sparse_init	(	const Field &	F,
		Sparse< Field, SparseMatrix_t::ELL > &	A,
		const IndexT *	row,
		const IndexT *	col,
		typename Field::ConstElement_ptr	dat,
		uint64_t	rowdim,
		uint64_t	coldim,
		uint64_t	nnz
	)

inline

◆ sparse_init() [11/18]

void sparse_init	(	const Field &	F,
		Sparse< Field, SparseMatrix_t::ELL_ZO > &	A,
		const IndexT *	row,
		const IndexT *	col,
		typename Field::ConstElement_ptr	dat,
		uint64_t	rowdim,
		uint64_t	coldim,
		uint64_t	nnz
	)

inline

◆ sparse_delete() [6/14]

void sparse_delete ( const Sparse< Field, SparseMatrix_t::ELL > & A )

inline

◆ sparse_delete() [7/14]

void sparse_delete ( const Sparse< Field, SparseMatrix_t::ELL_ZO > & A )

inline

◆ fspmv() [2/10]

void fspmv	(	const Field &	F,
		const Sparse< Field, SparseMatrix_t::ELL_R > &	A,
		typename Field::ConstElement_ptr	x,
		const typename Field::Element &	beta,
		typename Field::Element_ptr	y
	)

inline

◆ fspmv() [3/10]

void fspmv	(	const Field &	F,
		const Sparse< Field, SparseMatrix_t::ELL_R_ZO > &	A,
		typename Field::ConstElement_ptr	x,
		const typename Field::Element &	beta,
		typename Field::Element_ptr	y
	)

inline

◆ fspmm() [2/3]

void fspmm	(	const Field &	F,
		const Sparse< Field, SparseMatrix_t::ELL_R > &	A,
		const size_t	blockSize,
		const typename Field::Element_ptr &	x,
		const int	ldx,
		const typename Field::Element &	beta,
		typename Field::Element_ptr &	y,
		const int	ldy
	)

◆ fspmm() [3/3]

void fspmm	(	const Field &	F,
		const Sparse< Field, SparseMatrix_t::ELL_R_ZO > &	A,
		const size_t	blockSize,
		const typename Field::Element_ptr &	x,
		const int	ldx,
		const typename Field::Element &	beta,
		typename Field::Element_ptr &	y,
		const int	ldy
	)

◆ fspmv() [4/10]

void fspmv	(	const Field &	F,
		const Sparse< Field, SparseMatrix_t::ELL_R > &	A,
		typename Field::ConstElement_ptr	x,
		typename Field::Element_ptr	y,
		FieldCategories::GenericTag
	)

inline

◆ fspmv() [5/10]

void fspmv	(	const Field &	F,
		const Sparse< Field, SparseMatrix_t::ELL_R > &	A,
		typename Field::ConstElement_ptr	x,
		typename Field::Element_ptr	y,
		FieldCategories::UnparametricTag
	)

inline

◆ fspmv() [6/10]

void fspmv	(	const Field &	F,
		const Sparse< Field, SparseMatrix_t::ELL_R > &	A,
		typename Field::ConstElement_ptr	x,
		typename Field::Element_ptr	y,
		FieldCategories::ModularTag
	)

inline

◆ fspmv() [7/10]

void fspmv	(	const Field &	F,
		const Sparse< Field, SparseMatrix_t::ELL_R_ZO > &	A,
		typename Field::ConstElement_ptr	x,
		typename Field::Element_ptr	y,
		FieldCategories::GenericTag
	)

inline

◆ fspmv() [8/10]

void fspmv	(	const Field &	F,
		const Sparse< Field, SparseMatrix_t::ELL_R_ZO > &	A,
		typename Field::ConstElement_ptr	x,
		typename Field::Element_ptr	y,
		FieldCategories::UnparametricTag
	)

inline

◆ fspmv() [9/10]

void fspmv	(	const Field &	F,
		const Sparse< Field, SparseMatrix_t::ELL_R_ZO > &	A,
		typename Field::ConstElement_ptr	x,
		typename Field::Element_ptr	y,
		FieldCategories::ModularTag
	)

inline

◆ sparse_delete() [8/14]

void sparse_delete ( const Sparse< Field, SparseMatrix_t::ELL_R > & A )

inline

◆ sparse_delete() [9/14]

void sparse_delete ( const Sparse< Field, SparseMatrix_t::ELL_R_ZO > & A )

inline

◆ sparse_init() [12/18]

void sparse_init	(	const Field &	F,
		Sparse< Field, SparseMatrix_t::ELL_R > &	A,
		const IndexT *	row,
		const IndexT *	col,
		typename Field::ConstElement_ptr	dat,
		uint64_t	rowdim,
		uint64_t	coldim,
		uint64_t	nnz
	)

inline

◆ sparse_init() [13/18]

void sparse_init	(	const Field &	F,
		Sparse< Field, SparseMatrix_t::ELL_R_ZO > &	A,
		const IndexT *	row,
		const IndexT *	col,
		typename Field::ConstElement_ptr	dat,
		uint64_t	rowdim,
		uint64_t	coldim,
		uint64_t	nnz
	)

inline

◆ sparse_init() [14/18]

void sparse_init	(	const Field &	F,
		Sparse< Field, SparseMatrix_t::ELL_simd > &	A,
		const IndexT *	row,
		const IndexT *	col,
		typename Field::ConstElement_ptr	dat,
		uint64_t	rowdim,
		uint64_t	coldim,
		uint64_t	nnz
	)

inline

◆ sparse_init() [15/18]

void sparse_init	(	const Field &	F,
		Sparse< Field, SparseMatrix_t::ELL_simd_ZO > &	A,
		const IndexT *	row,
		const IndexT *	col,
		typename Field::ConstElement_ptr	dat,
		uint64_t	rowdim,
		uint64_t	coldim,
		uint64_t	nnz
	)

inline

◆ sparse_delete() [10/14]

void sparse_delete ( const Sparse< Field, SparseMatrix_t::ELL_simd > & A )

inline

◆ sparse_delete() [11/14]

void sparse_delete ( const Sparse< Field, SparseMatrix_t::ELL_simd_ZO > & A )

inline

◆ sparse_print() [2/3]

void sparse_print ( const Sparse< Field, SparseMatrix_t::ELL_simd > & A )

inline

◆ sparse_delete() [12/14]

void sparse_delete ( const Sparse< Field, SparseMatrix_t::HYB_ZO > & A )

inline

◆ sparse_init() [16/18]

void sparse_init	(	const Field &	F,
		Sparse< Field, SparseMatrix_t::HYB_ZO > &	A,
		const IndexT *	row,
		const IndexT *	col,
		typename Field::ConstElement_ptr	dat,
		uint64_t	rowdim,
		uint64_t	coldim,
		uint64_t	nnz
	)

inline

◆ operator<<()

std::ostream & operator<<	(	std::ostream &	os,
		const Sparse< _Field, SparseMatrix_t::HYB_ZO > &	A
	)

◆ readSmsFormat()

void readSmsFormat	(	const std::string &	path,
		const Field &	f,
		index_t *&	row,
		index_t *&	col,
		typename Field::Element_ptr &	val,
		index_t &	rowdim,
		index_t &	coldim,
		uint64_t &	nnz
	)

◆ readSprFormat()

void readSprFormat	(	const std::string &	path,
		const Field &	f,
		index_t *&	row,
		index_t *&	col,
		typename Field::Element_ptr &	val,
		index_t &	rowdim,
		index_t &	coldim,
		uint64_t &	nnz
	)

◆ getDataType() [1/4]

std::enable_if< std::is_integral< T >::value, int > getDataType ( )

