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1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 | /* -*- mode: C++; tab-width: 8; indent-tabs-mode: t; c-basic-offset: 8 -*- */
// vim:sts=8:sw=8:ts=8:noet:sr:cino=>s,f0,{0,g0,(0,\:0,t0,+0,=s
/* fflas.h
* Copyright (C) 2005 Clement Pernet
*
* Written by Clement Pernet <Clement.Pernet@imag.fr>
*
*
* ========LICENCE========
* This file is part of the library FFLAS-FFPACK.
*
* FFLAS-FFPACK is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
* ========LICENCE========
*.
*/
/** @file fflas.h
* @author Clément Pernet.
* @brief <b>F</b>inite <b>F</b>ield <b>L</b>inear <b>A</b>lgebra <b>S</b>ubroutines
*/
#ifndef __FFLASFFPACK_fflas_H
#define __FFLASFFPACK_fflas_H
#include <cmath>
#include <cstring>
#ifndef MAX
#define MAX(a,b) ((a < b)?b:a)
#endif
#ifndef MIN
#define MIN(a,b) ((a > b)?b:a)
#endif
#include "fflas-ffpack/config-blas.h"
#include "fflas-ffpack/field/unparametric.h"
#include "fflas-ffpack/field/modular-balanced.h"
#include "fflas-ffpack/field/modular-positive.h"
#define WINOTHRESHOLD __FFLASFFPACK_WINOTHRESHOLD
/* Thresholds determining which floating point representation to use, depending
* on the cardinality of the finite field. This is only used when the element
* representation is not a floating point type.
*/
#define FLOAT_DOUBLE_THRESHOLD_0 430
#define FLOAT_DOUBLE_THRESHOLD_1 350
#define FLOAT_DOUBLE_THRESHOLD_2 175
#include <float.h>
//#define LB_TRTR
/// @brief FFLAS: <b>F</b>inite <b>F</b>ield <b>L</b>inear <b>A</b>lgebra <b>S</b>ubroutines.
namespace FFLAS {
// public:
/// Is matrix transposed ?
enum FFLAS_TRANSPOSE
{
FflasNoTrans=111, /**< Matrix is not transposed */
FflasTrans =112 /**< Matrix is transposed */
};
/// Is triangular matrix's shape upper ?
enum FFLAS_UPLO
{
FflasUpper=121, /**< Triangular matrix is Upper triangular (if \f$i>j\f$ then \f$T_{i,j} = 0\f$)*/
FflasLower=122 /**< Triangular matrix is Lower triangular (if \f$i<j\f$ then \f$T_{i,j} = 0\f$)*/
};
/// Is Matrix diagonal implicit ?
enum FFLAS_DIAG
{
FflasNonUnit=131 , /**< Triangular matrix has an explicit general diagonal */
FflasUnit =132 /**< Triangular matrix has an implicit unit diagonal (\f$T_{i,i} = 1\f$)*//**< */
};
/// On what side ?
enum FFLAS_SIDE
{
FflasLeft = 141, /**< Operator applied on the left */
FflasRight = 142 /**< Operator applied on the rigth*/
};
/** \p FFLAS_BASE determines the type of the element representation for Matrix Mult kernel. */
enum FFLAS_BASE
{
FflasDouble = 151, /**< to use the double precision BLAS */
FflasFloat = 152, /**< to use the single precison BLAS */
FflasGeneric = 153 /**< for any other domain, that can not be converted to floating point integers */
};
/* Representations of Z with floating point elements*/
typedef FFPACK::UnparametricField<float> FloatDomain;
typedef FFPACK::UnparametricField<double> DoubleDomain;
namespace Protected {
// Prevents the instantiation of the class
// FFLAS(){}
template <class X,class Y>
class AreEqual {
public:
static const bool value = false;
};
template <class X>
class AreEqual<X,X> {
public:
static const bool value = true;
};
//-----------------------------------------------------------------------------
// Some conversion functions
//-----------------------------------------------------------------------------
//---------------------------------------------------------------------
// Finite Field matrix => double matrix
//---------------------------------------------------------------------
template<class Field>
void MatF2MatD (const Field& F,
DoubleDomain::Element* S, const size_t lds,
const typename Field::Element* E,
const size_t lde,const size_t m, const size_t n)
{
const typename Field::Element* Ei = E;
DoubleDomain::Element *Si=S;
size_t j;
for (; Ei < E+lde*m; Ei+=lde, Si += lds)
for ( j=0; j<n; ++j){
F.convert(*(Si+j),*(Ei+j));
}
}
//---------------------------------------------------------------------
// Finite Field matrix => float matrix
//---------------------------------------------------------------------
template<class Field>
void MatF2MatFl (const Field& F,
FloatDomain::Element* S, const size_t lds,
const typename Field::Element* E,
const size_t lde,const size_t m, const size_t n)
{
const typename Field::Element* Ei = E;
FloatDomain::Element *Si=S;
size_t j;
for (; Ei < E+lde*m; Ei+=lde, Si += lds)
for ( j=0; j<n; ++j){
F.convert(*(Si+j),*(Ei+j));
}
}
//---------------------------------------------------------------------
// Finite Field matrix => double matrix
// Special design for upper-triangular matrices
