| Current File : //usr/include/eigen3/Eigen/src/Core/products/GeneralBlockPanelKernel.h |
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_GENERAL_BLOCK_PANEL_H
#define EIGEN_GENERAL_BLOCK_PANEL_H
namespace Eigen {
namespace internal {
template<typename _LhsScalar, typename _RhsScalar, bool _ConjLhs=false, bool _ConjRhs=false>
class gebp_traits;
/** \internal \returns b if a<=0, and returns a otherwise. */
inline std::ptrdiff_t manage_caching_sizes_helper(std::ptrdiff_t a, std::ptrdiff_t b)
{
return a<=0 ? b : a;
}
#if EIGEN_ARCH_i386_OR_x86_64
const std::ptrdiff_t defaultL1CacheSize = 32*1024;
const std::ptrdiff_t defaultL2CacheSize = 256*1024;
const std::ptrdiff_t defaultL3CacheSize = 2*1024*1024;
#else
const std::ptrdiff_t defaultL1CacheSize = 16*1024;
const std::ptrdiff_t defaultL2CacheSize = 512*1024;
const std::ptrdiff_t defaultL3CacheSize = 512*1024;
#endif
/** \internal */
struct CacheSizes {
CacheSizes(): m_l1(-1),m_l2(-1),m_l3(-1) {
int l1CacheSize, l2CacheSize, l3CacheSize;
queryCacheSizes(l1CacheSize, l2CacheSize, l3CacheSize);
m_l1 = manage_caching_sizes_helper(l1CacheSize, defaultL1CacheSize);
m_l2 = manage_caching_sizes_helper(l2CacheSize, defaultL2CacheSize);
m_l3 = manage_caching_sizes_helper(l3CacheSize, defaultL3CacheSize);
}
std::ptrdiff_t m_l1;
std::ptrdiff_t m_l2;
std::ptrdiff_t m_l3;
};
/** \internal */
inline void manage_caching_sizes(Action action, std::ptrdiff_t* l1, std::ptrdiff_t* l2, std::ptrdiff_t* l3)
{
static CacheSizes m_cacheSizes;
if(action==SetAction)
{
// set the cpu cache size and cache all block sizes from a global cache size in byte
eigen_internal_assert(l1!=0 && l2!=0);
m_cacheSizes.m_l1 = *l1;
m_cacheSizes.m_l2 = *l2;
m_cacheSizes.m_l3 = *l3;
}
else if(action==GetAction)
{
eigen_internal_assert(l1!=0 && l2!=0);
*l1 = m_cacheSizes.m_l1;
*l2 = m_cacheSizes.m_l2;
*l3 = m_cacheSizes.m_l3;
}
else
{
eigen_internal_assert(false);
}
}
/* Helper for computeProductBlockingSizes.
*
* Given a m x k times k x n matrix product of scalar types \c LhsScalar and \c RhsScalar,
* this function computes the blocking size parameters along the respective dimensions
* for matrix products and related algorithms. The blocking sizes depends on various
* parameters:
* - the L1 and L2 cache sizes,
* - the register level blocking sizes defined by gebp_traits,
* - the number of scalars that fit into a packet (when vectorization is enabled).
*
* \sa setCpuCacheSizes */
template<typename LhsScalar, typename RhsScalar, int KcFactor, typename Index>
void evaluateProductBlockingSizesHeuristic(Index& k, Index& m, Index& n, Index num_threads = 1)
{
typedef gebp_traits<LhsScalar,RhsScalar> Traits;
// Explanations:
// Let's recall that the product algorithms form mc x kc vertical panels A' on the lhs and
// kc x nc blocks B' on the rhs. B' has to fit into L2/L3 cache. Moreover, A' is processed
// per mr x kc horizontal small panels where mr is the blocking size along the m dimension
// at the register level. This small horizontal panel has to stay within L1 cache.
std::ptrdiff_t l1, l2, l3;
manage_caching_sizes(GetAction, &l1, &l2, &l3);
if (num_threads > 1) {
typedef typename Traits::ResScalar ResScalar;
enum {
kdiv = KcFactor * (Traits::mr * sizeof(LhsScalar) + Traits::nr * sizeof(RhsScalar)),
ksub = Traits::mr * Traits::nr * sizeof(ResScalar),
kr = 8,
mr = Traits::mr,
nr = Traits::nr
};
// Increasing k gives us more time to prefetch the content of the "C"
// registers. However once the latency is hidden there is no point in
// increasing the value of k, so we'll cap it at 320 (value determined
// experimentally).
const Index k_cache = (numext::mini<Index>)((l1-ksub)/kdiv, 320);
if (k_cache < k) {
k = k_cache - (k_cache % kr);
eigen_internal_assert(k > 0);
}
const Index n_cache = (l2-l1) / (nr * sizeof(RhsScalar) * k);
const Index n_per_thread = numext::div_ceil(n, num_threads);
if (n_cache <= n_per_thread) {
// Don't exceed the capacity of the l2 cache.
eigen_internal_assert(n_cache >= static_cast<Index>(nr));
n = n_cache - (n_cache % nr);
eigen_internal_assert(n > 0);
} else {
n = (numext::mini<Index>)(n, (n_per_thread + nr - 1) - ((n_per_thread + nr - 1) % nr));
}
if (l3 > l2) {
// l3 is shared between all cores, so we'll give each thread its own chunk of l3.
const Index m_cache = (l3-l2) / (sizeof(LhsScalar) * k * num_threads);
const Index m_per_thread = numext::div_ceil(m, num_threads);
if(m_cache < m_per_thread && m_cache >= static_cast<Index>(mr)) {
m = m_cache - (m_cache % mr);
eigen_internal_assert(m > 0);
} else {
m = (numext::mini<Index>)(m, (m_per_thread + mr - 1) - ((m_per_thread + mr - 1) % mr));
}
}
}
else {
// In unit tests we do not want to use extra large matrices,
// so we reduce the cache size to check the blocking strategy is not flawed
#ifdef EIGEN_DEBUG_SMALL_PRODUCT_BLOCKS
l1 = 9*1024;
l2 = 32*1024;
l3 = 512*1024;
#endif
// Early return for small problems because the computation below are time consuming for small problems.
// Perhaps it would make more sense to consider k*n*m??
// Note that for very tiny problem, this function should be bypassed anyway
// because we use the coefficient-based implementation for them.
if((numext::maxi)(k,(numext::maxi)(m,n))<48)
return;
typedef typename Traits::ResScalar ResScalar;
enum {
k_peeling = 8,
k_div = KcFactor * (Traits::mr * sizeof(LhsScalar) + Traits::nr * sizeof(RhsScalar)),
k_sub = Traits::mr * Traits::nr * sizeof(ResScalar)
};
// ---- 1st level of blocking on L1, yields kc ----
// Blocking on the third dimension (i.e., k) is chosen so that an horizontal panel
// of size mr x kc of the lhs plus a vertical panel of kc x nr of the rhs both fits within L1 cache.
// We also include a register-level block of the result (mx x nr).
// (In an ideal world only the lhs panel would stay in L1)
// Moreover, kc has to be a multiple of 8 to be compatible with loop peeling, leading to a maximum blocking size of:
const Index max_kc = numext::maxi<Index>(((l1-k_sub)/k_div) & (~(k_peeling-1)),1);
const Index old_k = k;
if(k>max_kc)
{
// We are really blocking on the third dimension:
// -> reduce blocking size to make sure the last block is as large as possible
// while keeping the same number of sweeps over the result.
k = (k%max_kc)==0 ? max_kc
: max_kc - k_peeling * ((max_kc-1-(k%max_kc))/(k_peeling*(k/max_kc+1)));
eigen_internal_assert(((old_k/k) == (old_k/max_kc)) && "the number of sweeps has to remain the same");
}
// ---- 2nd level of blocking on max(L2,L3), yields nc ----
// TODO find a reliable way to get the actual amount of cache per core to use for 2nd level blocking, that is:
// actual_l2 = max(l2, l3/nb_core_sharing_l3)
// The number below is quite conservative: it is better to underestimate the cache size rather than overestimating it)
// For instance, it corresponds to 6MB of L3 shared among 4 cores.
#ifdef EIGEN_DEBUG_SMALL_PRODUCT_BLOCKS
const Index actual_l2 = l3;
#else
const Index actual_l2 = 1572864; // == 1.5 MB
#endif
// Here, nc is chosen such that a block of kc x nc of the rhs fit within half of L2.
// The second half is implicitly reserved to access the result and lhs coefficients.
// When k<max_kc, then nc can arbitrarily growth. In practice, it seems to be fruitful
// to limit this growth: we bound nc to growth by a factor x1.5.
// However, if the entire lhs block fit within L1, then we are not going to block on the rows at all,
// and it becomes fruitful to keep the packed rhs blocks in L1 if there is enough remaining space.
Index max_nc;
const Index lhs_bytes = m * k * sizeof(LhsScalar);
const Index remaining_l1 = l1- k_sub - lhs_bytes;
if(remaining_l1 >= Index(Traits::nr*sizeof(RhsScalar))*k)
{
// L1 blocking
max_nc = remaining_l1 / (k*sizeof(RhsScalar));
}
else
{
// L2 blocking
max_nc = (3*actual_l2)/(2*2*max_kc*sizeof(RhsScalar));
}
// WARNING Below, we assume that Traits::nr is a power of two.
Index nc = numext::mini<Index>(actual_l2/(2*k*sizeof(RhsScalar)), max_nc) & (~(Traits::nr-1));
if(n>nc)
{
// We are really blocking over the columns:
// -> reduce blocking size to make sure the last block is as large as possible
// while keeping the same number of sweeps over the packed lhs.
// Here we allow one more sweep if this gives us a perfect match, thus the commented "-1"
n = (n%nc)==0 ? nc
: (nc - Traits::nr * ((nc/*-1*/-(n%nc))/(Traits::nr*(n/nc+1))));
}
else if(old_k==k)
{
// So far, no blocking at all, i.e., kc==k, and nc==n.
// In this case, let's perform a blocking over the rows such that the packed lhs data is kept in cache L1/L2
// TODO: part of this blocking strategy is now implemented within the kernel itself, so the L1-based heuristic here should be obsolete.
Index problem_size = k*n*sizeof(LhsScalar);
Index actual_lm = actual_l2;
Index max_mc = m;
if(problem_size<=1024)
{
// problem is small enough to keep in L1
// Let's choose m such that lhs's block fit in 1/3 of L1
actual_lm = l1;
}
else if(l3!=0 && problem_size<=32768)
{
// we have both L2 and L3, and problem is small enough to be kept in L2
// Let's choose m such that lhs's block fit in 1/3 of L2
actual_lm = l2;
max_mc = (numext::mini<Index>)(576,max_mc);
}
Index mc = (numext::mini<Index>)(actual_lm/(3*k*sizeof(LhsScalar)), max_mc);
if (mc > Traits::mr) mc -= mc % Traits::mr;
else if (mc==0) return;
m = (m%mc)==0 ? mc
: (mc - Traits::mr * ((mc/*-1*/-(m%mc))/(Traits::mr*(m/mc+1))));
}
}
}
template <typename Index>
inline bool useSpecificBlockingSizes(Index& k, Index& m, Index& n)
{
#ifdef EIGEN_TEST_SPECIFIC_BLOCKING_SIZES
if (EIGEN_TEST_SPECIFIC_BLOCKING_SIZES) {
k = numext::mini<Index>(k, EIGEN_TEST_SPECIFIC_BLOCKING_SIZE_K);
m = numext::mini<Index>(m, EIGEN_TEST_SPECIFIC_BLOCKING_SIZE_M);
n = numext::mini<Index>(n, EIGEN_TEST_SPECIFIC_BLOCKING_SIZE_N);
return true;
}
#else
EIGEN_UNUSED_VARIABLE(k)
EIGEN_UNUSED_VARIABLE(m)
EIGEN_UNUSED_VARIABLE(n)
#endif
return false;
}
/** \brief Computes the blocking parameters for a m x k times k x n matrix product
*
* \param[in,out] k Input: the third dimension of the product. Output: the blocking size along the same dimension.