◆ getDataType() [2/4]

std::enable_if< std::is_floating_point< T >::value, int > getDataType ( )

◆ getDataType() [3/4]

std::enable_if< std::is_same< T, mpz_t >::value, int > getDataType ( )

◆ getDataType() [4/4]

int getDataType ( )

◆ readMachineType()

void readMachineType	(	const Field &	F,
		typename Field::Element &	modulo,
		typename Field::Element_ptr	val,
		std::ifstream &	file,
		const uint64_t	dims,
		const mask_t	data_type,
		const mask_t	field_desc
	)

◆ readDnsFormat()

void readDnsFormat	(	const std::string &	path,
		const Field &	F,
		index_t &	rowdim,
		index_t &	coldim,
		typename Field::Element_ptr &	val
	)

◆ writeDnsFormat()

void writeDnsFormat	(	const std::string &	path,
		const Field &	F,
		const index_t &	rowdim,
		const index_t &	coldim,
		typename Field::Element_ptr	A,
		index_t	ldA
	)

◆ fspmv() [10/10]

void fspmv	(	const Field &	F,
		const Sparse< Field, SparseMatrix_t::SELL_ZO > &	A,
		typename Field::ConstElement_ptr	x,
		typename Field::Element_ptr	y,
		FieldCategories::ModularTag
	)

inline

◆ sparse_delete() [13/14]

void sparse_delete ( const Sparse< Field, SparseMatrix_t::SELL > & A )

inline

◆ sparse_delete() [14/14]

void sparse_delete ( const Sparse< Field, SparseMatrix_t::SELL_ZO > & A )

inline

◆ sparse_print() [3/3]

void sparse_print ( const Sparse< Field, SparseMatrix_t::SELL > & A )

inline

◆ sparse_init() [17/18]

void sparse_init	(	const Field &	F,
		Sparse< Field, SparseMatrix_t::SELL > &	A,
		const IndexT *	row,
		const IndexT *	col,
		typename Field::ConstElement_ptr	dat,
		uint64_t	rowdim,
		uint64_t	coldim,
		uint64_t	nnz,
		uint64_t	sigma = `0`
	)

inline

◆ sparse_init() [18/18]

void sparse_init	(	const Field &	F,
		Sparse< Field, SparseMatrix_t::SELL_ZO > &	A,
		const IndexT *	row,
		const IndexT *	col,
		typename Field::ConstElement_ptr	dat,
		uint64_t	rowdim,
		uint64_t	coldim,
		uint64_t	nnz
	)

inline

◆ computeDeviation()

double computeDeviation	(	It	begin,
		It	end
	)

◆ getStat()

StatsMatrix getStat	(	const Field &	F,
		const index_t *	row,
		const index_t *	col,
		typename Field::ConstElement_ptr	val,
		uint64_t	rowdim,
		uint64_t	coldim,
		uint64_t	nnz
	)

◆ maxCardinality()

Field::Residu_t maxCardinality ( )

inline

◆ maxCardinality< Givaro::Modular< int64_t > >()

uint64_t maxCardinality< Givaro::Modular< int64_t > > ( )

inline

◆ maxCardinality< Givaro::Modular< int32_t > >()

uint32_t maxCardinality< Givaro::Modular< int32_t > > ( )

inline

◆ minCardinality()

Field::Residu_t minCardinality ( )

inline

◆ fflas_delete() [1/4]

void fflas_delete ( FFPACK::rns_double_elt_ptr A )

inline

◆ fflas_delete() [2/4]

void fflas_delete ( FFPACK::rns_double_elt_cstptr A )

inline

◆ fflas_new() [1/7]

FFPACK::rns_double_elt_ptr fflas_new	(	const FFPACK::RNSIntegerMod< FFPACK::rns_double > &	F,
		const size_t	m,
		const Alignment	align
	)

inline

◆ fflas_new() [2/7]

FFPACK::rns_double_elt_ptr fflas_new	(	const FFPACK::RNSIntegerMod< FFPACK::rns_double > &	F,
		const size_t	m,
		const size_t	n,
		const Alignment	align
	)

inline

◆ finit_rns() [1/2]

void finit_rns	(	const FFPACK::RNSIntegerMod< RNS > &	F,
		const size_t	m,
		const size_t	n,
		size_t	k,
		const Givaro::Integer *	B,
		const size_t	ldb,
		typename RNS::Element_ptr	A
	)

◆ finit_trans_rns()

void finit_trans_rns	(	const FFPACK::RNSIntegerMod< RNS > &	F,
		const size_t	m,
		const size_t	n,
		size_t	k,
		const Givaro::Integer *	B,
		const size_t	ldb,
		typename RNS::Element_ptr	A
	)

◆ fconvert_rns() [1/2]

void fconvert_rns	(	const FFPACK::RNSIntegerMod< RNS > &	F,
		const size_t	m,
		const size_t	n,
		Givaro::Integer	alpha,
		Givaro::Integer *	B,
		const size_t	ldb,
		typename RNS::ConstElement_ptr	A
	)

◆ fconvert_trans_rns()

void fconvert_trans_rns	(	const FFPACK::RNSIntegerMod< RNS > &	F,
		const size_t	m,
		const size_t	n,
		Givaro::Integer	alpha,
		Givaro::Integer *	B,
		const size_t	ldb,
		typename RNS::ConstElement_ptr	A
	)

◆ fflas_new() [3/7]

FFPACK::rns_double_elt_ptr fflas_new	(	const FFPACK::RNSInteger< FFPACK::rns_double > &	F,
		const size_t	m,
		const Alignment	align
	)

inline

◆ fflas_new() [4/7]

FFPACK::rns_double_elt_ptr fflas_new	(	const FFPACK::RNSInteger< FFPACK::rns_double > &	F,
		const size_t	m,
		const size_t	n,
		const Alignment	align
	)

inline

◆ finit_rns() [2/2]

void finit_rns	(	const FFPACK::RNSInteger< RNS > &	F,
		const size_t	m,
		const size_t	n,
		size_t	k,
		const Givaro::Integer *	B,
		const size_t	ldb,
		typename FFPACK::RNSInteger< RNS >::Element_ptr	A
	)

◆ fconvert_rns() [2/2]

void fconvert_rns	(	const FFPACK::RNSInteger< RNS > &	F,
		const size_t	m,
		const size_t	n,
		Givaro::Integer	alpha,
		Givaro::Integer *	B,
		const size_t	ldb,
		typename FFPACK::RNSInteger< RNS >::ConstElement_ptr	A
	)

◆ freduce() [8/11]

template INST_OR_DECL void freduce	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	n,
		FFLAS_ELT *	X,
		const size_t	incX
	)

freduce $x \gets x mod F$ .

Parameters

F	field
n	size of the vectors
X	vector in `F`
incX	stride of `X`

Bug:: use cblas_(d)scal when possible

◆ freduce() [9/11]

template INST_OR_DECL void freduce	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	n,
		const FFLAS_ELT *	Y,
		const size_t	incY,
		FFLAS_ELT *	X,
		const size_t	incX
	)

freduce $x \gets y mod F$ .

Parameters

F	field
n	size of the vectors
Y	vector of `Element`
incY	stride of `Y`
X	vector in `F`
incX	stride of `X`

Bug:: use cblas_(d)scal when possible

◆ finit() [7/8]

template INST_OR_DECL void finit	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	n,
		const FFLAS_ELT *	Y,
		const size_t	incY,
		FFLAS_ELT *	X,
		const size_t	incX
	)

finit $x \gets y mod F$ .