//---------------------------------------------------------------------
template<class Field>
void MatF2MatD_Triangular (const Field& F,
typename DoubleDomain::Element* S, const size_t lds,
const typename Field::Element* const E,
const size_t lde,
const size_t m, const size_t n){
const typename Field::Element* Ei = E;
typename DoubleDomain::Element* Si = S;
size_t i=0, j;
for ( ; i<m;++i, Ei+=lde, Si+=lds)
for ( j=i; j<n;++j)
F.convert(*(Si+j),*(Ei+j));
}
//---------------------------------------------------------------------
// Finite Field matrix => float matrix
// Special design for upper-triangular matrices
//---------------------------------------------------------------------
template<class Field>
void MatF2MatFl_Triangular (const Field& F,
typename FloatDomain::Element* S, const size_t lds,
const typename Field::Element* const E,
const size_t lde,
const size_t m, const size_t n){
const typename Field::Element* Ei = E;
typename FloatDomain::Element* Si = S;
size_t i=0, j;
for ( ; i<m;++i, Ei+=lde, Si+=lds)
for ( j=i; j<n;++j)
F.convert(*(Si+j),*(Ei+j));
}
//---------------------------------------------------------------------
// double matrix => Finite Field matrix
//---------------------------------------------------------------------
template<class Field>
void MatD2MatF (const Field& F,
typename Field::Element* S, const size_t lds,
const typename DoubleDomain::Element* E, const size_t lde,
const size_t m, const size_t n)
{
typename Field::Element* Si = S;
const DoubleDomain::Element* Ei =E;
size_t j;
for ( ; Si < S+m*lds; Si += lds, Ei+= lde){
for ( j=0; j<n;++j)
F.init( *(Si+j), *(Ei+j) );
}
}
//---------------------------------------------------------------------
// float matrix => Finite Field matrix
//---------------------------------------------------------------------
template<class Field>
void MatFl2MatF (const Field& F,
typename Field::Element* S, const size_t lds,
const typename FloatDomain::Element* E, const size_t lde,
const size_t m, const size_t n){
typename Field::Element* Si = S;
const FloatDomain::Element* Ei =E;
size_t j;
for ( ; Si < S+m*lds; Si += lds, Ei+= lde){
for ( j=0; j<n;++j)
F.init( *(Si+j), *(Ei+j) );
}
}
/**
* Computes the threshold parameters for the cascade
* Matmul algorithm.
*
*
* \param F Finite Field/Ring of the computation.
* \param k Common dimension of A and B, in the product A x B
* \param beta Computing \f$AB + \beta C\f$
* \param delayedDim Returns the size of blocks that can be multiplied
* over Z with no overflow
* \param base Returns the type of BLAS representation to use
* \param winoRecLevel Returns the number of recursion levels of
* Strassen-Winograd's algorithm to perform
* \param winoLevelProvided tells whether the user forced the number of
* recursive level of Winograd's algorithm
*
* @bib
* - Dumas, Giorgi, Pernet, arXiv cs/0601133 <a href=http://arxiv.org/abs/cs.SC/0601133>here</a>
*/
template <class Field>
void MatMulParameters (const Field& F,
const size_t k,
const typename Field::Element& beta,
size_t& delayedDim,
FFLAS_BASE& base,
size_t& winoRecLevel,
bool winoLevelProvided=false);
/**
* Computes the maximal size for delaying the modular reduction
* in a dotproduct.
*
* This is the default version assuming a conversion to a positive modular representation
*
* \param F Finite Field/Ring of the computation
* \param winoRecLevel Number of recusrive Strassen-Winograd levels (if any, 0 otherwise)
* \param beta Computing AB + beta C
* \param base Type of floating point representation for delayed modular computations
*
*/
template <class Field>
size_t DotProdBound (const Field& F,
const size_t winoRecLevel,
const typename Field::Element& beta,
const FFLAS_BASE base);
/**
* Internal function for the bound computation.
* Generic implementation for positive representations
*/
template <class Field>
double computeFactorWino (const Field& F, const size_t w);
template <class Field>
double computeFactorClassic (const Field& F);
/**
* Determines the type of floating point representation to convert to,
* for BLAS computations.
* \param F Finite Field/Ring of the computation
* \param w Number of recursive levels in Winograd's algorithm
*/
template <class Field>
FFLAS_BASE BaseCompute (const Field& F, const size_t w);
/**
* Computes the maximal size for delaying the modular reduction
* in a triangular system resolution.
*
* Compute the maximal dimension k, such that a unit diagonal triangular
* system of dimension k can be solved over Z without overflow of the
* underlying floating point representation.
*
* @bib
* - Dumas, Giorgi, Pernet 06, arXiv:cs/0601133.