* \param[in,out] m Input: the number of rows of the left hand side. Output: the blocking size along the same dimension.
* \param[in,out] n Input: the number of columns of the right hand side. Output: the blocking size along the same dimension.
*
* Given a m x k times k x n matrix product of scalar types \c LhsScalar and \c RhsScalar,
* this function computes the blocking size parameters along the respective dimensions
* for matrix products and related algorithms.
*
* The blocking size parameters may be evaluated:
* - either by a heuristic based on cache sizes;
* - or using fixed prescribed values (for testing purposes).
*
* \sa setCpuCacheSizes */
template<typename LhsScalar, typename RhsScalar, int KcFactor, typename Index>
void computeProductBlockingSizes(Index& k, Index& m, Index& n, Index num_threads = 1)
{
if (!useSpecificBlockingSizes(k, m, n)) {
evaluateProductBlockingSizesHeuristic<LhsScalar, RhsScalar, KcFactor, Index>(k, m, n, num_threads);
}
}
template<typename LhsScalar, typename RhsScalar, typename Index>
inline void computeProductBlockingSizes(Index& k, Index& m, Index& n, Index num_threads = 1)
{
computeProductBlockingSizes<LhsScalar,RhsScalar,1,Index>(k, m, n, num_threads);
}
#ifdef EIGEN_HAS_SINGLE_INSTRUCTION_CJMADD
#define CJMADD(CJ,A,B,C,T) C = CJ.pmadd(A,B,C);
#else
// FIXME (a bit overkill maybe ?)
template<typename CJ, typename A, typename B, typename C, typename T> struct gebp_madd_selector {
EIGEN_ALWAYS_INLINE static void run(const CJ& cj, A& a, B& b, C& c, T& /*t*/)
{
c = cj.pmadd(a,b,c);
}
};
template<typename CJ, typename T> struct gebp_madd_selector<CJ,T,T,T,T> {
EIGEN_ALWAYS_INLINE static void run(const CJ& cj, T& a, T& b, T& c, T& t)
{
t = b; t = cj.pmul(a,t); c = padd(c,t);
}
};
template<typename CJ, typename A, typename B, typename C, typename T>
EIGEN_STRONG_INLINE void gebp_madd(const CJ& cj, A& a, B& b, C& c, T& t)
{
gebp_madd_selector<CJ,A,B,C,T>::run(cj,a,b,c,t);
}
#define CJMADD(CJ,A,B,C,T) gebp_madd(CJ,A,B,C,T);
// #define CJMADD(CJ,A,B,C,T) T = B; T = CJ.pmul(A,T); C = padd(C,T);
#endif
/* Vectorization logic
* real*real: unpack rhs to constant packets, ...
*
* cd*cd : unpack rhs to (b_r,b_r), (b_i,b_i), mul to get (a_r b_r,a_i b_r) (a_r b_i,a_i b_i),
* storing each res packet into two packets (2x2),
* at the end combine them: swap the second and addsub them
* cf*cf : same but with 2x4 blocks
* cplx*real : unpack rhs to constant packets, ...
* real*cplx : load lhs as (a0,a0,a1,a1), and mul as usual
*/
template<typename _LhsScalar, typename _RhsScalar, bool _ConjLhs, bool _ConjRhs>
class gebp_traits
{
public:
typedef _LhsScalar LhsScalar;
typedef _RhsScalar RhsScalar;
typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
enum {
ConjLhs = _ConjLhs,
ConjRhs = _ConjRhs,
Vectorizable = packet_traits<LhsScalar>::Vectorizable && packet_traits<RhsScalar>::Vectorizable,
LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,
RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,
ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1,
NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,
// register block size along the N direction must be 1 or 4
nr = 4,
// register block size along the M direction (currently, this one cannot be modified)
default_mr = (EIGEN_PLAIN_ENUM_MIN(16,NumberOfRegisters)/2/nr)*LhsPacketSize,
#if defined(EIGEN_HAS_SINGLE_INSTRUCTION_MADD) && !defined(EIGEN_VECTORIZE_ALTIVEC) && !defined(EIGEN_VECTORIZE_VSX)
// we assume 16 registers
// See bug 992, if the scalar type is not vectorizable but that EIGEN_HAS_SINGLE_INSTRUCTION_MADD is defined,
// then using 3*LhsPacketSize triggers non-implemented paths in syrk.
mr = Vectorizable ? 3*LhsPacketSize : default_mr,
#else
mr = default_mr,
#endif
LhsProgress = LhsPacketSize,
RhsProgress = 1
};
typedef typename packet_traits<LhsScalar>::type _LhsPacket;
typedef typename packet_traits<RhsScalar>::type _RhsPacket;
typedef typename packet_traits<ResScalar>::type _ResPacket;
typedef typename conditional<Vectorizable,_LhsPacket,LhsScalar>::type LhsPacket;
typedef typename conditional<Vectorizable,_RhsPacket,RhsScalar>::type RhsPacket;
typedef typename conditional<Vectorizable,_ResPacket,ResScalar>::type ResPacket;
typedef ResPacket AccPacket;
EIGEN_STRONG_INLINE void initAcc(AccPacket& p)
{
p = pset1<ResPacket>(ResScalar(0));
}
EIGEN_STRONG_INLINE void broadcastRhs(const RhsScalar* b, RhsPacket& b0, RhsPacket& b1, RhsPacket& b2, RhsPacket& b3)
{
pbroadcast4(b, b0, b1, b2, b3);
}
// EIGEN_STRONG_INLINE void broadcastRhs(const RhsScalar* b, RhsPacket& b0, RhsPacket& b1)
// {
// pbroadcast2(b, b0, b1);
// }
template<typename RhsPacketType>
EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacketType& dest) const
{
dest = pset1<RhsPacketType>(*b);
}
EIGEN_STRONG_INLINE void loadRhsQuad(const RhsScalar* b, RhsPacket& dest) const
{
dest = ploadquad<RhsPacket>(b);
}
template<typename LhsPacketType>
EIGEN_STRONG_INLINE void loadLhs(const LhsScalar* a, LhsPacketType& dest) const
{
dest = pload<LhsPacketType>(a);
}
template<typename LhsPacketType>
EIGEN_STRONG_INLINE void loadLhsUnaligned(const LhsScalar* a, LhsPacketType& dest) const
{
dest = ploadu<LhsPacketType>(a);
}
template<typename LhsPacketType, typename RhsPacketType, typename AccPacketType>
EIGEN_STRONG_INLINE void madd(const LhsPacketType& a, const RhsPacketType& b, AccPacketType& c, AccPacketType& tmp) const
{
conj_helper<LhsPacketType,RhsPacketType,ConjLhs,ConjRhs> cj;
// It would be a lot cleaner to call pmadd all the time. Unfortunately if we
// let gcc allocate the register in which to store the result of the pmul
// (in the case where there is no FMA) gcc fails to figure out how to avoid
// spilling register.
#ifdef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
EIGEN_UNUSED_VARIABLE(tmp);
c = cj.pmadd(a,b,c);
#else
tmp = b; tmp = cj.pmul(a,tmp); c = padd(c,tmp);
#endif
}
EIGEN_STRONG_INLINE void acc(const AccPacket& c, const ResPacket& alpha, ResPacket& r) const
{
r = pmadd(c,alpha,r);
}
template<typename ResPacketHalf>
EIGEN_STRONG_INLINE void acc(const ResPacketHalf& c, const ResPacketHalf& alpha, ResPacketHalf& r) const
{
r = pmadd(c,alpha,r);
}
};
template<typename RealScalar, bool _ConjLhs>
class gebp_traits<std::complex<RealScalar>, RealScalar, _ConjLhs, false>
{
public:
typedef std::complex<RealScalar> LhsScalar;
typedef RealScalar RhsScalar;
typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
enum {
ConjLhs = _ConjLhs,
ConjRhs = false,
Vectorizable = packet_traits<LhsScalar>::Vectorizable && packet_traits<RhsScalar>::Vectorizable,
LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,
RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,
ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1,
NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,
nr = 4,
#if defined(EIGEN_HAS_SINGLE_INSTRUCTION_MADD) && !defined(EIGEN_VECTORIZE_ALTIVEC) && !defined(EIGEN_VECTORIZE_VSX)
// we assume 16 registers
mr = 3*LhsPacketSize,
#else
mr = (EIGEN_PLAIN_ENUM_MIN(16,NumberOfRegisters)/2/nr)*LhsPacketSize,
#endif
LhsProgress = LhsPacketSize,
RhsProgress = 1
};
typedef typename packet_traits<LhsScalar>::type _LhsPacket;
typedef typename packet_traits<RhsScalar>::type _RhsPacket;
typedef typename packet_traits<ResScalar>::type _ResPacket;
typedef typename conditional<Vectorizable,_LhsPacket,LhsScalar>::type LhsPacket;
typedef typename conditional<Vectorizable,_RhsPacket,RhsScalar>::type RhsPacket;
typedef typename conditional<Vectorizable,_ResPacket,ResScalar>::type ResPacket;
typedef ResPacket AccPacket;
EIGEN_STRONG_INLINE void initAcc(AccPacket& p)
{
p = pset1<ResPacket>(ResScalar(0));
}
EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacket& dest) const
{
dest = pset1<RhsPacket>(*b);
}
EIGEN_STRONG_INLINE void loadRhsQuad(const RhsScalar* b, RhsPacket& dest) const
{
dest = pset1<RhsPacket>(*b);
}
EIGEN_STRONG_INLINE void loadLhs(const LhsScalar* a, LhsPacket& dest) const
{
dest = pload<LhsPacket>(a);
}
EIGEN_STRONG_INLINE void loadLhsUnaligned(const LhsScalar* a, LhsPacket& dest) const