Parameters

F	field
n	size of the vectors
Y	vector of `OtherElement`
incY	stride of `Y`
X	vector in `F`
incX	stride of `X`

Bug:: use cblas_(d)scal when possible

◆ fconvert() [3/3]

template INST_OR_DECL void fconvert	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	n,
		FFLAS_ELT *	X,
		const size_t	incX,
		const FFLAS_ELT *	Y,
		const size_t	incY
	)

fconvert $x \gets y mod F$ .

Parameters

F	field
n	size of the vectors
Y	vector of `F`
incY	stride of `Y`
X	vector in `OtherElement`
incX	stride of `X`

Bug:: use cblas_(d)scal when possible

◆ fnegin() [3/4]

template INST_OR_DECL void fnegin	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	n,
		FFLAS_ELT *	X,
		const size_t	incX
	)

fnegin $x \gets - x$ .

Parameters

F	field
n	size of the vectors
X	vector in `F`
incX	stride of `X`

Bug:: use cblas_(d)scal when possible

◆ fneg() [3/4]

template INST_OR_DECL void fneg	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	n,
		const FFLAS_ELT *	Y,
		const size_t	incY,
		FFLAS_ELT *	X,
		const size_t	incX
	)

fneg $x \gets - y$ .

Parameters

F	field
n	size of the vectors
X	vector in `F`
incX	stride of `X`
Y	vector in `F`
incY	stride of `Y`

Bug:: use cblas_(d)scal when possible

◆ fzero() [4/5]

template INST_OR_DECL void fzero	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	n,
		FFLAS_ELT *	X,
		const size_t	incX
	)

fzero : $A \gets 0$ .

Parameters

F	field
n	number of elements to zero
X	vector in `F`
incX	stride of `X`

◆ fiszero() [3/4]

template INST_OR_DECL bool fiszero	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	n,
		const FFLAS_ELT *	X,
		const size_t	incX
	)

fiszero : test .

Parameters

F	field
n	vector dimension
X	vector in `F`
incX	increment of `X`

◆ fequal() [3/4]

template INST_OR_DECL bool fequal	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	n,
		const FFLAS_ELT *	X,
		const size_t	incX,
		const FFLAS_ELT *	Y,
		const size_t	incY
	)

fequal : test .

Parameters

F	field
n	vector dimension
X	vector in `F`
incX	increment of `X`
Y	vector in `F`
incY	increment of `Y`

◆ fassign() [9/10]

template INST_OR_DECL void fassign	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	N,
		const FFLAS_ELT *	Y,
		const size_t	incY,
		FFLAS_ELT *	X,
		const size_t	incX
	)

fassign : $x \gets y$ .

X is preallocated

Todo:: variant for triagular matrix

Parameters

	F	field
	N	size of the vectors
[out]	X	vector in `F`
	incX	stride of `X`
[in]	Y	vector in `F`
	incY	stride of `Y`

◆ fscalin() [9/10]

template INST_OR_DECL void fscalin	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	n,
		const FFLAS_ELT	alpha,
		FFLAS_ELT *	X,
		const size_t	incX
	)

fscalin $x \gets \alpha \cdot x$ .

Parameters

F	field
n	size of the vectors
alpha	scalar
X	vector in `F`
incX	stride of `X`

Bug:: use cblas_(d)scal when possible

Todo:: check if comparison with +/-1,0 is necessary.

◆ fscal() [9/10]

template INST_OR_DECL void fscal	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	n,
		const FFLAS_ELT	alpha,
		const FFLAS_ELT *	X,
		const size_t	incX,
		FFLAS_ELT *	Y,
		const size_t	incY
	)

fscal $y \gets \alpha \cdot x$ .

Parameters

	F	field
	n	size of the vectors
	alpha	scalar
[in]	X	vector in `F`
	incX	stride of `X`
[out]	Y	vector in `F`
	incY	stride of `Y`

Bug:: use cblas_(d)scal when possible

Todo:: check if comparison with +/-1,0 is necessary.

◆ faxpy() [5/6]

template INST_OR_DECL void faxpy	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	N,
		const FFLAS_ELT	alpha,
		const FFLAS_ELT *	X,
		const size_t	incX,
		FFLAS_ELT *	Y,
		const size_t	incY
	)

faxpy : $y \gets \alpha \cdot x + y$ .

Parameters

	F	field
	N	size of the vectors
	alpha	scalar
[in]	X	vector in `F`
	incX	stride of `X`
[in,out]	Y	vector in `F`
	incY	stride of `Y`

◆ fdot() [10/11]

template INST_OR_DECL FFLAS_ELT fdot	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	N,
		const FFLAS_ELT *	X,
		const size_t	incX,
		const FFLAS_ELT *	Y,
		const size_t	incY
	)

faxpby : $y \gets \alpha \cdot x + \beta \cdot y$ .

Parameters

	F	field
	N	size of the vectors
	alpha	scalar
[in]	X	vector in `F`
	incX	stride of `X`
	beta	scalar
[in,out]	Y	vector in `F`
	incY	stride of `Y`

Note: this is a catlas function

fdot: dot product .

Parameters

F	field
N	size of the vectors
X	vector in `F`
incX	stride of `X`
Y	vector in `F`
incY	stride of `Y`

◆ fswap() [2/2]

template INST_OR_DECL void fswap	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	N,
		FFLAS_ELT *	X,
		const size_t	incX,
		FFLAS_ELT *	Y,
		const size_t	incY
	)

fswap: $X \leftrightarrow Y$ .

Bug:: use cblas_dswap when double

Parameters

F	field
N	size of the vectors
X	vector in `F`
incX	stride of `X`
Y	vector in `F`
incY	stride of `Y`

◆ fadd() [5/8]

template INST_OR_DECL void fadd	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	N,
		const FFLAS_ELT *	A,
		const size_t	inca,
		const FFLAS_ELT *	B,
		const size_t	incb,
		FFLAS_ELT *	C,
		const size_t	incc
	)

◆ fsub() [3/4]

template INST_OR_DECL void fsub	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	N,
		const FFLAS_ELT *	A,
		const size_t	inca,
		const FFLAS_ELT *	B,
		const size_t	incb,
		FFLAS_ELT *	C,
		const size_t	incc
	)

◆ faddin() [4/5]

template INST_OR_DECL void faddin	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	N,
		const FFLAS_ELT *	B,
		const size_t	incb,
		FFLAS_ELT *	C,
		const size_t	incc
	)

◆ fadd() [6/8]

template INST_OR_DECL void fadd	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	N,
		const FFLAS_ELT *	A,
		const size_t	inca,
		const FFLAS_ELT	alpha,
		const FFLAS_ELT *	B,
		const size_t	incb,
		FFLAS_ELT *	C,
		const size_t	incc
	)

◆ fassign() [10/10]

template INST_OR_DECL void fassign	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	m,
		const size_t	n,
		const FFLAS_ELT *	B,
		const size_t	ldb,
		FFLAS_ELT *	A,
		const size_t	lda
	)

fassign : $A \gets B$ .

Parameters

F	field
m	number of rows to copy
n	number of cols to copy
A	matrix in `F`
lda	stride of `A`
B	vector in `F`
ldb	stride of `B`

◆ fzero() [5/5]

template INST_OR_DECL void fzero	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	m,
		const size_t	n,
		FFLAS_ELT *	A,
		const size_t	lda
	)

fzero : $A \gets 0$ .

Parameters

F	field
m	number of rows to zero
n	number of cols to zero
A	matrix in `F`
lda	stride of `A`

Warning: may be buggy if Element is larger than int

◆ fequal() [4/4]

template INST_OR_DECL bool fequal	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	m,
		const size_t	n,
		const FFLAS_ELT *	A,
		const size_t	lda,
		const FFLAS_ELT *	B,
		const size_t	ldb
	)

fequal : test .