*
* \param F Finite Field/Ring of the computation
*
*/
template <class Field>
size_t TRSMBound (const Field& F);
template <class Field>
void DynamicPealing( 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* A, const size_t lda,
const typename Field::Element* B, const size_t ldb,
const typename Field::Element beta,
typename Field::Element* C, const size_t ldc,
const size_t ); //kmax
template <class Field>
void MatVectProd (const Field& F,
const FFLAS_TRANSPOSE TransA,
const size_t M, const size_t N,
const typename Field::Element alpha,
const typename Field::Element * A, const size_t lda,
const typename Field::Element * X, const size_t incX,
const typename Field::Element beta,
typename Field::Element * Y, const size_t incY);
template <class Field>
void ClassicMatmul(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 * A, const size_t lda,
const typename Field::Element * B, const size_t ldb,
const typename Field::Element beta,
typename Field::Element * C, const size_t ldc,
const size_t kmax, const FFLAS_BASE base );
// Winograd Multiplication alpha.A(n*k) * B(k*m) + beta . C(n*m)
// WinoCalc performs the 22 Winograd operations
template <class Field>
void WinoCalc (const Field& F,
const FFLAS_TRANSPOSE ta,
const FFLAS_TRANSPOSE tb,
const size_t mr, const size_t nr,const size_t kr,
const typename Field::Element alpha,
const typename Field::Element* A,const size_t lda,
const typename Field::Element* B,const size_t ldb,
const typename Field::Element beta,
typename Field::Element * C, const size_t ldc,
const size_t kmax, const size_t w, const FFLAS_BASE base);
template<class Field>
void WinoMain (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* A,const size_t lda,
const typename Field::Element* B,const size_t ldb,
const typename Field::Element beta,
typename Field::Element * C, const size_t ldc,
const size_t kmax, const size_t w, const FFLAS_BASE base);
// Specialized routines for ftrsm
template <class Element>
class ftrsmLeftUpperNoTransNonUnit;
template <class Element>
class ftrsmLeftUpperNoTransUnit;
template <class Element>
class ftrsmLeftUpperTransNonUnit;
template <class Element>
class ftrsmLeftUpperTransUnit;
template <class Element>
class ftrsmLeftLowerNoTransNonUnit;
template <class Element>
class ftrsmLeftLowerNoTransUnit;
template <class Element>
class ftrsmLeftLowerTransNonUnit;
template <class Element>
class ftrsmLeftLowerTransUnit;
template <class Element>
class ftrsmRightUpperNoTransNonUnit;
template <class Element>
class ftrsmRightUpperNoTransUnit;
template <class Element>
class ftrsmRightUpperTransNonUnit;
template <class Element>
class ftrsmRightUpperTransUnit;
template <class Element>
class ftrsmRightLowerNoTransNonUnit;
template <class Element>
class ftrsmRightLowerNoTransUnit;
template <class Element>
class ftrsmRightLowerTransNonUnit;
template <class Element>
class ftrsmRightLowerTransUnit;
// Specialized routines for ftrmm
template <class Element>
class ftrmmLeftUpperNoTransNonUnit;
template <class Element>
class ftrmmLeftUpperNoTransUnit;
template <class Element>
class ftrmmLeftUpperTransNonUnit;
template <class Element>
class ftrmmLeftUpperTransUnit;
template <class Element>
class ftrmmLeftLowerNoTransNonUnit;
template <class Element>
class ftrmmLeftLowerNoTransUnit;
template <class Element>
class ftrmmLeftLowerTransNonUnit;
template <class Element>
class ftrmmLeftLowerTransUnit;
template <class Element>
class ftrmmRightUpperNoTransNonUnit;
template <class Element>
class ftrmmRightUpperNoTransUnit;
template <class Element>
class ftrmmRightUpperTransNonUnit;
template <class Element>
class ftrmmRightUpperTransUnit;
template <class Element>
class ftrmmRightLowerNoTransNonUnit;
template <class Element>
class ftrmmRightLowerNoTransUnit;
template <class Element>
class ftrmmRightLowerTransNonUnit;
template <class Element>
class ftrmmRightLowerTransUnit;
// BB : ça peut servir...