{
dest = ploadu<LhsPacket>(a);
}
EIGEN_STRONG_INLINE void broadcastRhs(const RhsScalar* b, RhsPacket& b0, RhsPacket& b1, RhsPacket& b2, RhsPacket& b3)
{
pbroadcast4(b, b0, b1, b2, b3);
}
// EIGEN_STRONG_INLINE void broadcastRhs(const RhsScalar* b, RhsPacket& b0, RhsPacket& b1)
// {
// pbroadcast2(b, b0, b1);
// }
EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacket& b, AccPacket& c, RhsPacket& tmp) const
{
madd_impl(a, b, c, tmp, typename conditional<Vectorizable,true_type,false_type>::type());
}
EIGEN_STRONG_INLINE void madd_impl(const LhsPacket& a, const RhsPacket& b, AccPacket& c, RhsPacket& tmp, const true_type&) const
{
#ifdef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
EIGEN_UNUSED_VARIABLE(tmp);
c.v = pmadd(a.v,b,c.v);
#else
tmp = b; tmp = pmul(a.v,tmp); c.v = padd(c.v,tmp);
#endif
}
EIGEN_STRONG_INLINE void madd_impl(const LhsScalar& a, const RhsScalar& b, ResScalar& c, RhsScalar& /*tmp*/, const false_type&) const
{
c += a * b;
}
EIGEN_STRONG_INLINE void acc(const AccPacket& c, const ResPacket& alpha, ResPacket& r) const
{
r = cj.pmadd(c,alpha,r);
}
protected:
conj_helper<ResPacket,ResPacket,ConjLhs,false> cj;
};
template<typename Packet>
struct DoublePacket
{
Packet first;
Packet second;
};
template<typename Packet>
DoublePacket<Packet> padd(const DoublePacket<Packet> &a, const DoublePacket<Packet> &b)
{
DoublePacket<Packet> res;
res.first = padd(a.first, b.first);
res.second = padd(a.second,b.second);
return res;
}
template<typename Packet>
const DoublePacket<Packet>& predux_downto4(const DoublePacket<Packet> &a)
{
return a;
}
template<typename Packet> struct unpacket_traits<DoublePacket<Packet> > { typedef DoublePacket<Packet> half; };
// template<typename Packet>
// DoublePacket<Packet> pmadd(const DoublePacket<Packet> &a, const DoublePacket<Packet> &b)
// {
// DoublePacket<Packet> res;
// res.first = padd(a.first, b.first);
// res.second = padd(a.second,b.second);
// return res;
// }
template<typename RealScalar, bool _ConjLhs, bool _ConjRhs>
class gebp_traits<std::complex<RealScalar>, std::complex<RealScalar>, _ConjLhs, _ConjRhs >
{
public:
typedef std::complex<RealScalar> Scalar;
typedef std::complex<RealScalar> LhsScalar;
typedef std::complex<RealScalar> RhsScalar;
typedef std::complex<RealScalar> ResScalar;
enum {
ConjLhs = _ConjLhs,
ConjRhs = _ConjRhs,
Vectorizable = packet_traits<RealScalar>::Vectorizable
&& packet_traits<Scalar>::Vectorizable,
RealPacketSize = Vectorizable ? packet_traits<RealScalar>::size : 1,
ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1,
LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,
RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,
// FIXME: should depend on NumberOfRegisters
nr = 4,
mr = ResPacketSize,
LhsProgress = ResPacketSize,
RhsProgress = 1
};
typedef typename packet_traits<RealScalar>::type RealPacket;
typedef typename packet_traits<Scalar>::type ScalarPacket;
typedef DoublePacket<RealPacket> DoublePacketType;
typedef typename conditional<Vectorizable,RealPacket, Scalar>::type LhsPacket;
typedef typename conditional<Vectorizable,DoublePacketType,Scalar>::type RhsPacket;
typedef typename conditional<Vectorizable,ScalarPacket,Scalar>::type ResPacket;
typedef typename conditional<Vectorizable,DoublePacketType,Scalar>::type AccPacket;
EIGEN_STRONG_INLINE void initAcc(Scalar& p) { p = Scalar(0); }
EIGEN_STRONG_INLINE void initAcc(DoublePacketType& p)
{
p.first = pset1<RealPacket>(RealScalar(0));
p.second = pset1<RealPacket>(RealScalar(0));
}
// Scalar path
EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, ResPacket& dest) const
{
dest = pset1<ResPacket>(*b);
}
// Vectorized path
EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, DoublePacketType& dest) const
{
dest.first = pset1<RealPacket>(real(*b));
dest.second = pset1<RealPacket>(imag(*b));
}
EIGEN_STRONG_INLINE void loadRhsQuad(const RhsScalar* b, ResPacket& dest) const
{
loadRhs(b,dest);
}
EIGEN_STRONG_INLINE void loadRhsQuad(const RhsScalar* b, DoublePacketType& dest) const
{
eigen_internal_assert(unpacket_traits<ScalarPacket>::size<=4);
loadRhs(b,dest);
}
EIGEN_STRONG_INLINE void broadcastRhs(const RhsScalar* b, RhsPacket& b0, RhsPacket& b1, RhsPacket& b2, RhsPacket& b3)
{
// FIXME not sure that's the best way to implement it!
loadRhs(b+0, b0);
loadRhs(b+1, b1);
loadRhs(b+2, b2);
loadRhs(b+3, b3);
}
// Vectorized path
EIGEN_STRONG_INLINE void broadcastRhs(const RhsScalar* b, DoublePacketType& b0, DoublePacketType& b1)
{
// FIXME not sure that's the best way to implement it!
loadRhs(b+0, b0);
loadRhs(b+1, b1);
}
// Scalar path
EIGEN_STRONG_INLINE void broadcastRhs(const RhsScalar* b, RhsScalar& b0, RhsScalar& b1)
{
// FIXME not sure that's the best way to implement it!
loadRhs(b+0, b0);
loadRhs(b+1, b1);
}
// nothing special here
EIGEN_STRONG_INLINE void loadLhs(const LhsScalar* a, LhsPacket& dest) const
{
dest = pload<LhsPacket>((const typename unpacket_traits<LhsPacket>::type*)(a));
}
EIGEN_STRONG_INLINE void loadLhsUnaligned(const LhsScalar* a, LhsPacket& dest) const
{
dest = ploadu<LhsPacket>((const typename unpacket_traits<LhsPacket>::type*)(a));
}
EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacket& b, DoublePacketType& c, RhsPacket& /*tmp*/) const
{
c.first = padd(pmul(a,b.first), c.first);
c.second = padd(pmul(a,b.second),c.second);
}
EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacket& b, ResPacket& c, RhsPacket& /*tmp*/) const
{
c = cj.pmadd(a,b,c);
}
EIGEN_STRONG_INLINE void acc(const Scalar& c, const Scalar& alpha, Scalar& r) const { r += alpha * c; }
EIGEN_STRONG_INLINE void acc(const DoublePacketType& c, const ResPacket& alpha, ResPacket& r) const
{
// assemble c
ResPacket tmp;
if((!ConjLhs)&&(!ConjRhs))
{
tmp = pcplxflip(pconj(ResPacket(c.second)));
tmp = padd(ResPacket(c.first),tmp);
}
else if((!ConjLhs)&&(ConjRhs))
{
tmp = pconj(pcplxflip(ResPacket(c.second)));
tmp = padd(ResPacket(c.first),tmp);
}
else if((ConjLhs)&&(!ConjRhs))
{
tmp = pcplxflip(ResPacket(c.second));
tmp = padd(pconj(ResPacket(c.first)),tmp);
}
else if((ConjLhs)&&(ConjRhs))
{
tmp = pcplxflip(ResPacket(c.second));
tmp = psub(pconj(ResPacket(c.first)),tmp);
}
r = pmadd(tmp,alpha,r);
}
protected:
conj_helper<LhsScalar,RhsScalar,ConjLhs,ConjRhs> cj;
};
template<typename RealScalar, bool _ConjRhs>
class gebp_traits<RealScalar, std::complex<RealScalar>, false, _ConjRhs >
{
public:
typedef std::complex<RealScalar> Scalar;
typedef RealScalar LhsScalar;
typedef Scalar RhsScalar;
typedef Scalar ResScalar;
enum {
ConjLhs = false,
ConjRhs = _ConjRhs,
Vectorizable = packet_traits<RealScalar>::Vectorizable
&& packet_traits<Scalar>::Vectorizable,
LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,
RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,
ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1,
NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,
// FIXME: should depend on NumberOfRegisters
nr = 4,
mr = (EIGEN_PLAIN_ENUM_MIN(16,NumberOfRegisters)/2/nr)*ResPacketSize,
LhsProgress = ResPacketSize,
RhsProgress = 1
};
typedef typename packet_traits<LhsScalar>::type _LhsPacket;
typedef typename packet_traits<RhsScalar>::type _RhsPacket;
typedef typename packet_traits<ResScalar>::type _ResPacket;
typedef typename conditional<Vectorizable,_LhsPacket,LhsScalar>::type LhsPacket;
typedef typename conditional<Vectorizable,_RhsPacket,RhsScalar>::type RhsPacket;
typedef typename conditional<Vectorizable,_ResPacket,ResScalar>::type ResPacket;
typedef ResPacket AccPacket;
EIGEN_STRONG_INLINE void initAcc(AccPacket& p)
{
p = pset1<ResPacket>(ResScalar(0));
}
EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacket& dest) const
{
dest = pset1<RhsPacket>(*b);
}
void broadcastRhs(const RhsScalar* b, RhsPacket& b0, RhsPacket& b1, RhsPacket& b2, RhsPacket& b3)
{
pbroadcast4(b, b0, b1, b2, b3);
}
// EIGEN_STRONG_INLINE void broadcastRhs(const RhsScalar* b, RhsPacket& b0, RhsPacket& b1)
// {
// // FIXME not sure that's the best way to implement it!