Parameters

F	field
m	row dimension
n	column dimension
A	m x n matrix in `F`
lda	leading dimension of A
B	m x n matrix in `F`
ldb	leading dimension of B

◆ fiszero() [4/4]

template INST_OR_DECL bool fiszero	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	m,
		const size_t	n,
		const FFLAS_ELT *	A,
		const size_t	lda
	)

fiszero : test .

Parameters

F	field
m	row dimension
n	column dimension
A	m x n matrix in `F`
lda	leading dimension of A

◆ fidentity() [3/4]

template INST_OR_DECL void fidentity	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	m,
		const size_t	n,
		FFLAS_ELT *	A,
		const size_t	lda,
		const FFLAS_ELT &	d
	)

creates a diagonal matrix

◆ fidentity() [4/4]

template INST_OR_DECL void fidentity	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	m,
		const size_t	n,
		FFLAS_ELT *	A,
		const size_t	lda
	)

creates a diagonal matrix

◆ freduce() [10/11]

template INST_OR_DECL void freduce	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	m,
		const size_t	n,
		FFLAS_ELT *	A,
		const size_t	lda
	)

freduce $A \gets A mod F$ .

Parameters

F	field
m	number of rows
n	number of cols
A	matrix in `F`
lda	stride of `A`

◆ freduce() [11/11]

template INST_OR_DECL void freduce	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	m,
		const size_t	n,
		const FFLAS_ELT *	B,
		const size_t	ldb,
		FFLAS_ELT *	A,
		const size_t	lda
	)

freduce $A \gets B mod F$ .

Parameters

F	field
m	number of rows
n	number of cols
A	matrix in `F`
lda	stride of `A`
B	matrix in `Element`
ldb	stride of `B`

◆ finit() [8/8]

template INST_OR_DECL void finit	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	m,
		const size_t	n,
		const FFLAS_ELT *	B,
		const size_t	ldb,
		FFLAS_ELT *	A,
		const size_t	lda
	)

finit $A \gets B mod F$ .

Parameters

F	field
m	number of rows
n	number of cols
A	matrix in `F`
lda	stride of `A`
B	matrix in `F`
ldb	stride of `B`

◆ fnegin() [4/4]

template INST_OR_DECL void fnegin	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	m,
		const size_t	n,
		FFLAS_ELT *	A,
		const size_t	lda
	)

fnegin $A \gets - A$ .

Parameters

F	field
m	number of rows
n	number of cols
A	matrix in `F`
lda	stride of `A`

◆ fneg() [4/4]

template INST_OR_DECL void fneg	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	m,
		const size_t	n,
		const FFLAS_ELT *	B,
		const size_t	ldb,
		FFLAS_ELT *	A,
		const size_t	lda
	)

fneg $A \gets - B$ .

Parameters

F	field
m	number of rows
n	number of cols
A	matrix in `F`
lda	stride of `A`

◆ fscalin() [10/10]

template INST_OR_DECL void fscalin	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	m,
		const size_t	n,
		const FFLAS_ELT	alpha,
		FFLAS_ELT *	A,
		const size_t	lda
	)

fscalin $A \gets a \cdot A$ .

Parameters

F	field
m	number of rows
n	number of cols
alpha	homotecie scalar
A	matrix in `F`
lda	stride of `A`

◆ fscal() [10/10]

template INST_OR_DECL void fscal	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	m,
		const size_t	n,
		const FFLAS_ELT	alpha,
		const FFLAS_ELT *	A,
		const size_t	lda,
		FFLAS_ELT *	B,
		const size_t	ldb
	)

fscal $B \gets a \cdot A$ .

Parameters

	F	field
	m	number of rows
	n	number of cols
	alpha	homotecie scalar
[in]	A	matrix in `F`
	lda	stride of `A`
[out]	B	matrix in `F`
	ldb	stride of `B`

◆ faxpy() [6/6]

template INST_OR_DECL void faxpy	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	m,
		const size_t	n,
		const FFLAS_ELT	alpha,
		const FFLAS_ELT *	X,
		const size_t	ldx,
		FFLAS_ELT *	Y,
		const size_t	ldy
	)

faxpy : $y \gets \alpha \cdot x + y$ .

Parameters

	F	field
	m	row dimension
	n	column dimension
	alpha	scalar
[in]	X	vector in `F`
	ldx	leading dimension of `X`
[in,out]	Y	vector in `F`
	ldy	leading dimension of `Y`

◆ fmove() [2/2]

template INST_OR_DECL void fmove	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	m,
		const size_t	n,
		FFLAS_ELT *	A,
		const size_t	lda,
		FFLAS_ELT *	B,
		const size_t	ldb
	)

faxpby : $y \gets \alpha \cdot x + \beta \cdot y$ .

Parameters

	F	field
	m	row dimension
	n	column dimension
	alpha	scalar
[in]	X	vector in `F`
	ldx	leading dimension of `X`
	beta	scalar
[in,out]	Y	vector in `F`
	ldy	leading dimension of `Y`

Note: this is a catlas function

fmove : $A \gets B$ and $B \gets 0$ .

Parameters

F	field
m	number of rows to copy
n	number of cols to copy
A	matrix in `F`
lda	stride of `A`
B	vector in `F`
ldb	stride of `B`

◆ fadd() [7/8]

template INST_OR_DECL void fadd	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	M,
		const size_t	N,
		const FFLAS_ELT *	A,
		const size_t	lda,
		const FFLAS_ELT *	B,
		const size_t	ldb,
		FFLAS_ELT *	C,
		const size_t	ldc
	)

fadd : matrix addition.

Computes C = A + B.

Parameters

F	field
M	rows
N	cols
A	dense matrix of size `MxN`
lda	leading dimension of `A`
B	dense matrix of size `MxN`
ldb	leading dimension of `B`
C	dense matrix of size `MxN`
ldc	leading dimension of `C`

◆ fsub() [4/4]

template INST_OR_DECL void fsub	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	M,
		const size_t	N,
		const FFLAS_ELT *	A,
		const size_t	lda,
		const FFLAS_ELT *	B,
		const size_t	ldb,
		FFLAS_ELT *	C,
		const size_t	ldc
	)

fsub : matrix subtraction.

Computes C = A - B.

Parameters

F	field
M	rows
N	cols
A	dense matrix of size `MxN`
lda	leading dimension of `A`
B	dense matrix of size `MxN`
ldb	leading dimension of `B`
C	dense matrix of size `MxN`
ldc	leading dimension of `C`

◆ fsubin() [3/3]

template INST_OR_DECL void fsubin	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	M,
		const size_t	N,
		const FFLAS_ELT *	B,
		const size_t	ldb,
		FFLAS_ELT *	C,
		const size_t	ldc
	)

fsubin C = C - B

◆ fadd() [8/8]

template INST_OR_DECL void fadd	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	M,
		const size_t	N,
		const FFLAS_ELT *	A,
		const size_t	lda,
		const FFLAS_ELT	alpha,
		const FFLAS_ELT *	B,
		const size_t	ldb,
		FFLAS_ELT *	C,
		const size_t	ldc
	)

fadd : matrix addition with scaling.

Computes C = A + alpha B.