#ifdef LB_TRTR
template <class Element>
class ftrtrLeftUpperNoTransNonUnitNonUnit;
template <class Element>
class ftrtrLeftUpperNoTransUnitNonUnit;
template <class Element>
class ftrtrLeftUpperTransNonUnitNonUnit;
template <class Element>
class ftrtrLeftUpperTransUnitNonUnit;
template <class Element>
class ftrtrLeftLowerNoTransNonUnitNonUnit;
template <class Element>
class ftrtrLeftLowerNoTransUnitNonUnit;
template <class Element>
class ftrtrLeftLowerTransNonUnitNonUnit;
template <class Element>
class ftrtrLeftLowerTransUnitNonUnit;
template <class Element>
class ftrtrLeftUpperNoTransNonUnitUnit;
template <class Element>
class ftrtrLeftUpperNoTransUnitUnit;
template <class Element>
class ftrtrLeftUpperTransNonUnitUnit;
template <class Element>
class ftrtrLeftUpperTransUnitUnit;
template <class Element>
class ftrtrLeftLowerNoTransNonUnitUnit;
template <class Element>
class ftrtrLeftLowerNoTransUnitUnit;
template <class Element>
class ftrtrLeftLowerTransNonUnitUnit;
template <class Element>
class ftrtrLeftLowerTransUnitUnit;
template <class Element>
class ftrtrRightUpperNoTransNonUnitNonUnit;
template <class Element>
class ftrtrRightUpperNoTransUnitNonUnit;
template <class Element>
class ftrtrRightUpperTransNonUnitNonUnit;
template <class Element>
class ftrtrRightUpperTransUnitNonUnit;
template <class Element>
class ftrtrRightLowerNoTransNonUnitNonUnit;
template <class Element>
class ftrtrRightLowerNoTransUnitNonUnit;
template <class Element>
class ftrtrRightLowerTransNonUnitNonUnit;
template <class Element>
class ftrtrRightLowerTransUnitNonUnit;
template <class Element>
class ftrtrRightUpperNoTransNonUnitUnit;
template <class Element>
class ftrtrRightUpperNoTransUnitUnit;
template <class Element>
class ftrtrRightUpperTransNonUnitUnit;
template <class Element>
class ftrtrRightUpperTransUnitUnit;
template <class Element>
class ftrtrRightLowerNoTransNonUnitUnit;
template <class Element>
class ftrtrRightLowerNoTransUnitUnit;
template <class Element>
class ftrtrRightLowerTransNonUnitUnit;
template <class Element>
class ftrtrRightLowerTransUnitUnit;
#endif
template<class Element>
class faddmTrans;
template<class Element>
class faddmNoTrans;
template<class Element>
class fsubmTrans;
template<class Element>
class fsubmNoTrans;
template<class Element>
class faddmTransTrans;
template<class Element>
class faddmNoTransTrans;
template<class Element>
class faddmTransNoTrans;
template<class Element>
class faddmNoTransNoTrans;
template<class Element>
class fsubmTransTrans;
template<class Element>
class fsubmNoTransTrans;
template<class Element>
class fsubmTransNoTrans;
template<class Element>
class fsubmNoTransNoTrans;
} // protected
//---------------------------------------------------------------------
// Level 1 routines
//---------------------------------------------------------------------
/** \brief fzero : \f$A \gets 0 \f$.
* @param F field
* @param n number of elements to zero
* \param X vector in \p F
* \param incX stride of \p X
*/
template<class Field>
void
fzero (const Field& F, const size_t n,
typename Field::Element *X, const size_t incX)
{
if (incX == 1) { // contigous data
// memset(X,(int)F.zero,n); // might be bogus ?
for (size_t i = 0 ; i < n ; ++i)
F.assign(*(X+i), F.zero);
}
else { // not contiguous (strided)
for (size_t i = 0 ; i < n ; ++i)
F.assign(*(X+i*incX), F.zero);
}
}
/** fscal
* \f$x \gets a \cdot x\f$.
* @param F field
* @param n size of the vectors
* @param alpha homotéti scalar
* \param X vector in \p F
* \param incX stride of \p X
* @bug use cblas_(d)scal when possible
* @internal
* @todo check if comparison with +/-1,0 is necessary.
*/
template<class Field>
void
fscal (const Field& F, const size_t n, const typename Field::Element alpha,
typename Field::Element * X, const size_t incX)
{
typedef typename Field::Element Element ;
if (F.isOne(alpha))
return ;
Element * Xi = X;
if (F.areEqual(alpha,F.mOne)){
for (; Xi < X+n*incX; Xi+=incX )
F.negin( *Xi );
return;
}
if (F.isZero(alpha)){
fzero(F,n,X,incX);
return;
}
for (; Xi < X+n*incX; Xi+=incX )
F.mulin( *Xi, alpha );
}
/** \brief fcopy : \f$x \gets y \f$.
* X is preallocated
* @param F field
* @param N size of the vectors
* \param [out] X vector in \p F
* \param incX stride of \p X
* \param [in] Y vector in \p F
* \param incY stride of \p Y
*/
template<class Field>
void
fcopy (const Field& F, const size_t N,
typename Field::Element * X, const size_t incX,
const typename Field::Element * Y, const size_t incY );
/** \brief faxpy : \f$y \gets \alpha \cdot x + y\f$.
* @param F field
* @param N size of the vectors
* @param alpha scalar
* \param X vector in \p F
* \param incX stride of \p X
* \param Y vector in \p F
* \param incY stride of \p Y
*/
template<class Field>
void
faxpy (const Field& F, const size_t N,
const typename Field::Element alpha,
const typename Field::Element * X, const size_t incX,
typename Field::Element * Y, const size_t incY );
/** \brief fdot: dot product \f$x^T y\f$.