// b0 = pload1<RhsPacket>(b+0);
// b1 = pload1<RhsPacket>(b+1);
// }
EIGEN_STRONG_INLINE void loadLhs(const LhsScalar* a, LhsPacket& dest) const
{
dest = ploaddup<LhsPacket>(a);
}
EIGEN_STRONG_INLINE void loadRhsQuad(const RhsScalar* b, RhsPacket& dest) const
{
eigen_internal_assert(unpacket_traits<RhsPacket>::size<=4);
loadRhs(b,dest);
}
EIGEN_STRONG_INLINE void loadLhsUnaligned(const LhsScalar* a, LhsPacket& dest) const
{
dest = ploaddup<LhsPacket>(a);
}
EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacket& b, AccPacket& c, RhsPacket& tmp) const
{
madd_impl(a, b, c, tmp, typename conditional<Vectorizable,true_type,false_type>::type());
}
EIGEN_STRONG_INLINE void madd_impl(const LhsPacket& a, const RhsPacket& b, AccPacket& c, RhsPacket& tmp, const true_type&) const
{
#ifdef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
EIGEN_UNUSED_VARIABLE(tmp);
c.v = pmadd(a,b.v,c.v);
#else
tmp = b; tmp.v = pmul(a,tmp.v); c = padd(c,tmp);
#endif
}
EIGEN_STRONG_INLINE void madd_impl(const LhsScalar& a, const RhsScalar& b, ResScalar& c, RhsScalar& /*tmp*/, const false_type&) const
{
c += a * b;
}
EIGEN_STRONG_INLINE void acc(const AccPacket& c, const ResPacket& alpha, ResPacket& r) const
{
r = cj.pmadd(alpha,c,r);
}
protected:
conj_helper<ResPacket,ResPacket,false,ConjRhs> cj;
};
/* optimized GEneral packed Block * packed Panel product kernel
*
* Mixing type logic: C += A * B
* | A | B | comments
* |real |cplx | no vectorization yet, would require to pack A with duplication
* |cplx |real | easy vectorization
*/
template<typename LhsScalar, typename RhsScalar, typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
struct gebp_kernel
{
typedef gebp_traits<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> Traits;
typedef typename Traits::ResScalar ResScalar;
typedef typename Traits::LhsPacket LhsPacket;
typedef typename Traits::RhsPacket RhsPacket;
typedef typename Traits::ResPacket ResPacket;
typedef typename Traits::AccPacket AccPacket;
typedef gebp_traits<RhsScalar,LhsScalar,ConjugateRhs,ConjugateLhs> SwappedTraits;
typedef typename SwappedTraits::ResScalar SResScalar;
typedef typename SwappedTraits::LhsPacket SLhsPacket;
typedef typename SwappedTraits::RhsPacket SRhsPacket;
typedef typename SwappedTraits::ResPacket SResPacket;
typedef typename SwappedTraits::AccPacket SAccPacket;
typedef typename DataMapper::LinearMapper LinearMapper;
enum {
Vectorizable = Traits::Vectorizable,
LhsProgress = Traits::LhsProgress,
RhsProgress = Traits::RhsProgress,
ResPacketSize = Traits::ResPacketSize
};
EIGEN_DONT_INLINE
void operator()(const DataMapper& res, const LhsScalar* blockA, const RhsScalar* blockB,
Index rows, Index depth, Index cols, ResScalar alpha,
Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0);
};
template<typename LhsScalar, typename RhsScalar, typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
EIGEN_DONT_INLINE
void gebp_kernel<LhsScalar,RhsScalar,Index,DataMapper,mr,nr,ConjugateLhs,ConjugateRhs>
::operator()(const DataMapper& res, const LhsScalar* blockA, const RhsScalar* blockB,
Index rows, Index depth, Index cols, ResScalar alpha,
Index strideA, Index strideB, Index offsetA, Index offsetB)
{
Traits traits;
SwappedTraits straits;
if(strideA==-1) strideA = depth;
if(strideB==-1) strideB = depth;
conj_helper<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> cj;
Index packet_cols4 = nr>=4 ? (cols/4) * 4 : 0;
const Index peeled_mc3 = mr>=3*Traits::LhsProgress ? (rows/(3*LhsProgress))*(3*LhsProgress) : 0;
const Index peeled_mc2 = mr>=2*Traits::LhsProgress ? peeled_mc3+((rows-peeled_mc3)/(2*LhsProgress))*(2*LhsProgress) : 0;
const Index peeled_mc1 = mr>=1*Traits::LhsProgress ? (rows/(1*LhsProgress))*(1*LhsProgress) : 0;
enum { pk = 8 }; // NOTE Such a large peeling factor is important for large matrices (~ +5% when >1000 on Haswell)
const Index peeled_kc = depth & ~(pk-1);
const Index prefetch_res_offset = 32/sizeof(ResScalar);
// const Index depth2 = depth & ~1;
//---------- Process 3 * LhsProgress rows at once ----------
// This corresponds to 3*LhsProgress x nr register blocks.
// Usually, make sense only with FMA
if(mr>=3*Traits::LhsProgress)
{
// Here, the general idea is to loop on each largest micro horizontal panel of the lhs (3*Traits::LhsProgress x depth)
// and on each largest micro vertical panel of the rhs (depth * nr).
// Blocking sizes, i.e., 'depth' has been computed so that the micro horizontal panel of the lhs fit in L1.
// However, if depth is too small, we can extend the number of rows of these horizontal panels.
// This actual number of rows is computed as follow:
const Index l1 = defaultL1CacheSize; // in Bytes, TODO, l1 should be passed to this function.
// The max(1, ...) here is needed because we may be using blocking params larger than what our known l1 cache size
// suggests we should be using: either because our known l1 cache size is inaccurate (e.g. on Android, we can only guess),
// or because we are testing specific blocking sizes.
const Index actual_panel_rows = (3*LhsProgress) * std::max<Index>(1,( (l1 - sizeof(ResScalar)*mr*nr - depth*nr*sizeof(RhsScalar)) / (depth * sizeof(LhsScalar) * 3*LhsProgress) ));
for(Index i1=0; i1<peeled_mc3; i1+=actual_panel_rows)
{
const Index actual_panel_end = (std::min)(i1+actual_panel_rows, peeled_mc3);
for(Index j2=0; j2<packet_cols4; j2+=nr)
{
for(Index i=i1; i<actual_panel_end; i+=3*LhsProgress)
{
// We selected a 3*Traits::LhsProgress x nr micro block of res which is entirely
// stored into 3 x nr registers.
const LhsScalar* blA = &blockA[i*strideA+offsetA*(3*LhsProgress)];
prefetch(&blA[0]);
// gets res block as register
AccPacket C0, C1, C2, C3,
C4, C5, C6, C7,
C8, C9, C10, C11;
traits.initAcc(C0); traits.initAcc(C1); traits.initAcc(C2); traits.initAcc(C3);
traits.initAcc(C4); traits.initAcc(C5); traits.initAcc(C6); traits.initAcc(C7);
traits.initAcc(C8); traits.initAcc(C9); traits.initAcc(C10); traits.initAcc(C11);
LinearMapper r0 = res.getLinearMapper(i, j2 + 0);
LinearMapper r1 = res.getLinearMapper(i, j2 + 1);
LinearMapper r2 = res.getLinearMapper(i, j2 + 2);
LinearMapper r3 = res.getLinearMapper(i, j2 + 3);
r0.prefetch(0);
r1.prefetch(0);
r2.prefetch(0);
r3.prefetch(0);
// performs "inner" products
const RhsScalar* blB = &blockB[j2*strideB+offsetB*nr];
prefetch(&blB[0]);
LhsPacket A0, A1;
for(Index k=0; k<peeled_kc; k+=pk)
{
EIGEN_ASM_COMMENT("begin gebp micro kernel 3pX4");
RhsPacket B_0, T0;
LhsPacket A2;
#define EIGEN_GEBP_ONESTEP(K) \
do { \
EIGEN_ASM_COMMENT("begin step of gebp micro kernel 3pX4"); \
EIGEN_ASM_COMMENT("Note: these asm comments work around bug 935!"); \
internal::prefetch(blA+(3*K+16)*LhsProgress); \
if (EIGEN_ARCH_ARM) { internal::prefetch(blB+(4*K+16)*RhsProgress); } /* Bug 953 */ \
traits.loadLhs(&blA[(0+3*K)*LhsProgress], A0); \
traits.loadLhs(&blA[(1+3*K)*LhsProgress], A1); \
traits.loadLhs(&blA[(2+3*K)*LhsProgress], A2); \
traits.loadRhs(blB + (0+4*K)*Traits::RhsProgress, B_0); \
traits.madd(A0, B_0, C0, T0); \
traits.madd(A1, B_0, C4, T0); \
traits.madd(A2, B_0, C8, B_0); \
traits.loadRhs(blB + (1+4*K)*Traits::RhsProgress, B_0); \
traits.madd(A0, B_0, C1, T0); \
traits.madd(A1, B_0, C5, T0); \
traits.madd(A2, B_0, C9, B_0); \
traits.loadRhs(blB + (2+4*K)*Traits::RhsProgress, B_0); \
traits.madd(A0, B_0, C2, T0); \
traits.madd(A1, B_0, C6, T0); \
traits.madd(A2, B_0, C10, B_0); \
traits.loadRhs(blB + (3+4*K)*Traits::RhsProgress, B_0); \
traits.madd(A0, B_0, C3 , T0); \
traits.madd(A1, B_0, C7, T0); \
traits.madd(A2, B_0, C11, B_0); \
EIGEN_ASM_COMMENT("end step of gebp micro kernel 3pX4"); \
} while(false)
internal::prefetch(blB);
EIGEN_GEBP_ONESTEP(0);
EIGEN_GEBP_ONESTEP(1);
EIGEN_GEBP_ONESTEP(2);
EIGEN_GEBP_ONESTEP(3);
EIGEN_GEBP_ONESTEP(4);
EIGEN_GEBP_ONESTEP(5);
EIGEN_GEBP_ONESTEP(6);
EIGEN_GEBP_ONESTEP(7);
blB += pk*4*RhsProgress;
blA += pk*3*Traits::LhsProgress;
EIGEN_ASM_COMMENT("end gebp micro kernel 3pX4");
}
// process remaining peeled loop
for(Index k=peeled_kc; k<depth; k++)
{
RhsPacket B_0, T0;
LhsPacket A2;
EIGEN_GEBP_ONESTEP(0);
blB += 4*RhsProgress;
blA += 3*Traits::LhsProgress;
}
#undef EIGEN_GEBP_ONESTEP
ResPacket R0, R1, R2;
ResPacket alphav = pset1<ResPacket>(alpha);
R0 = r0.loadPacket(0 * Traits::ResPacketSize);
R1 = r0.loadPacket(1 * Traits::ResPacketSize);
R2 = r0.loadPacket(2 * Traits::ResPacketSize);
traits.acc(C0, alphav, R0);
traits.acc(C4, alphav, R1);
traits.acc(C8, alphav, R2);
r0.storePacket(0 * Traits::ResPacketSize, R0);
r0.storePacket(1 * Traits::ResPacketSize, R1);
r0.storePacket(2 * Traits::ResPacketSize, R2);
R0 = r1.loadPacket(0 * Traits::ResPacketSize);
R1 = r1.loadPacket(1 * Traits::ResPacketSize);
R2 = r1.loadPacket(2 * Traits::ResPacketSize);
traits.acc(C1, alphav, R0);
traits.acc(C5, alphav, R1);
traits.acc(C9, alphav, R2);
r1.storePacket(0 * Traits::ResPacketSize, R0);
r1.storePacket(1 * Traits::ResPacketSize, R1);
r1.storePacket(2 * Traits::ResPacketSize, R2);
R0 = r2.loadPacket(0 * Traits::ResPacketSize);
R1 = r2.loadPacket(1 * Traits::ResPacketSize);
R2 = r2.loadPacket(2 * Traits::ResPacketSize);
traits.acc(C2, alphav, R0);
traits.acc(C6, alphav, R1);
traits.acc(C10, alphav, R2);
r2.storePacket(0 * Traits::ResPacketSize, R0);
r2.storePacket(1 * Traits::ResPacketSize, R1);
r2.storePacket(2 * Traits::ResPacketSize, R2);
R0 = r3.loadPacket(0 * Traits::ResPacketSize);
R1 = r3.loadPacket(1 * Traits::ResPacketSize);
R2 = r3.loadPacket(2 * Traits::ResPacketSize);
traits.acc(C3, alphav, R0);
traits.acc(C7, alphav, R1);
traits.acc(C11, alphav, R2);
r3.storePacket(0 * Traits::ResPacketSize, R0);
r3.storePacket(1 * Traits::ResPacketSize, R1);
r3.storePacket(2 * Traits::ResPacketSize, R2);
}
}
// Deal with remaining columns of the rhs
for(Index j2=packet_cols4; j2<cols; j2++)
{
for(Index i=i1; i<actual_panel_end; i+=3*LhsProgress)
{
// One column at a time
const LhsScalar* blA = &blockA[i*strideA+offsetA*(3*Traits::LhsProgress)];
prefetch(&blA[0]);
// gets res block as register
AccPacket C0, C4, C8;
traits.initAcc(C0);
traits.initAcc(C4);
traits.initAcc(C8);
LinearMapper r0 = res.getLinearMapper(i, j2);
r0.prefetch(0);
// performs "inner" products
const RhsScalar* blB = &blockB[j2*strideB+offsetB];
LhsPacket A0, A1, A2;
for(Index k=0; k<peeled_kc; k+=pk)
{
EIGEN_ASM_COMMENT("begin gebp micro kernel 3pX1");
RhsPacket B_0;
#define EIGEN_GEBGP_ONESTEP(K) \
do { \
EIGEN_ASM_COMMENT("begin step of gebp micro kernel 3pX1"); \
EIGEN_ASM_COMMENT("Note: these asm comments work around bug 935!"); \
traits.loadLhs(&blA[(0+3*K)*LhsProgress], A0); \
traits.loadLhs(&blA[(1+3*K)*LhsProgress], A1); \
traits.loadLhs(&blA[(2+3*K)*LhsProgress], A2); \
traits.loadRhs(&blB[(0+K)*RhsProgress], B_0); \
traits.madd(A0, B_0, C0, B_0); \
traits.madd(A1, B_0, C4, B_0); \
traits.madd(A2, B_0, C8, B_0); \
EIGEN_ASM_COMMENT("end step of gebp micro kernel 3pX1"); \
} while(false)
EIGEN_GEBGP_ONESTEP(0);
EIGEN_GEBGP_ONESTEP(1);
EIGEN_GEBGP_ONESTEP(2);
EIGEN_GEBGP_ONESTEP(3);
EIGEN_GEBGP_ONESTEP(4);
EIGEN_GEBGP_ONESTEP(5);
EIGEN_GEBGP_ONESTEP(6);
EIGEN_GEBGP_ONESTEP(7);
blB += pk*RhsProgress;
blA += pk*3*Traits::LhsProgress;
EIGEN_ASM_COMMENT("end gebp micro kernel 3pX1");
}
// process remaining peeled loop
for(Index k=peeled_kc; k<depth; k++)
{
RhsPacket B_0;
EIGEN_GEBGP_ONESTEP(0);
blB += RhsProgress;
blA += 3*Traits::LhsProgress;
}
#undef EIGEN_GEBGP_ONESTEP
ResPacket R0, R1, R2;
ResPacket alphav = pset1<ResPacket>(alpha);
R0 = r0.loadPacket(0 * Traits::ResPacketSize);
R1 = r0.loadPacket(1 * Traits::ResPacketSize);
R2 = r0.loadPacket(2 * Traits::ResPacketSize);
traits.acc(C0, alphav, R0);
traits.acc(C4, alphav, R1);
traits.acc(C8, alphav, R2);
r0.storePacket(0 * Traits::ResPacketSize, R0);
r0.storePacket(1 * Traits::ResPacketSize, R1);
r0.storePacket(2 * Traits::ResPacketSize, R2);
}
}
}
}
//---------- Process 2 * LhsProgress rows at once ----------
if(mr>=2*Traits::LhsProgress)
{
const Index l1 = defaultL1CacheSize; // in Bytes, TODO, l1 should be passed to this function.