Parameters

F	field
M	rows
N	cols
A	dense matrix of size `MxN`
lda	leading dimension of `A`
alpha	some scalar
B	dense matrix of size `MxN`
ldb	leading dimension of `B`
C	dense matrix of size `MxN`
ldc	leading dimension of `C`

◆ faddin() [5/5]

template INST_OR_DECL void faddin	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	M,
		const size_t	N,
		const FFLAS_ELT *	B,
		const size_t	ldb,
		FFLAS_ELT *	C,
		const size_t	ldc
	)

faddin

◆ fgemv() [17/19]

template INST_OR_DECL FFLAS_ELT * fgemv	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const FFLAS_TRANSPOSE	TransA,
		const size_t	M,
		const size_t	N,
		const FFLAS_ELT	alpha,
		const FFLAS_ELT *	A,
		const size_t	lda,
		const FFLAS_ELT *	X,
		const size_t	incX,
		const FFLAS_ELT	beta,
		FFLAS_ELT *	Y,
		const size_t	incY
	)

finite prime FFLAS_FIELD<FFLAS_ELT> GEneral Matrix Vector multiplication.

Computes $Y \gets \alpha \mathrm{op}(A) X + \beta Y$ .

Parameters

	F	field
	TransA	if `TransA==FflasTrans` then $\mathrm{op}(A)=A^t$ .
	M	rows
	N	cols
	alpha	scalar
	A	dense matrix of size `MxN`
	lda	leading dimension of `A`
	X	dense vector of size `N`
	incX	stride of `X`
	beta	scalar
[out]	Y	dense vector of size `M`
	incY	stride of `Y`

◆ fger() [12/12]

template INST_OR_DECL void fger	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const size_t	M,
		const size_t	N,
		const FFLAS_ELT	alpha,
		const FFLAS_ELT *	x,
		const size_t	incx,
		const FFLAS_ELT *	y,
		const size_t	incy,
		FFLAS_ELT *	A,
		const size_t	lda
	)

fger: rank one update of a general matrix

Computes $A \gets \alpha x . y^T + A$

Parameters

	F	field
	M	rows
	N	cols
	alpha	scalar
[in,out]	A	dense matrix of size `MxN` and leading dimension `lda`
	lda	leading dimension of `A`
	x	dense vector of size `M`
	incx	stride of `X`
	y	dense vector of size `N`
	incy	stride of `Y`

◆ ftrsv() [2/2]

template INST_OR_DECL void ftrsv	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const FFLAS_UPLO	Uplo,
		const FFLAS_TRANSPOSE	TransA,
		const FFLAS_DIAG	Diag,
		const size_t	N,
		const FFLAS_ELT *	A,
		const size_t	lda,
		FFLAS_ELT *	X,
		int	incX
	)

ftrsv: TRiangular System solve with Vector Computes $X \gets \mathrm{op}(A^{-1}) X$

Parameters

F	field
X	vector of size `N` on a field `F`
incX	stride of `X`
A	a matrix of leading dimension `lda` and size `N`
lda	leading dimension of `A`
N	number of rows or columns of `A` according to `TransA`
TransA	if `TransA==FflasTrans` then $\mathrm{op}(A)=A^t$ .
Diag	if `Diag==FflasUnit` then `A` is unit.
Uplo	if `Uplo==FflasUpper` then `A` is upper triangular

◆ ftrsm() [9/9]

template INST_OR_DECL void ftrsm	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const FFLAS_SIDE	Side,
		const FFLAS_UPLO	Uplo,
		const FFLAS_TRANSPOSE	TransA,
		const FFLAS_DIAG	Diag,
		const size_t	M,
		const size_t	N,
		const FFLAS_ELT	alpha,
		const FFLAS_ELT *	A,
		const size_t	lda,
		FFLAS_ELT *	B,
		const size_t	ldb
	)

ftrsm: TRiangular System solve with Matrix.

Computes $B \gets \alpha \mathrm{op}(A^{-1}) B$ or $B \gets \alpha B \mathrm{op}(A^{-1})$ .

Parameters

F	field
Side	if `Side==FflasLeft` then $B \gets \alpha \mathrm{op}(A^{-1}) B$ is computed.
Uplo	if `Uplo==FflasUpper` then `A` is upper triangular
TransA	if `TransA==FflasTrans` then $\mathrm{op}(A)=A^t$ .
Diag	if `Diag==FflasUnit` then `A` is unit.
M	rows of `B`
N	cols of `B`
alpha	scalar
A	triangular invertible matrix. If `Side==FflasLeft` then `A` is $N\times N$ , otherwise `A` is $M\times M$
lda	leading dim of `A`
B	matrix of size `MxN`
ldb	leading dim of `B`

Bug:: $\alpha$ must be non zero.

◆ ftrmm() [3/3]

template INST_OR_DECL void ftrmm	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const FFLAS_SIDE	Side,
		const FFLAS_UPLO	Uplo,
		const FFLAS_TRANSPOSE	TransA,
		const FFLAS_DIAG	Diag,
		const size_t	M,
		const size_t	N,
		const FFLAS_ELT	alpha,
		const FFLAS_ELT *	A,
		const size_t	lda,
		FFLAS_ELT *	B,
		const size_t	ldb
	)

ftrmm: TRiangular Matrix Multiply.

Computes $B \gets \alpha \mathrm{op}(A) B$ or $B \gets \alpha B \mathrm{op}(A)$ .

Parameters

F	field
Side	if `Side==FflasLeft` then $B \gets \alpha \mathrm{op}(A) B$ is computed.
Uplo	if `Uplo==FflasUpper` then `A` is upper triangular
TransA	if `TransA==FflasTrans` then $\mathrm{op}(A)=A^t$ .
Diag	if `Diag==FflasUnit` then `A` is implicitly unit.
M	rows of `B`
N	cols of `B`
alpha	scalar
A	triangular matrix. If `Side==FflasLeft` then `A` is $N\times N$ , otherwise `A` is $M\times M$
lda	leading dim of `A`
B	matrix of size `MxN`
ldb	leading dim of `B`

◆ fgemm() [20/23]

template INST_OR_DECL FFLAS_ELT * fgemm	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const FFLAS_ELT	alpha,
		const FFLAS_ELT *	A,
		const size_t	lda,
		const FFLAS_ELT *	B,
		const size_t	ldb,
		const FFLAS_ELT	beta,
		FFLAS_ELT *	C,
		const size_t	ldc
	)

fgemm: Field GEneral Matrix Multiply.

Computes $C = \alpha \mathrm{op}(A) \times \mathrm{op}(B) + \beta C$ Automatically set Winograd recursion level

Parameters

F	field.
ta	if `ta==FflasTrans` then $\mathrm{op}(A)=A^t$ , else $\mathrm{op}(A)=A$ ,
tb	same for matrix `B`
m	see `A`
n	see `B`
k	see `A`
alpha	scalar
beta	scalar
A	$\mathrm{op}(A)$ is $m \times k$
B	$\mathrm{op}(B)$ is $k \times n$
C	is $m \times n$
lda	leading dimension of `A`
ldb	leading dimension of `B`
ldc	leading dimension of `C`
w	recursive levels of Winograd's algorithm are used. No argument (or -1) does auto computation of `w`.