* @param F field
* @param N size of the vectors
* \param X vector in \p F
* \param incX stride of \p X
* \param Y vector in \p F
* \param incY stride of \p Y
*/
template<class Field>
typename Field::Element
fdot (const Field& F, const size_t N,
const typename Field::Element * X, const size_t incX,
const typename Field::Element * Y, const size_t incY );
/** \brief fswap: \f$ X \leftrightarrow Y\f$.
* @param F field
* @param N size of the vectors
* \param X vector in \p F
* \param incX stride of \p X
* \param Y vector in \p F
* \param incY stride of \p Y
*/
template<class Field>
void
fswap (const Field& F, const size_t N, typename Field::Element * X, const size_t incX,
typename Field::Element * Y, const size_t incY )
{
typename Field::Element tmp;
typename Field::Element * Xi = X;
typename Field::Element * Yi=Y;
for (; Xi < X+N*incX; Xi+=incX, Yi+=incY ){
F.assign( tmp, *Xi );
F.assign( *Xi, *Yi );
F.assign( *Yi, tmp );
}
}
//---------------------------------------------------------------------
// Level 2 routines
//---------------------------------------------------------------------
/** \brief fcopy : \f$A \gets B \f$.
* @param F field
* @param m number of rows to copy
* @param n number of cols to copy
* \param A matrix in \p F
* \param lda stride of \p A
* \param B vector in \p F
* \param ldb stride of \p B
*/
template<class Field>
void
fcopy (const Field& F, const size_t m, const size_t n,
typename Field::Element * A, const size_t lda,
const typename Field::Element * B, const size_t ldb ) ;
/** \brief fzero : \f$A \gets 0 \f$.
* @param F field
* @param m number of rows to zero
* @param n number of cols to zero
* \param A matrix in \p F
* \param lda stride of \p A
* @warning may be buggy if Element is larger than int
*/
template<class Field>
void
fzero (const Field& F, const size_t m, const size_t n,
typename Field::Element * A, const size_t lda)
{
/* use memset only with Elements that are ok */
if (n == lda) { // contigous data
// memset(A,(int) F.zero,m*n); // might be bogus ?
fzero(F,m*n,A,1);
}
else { // not contiguous (strided)
for (size_t i = 0 ; i < m ; ++i)
// memset(A+i*lda,(int) F.zero,n) ; // might be bogus ?
fzero(F,n,A+i*lda,1);
}
}
/** fscal
* \f$A \gets a \cdot A\f$.
* @param F field
* @param m number of rows
* @param n number of cols
* @param alpha homotecie scalar
* \param A matrix in \p F
* \param lda stride of \p A
* @internal
*/
template<class Field>
void
fscal (const Field& F, const size_t m , const size_t n,
const typename Field::Element alpha,
typename Field::Element * A, const size_t lda)
{
typedef typename Field::Element Element ;
if (F.isOne(alpha)) {
return ;
}
else {
if (lda == n) {
fscal(F,n*m,alpha,A,1);
}
else {
for (size_t i = 0 ; i < m ; ++i)
fscal(F,n,alpha,A+i*lda,1);
}
return;
}
}
/** \brief fmove : \f$A \gets B \f$ and \f$ B \gets 0\f$.
* @param F field
* @param m number of rows to copy
* @param n number of cols to copy
* \param A matrix in \p F
* \param lda stride of \p A
* \param B vector in \p F
* \param ldb stride of \p B
*/
template<class Field>
void
fmove (const Field& F, const size_t m, const size_t n,
typename Field::Element * A, const size_t lda,
typename Field::Element * B, const size_t ldb )
{
fcopy(F,m,n,A,lda,B,ldb);
fzero(F,m,n,B,ldb);
}
/** fadd : matrix addition.
* Computes \p C = \p A + \p B.
* @param F field
* @param M rows
* @param N cols
* @param A dense matrix of size \c MxN
* @param lda leading dimension of \p A
* @param B dense matrix of size \c MxN
* @param ldb leading dimension of \p B
* @param C dense matrix of size \c MxN
* @param ldc leading dimension of \p C
*/
template <class Field>
void
fadd (const Field& F, const size_t M, const size_t N,
const typename Field::Element* A, const size_t lda,
const typename Field::Element* B, const size_t ldb,
typename Field::Element* C, const size_t ldc)
{
const typename Field::Element *Ai = A, *Bi = B;
typename Field::Element *Ci = C;
for (; Ai < A+M*lda; Ai+=lda, Bi+=ldb, Ci+=ldc)
for (size_t i=0; i<N; i++)
F.add (Ci[i], Ai[i], Bi[i]);
}
/** fsub : matrix subtraction.
* Computes \p C = \p A - \p B.