// The max(1, ...) here is needed because we may be using blocking params larger than what our known l1 cache size
// suggests we should be using: either because our known l1 cache size is inaccurate (e.g. on Android, we can only guess),
// or because we are testing specific blocking sizes.
Index actual_panel_rows = (2*LhsProgress) * std::max<Index>(1,( (l1 - sizeof(ResScalar)*mr*nr - depth*nr*sizeof(RhsScalar)) / (depth * sizeof(LhsScalar) * 2*LhsProgress) ));
for(Index i1=peeled_mc3; i1<peeled_mc2; i1+=actual_panel_rows)
{
Index actual_panel_end = (std::min)(i1+actual_panel_rows, peeled_mc2);
for(Index j2=0; j2<packet_cols4; j2+=nr)
{
for(Index i=i1; i<actual_panel_end; i+=2*LhsProgress)
{
// We selected a 2*Traits::LhsProgress x nr micro block of res which is entirely
// stored into 2 x nr registers.
const LhsScalar* blA = &blockA[i*strideA+offsetA*(2*Traits::LhsProgress)];
prefetch(&blA[0]);
// gets res block as register
AccPacket C0, C1, C2, C3,
C4, C5, C6, C7;
traits.initAcc(C0); traits.initAcc(C1); traits.initAcc(C2); traits.initAcc(C3);
traits.initAcc(C4); traits.initAcc(C5); traits.initAcc(C6); traits.initAcc(C7);
LinearMapper r0 = res.getLinearMapper(i, j2 + 0);
LinearMapper r1 = res.getLinearMapper(i, j2 + 1);
LinearMapper r2 = res.getLinearMapper(i, j2 + 2);
LinearMapper r3 = res.getLinearMapper(i, j2 + 3);
r0.prefetch(prefetch_res_offset);
r1.prefetch(prefetch_res_offset);
r2.prefetch(prefetch_res_offset);
r3.prefetch(prefetch_res_offset);
// performs "inner" products
const RhsScalar* blB = &blockB[j2*strideB+offsetB*nr];
prefetch(&blB[0]);
LhsPacket A0, A1;
for(Index k=0; k<peeled_kc; k+=pk)
{
EIGEN_ASM_COMMENT("begin gebp micro kernel 2pX4");
RhsPacket B_0, B1, B2, B3, T0;
// NOTE: the begin/end asm comments below work around bug 935!
// but they are not enough for gcc>=6 without FMA (bug 1637)
#if EIGEN_GNUC_AT_LEAST(6,0) && defined(EIGEN_VECTORIZE_SSE)
#define EIGEN_GEBP_2PX4_SPILLING_WORKAROUND __asm__ ("" : [a0] "+x,m" (A0),[a1] "+x,m" (A1));
#else
#define EIGEN_GEBP_2PX4_SPILLING_WORKAROUND
#endif
#define EIGEN_GEBGP_ONESTEP(K) \
do { \
EIGEN_ASM_COMMENT("begin step of gebp micro kernel 2pX4"); \
traits.loadLhs(&blA[(0+2*K)*LhsProgress], A0); \
traits.loadLhs(&blA[(1+2*K)*LhsProgress], A1); \
traits.broadcastRhs(&blB[(0+4*K)*RhsProgress], B_0, B1, B2, B3); \
traits.madd(A0, B_0, C0, T0); \
traits.madd(A1, B_0, C4, B_0); \
traits.madd(A0, B1, C1, T0); \
traits.madd(A1, B1, C5, B1); \
traits.madd(A0, B2, C2, T0); \
traits.madd(A1, B2, C6, B2); \
traits.madd(A0, B3, C3, T0); \
traits.madd(A1, B3, C7, B3); \
EIGEN_GEBP_2PX4_SPILLING_WORKAROUND \
EIGEN_ASM_COMMENT("end step of gebp micro kernel 2pX4"); \
} while(false)
internal::prefetch(blB+(48+0));
EIGEN_GEBGP_ONESTEP(0);
EIGEN_GEBGP_ONESTEP(1);
EIGEN_GEBGP_ONESTEP(2);
EIGEN_GEBGP_ONESTEP(3);
internal::prefetch(blB+(48+16));
EIGEN_GEBGP_ONESTEP(4);
EIGEN_GEBGP_ONESTEP(5);
EIGEN_GEBGP_ONESTEP(6);
EIGEN_GEBGP_ONESTEP(7);
blB += pk*4*RhsProgress;
blA += pk*(2*Traits::LhsProgress);
EIGEN_ASM_COMMENT("end gebp micro kernel 2pX4");
}
// process remaining peeled loop
for(Index k=peeled_kc; k<depth; k++)
{
RhsPacket B_0, B1, B2, B3, T0;
EIGEN_GEBGP_ONESTEP(0);
blB += 4*RhsProgress;
blA += 2*Traits::LhsProgress;
}
#undef EIGEN_GEBGP_ONESTEP
ResPacket R0, R1, R2, R3;
ResPacket alphav = pset1<ResPacket>(alpha);
R0 = r0.loadPacket(0 * Traits::ResPacketSize);
R1 = r0.loadPacket(1 * Traits::ResPacketSize);
R2 = r1.loadPacket(0 * Traits::ResPacketSize);
R3 = r1.loadPacket(1 * Traits::ResPacketSize);
traits.acc(C0, alphav, R0);
traits.acc(C4, alphav, R1);
traits.acc(C1, alphav, R2);
traits.acc(C5, alphav, R3);
r0.storePacket(0 * Traits::ResPacketSize, R0);
r0.storePacket(1 * Traits::ResPacketSize, R1);
r1.storePacket(0 * Traits::ResPacketSize, R2);
r1.storePacket(1 * Traits::ResPacketSize, R3);
R0 = r2.loadPacket(0 * Traits::ResPacketSize);
R1 = r2.loadPacket(1 * Traits::ResPacketSize);
R2 = r3.loadPacket(0 * Traits::ResPacketSize);
R3 = r3.loadPacket(1 * Traits::ResPacketSize);
traits.acc(C2, alphav, R0);
traits.acc(C6, alphav, R1);
traits.acc(C3, alphav, R2);
traits.acc(C7, alphav, R3);
r2.storePacket(0 * Traits::ResPacketSize, R0);
r2.storePacket(1 * Traits::ResPacketSize, R1);
r3.storePacket(0 * Traits::ResPacketSize, R2);
r3.storePacket(1 * Traits::ResPacketSize, R3);
}
}
// Deal with remaining columns of the rhs
for(Index j2=packet_cols4; j2<cols; j2++)
{
for(Index i=i1; i<actual_panel_end; i+=2*LhsProgress)
{
// One column at a time
const LhsScalar* blA = &blockA[i*strideA+offsetA*(2*Traits::LhsProgress)];
prefetch(&blA[0]);
// gets res block as register
AccPacket C0, C4;
traits.initAcc(C0);
traits.initAcc(C4);
LinearMapper r0 = res.getLinearMapper(i, j2);
r0.prefetch(prefetch_res_offset);
// performs "inner" products
const RhsScalar* blB = &blockB[j2*strideB+offsetB];
LhsPacket A0, A1;
for(Index k=0; k<peeled_kc; k+=pk)
{
EIGEN_ASM_COMMENT("begin gebp micro kernel 2pX1");
RhsPacket B_0, B1;
#define EIGEN_GEBGP_ONESTEP(K) \
do { \
EIGEN_ASM_COMMENT("begin step of gebp micro kernel 2pX1"); \
EIGEN_ASM_COMMENT("Note: these asm comments work around bug 935!"); \
traits.loadLhs(&blA[(0+2*K)*LhsProgress], A0); \
traits.loadLhs(&blA[(1+2*K)*LhsProgress], A1); \
traits.loadRhs(&blB[(0+K)*RhsProgress], B_0); \
traits.madd(A0, B_0, C0, B1); \
traits.madd(A1, B_0, C4, B_0); \
EIGEN_ASM_COMMENT("end step of gebp micro kernel 2pX1"); \
} while(false)
EIGEN_GEBGP_ONESTEP(0);
EIGEN_GEBGP_ONESTEP(1);
EIGEN_GEBGP_ONESTEP(2);
EIGEN_GEBGP_ONESTEP(3);
EIGEN_GEBGP_ONESTEP(4);
EIGEN_GEBGP_ONESTEP(5);
EIGEN_GEBGP_ONESTEP(6);
EIGEN_GEBGP_ONESTEP(7);
blB += pk*RhsProgress;
blA += pk*2*Traits::LhsProgress;
EIGEN_ASM_COMMENT("end gebp micro kernel 2pX1");
}
// process remaining peeled loop
for(Index k=peeled_kc; k<depth; k++)
{
RhsPacket B_0, B1;
EIGEN_GEBGP_ONESTEP(0);
blB += RhsProgress;
blA += 2*Traits::LhsProgress;
}
#undef EIGEN_GEBGP_ONESTEP
ResPacket R0, R1;
ResPacket alphav = pset1<ResPacket>(alpha);
R0 = r0.loadPacket(0 * Traits::ResPacketSize);
R1 = r0.loadPacket(1 * Traits::ResPacketSize);
traits.acc(C0, alphav, R0);
traits.acc(C4, alphav, R1);
r0.storePacket(0 * Traits::ResPacketSize, R0);
r0.storePacket(1 * Traits::ResPacketSize, R1);
}
}
}
}
//---------- Process 1 * LhsProgress rows at once ----------
if(mr>=1*Traits::LhsProgress)
{
// loops on each largest micro horizontal panel of lhs (1*LhsProgress x depth)
for(Index i=peeled_mc2; i<peeled_mc1; i+=1*LhsProgress)
{
// loops on each largest micro vertical panel of rhs (depth * nr)
for(Index j2=0; j2<packet_cols4; j2+=nr)
{
// We select a 1*Traits::LhsProgress x nr micro block of res which is entirely
// stored into 1 x nr registers.