Warning: $\alpha$ must be invertible

◆ fgemm() [21/23]

template INST_OR_DECL FFLAS_ELT * fgemm	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const FFLAS_ELT	alpha,
		const FFLAS_ELT *	A,
		const size_t	lda,
		const FFLAS_ELT *	B,
		const size_t	ldb,
		const FFLAS_ELT	beta,
		FFLAS_ELT *	C,
		const size_t	ldc,
		const ParSeqHelper::Sequential	seq
	)

◆ fgemm() [22/23]

template INST_OR_DECL FFLAS_ELT * fgemm	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const FFLAS_ELT	alpha,
		const FFLAS_ELT *	A,
		const size_t	lda,
		const FFLAS_ELT *	B,
		const size_t	ldb,
		const FFLAS_ELT	beta,
		FFLAS_ELT *	C,
		const size_t	ldc,
		const ParSeqHelper::Parallel< CuttingStrategy::Recursive, StrategyParameter::TwoDAdaptive >	par
	)

◆ fgemm() [23/23]

template INST_OR_DECL FFLAS_ELT * fgemm	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const FFLAS_ELT	alpha,
		const FFLAS_ELT *	A,
		const size_t	lda,
		const FFLAS_ELT *	B,
		const size_t	ldb,
		const FFLAS_ELT	beta,
		FFLAS_ELT *	C,
		const size_t	ldc,
		const ParSeqHelper::Parallel< CuttingStrategy::Block, StrategyParameter::Threads >	par
	)

◆ fsquare() [6/6]

template INST_OR_DECL FFLAS_ELT * fsquare	(	const FFLAS_FIELD< FFLAS_ELT > &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	n,
		const FFLAS_ELT	alpha,
		const FFLAS_ELT *	A,
		const size_t	lda,
		const FFLAS_ELT	beta,
		FFLAS_ELT *	C,
		const size_t	ldc
	)

fsquare: Squares a matrix.

compute $C \gets \alpha \mathrm{op}(A) \mathrm{op}(A) + \beta C$ over a FFLAS_FIELD <FFLAS_ELT> F Avoid the conversion of B

Parameters

ta	if `ta==FflasTrans`, $\mathrm{op}(A)=A^T$ .
F	field
n	size of `A`
alpha	scalar
beta	scalar
A	dense matrix of size `nxn`
lda	leading dimension of `A`
C	dense matrix of size `nxn`
ldc	leading dimension of `C`

◆ BlockCuts() [1/2]

void BlockCuts	(	size_t &	RBLOCKSIZE,
		size_t &	CBLOCKSIZE,
		const size_t	m,
		const size_t	n,
		const size_t	numthreads
	)

inline

◆ BlockCuts< CuttingStrategy::Single, StrategyParameter::Threads >()

void BlockCuts< CuttingStrategy::Single, StrategyParameter::Threads >	(	size_t &	RBLOCKSIZE,
		size_t &	CBLOCKSIZE,
		const size_t	m,
		const size_t	n,
		const size_t	numthreads
	)

inline

◆ BlockCuts< CuttingStrategy::Row, StrategyParameter::Fixed >()

void BlockCuts< CuttingStrategy::Row, StrategyParameter::Fixed >	(	size_t &	RBLOCKSIZE,
		size_t &	CBLOCKSIZE,
		const size_t	m,
		const size_t	n,
		const size_t	numthreads
	)

inline

◆ BlockCuts< CuttingStrategy::Row, StrategyParameter::Grain >()

void BlockCuts< CuttingStrategy::Row, StrategyParameter::Grain >	(	size_t &	RBLOCKSIZE,
		size_t &	CBLOCKSIZE,
		const size_t	m,
		const size_t	n,
		const size_t	grainsize
	)

inline

◆ BlockCuts< CuttingStrategy::Block, StrategyParameter::Grain >()

void BlockCuts< CuttingStrategy::Block, StrategyParameter::Grain >	(	size_t &	RBLOCKSIZE,
		size_t &	CBLOCKSIZE,
		const size_t	m,
		const size_t	n,
		const size_t	grainsize
	)

inline

◆ BlockCuts< CuttingStrategy::Column, StrategyParameter::Fixed >()

void BlockCuts< CuttingStrategy::Column, StrategyParameter::Fixed >	(	size_t &	RBLOCKSIZE,
		size_t &	CBLOCKSIZE,
		const size_t	m,
		const size_t	n,
		const size_t	numthreads
	)

inline

◆ BlockCuts< CuttingStrategy::Column, StrategyParameter::Grain >()

void BlockCuts< CuttingStrategy::Column, StrategyParameter::Grain >	(	size_t &	RBLOCKSIZE,
		size_t &	CBLOCKSIZE,
		const size_t	m,
		const size_t	n,
		const size_t	grainsize
	)

inline

◆ BlockCuts< CuttingStrategy::Block, StrategyParameter::Fixed >()

void BlockCuts< CuttingStrategy::Block, StrategyParameter::Fixed >	(	size_t &	RBLOCKSIZE,
		size_t &	CBLOCKSIZE,
		const size_t	m,
		const size_t	n,
		const size_t	numthreads
	)

inline

◆ BlockCuts< CuttingStrategy::Row, StrategyParameter::Threads >()

void BlockCuts< CuttingStrategy::Row, StrategyParameter::Threads >	(	size_t &	RBLOCKSIZE,
		size_t &	CBLOCKSIZE,
		const size_t	m,
		const size_t	n,
		const size_t	numthreads
	)

inline

◆ BlockCuts< CuttingStrategy::Column, StrategyParameter::Threads >()

void BlockCuts< CuttingStrategy::Column, StrategyParameter::Threads >	(	size_t &	RBLOCKSIZE,
		size_t &	CBLOCKSIZE,
		const size_t	m,
		const size_t	n,
		const size_t	numthreads
	)

inline

◆ BlockCuts< CuttingStrategy::Block, StrategyParameter::Threads >()

void BlockCuts< CuttingStrategy::Block, StrategyParameter::Threads >	(	size_t &	RBLOCKSIZE,
		size_t &	CBLOCKSIZE,
		const size_t	m,
		const size_t	n,
		const size_t	numthreads
	)

inline

◆ BlockCuts() [2/2]

void BlockCuts	(	size_t &	rowBlockSize,
		size_t &	colBlockSize,
		size_t &	lastRBS,
		size_t &	lastCBS,
		size_t &	changeRBS,
		size_t &	changeCBS,
		size_t &	numRowBlock,
		size_t &	numColBlock,
		size_t	m,
		size_t	n,
		const size_t	numthreads
	)

inline

◆ pfzero()

void pfzero	(	const Field &	F,
		size_t	m,
		size_t	n,
		typename Field::Element_ptr	C,
		size_t	BS = `0`
	)

◆ pfrand()

void pfrand	(	const Field &	F,
		RandIter &	G,
		size_t	m,
		size_t	n,
		typename Field::Element_ptr	C,
		size_t	BS = `0`
	)

◆ fdot() [11/11]

Field::Element & fdot	(	const Field &	F,
		const size_t	N,
		typename Field::ConstElement_ptr	x,
		const size_t	incx,
		typename Field::ConstElement_ptr	y,
		const size_t	incy,
		typename Field::Element &	d,
		const ParSeqHelper::Parallel< Cut, Param >	par
	)

inline

◆ pfgemm() [2/7]

Field::Element * pfgemm	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		const typename Field::ConstElement_ptr	A,
		const size_t	lda,
		const typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		const typename Field::Element	beta,
		typename Field::Element *	C,
		const size_t	ldc,
		MMHelper< Field, AlgoT, FieldTrait, ParSeqHelper::Parallel< CuttingStrategy::Block, StrategyParameter::Threads > > &	H
	)

◆ pfgemm() [3/7]

Field::Element * pfgemm	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		const typename Field::ConstElement_ptr	AA,
		const size_t	lda,
		const typename Field::ConstElement_ptr	BB,
		const size_t	ldb,
		const typename Field::Element	beta,
		typename Field::Element *	C,
		const size_t	ldc,
		MMHelper< Field, AlgoT, FieldTrait, ParSeqHelper::Parallel< CuttingStrategy::Recursive, StrategyParameter::ThreeDAdaptive > > &	H
	)

◆ pfgemm() [4/7]