* @param F field
* @param M rows
* @param N cols
* @param A dense matrix of size \c MxN
* @param lda leading dimension of \p A
* @param B dense matrix of size \c MxN
* @param ldb leading dimension of \p B
* @param C dense matrix of size \c MxN
* @param ldc leading dimension of \p C
*/
template <class Field>
void
fsub (const Field& F, const size_t M, const size_t N,
const typename Field::Element* A, const size_t lda,
const typename Field::Element* B, const size_t ldb,
typename Field::Element* C, const size_t ldc)
{
const typename Field::Element * Ai = A, *Bi = B;
typename Field::Element *Ci = C;
for (; Ai < A+M*lda; Ai+=lda, Bi+=ldb, Ci+=ldc)
for (size_t i=0; i<N; i++)
F.sub (Ci[i], Ai[i], Bi[i]);
}
//! fsubin
template <class Field>
void
fsubin (const Field& F, const size_t M, const size_t N,
const typename Field::Element* B, const size_t ldb,
typename Field::Element* C, const size_t ldc)
{
const typename Field::Element * Bi = B;
typename Field::Element *Ci = C;
for (; Ci < C+M*ldc; Bi+=ldb, Ci+=ldc)
for (size_t i=0; i<N; i++)
F.subin (Ci[i], Bi[i]);
}
//! faddin
template <class Field>
void
faddin (const Field& F, const size_t M, const size_t N,
const typename Field::Element* B, const size_t ldb,
typename Field::Element* C, const size_t ldc)
{
const typename Field::Element * Bi = B;
typename Field::Element *Ci = C;
for (; Ci < C+M*ldc; Bi+=ldb, Ci+=ldc)
for (size_t i=0; i<N; i++)
F.addin (Ci[i], Bi[i]);
}
/** @brief finite prime Field GEneral Matrix Vector multiplication.
*
* Computes \f$Y \gets \alpha \mathrm{op}(A) X + \beta Y \f$.
* @param F field
* \param TransA if \c TransA==FflasTrans then \f$\mathrm{op}(A)=A^t\f$.
* @param M rows
* @param N cols
* @param alpha scalar
* @param A dense matrix of size \c MxN
* @param lda leading dimension of \p A
* @param X dense vector of size \c N
* @param incX stride of \p X
* @param beta scalar
* @param[out] Y dense vector of size \c M
* @param incY stride of \p Y
*/
template<class Field>
void
fgemv (const Field& F, const FFLAS_TRANSPOSE TransA,
const size_t M, const size_t N,
const typename Field::Element alpha,
const typename Field::Element * A, const size_t lda,
const typename Field::Element * X, const size_t incX,
const typename Field::Element beta,
typename Field::Element * Y, const size_t incY);
/** @brief fger: GEneral ?
*
* Computes \f$A \gets \alpha x . y^T + A\f$
* @param F field
* @param M rows
* @param N cols
* @param alpha scalar
* @param[in,out] A dense matrix of size \c MxN and leading dimension \p lda
* @param lda leading dimension of \p A
* @param x dense vector of size \c M
* @param incx stride of \p X
* @param y dense vector of size \c N
* @param incy stride of \p Y
*/
template<class Field>
void
fger (const Field& F, const size_t M, const size_t N,
const typename Field::Element alpha,
const typename Field::Element * x, const size_t incx,
const typename Field::Element * y, const size_t incy,
typename Field::Element * A, const size_t lda);
/** @brief ftrsv: TRiangular System solve with Vector
* Computes \f$ X \gets \mathrm{op}(A^{-1}) X\f$
* @param F field
* @param X vector of size \p N on a field \p F
* @param incX stride of \p X
* @param A a matrix of leading dimension \p lda and size \p N
* @param lda leading dimension of \p A
* @param N number of rows or columns of \p A according to \p TransA
* \param TransA if \c TransA==FflasTrans then \f$\mathrm{op}(A)=A^t\f$.
* \param Diag if \c Diag==FflasUnit then \p A is unit.
* \param Uplo if \c Uplo==FflasUpper then \p A is upper triangular
*/
template<class Field>
void
ftrsv (const Field& F, const FFLAS_UPLO Uplo,
const FFLAS_TRANSPOSE TransA, const FFLAS_DIAG Diag,
const size_t N,const typename Field::Element * A, const size_t lda,
typename Field::Element * X, int incX);
//---------------------------------------------------------------------
// Level 3 routines
//---------------------------------------------------------------------
/** @brief ftrsm: <b>TR</b>iangular <b>S</b>ystem solve with <b>M</b>atrix.
* Computes \f$ B \gets \alpha \mathrm{op}(A^{-1}) B\f$ or \f$B \gets \alpha B \mathrm{op}(A^{-1})\f$.
* \param F field
* \param Side if \c Side==FflasLeft then \f$ B \gets \alpha \mathrm{op}(A^{-1}) B\f$ is computed.
* \param Uplo if \c Uplo==FflasUpper then \p A is upper triangular
* \param TransA if \c TransA==FflasTrans then \f$\mathrm{op}(A)=A^t\f$.
* \param Diag if \c Diag==FflasUnit then \p A is unit.
* \param M rows of \p B
* \param N cols of \p B
* @param alpha scalar
* \param A triangular invertible matrix. If \c Side==FflasLeft then \p A is \f$N\times N\f$, otherwise \p A is \f$M\times M\f$
* @param lda leading dim of \p A
* @param B matrix of size \p MxN
* @param ldb leading dim of \p B
* @bug unsafe with \c Trans==FflasTrans (debugging in progress)
* @bug \f$\alpha\f$ must be non zero.