const LhsScalar* blA = &blockA[i*strideA+offsetA*(1*Traits::LhsProgress)];
prefetch(&blA[0]);
// gets res block as register
AccPacket C0, C1, C2, C3;
traits.initAcc(C0);
traits.initAcc(C1);
traits.initAcc(C2);
traits.initAcc(C3);
LinearMapper r0 = res.getLinearMapper(i, j2 + 0);
LinearMapper r1 = res.getLinearMapper(i, j2 + 1);
LinearMapper r2 = res.getLinearMapper(i, j2 + 2);
LinearMapper r3 = res.getLinearMapper(i, j2 + 3);
r0.prefetch(prefetch_res_offset);
r1.prefetch(prefetch_res_offset);
r2.prefetch(prefetch_res_offset);
r3.prefetch(prefetch_res_offset);
// performs "inner" products
const RhsScalar* blB = &blockB[j2*strideB+offsetB*nr];
prefetch(&blB[0]);
LhsPacket A0;
for(Index k=0; k<peeled_kc; k+=pk)
{
EIGEN_ASM_COMMENT("begin gebp micro kernel 1pX4");
RhsPacket B_0, B1, B2, B3;
#define EIGEN_GEBGP_ONESTEP(K) \
do { \
EIGEN_ASM_COMMENT("begin step of gebp micro kernel 1pX4"); \
EIGEN_ASM_COMMENT("Note: these asm comments work around bug 935!"); \
traits.loadLhs(&blA[(0+1*K)*LhsProgress], A0); \
traits.broadcastRhs(&blB[(0+4*K)*RhsProgress], B_0, B1, B2, B3); \
traits.madd(A0, B_0, C0, B_0); \
traits.madd(A0, B1, C1, B1); \
traits.madd(A0, B2, C2, B2); \
traits.madd(A0, B3, C3, B3); \
EIGEN_ASM_COMMENT("end step of gebp micro kernel 1pX4"); \
} while(false)
internal::prefetch(blB+(48+0));
EIGEN_GEBGP_ONESTEP(0);
EIGEN_GEBGP_ONESTEP(1);
EIGEN_GEBGP_ONESTEP(2);
EIGEN_GEBGP_ONESTEP(3);
internal::prefetch(blB+(48+16));
EIGEN_GEBGP_ONESTEP(4);
EIGEN_GEBGP_ONESTEP(5);
EIGEN_GEBGP_ONESTEP(6);
EIGEN_GEBGP_ONESTEP(7);
blB += pk*4*RhsProgress;
blA += pk*1*LhsProgress;
EIGEN_ASM_COMMENT("end gebp micro kernel 1pX4");
}
// process remaining peeled loop
for(Index k=peeled_kc; k<depth; k++)
{
RhsPacket B_0, B1, B2, B3;
EIGEN_GEBGP_ONESTEP(0);
blB += 4*RhsProgress;
blA += 1*LhsProgress;
}
#undef EIGEN_GEBGP_ONESTEP
ResPacket R0, R1;
ResPacket alphav = pset1<ResPacket>(alpha);
R0 = r0.loadPacket(0 * Traits::ResPacketSize);
R1 = r1.loadPacket(0 * Traits::ResPacketSize);
traits.acc(C0, alphav, R0);
traits.acc(C1, alphav, R1);
r0.storePacket(0 * Traits::ResPacketSize, R0);
r1.storePacket(0 * Traits::ResPacketSize, R1);
R0 = r2.loadPacket(0 * Traits::ResPacketSize);
R1 = r3.loadPacket(0 * Traits::ResPacketSize);
traits.acc(C2, alphav, R0);
traits.acc(C3, alphav, R1);
r2.storePacket(0 * Traits::ResPacketSize, R0);
r3.storePacket(0 * Traits::ResPacketSize, R1);
}
// Deal with remaining columns of the rhs
for(Index j2=packet_cols4; j2<cols; j2++)
{
// One column at a time
const LhsScalar* blA = &blockA[i*strideA+offsetA*(1*Traits::LhsProgress)];
prefetch(&blA[0]);
// gets res block as register
AccPacket C0;
traits.initAcc(C0);
LinearMapper r0 = res.getLinearMapper(i, j2);
// performs "inner" products
const RhsScalar* blB = &blockB[j2*strideB+offsetB];
LhsPacket A0;
for(Index k=0; k<peeled_kc; k+=pk)
{
EIGEN_ASM_COMMENT("begin gebp micro kernel 1pX1");
RhsPacket B_0;
#define EIGEN_GEBGP_ONESTEP(K) \
do { \
EIGEN_ASM_COMMENT("begin step of gebp micro kernel 1pX1"); \
EIGEN_ASM_COMMENT("Note: these asm comments work around bug 935!"); \
traits.loadLhs(&blA[(0+1*K)*LhsProgress], A0); \
traits.loadRhs(&blB[(0+K)*RhsProgress], B_0); \
traits.madd(A0, B_0, C0, B_0); \
EIGEN_ASM_COMMENT("end step of gebp micro kernel 1pX1"); \
} while(false);
EIGEN_GEBGP_ONESTEP(0);
EIGEN_GEBGP_ONESTEP(1);
EIGEN_GEBGP_ONESTEP(2);
EIGEN_GEBGP_ONESTEP(3);
EIGEN_GEBGP_ONESTEP(4);
EIGEN_GEBGP_ONESTEP(5);
EIGEN_GEBGP_ONESTEP(6);
EIGEN_GEBGP_ONESTEP(7);
blB += pk*RhsProgress;
blA += pk*1*Traits::LhsProgress;
EIGEN_ASM_COMMENT("end gebp micro kernel 1pX1");
}
// process remaining peeled loop
for(Index k=peeled_kc; k<depth; k++)
{
RhsPacket B_0;
EIGEN_GEBGP_ONESTEP(0);
blB += RhsProgress;
blA += 1*Traits::LhsProgress;
}
#undef EIGEN_GEBGP_ONESTEP
ResPacket R0;
ResPacket alphav = pset1<ResPacket>(alpha);
R0 = r0.loadPacket(0 * Traits::ResPacketSize);
traits.acc(C0, alphav, R0);
r0.storePacket(0 * Traits::ResPacketSize, R0);
}
}
}
//---------- Process remaining rows, 1 at once ----------
if(peeled_mc1<rows)
{
// loop on each panel of the rhs
for(Index j2=0; j2<packet_cols4; j2+=nr)
{
// loop on each row of the lhs (1*LhsProgress x depth)
for(Index i=peeled_mc1; i<rows; i+=1)
{
const LhsScalar* blA = &blockA[i*strideA+offsetA];
prefetch(&blA[0]);
const RhsScalar* blB = &blockB[j2*strideB+offsetB*nr];
// The following piece of code wont work for 512 bit registers
// Moreover, if LhsProgress==8 it assumes that there is a half packet of the same size
// as nr (which is currently 4) for the return type.