Field::Element * pfgemm	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		const typename Field::ConstElement_ptr	AA,
		const size_t	lda,
		const typename Field::ConstElement_ptr	BB,
		const size_t	ldb,
		const typename Field::Element	beta,
		typename Field::Element *	C,
		const size_t	ldc,
		MMHelper< Field, AlgoT, FieldTrait, ParSeqHelper::Parallel< CuttingStrategy::Recursive, StrategyParameter::TwoDAdaptive > > &	H
	)

◆ pfgemm() [5/7]

Field::Element * pfgemm	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		const typename Field::ConstElement_ptr	AA,
		const size_t	lda,
		const typename Field::ConstElement_ptr	BB,
		const size_t	ldb,
		const typename Field::Element	beta,
		typename Field::Element *	C,
		const size_t	ldc,
		MMHelper< Field, AlgoT, FieldTrait, ParSeqHelper::Parallel< CuttingStrategy::Recursive, StrategyParameter::TwoD > > &	H
	)

◆ pfgemm() [6/7]

Field::Element_ptr pfgemm	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		const typename Field::ConstElement_ptr	A,
		const size_t	lda,
		const typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		MMHelper< Field, AlgoT, FieldTrait, ParSeqHelper::Parallel< CuttingStrategy::Recursive, StrategyParameter::ThreeD > > &	H
	)

◆ pfgemm() [7/7]

Field::Element * pfgemm	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const FFLAS_TRANSPOSE	tb,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const typename Field::Element	alpha,
		const typename Field::ConstElement_ptr	A,
		const size_t	lda,
		const typename Field::ConstElement_ptr	B,
		const size_t	ldb,
		const typename Field::Element	beta,
		typename Field::Element_ptr	C,
		const size_t	ldc,
		MMHelper< Field, AlgoT, FieldTrait, ParSeqHelper::Parallel< CuttingStrategy::Recursive, StrategyParameter::ThreeDInPlace > > &	H
	)

◆ fgemv() [18/19]

Field::Element_ptr fgemv	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	m,
		const size_t	n,
		const typename Field::Element	alpha,
		const typename Field::ConstElement_ptr	A,
		const size_t	lda,
		const typename Field::ConstElement_ptr	X,
		const size_t	incX,
		const typename Field::Element	beta,
		typename Field::Element_ptr	Y,
		const size_t	incY,
		MMHelper< Field, AlgoT, FieldTrait, ParSeqHelper::Parallel< CuttingStrategy::Recursive, StrategyParameter::Threads > > &	H
	)

◆ fgemv() [19/19]

Field::Element_ptr fgemv	(	const Field &	F,
		const FFLAS_TRANSPOSE	ta,
		const size_t	m,
		const size_t	n,
		const typename Field::Element	alpha,
		const typename Field::ConstElement_ptr	A,
		const size_t	lda,
		const typename Field::ConstElement_ptr	X,
		const size_t	incX,
		const typename Field::Element	beta,
		typename Field::Element_ptr	Y,
		const size_t	incY,
		MMHelper< Field, AlgoT, FieldTrait, ParSeqHelper::Parallel< CuttingStrategy::Row, Cut > > &	H
	)

◆ parseArguments()

void parseArguments	(	int	argc,
		char **	argv,
		Argument *	args,
		bool	printDefaults = `true`
	)

◆ getArgumentValue()

char * getArgumentValue	(	int	argc,
		char **	argv,
		int	i
	)

Get the value of an argument and avoid core dump when no value was given after an argument.

Parameters

argv	argument value list
i	argument index

Returns: char* argument value

◆ writeCommandString()

std::ostream & writeCommandString	(	std::ostream &	os,
		Argument *	args,
		const char *	programName = `nullptr`
	)

writes the values of all arguments, preceded by the programName

◆ WriteMatrix() [1/2]

std::ostream & WriteMatrix	(	std::ostream &	c,
		const Field &	F,
		size_t	m,
		size_t	n,
		typename Field::ConstElement_ptr	A,
		size_t	lda,
		FFLAS_FORMAT	format,
		bool	column_major
	)

inline

WriteMatrix: write a matrix to an output stream.

Parameters

c	output stream
F	base field
m	row dimension
n	column dimension
A	matrix
format	input format (FflasAuto, FflasDense, FflasSMS, FflasBinary)
column_major	whether the matrix is stored in column or row major (row by default)

◆ preamble()

void preamble	(	std::ifstream &	ifs,
		FFLAS_FORMAT &	format
	)

inline

◆ ReadMatrix() [1/2]

Field::Element_ptr ReadMatrix	(	std::ifstream &	ifs,
		Field &	F,
		size_t &	m,
		size_t &	n,
		typename Field::Element_ptr &	A,
		FFLAS_FORMAT	format = `FflasAuto`
	)

ReadMatrix: read a matrix from an input stream.

Parameters

	ifs	input stream
	F	base field
[out]	m	row dimension
[out]	n	column dimension
[out]	A	output matrix
	format	input format (FflasAuto, FflasDense, FflasSMS, FflasBinary)

◆ ReadMatrix() [2/2]

Field::Element_ptr ReadMatrix	(	const std::string &	matrix_file,
		Field &	F,
		size_t &	m,
		size_t &	n,
		typename Field::Element_ptr &	A,
		FFLAS_FORMAT	format = `FflasAuto`
	)

inline

ReadMatrix: read a matrix from a file.

Parameters

	matrix_file	filename
	F	base field
[out]	m	row dimension
[out]	n	column dimension
[out]	A	output matrix
	format	input format (FflasAuto, FflasDense, FflasSMS, FflasBinary)

◆ WriteMatrix() [2/2]

void WriteMatrix	(	std::string &	matrix_file,
		const Field &	F,
		int	m,
		int	n,
		typename Field::ConstElement_ptr	A,
		size_t	lda,
		FFLAS_FORMAT	format = `FflasDense`,
		bool	column_major = `false`
	)

WriteMatrix: write a matrix to a file.

Parameters

matrix_file	file name
F	base field
m	row dimension
n	column dimension
A	matrix
format	input format (FflasAuto, FflasDense, FflasSMS, FflasBinary)
column_major	whether the matrix is stored in column or row major (row by default)

◆ WritePermutation()

std::ostream & WritePermutation	(	std::ostream &	c,
		const size_t *	P,
		size_t	N
	)

inline

WritePermutation: write a permutation matrix to an output stream.

Parameters

c	output stream
P	permutation
N	size of the permutation

◆ alignable()

bool alignable ( )

inline

◆ alignable< Givaro::Integer * >()

bool alignable< Givaro::Integer * > ( )

inline

◆ fflas_new() [5/7]

Field::Element_ptr fflas_new	(	const Field &	F,
		const size_t	m,
		const Alignment	align = `Alignment::DEFAULT`
	)

inline

◆ fflas_new() [6/7]

Field::Element_ptr fflas_new	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		const Alignment	align = `Alignment::DEFAULT`
	)

inline

◆ fflas_new() [7/7]

Element * fflas_new	(	const size_t	m,
		const Alignment	align = `Alignment::DEFAULT`
	)

inline

◆ fflas_delete() [3/4]

void fflas_delete ( Element_ptr A )

inline

◆ fflas_delete() [4/4]

void fflas_delete	(	Ptr	p,
		Args ...	args
	)

inline

◆ prefetch()

void prefetch ( const int64_t * )

inline

◆ getTLBSize()

void getTLBSize ( int & tlb )

inline

◆ queryCacheSizes()

void queryCacheSizes	(	int &	l1,
		int &	l2,
		int &	l3
	)

inline

Queries and returns the cache sizes in Bytes of the L1, L2, and L3 data caches respectively