*/
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 * A, const size_t lda,
typename Field::Element * B, const size_t ldb);
/** @brief ftrmm: <b>TR</b>iangular <b>M</b>atrix <b>M</b>ultiply.
* Computes \f$ B \gets \alpha \mathrm{op}(A) B\f$ or \f$B \gets \alpha B \mathrm{op}(A)\f$.
* @param F field
* \param Side if \c Side==FflasLeft then \f$ B \gets \alpha \mathrm{op}(A) B\f$ is computed.
* \param Uplo if \c Uplo==FflasUpper then \p A is upper triangular
* \param TransA if \c TransA==FflasTrans then \f$\mathrm{op}(A)=A^t\f$.
* \param Diag if \c Diag==FflasUnit then \p A is implicitly unit.
* \param M rows of \p B
* \param N cols of \p B
* @param alpha scalar
* \param A triangular matrix. If \c Side==FflasLeft then \p A is \f$N\times N\f$, otherwise \p A is \f$M\times M\f$
* @param lda leading dim of \p A
* @param B matrix of size \p MxN
* @param ldb leading dim of \p B
* @bug unsafe with \c Trans==FflasTrans (debugging in progress)
*/
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::Element * A, const size_t lda,
typename Field::Element * B, const size_t ldb);
/** @brief fgemm: <b>F</b>ield <b>GE</b>neral <b>M</b>atrix <b>M</b>ultiply.
*
* Computes \f$C = \alpha \mathrm{op}(A) \times \mathrm{op}(B) + \beta C\f$
* \param F field.
* \param ta if \c ta==FflasTrans then \f$\mathrm{op}(A)=A^t\f$, else \f$\mathrm{op}(A)=A\f$,
* \param tb same for \p B
* \param m see \p A
* \param k see \p A
* \param n see \p B
* \param alpha scalar
* \param beta scalar
* \param A \f$\mathrm{op}(A)\f$ is \f$m \times k\f$
* \param B \f$\mathrm{op}(B)\f$ is \f$k \times n\f$
* \param C \f$C\f$ is \f$m \times n\f$
* \param lda leading dimension of \p A
* \param ldb leading dimension of \p B
* \param ldc leading dimension of \p C
* \param w recursive levels of Winograd's algorithm are used
* @warning \f$\alpha\f$ \e must be invertible
*/
template<class Field>
typename Field::Element*
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,
const typename Field::Element* A, const size_t lda,
const typename Field::Element* B, const size_t ldb,
const typename Field::Element beta,
typename Field::Element* C, const size_t ldc,
const size_t w)
{
if (!(m && n && k)) return C;
if (F.isZero (alpha)){
fscal(F, m, n, beta, C, ldc);
return C;
}
size_t kmax = 0;
size_t winolevel = w;
FFLAS_BASE base;
Protected::MatMulParameters (F, MIN(MIN(m,n),k), beta, kmax, base,
winolevel, true);
Protected::WinoMain (F, ta, tb, m, n, k, alpha, A, lda, B, ldb, beta,
C, ldc, kmax, winolevel, base);
return C;
}
/** @brief fgemm: <b>F</b>ield <b>GE</b>neral <b>M</b>atrix <b>M</b>ultiply.
*
* Computes \f$C = \alpha \mathrm{op}(A) \mathrm{op}(B) + \beta C\f$.
* Automatically set Winograd recursion level
* \param F field.
* \param ta if \c ta==FflasTrans then \f$\mathrm{op}(A)=A^t\f$, else \f$\mathrm{op}(A)=A\f$,
* \param tb same for matrix \p B
* \param m see \p A
* \param k see \p A
* \param n see \p B
* \param alpha scalar
* \param beta scalar
* \param A \f$\mathrm{op}(A)\f$ is \f$m \times k\f$
* \param B \f$\mathrm{op}(B)\f$ is \f$k \times n\f$
* \param C \f$C\f$ is \f$m \times n\f$
* \param lda leading dimension of \p A
* \param ldb leading dimension of \p B
* \param ldc leading dimension of \p C
* @warning \f$\alpha\f$ \e must be invertible
*/
template<class Field>
typename Field::Element*
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,
const typename Field::Element* A, const size_t lda,
const typename Field::Element* B, const size_t ldb,
const typename Field::Element beta,
typename Field::Element* C, const size_t ldc)
{
if (!(m && n && k)) return C;
if (F.isZero (alpha)){
for (size_t i = 0; i<m; ++i)
fscal(F, n, beta, C + i*ldc, 1);
return C;
}
#ifdef _LB_DEBUG
/* check if alpha is invertible. XXX do it in F.isInvertible(Element&) ? */
typename Field::Element e ;
F.init(e,1UL);
F.divin(e,alpha);
F.mulin(e,alpha);
FFLASFFPACK_check(F.isOne(e));
#endif
size_t w, kmax;
FFLAS_BASE base;
Protected::MatMulParameters (F, MIN(MIN(m,n),k), beta, kmax, base, w);
Protected::WinoMain (F, ta, tb, m, n, k, alpha, A, lda, B, ldb, beta,
C, ldc, kmax, w, base);
return C;
}
/** @brief fsquare: Squares a matrix.