const int SResPacketHalfSize = unpacket_traits<typename unpacket_traits<SResPacket>::half>::size;
if ((SwappedTraits::LhsProgress % 4) == 0 &&
(SwappedTraits::LhsProgress <= 8) &&
(SwappedTraits::LhsProgress!=8 || SResPacketHalfSize==nr))
{
SAccPacket C0, C1, C2, C3;
straits.initAcc(C0);
straits.initAcc(C1);
straits.initAcc(C2);
straits.initAcc(C3);
const Index spk = (std::max)(1,SwappedTraits::LhsProgress/4);
const Index endk = (depth/spk)*spk;
const Index endk4 = (depth/(spk*4))*(spk*4);
Index k=0;
for(; k<endk4; k+=4*spk)
{
SLhsPacket A0,A1;
SRhsPacket B_0,B_1;
straits.loadLhsUnaligned(blB+0*SwappedTraits::LhsProgress, A0);
straits.loadLhsUnaligned(blB+1*SwappedTraits::LhsProgress, A1);
straits.loadRhsQuad(blA+0*spk, B_0);
straits.loadRhsQuad(blA+1*spk, B_1);
straits.madd(A0,B_0,C0,B_0);
straits.madd(A1,B_1,C1,B_1);
straits.loadLhsUnaligned(blB+2*SwappedTraits::LhsProgress, A0);
straits.loadLhsUnaligned(blB+3*SwappedTraits::LhsProgress, A1);
straits.loadRhsQuad(blA+2*spk, B_0);
straits.loadRhsQuad(blA+3*spk, B_1);
straits.madd(A0,B_0,C2,B_0);
straits.madd(A1,B_1,C3,B_1);
blB += 4*SwappedTraits::LhsProgress;
blA += 4*spk;
}
C0 = padd(padd(C0,C1),padd(C2,C3));
for(; k<endk; k+=spk)
{
SLhsPacket A0;
SRhsPacket B_0;
straits.loadLhsUnaligned(blB, A0);
straits.loadRhsQuad(blA, B_0);
straits.madd(A0,B_0,C0,B_0);
blB += SwappedTraits::LhsProgress;
blA += spk;
}
if(SwappedTraits::LhsProgress==8)
{
// Special case where we have to first reduce the accumulation register C0
typedef typename conditional<SwappedTraits::LhsProgress>=8,typename unpacket_traits<SResPacket>::half,SResPacket>::type SResPacketHalf;
typedef typename conditional<SwappedTraits::LhsProgress>=8,typename unpacket_traits<SLhsPacket>::half,SLhsPacket>::type SLhsPacketHalf;
typedef typename conditional<SwappedTraits::LhsProgress>=8,typename unpacket_traits<SLhsPacket>::half,SRhsPacket>::type SRhsPacketHalf;
typedef typename conditional<SwappedTraits::LhsProgress>=8,typename unpacket_traits<SAccPacket>::half,SAccPacket>::type SAccPacketHalf;
SResPacketHalf R = res.template gatherPacket<SResPacketHalf>(i, j2);
SResPacketHalf alphav = pset1<SResPacketHalf>(alpha);
if(depth-endk>0)
{
// We have to handle the last row of the rhs which corresponds to a half-packet
SLhsPacketHalf a0;
SRhsPacketHalf b0;
straits.loadLhsUnaligned(blB, a0);
straits.loadRhs(blA, b0);
SAccPacketHalf c0 = predux_downto4(C0);
straits.madd(a0,b0,c0,b0);
straits.acc(c0, alphav, R);
}
else
{
straits.acc(predux_downto4(C0), alphav, R);
}
res.scatterPacket(i, j2, R);
}
else
{
SResPacket R = res.template gatherPacket<SResPacket>(i, j2);
SResPacket alphav = pset1<SResPacket>(alpha);
straits.acc(C0, alphav, R);
res.scatterPacket(i, j2, R);
}
}
else // scalar path
{
// get a 1 x 4 res block as registers
ResScalar C0(0), C1(0), C2(0), C3(0);
for(Index k=0; k<depth; k++)
{
LhsScalar A0;
RhsScalar B_0, B_1;
A0 = blA[k];
B_0 = blB[0];
B_1 = blB[1];
CJMADD(cj,A0,B_0,C0, B_0);
CJMADD(cj,A0,B_1,C1, B_1);
B_0 = blB[2];
B_1 = blB[3];
CJMADD(cj,A0,B_0,C2, B_0);
CJMADD(cj,A0,B_1,C3, B_1);
blB += 4;
}
res(i, j2 + 0) += alpha * C0;
res(i, j2 + 1) += alpha * C1;
res(i, j2 + 2) += alpha * C2;
res(i, j2 + 3) += alpha * C3;
}
}
}
// remaining columns
for(Index j2=packet_cols4; j2<cols; j2++)
{
// loop on each row of the lhs (1*LhsProgress x depth)
for(Index i=peeled_mc1; i<rows; i+=1)
{
const LhsScalar* blA = &blockA[i*strideA+offsetA];
prefetch(&blA[0]);
// gets a 1 x 1 res block as registers
ResScalar C0(0);
const RhsScalar* blB = &blockB[j2*strideB+offsetB];
for(Index k=0; k<depth; k++)
{
LhsScalar A0 = blA[k];
RhsScalar B_0 = blB[k];
CJMADD(cj, A0, B_0, C0, B_0);
}
res(i, j2) += alpha * C0;
}
}
}
}
#undef CJMADD
// pack a block of the lhs
// The traversal is as follow (mr==4):
// 0 4 8 12 ...
// 1 5 9 13 ...
// 2 6 10 14 ...
// 3 7 11 15 ...
//
// 16 20 24 28 ...
// 17 21 25 29 ...
// 18 22 26 30 ...
// 19 23 27 31 ...
//
// 32 33 34 35 ...
// 36 36 38 39 ...
template<typename Scalar, typename Index, typename DataMapper, int Pack1, int Pack2, bool Conjugate, bool PanelMode>
struct gemm_pack_lhs<Scalar, Index, DataMapper, Pack1, Pack2, ColMajor, Conjugate, PanelMode>
{
typedef typename DataMapper::LinearMapper LinearMapper;
EIGEN_DONT_INLINE void operator()(Scalar* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride=0, Index offset=0);
};
template<typename Scalar, typename Index, typename DataMapper, int Pack1, int Pack2, bool Conjugate, bool PanelMode>
EIGEN_DONT_INLINE void gemm_pack_lhs<Scalar, Index, DataMapper, Pack1, Pack2, ColMajor, Conjugate, PanelMode>
::operator()(Scalar* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
{
typedef typename packet_traits<Scalar>::type Packet;
enum { PacketSize = packet_traits<Scalar>::size };
EIGEN_ASM_COMMENT("EIGEN PRODUCT PACK LHS");
EIGEN_UNUSED_VARIABLE(stride);
EIGEN_UNUSED_VARIABLE(offset);
eigen_assert(((!PanelMode) && stride==0 && offset==0) || (PanelMode && stride>=depth && offset<=stride));
eigen_assert( ((Pack1%PacketSize)==0 && Pack1<=4*PacketSize) || (Pack1<=4) );
conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
Index count = 0;
const Index peeled_mc3 = Pack1>=3*PacketSize ? (rows/(3*PacketSize))*(3*PacketSize) : 0;
const Index peeled_mc2 = Pack1>=2*PacketSize ? peeled_mc3+((rows-peeled_mc3)/(2*PacketSize))*(2*PacketSize) : 0;
const Index peeled_mc1 = Pack1>=1*PacketSize ? (rows/(1*PacketSize))*(1*PacketSize) : 0;
const Index peeled_mc0 = Pack2>=1*PacketSize ? peeled_mc1
: Pack2>1 ? (rows/Pack2)*Pack2 : 0;
Index i=0;
// Pack 3 packets
if(Pack1>=3*PacketSize)
{
for(; i<peeled_mc3; i+=3*PacketSize)
{
if(PanelMode) count += (3*PacketSize) * offset;
for(Index k=0; k<depth; k++)
{
Packet A, B, C;
A = lhs.loadPacket(i+0*PacketSize, k);
B = lhs.loadPacket(i+1*PacketSize, k);
C = lhs.loadPacket(i+2*PacketSize, k);
pstore(blockA+count, cj.pconj(A)); count+=PacketSize;
pstore(blockA+count, cj.pconj(B)); count+=PacketSize;
pstore(blockA+count, cj.pconj(C)); count+=PacketSize;
}
if(PanelMode) count += (3*PacketSize) * (stride-offset-depth);
}
}
// Pack 2 packets
if(Pack1>=2*PacketSize)
{
for(; i<peeled_mc2; i+=2*PacketSize)
{
if(PanelMode) count += (2*PacketSize) * offset;
for(Index k=0; k<depth; k++)
{
Packet A, B;
A = lhs.loadPacket(i+0*PacketSize, k);
B = lhs.loadPacket(i+1*PacketSize, k);
pstore(blockA+count, cj.pconj(A)); count+=PacketSize;
pstore(blockA+count, cj.pconj(B)); count+=PacketSize;
}
if(PanelMode) count += (2*PacketSize) * (stride-offset-depth);
}
}
// Pack 1 packets
if(Pack1>=1*PacketSize)
{
for(; i<peeled_mc1; i+=1*PacketSize)
{
if(PanelMode) count += (1*PacketSize) * offset;
for(Index k=0; k<depth; k++)
{
Packet A;
A = lhs.loadPacket(i+0*PacketSize, k);
pstore(blockA+count, cj.pconj(A));
count+=PacketSize;
}
if(PanelMode) count += (1*PacketSize) * (stride-offset-depth);
}
}
// Pack scalars
if(Pack2<PacketSize && Pack2>1)
{
for(; i<peeled_mc0; i+=Pack2)
{
if(PanelMode) count += Pack2 * offset;
for(Index k=0; k<depth; k++)
for(Index w=0; w<Pack2; w++)
blockA[count++] = cj(lhs(i+w, k));
if(PanelMode) count += Pack2 * (stride-offset-depth);
}
}
for(; i<rows; i++)
{
if(PanelMode) count += offset;
for(Index k=0; k<depth; k++)
blockA[count++] = cj(lhs(i, k));
if(PanelMode) count += (stride-offset-depth);
}
}
template<typename Scalar, typename Index, typename DataMapper, int Pack1, int Pack2, bool Conjugate, bool PanelMode>
struct gemm_pack_lhs<Scalar, Index, DataMapper, Pack1, Pack2, RowMajor, Conjugate, PanelMode>
{
typedef typename DataMapper::LinearMapper LinearMapper;
EIGEN_DONT_INLINE void operator()(Scalar* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride=0, Index offset=0);
};
template<typename Scalar, typename Index, typename DataMapper, int Pack1, int Pack2, bool Conjugate, bool PanelMode>
EIGEN_DONT_INLINE void gemm_pack_lhs<Scalar, Index, DataMapper, Pack1, Pack2, RowMajor, Conjugate, PanelMode>
::operator()(Scalar* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
{
typedef typename packet_traits<Scalar>::type Packet;
enum { PacketSize = packet_traits<Scalar>::size };
EIGEN_ASM_COMMENT("EIGEN PRODUCT PACK LHS");
EIGEN_UNUSED_VARIABLE(stride);
EIGEN_UNUSED_VARIABLE(offset);
eigen_assert(((!PanelMode) && stride==0 && offset==0) || (PanelMode && stride>=depth && offset<=stride));
conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
Index count = 0;
// const Index peeled_mc3 = Pack1>=3*PacketSize ? (rows/(3*PacketSize))*(3*PacketSize) : 0;
// const Index peeled_mc2 = Pack1>=2*PacketSize ? peeled_mc3+((rows-peeled_mc3)/(2*PacketSize))*(2*PacketSize) : 0;
// const Index peeled_mc1 = Pack1>=1*PacketSize ? (rows/(1*PacketSize))*(1*PacketSize) : 0;
int pack = Pack1;
Index i = 0;
while(pack>0)
{
Index remaining_rows = rows-i;
Index peeled_mc = i+(remaining_rows/pack)*pack;
for(; i<peeled_mc; i+=pack)
{
if(PanelMode) count += pack * offset;
const Index peeled_k = (depth/PacketSize)*PacketSize;
Index k=0;
if(pack>=PacketSize)
{
for(; k<peeled_k; k+=PacketSize)
{
for (Index m = 0; m < pack; m += PacketSize)
{
PacketBlock<Packet> kernel;
for (int p = 0; p < PacketSize; ++p) kernel.packet[p] = lhs.loadPacket(i+p+m, k);
ptranspose(kernel);
for (int p = 0; p < PacketSize; ++p) pstore(blockA+count+m+(pack)*p, cj.pconj(kernel.packet[p]));
}
count += PacketSize*pack;
}
}
for(; k<depth; k++)
{
Index w=0;
for(; w<pack-3; w+=4)
{
Scalar a(cj(lhs(i+w+0, k))),
b(cj(lhs(i+w+1, k))),
c(cj(lhs(i+w+2, k))),
d(cj(lhs(i+w+3, k)));
blockA[count++] = a;
blockA[count++] = b;
blockA[count++] = c;
blockA[count++] = d;
}
if(pack%4)
for(;w<pack;++w)
blockA[count++] = cj(lhs(i+w, k));
}
if(PanelMode) count += pack * (stride-offset-depth);
}
pack -= PacketSize;
if(pack<Pack2 && (pack+PacketSize)!=Pack2)
pack = Pack2;
}
for(; i<rows; i++)
{
if(PanelMode) count += offset;
for(Index k=0; k<depth; k++)
blockA[count++] = cj(lhs(i, k));
if(PanelMode) count += (stride-offset-depth);
}
}
// copy a complete panel of the rhs
// this version is optimized for column major matrices
// The traversal order is as follow: (nr==4):
// 0 1 2 3 12 13 14 15 24 27
// 4 5 6 7 16 17 18 19 25 28
// 8 9 10 11 20 21 22 23 26 29
// . . . . . . . . . .