◆ queryL1CacheSize()

int queryL1CacheSize ( )

inline

Returns: the size in Bytes of the L1 data cache

◆ queryTopLevelCacheSize()

int queryTopLevelCacheSize ( )

inline

Returns: the size in Bytes of the L2 or L3 cache if this later is present

◆ getSeed()

uint64_t getSeed ( )

◆ pack_word() [1/2]

void pack_word	(	pack_T *	packed,
		const wide_T *	words,
		int32_t	stride,
		Packer< pack_T, Nb > &	packer
	)

◆ pack_word() [2/2]

void pack_word	(	double *	packed,
		const wide_T *	words,
		int32_t	stride,
		Packer< double, 2 > &	packer
	)

◆ pack_word_part() [1/2]

void pack_word_part	(	pack_T *	packed,
		int32_t	nb,
		const wide_T *	words,
		int32_t	stride,
		Packer< pack_T, Nb > &	packer
	)

◆ pack_word_part() [2/2]

void pack_word_part	(	double *	packed,
		int32_t	nb,
		const wide_T *	words,
		int32_t	stride,
		Packer< double, 2 > &	packer
	)

◆ unpack_word() [1/2]

void unpack_word	(	wide_T *	words,
		int32_t	stride,
		const pack_T *	packed,
		Packer< pack_T, Nb > &	packer
	)

◆ unpack_word() [2/2]

void unpack_word	(	wide_T *	words,
		int32_t	stride,
		const double *	packed,
		Packer< double, 2 > &	packer
	)

◆ unpack_word_part() [1/2]

void unpack_word_part	(	wide_T *	words,
		int32_t	stride,
		const pack_T *	packed,
		int32_t	nb,
		Packer< pack_T, Nb > &	packer
	)

◆ unpack_word_part() [2/2]

void unpack_word_part	(	wide_T *	words,
		int32_t	stride,
		const double *	packed,
		int32_t	nb,
		Packer< double, 2 > &	packer
	)

◆ pack_matrix()

void pack_matrix	(	pack_T *	packed,
		int32_t	row_p,
		int32_t	col_p,
		int32_t	ldm_p,
		const wide_T *	elemts,
		int32_t	row_e,
		int32_t	col_e,
		int32_t	ldm_e,
		Packer< pack_T, Nb > &	packer
	)

◆ unpack_matrix()

void unpack_matrix	(	wide_T *	elemts,
		int32_t	row_e,
		int32_t	col_e,
		int32_t	ldm_e,
		const pack_T *	packed,
		int32_t	row_p,
		int32_t	col_p,
		int32_t	ldm_p,
		Packer< pack_T, Nb > &	packer
	)

◆ fgemm_compressed()

void fgemm_compressed	(	const Field &	F,
		int	m,
		int	n,
		int	k,
		const typename Field::Element *	A,
		int	lda,
		const typename Field::Element *	B,
		int	ldb,
		typename Field::Element *	C,
		int	ldc
	)

Bug:: don't zero all, just the "border"

Bug:: don't zero all, just the "border"

Bug:: don't zero all, just the "border"

◆ finit_fuzzy()

void finit_fuzzy	(	Field &	F,
		size_t	m,
		size_t	n,
		double *	C,
		size_t	ldc
	)

◆ add()

void add	(	const size_t	m,
		const size_t	n,
		double	a,
		const double *	A,
		const size_t	lda,
		const double *	B,
		const size_t	ldb,
		double *	C,
		const size_t	ldc
	)

◆ subadd()

void subadd	(	const size_t	m,
		const size_t	n,
		const double *	A,
		const size_t	lda,
		const double *	B,
		const size_t	ldb,
		double *	C,
		const size_t	ldc
	)

◆ negadd()

void negadd	(	const size_t	m,
		const size_t	n,
		const double *	A,
		const size_t	lda,
		const double *	B,
		const size_t	ldb,
		double *	C,
		const size_t	ldc
	)

◆ addsub()

void addsub	(	const size_t	m,
		const size_t	n,
		const double *	A,
		const size_t	lda,
		const double *	B,
		const size_t	ldb,
		double *	C,
		const size_t	ldc
	)

◆ addscalinf()

void addscalinf	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		const double *	B,
		const size_t	ldb,
		double	e,
		double *	C,
		const size_t	ldc
	)

◆ subscalinf()

void subscalinf	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		const double *	B,
		const size_t	ldb,
		double	e,
		double *	C,
		const size_t	ldc
	)

◆ subscal()

void subscal	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		const double *	D,
		const size_t	ldd,
		const double *	B,
		const size_t	ldb,
		double	e,
		double *	C,
		const size_t	ldc
	)

◆ addscal()

void addscal	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		const double *	D,
		const size_t	ldd,
		const double *	B,
		const size_t	ldb,
		double	e,
		double *	C,
		const size_t	ldc
	)

◆ subscalacc()

void subscalacc	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		const double *	D,
		const size_t	ldd,
		const double *	B,
		const size_t	ldb,
		double	e,
		double *	C,
		const size_t	ldc
	)

◆ gemm_fflas()

double * gemm_fflas	(	const Field &	F,
		const size_t	m,
		const size_t	n,
		const size_t	k,
		const double *	A,
		size_t	lda,
		const double *	B,
		size_t	ldb,
		double *	C,
		size_t	ldc,
		int	rec = `0`
	)

Namespaces

Data Structures

Typedefs

Enumerations

Functions

Typedef Documentation

◆ Checker_fgemm

◆ Checker_ftrsm

◆ ForceCheck_fgemm

◆ ForceCheck_ftrsm

◆ ZOSparseMatrix

◆ NotZOSparseMatrix

◆ SimdSparseMatrix

◆ NoSimdSparseMatrix

◆ MKLSparseMatrixFormat

◆ NotMKLSparseMatrixFormat

◆ has_plus

◆ has_minus

◆ has_equal

◆ has_plus_eq

◆ has_minus_eq

◆ has_mul

◆ has_mul_eq

◆ Timer

◆ BaseTimer

◆ UserTimer

◆ SysTimer

Enumeration Type Documentation

◆ FFLAS_ORDER

◆ FFLAS_TRANSPOSE

◆ FFLAS_UPLO

◆ FFLAS_DIAG

◆ FFLAS_SIDE

◆ FFLAS_BASE

◆ number_kind

◆ SparseMatrix_t

◆ FFLAS_FORMAT

Function Documentation

◆ InfNorm()

◆ min3()

◆ max3()

◆ min4()

◆ max4()

◆ fadd() [1/8]

◆ faddin() [1/5]

◆ fsub() [1/4]

◆ fsubin() [1/3]

◆ fadd() [2/8]

◆ pfadd()

◆ pfsub()

◆ pfaddin()

◆ pfsubin()

◆ fadd() [3/8]

◆ fsub() [2/4]

◆ faddin() [2/5]

◆ faddin() [3/5]

◆ fsubin() [2/3]

◆ fadd() [4/8]

◆ fassign() [1/10]

◆ fassign() [2/10]

◆ fassign() [3/10]

◆ fassign() [4/10]

◆ fassign() [5/10]

◆ fassign() [6/10]

◆ fassign() [7/10]

◆ fassign() [8/10]

◆ faxpy() [1/6]

◆ faxpy() [2/6]

◆ faxpy() [3/6]

◆ faxpy() [4/6]

◆ fdot() [1/11]

◆ fdot() [2/11]

◆ fdot() [3/11]

◆ fdot() [4/11]

◆ fdot() [5/11]

◆ fdot() [6/11]

◆ fdot() [7/11]

◆ fdot() [8/11]

◆ fgemm() [1/23]

◆ fgemm() [2/23]