* compute \f$ C \gets \alpha \mathrm{op}(A) \mathrm{op}(A) + \beta C\f$ over a Field \p F
* Avoid the conversion of B
* @param ta if \c ta==FflasTrans, \f$\mathrm{op}(A)=A^T\f$.
* @param F field
* @param n size of \p A
* @param alpha scalar
* @param beta scalar
* @param A dense matrix of size \c nxn
* @param lda leading dimension of \p A
* @param C dense matrix of size \c nxn
* @param ldc leading dimension of \p C
*/
template<class Field>
typename Field::Element* fsquare (const Field& F,
const FFLAS_TRANSPOSE ta,
const size_t n,
const typename Field::Element alpha,
const typename Field::Element* A,
const size_t lda,
const typename Field::Element beta,
typename Field::Element* C,
const size_t ldc);
#ifdef LB_TRTR
// BB
/** @brief ftrtr: Triangular-Triangular matrix multiplication.
* \f$B \gets \alpha \mathrm{op}(A) \times B\f$ (for FFLAS_SIDE::FflasLeft)
* A and B are triangular, with B UpLo
* and op(A) = A, A^T according to TransA
* A and B can be (non)unit
*
*/
template<class Field>
typename Field::Element* ftrtr (const Field& F, const FFLAS_SIDE Side,
const FFLAS_UPLO Uplo,
const FFLAS_TRANSPOSE TransA,
const FFLAS_DIAG ADiag,
const FFLAS_DIAG BDiag,
const size_t M,
const typename Field::Element alpha,
typename Field::Element * A, const size_t lda,
typename Field::Element * B, const size_t ldb);
#endif
/** faddm.
* A <- A+op(B)
* with op(B) = B or B^T
*/
template<class Field>
void faddm(const Field & F,
const FFLAS_TRANSPOSE transA,
const size_t M, const size_t N,
const typename Field::Element * A, const size_t lda,
typename Field::Element * B, const size_t ldb);
/** faddm.
* C <- op(A)+op(B)
* with op(B) = B or B^T
*/
template<class Field>
void faddm(const Field & F,
const FFLAS_TRANSPOSE transA,
const FFLAS_TRANSPOSE transB,
const size_t M, const size_t N,
const typename Field::Element * A, const size_t lda,
const typename Field::Element * B, const size_t ldb,
typename Field::Element * C, const size_t ldc );
/** fsubm.
* A <- A-op(B)
* with op(B) = B or B^T
*/
template<class Field>
void fsubm(const Field & F,
const FFLAS_TRANSPOSE transA,
const size_t M, const size_t N,
const typename Field::Element * A, const size_t lda,
typename Field::Element * B, const size_t ldb) ;
/** fsubm.
* C <- op(A)-op(B)
* with op(B) = B or B^T
*/
template<class Field>
void fsubm(const Field & F,
const FFLAS_TRANSPOSE transA,
const FFLAS_TRANSPOSE transB,
const size_t M, const size_t N,
const typename Field::Element * A, const size_t lda,
const typename Field::Element * B, const size_t ldb,
typename Field::Element * C, const size_t ldc );
/** MatCopy makes a copy of the matrix M into a new allocated space.
* @param F field
* @param M rows of \p A
* @param N cols of \p A
* @param A matrix to be copied
* @param lda leading dimension of \p A
* @return a copy \p C of \p A with stride \p N
* @warning \p A and \p C belong to the same field.
*/
template<class Field>
typename Field::Element* MatCopy (const Field& F,
const size_t M, const size_t N,
const typename Field::Element * A,
const size_t lda)
{
typename Field::Element * C = new typename Field::Element[M*N];
for (size_t i = 0; i < N; ++i)
for (size_t j = 0; j < N; ++j)
F.assign(*(C + i*N + j),*(A + i*lda + j));
return C;
}
/** \brief Computes the number of recursive levels to perform.
*
* \param m the common dimension in the product AxB
*/
size_t WinoSteps (const size_t m);
} // class FFLAS
#include "fflas_bounds.inl"
#include "fflas_fgemm.inl"
#include "fflas_fgemv.inl"
#include "fflas_fger.inl"
#include "fflas_ftrsm.inl"
#include "fflas_ftrmm.inl"
#include "fflas_ftrsv.inl"
#include "fflas_faxpy.inl"
#include "fflas_fdot.inl"
#include "fflas_fcopy.inl"
//BB
#ifdef LB_TRTR
#include "fflas_ftrtr.inl"
#endif
#include "fflas_faddm.inl"
#undef LB_TRTR
#endif // __FFLASFFPACK_fflas_H
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