template<typename Scalar, typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
struct gemm_pack_rhs<Scalar, Index, DataMapper, nr, ColMajor, Conjugate, PanelMode>
{
typedef typename packet_traits<Scalar>::type Packet;
typedef typename DataMapper::LinearMapper LinearMapper;
enum { PacketSize = packet_traits<Scalar>::size };
EIGEN_DONT_INLINE void operator()(Scalar* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride=0, Index offset=0);
};
template<typename Scalar, typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
EIGEN_DONT_INLINE void gemm_pack_rhs<Scalar, Index, DataMapper, nr, ColMajor, Conjugate, PanelMode>
::operator()(Scalar* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
{
EIGEN_ASM_COMMENT("EIGEN PRODUCT PACK RHS COLMAJOR");
EIGEN_UNUSED_VARIABLE(stride);
EIGEN_UNUSED_VARIABLE(offset);
eigen_assert(((!PanelMode) && stride==0 && offset==0) || (PanelMode && stride>=depth && offset<=stride));
conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
Index packet_cols8 = nr>=8 ? (cols/8) * 8 : 0;
Index packet_cols4 = nr>=4 ? (cols/4) * 4 : 0;
Index count = 0;
const Index peeled_k = (depth/PacketSize)*PacketSize;
// if(nr>=8)
// {
// for(Index j2=0; j2<packet_cols8; j2+=8)
// {
// // skip what we have before
// if(PanelMode) count += 8 * offset;
// const Scalar* b0 = &rhs[(j2+0)*rhsStride];
// const Scalar* b1 = &rhs[(j2+1)*rhsStride];
// const Scalar* b2 = &rhs[(j2+2)*rhsStride];
// const Scalar* b3 = &rhs[(j2+3)*rhsStride];
// const Scalar* b4 = &rhs[(j2+4)*rhsStride];
// const Scalar* b5 = &rhs[(j2+5)*rhsStride];
// const Scalar* b6 = &rhs[(j2+6)*rhsStride];
// const Scalar* b7 = &rhs[(j2+7)*rhsStride];
// Index k=0;
// if(PacketSize==8) // TODO enbale vectorized transposition for PacketSize==4
// {
// for(; k<peeled_k; k+=PacketSize) {
// PacketBlock<Packet> kernel;
// for (int p = 0; p < PacketSize; ++p) {
// kernel.packet[p] = ploadu<Packet>(&rhs[(j2+p)*rhsStride+k]);
// }
// ptranspose(kernel);
// for (int p = 0; p < PacketSize; ++p) {
// pstoreu(blockB+count, cj.pconj(kernel.packet[p]));
// count+=PacketSize;
// }
// }
// }
// for(; k<depth; k++)
// {
// blockB[count+0] = cj(b0[k]);
// blockB[count+1] = cj(b1[k]);
// blockB[count+2] = cj(b2[k]);
// blockB[count+3] = cj(b3[k]);
// blockB[count+4] = cj(b4[k]);
// blockB[count+5] = cj(b5[k]);
// blockB[count+6] = cj(b6[k]);
// blockB[count+7] = cj(b7[k]);
// count += 8;
// }
// // skip what we have after
// if(PanelMode) count += 8 * (stride-offset-depth);
// }
// }
if(nr>=4)
{
for(Index j2=packet_cols8; j2<packet_cols4; j2+=4)
{
// skip what we have before
if(PanelMode) count += 4 * offset;
const LinearMapper dm0 = rhs.getLinearMapper(0, j2 + 0);
const LinearMapper dm1 = rhs.getLinearMapper(0, j2 + 1);
const LinearMapper dm2 = rhs.getLinearMapper(0, j2 + 2);
const LinearMapper dm3 = rhs.getLinearMapper(0, j2 + 3);
Index k=0;
if((PacketSize%4)==0) // TODO enable vectorized transposition for PacketSize==2 ??
{
for(; k<peeled_k; k+=PacketSize) {
PacketBlock<Packet,(PacketSize%4)==0?4:PacketSize> kernel;
kernel.packet[0] = dm0.loadPacket(k);
kernel.packet[1%PacketSize] = dm1.loadPacket(k);
kernel.packet[2%PacketSize] = dm2.loadPacket(k);
kernel.packet[3%PacketSize] = dm3.loadPacket(k);
ptranspose(kernel);
pstoreu(blockB+count+0*PacketSize, cj.pconj(kernel.packet[0]));
pstoreu(blockB+count+1*PacketSize, cj.pconj(kernel.packet[1%PacketSize]));
pstoreu(blockB+count+2*PacketSize, cj.pconj(kernel.packet[2%PacketSize]));
pstoreu(blockB+count+3*PacketSize, cj.pconj(kernel.packet[3%PacketSize]));
count+=4*PacketSize;
}
}
for(; k<depth; k++)
{
blockB[count+0] = cj(dm0(k));
blockB[count+1] = cj(dm1(k));
blockB[count+2] = cj(dm2(k));
blockB[count+3] = cj(dm3(k));
count += 4;
}
// skip what we have after
if(PanelMode) count += 4 * (stride-offset-depth);
}
}
// copy the remaining columns one at a time (nr==1)
for(Index j2=packet_cols4; j2<cols; ++j2)
{
if(PanelMode) count += offset;
const LinearMapper dm0 = rhs.getLinearMapper(0, j2);
for(Index k=0; k<depth; k++)
{
blockB[count] = cj(dm0(k));
count += 1;
}
if(PanelMode) count += (stride-offset-depth);
}
}
// this version is optimized for row major matrices
template<typename Scalar, typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
struct gemm_pack_rhs<Scalar, Index, DataMapper, nr, RowMajor, Conjugate, PanelMode>
{
typedef typename packet_traits<Scalar>::type Packet;
typedef typename DataMapper::LinearMapper LinearMapper;
enum { PacketSize = packet_traits<Scalar>::size };
EIGEN_DONT_INLINE void operator()(Scalar* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride=0, Index offset=0);
};
template<typename Scalar, typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
EIGEN_DONT_INLINE void gemm_pack_rhs<Scalar, Index, DataMapper, nr, RowMajor, Conjugate, PanelMode>
::operator()(Scalar* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
{
EIGEN_ASM_COMMENT("EIGEN PRODUCT PACK RHS ROWMAJOR");
EIGEN_UNUSED_VARIABLE(stride);
EIGEN_UNUSED_VARIABLE(offset);
eigen_assert(((!PanelMode) && stride==0 && offset==0) || (PanelMode && stride>=depth && offset<=stride));
conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
Index packet_cols8 = nr>=8 ? (cols/8) * 8 : 0;
Index packet_cols4 = nr>=4 ? (cols/4) * 4 : 0;
Index count = 0;
// if(nr>=8)
// {
// for(Index j2=0; j2<packet_cols8; j2+=8)
// {
// // skip what we have before
// if(PanelMode) count += 8 * offset;
// for(Index k=0; k<depth; k++)
// {
// if (PacketSize==8) {
// Packet A = ploadu<Packet>(&rhs[k*rhsStride + j2]);
// pstoreu(blockB+count, cj.pconj(A));
// } else if (PacketSize==4) {
// Packet A = ploadu<Packet>(&rhs[k*rhsStride + j2]);
// Packet B = ploadu<Packet>(&rhs[k*rhsStride + j2 + PacketSize]);
// pstoreu(blockB+count, cj.pconj(A));
// pstoreu(blockB+count+PacketSize, cj.pconj(B));
// } else {
// const Scalar* b0 = &rhs[k*rhsStride + j2];
// blockB[count+0] = cj(b0[0]);
// blockB[count+1] = cj(b0[1]);
// blockB[count+2] = cj(b0[2]);
// blockB[count+3] = cj(b0[3]);
// blockB[count+4] = cj(b0[4]);
// blockB[count+5] = cj(b0[5]);
// blockB[count+6] = cj(b0[6]);
// blockB[count+7] = cj(b0[7]);
// }
// count += 8;
// }
// // skip what we have after
// if(PanelMode) count += 8 * (stride-offset-depth);
// }
// }
if(nr>=4)
{
for(Index j2=packet_cols8; j2<packet_cols4; j2+=4)
{
// skip what we have before
if(PanelMode) count += 4 * offset;
for(Index k=0; k<depth; k++)
{
if (PacketSize==4) {
Packet A = rhs.loadPacket(k, j2);
pstoreu(blockB+count, cj.pconj(A));
count += PacketSize;
} else {
const LinearMapper dm0 = rhs.getLinearMapper(k, j2);
blockB[count+0] = cj(dm0(0));
blockB[count+1] = cj(dm0(1));
blockB[count+2] = cj(dm0(2));
blockB[count+3] = cj(dm0(3));
count += 4;
}
}
// skip what we have after
if(PanelMode) count += 4 * (stride-offset-depth);
}
}
// copy the remaining columns one at a time (nr==1)
for(Index j2=packet_cols4; j2<cols; ++j2)
{
if(PanelMode) count += offset;
for(Index k=0; k<depth; k++)
{
blockB[count] = cj(rhs(k, j2));
count += 1;
}
if(PanelMode) count += stride-offset-depth;
}
}
} // end namespace internal
/** \returns the currently set level 1 cpu cache size (in bytes) used to estimate the ideal blocking size parameters.
* \sa setCpuCacheSize */
inline std::ptrdiff_t l1CacheSize()
{
std::ptrdiff_t l1, l2, l3;
internal::manage_caching_sizes(GetAction, &l1, &l2, &l3);
return l1;
}
/** \returns the currently set level 2 cpu cache size (in bytes) used to estimate the ideal blocking size parameters.
* \sa setCpuCacheSize */
inline std::ptrdiff_t l2CacheSize()
{
std::ptrdiff_t l1, l2, l3;
internal::manage_caching_sizes(GetAction, &l1, &l2, &l3);
return l2;
}
/** \returns the currently set level 3 cpu cache size (in bytes) used to estimate the ideal blocking size paramete\
rs.
* \sa setCpuCacheSize */
inline std::ptrdiff_t l3CacheSize()
{
std::ptrdiff_t l1, l2, l3;
internal::manage_caching_sizes(GetAction, &l1, &l2, &l3);
return l3;
}
/** Set the cpu L1 and L2 cache sizes (in bytes).
* These values are use to adjust the size of the blocks
* for the algorithms working per blocks.
*
* \sa computeProductBlockingSizes */
inline void setCpuCacheSizes(std::ptrdiff_t l1, std::ptrdiff_t l2, std::ptrdiff_t l3)
{
internal::manage_caching_sizes(SetAction, &l1, &l2, &l3);
}
} // end namespace Eigen
#endif // EIGEN_GENERAL_BLOCK_PANEL_H