double* ttm (double *X, const int Dim, long int *XDimSize,
double *U, long int *UDimSize, char tflag,
double *Y, long int *YDimSize,
int ModeComn, int *ModeCom, int ModeComLen)
{
//Decide transa and transb according to tflag and ModeComn and ModeCom's relationship.
CBLAS_TRANSPOSE transa = CblasNoTrans;
CBLAS_TRANSPOSE transb = CblasNoTrans;
long int m,n,k;
double alpha, beta;
long int rsu,csu,rsx,csx,rsy,csy;
long int XLoopStride = 0, YLoopStride = 0;
alpha = 1.0;
beta = 1.0;
/****Generated TM algo according to different modes and dimensions ***/
m = 10;
n = 1000;
k = 1000;
rsu = 1000;
csu = 1;
rsx = 1000;
csx = 1;
rsy = 1000;
csy = 1;
#pragma omp parallel for default(shared) schedule(static) num_threads(1)
for (long int i0=0;i0<1000;i0++)
{
mkl_set_dynamic(0);
mkl_set_num_threads_local(8);
XLoopStride = i0*1000000;
YLoopStride = i0*10000;
cblas_dgemm(CblasRowMajor, transa, transb,
m, n, k,
alpha,
U, rsu,
X+XLoopStride, rsx,
beta,
Y+YLoopStride, rsy);
}
return Y;
}
double FastMatmul(Matrix<Scalar>& A, Matrix<Scalar>& B, Matrix<Scalar>& C,
int num_steps, double x=1e-8, Scalar alpha=Scalar(1.0), Scalar beta=Scalar(0.0)) {
MemoryManager<Scalar> mem_mngr;
#ifdef _PARALLEL_
mem_mngr.Allocate(2, 2, 2, 8, num_steps, A.m(), A.n(), B.n());
#endif
A.set_multiplier(alpha);
int num_multiplies_per_step = 8;
int total_multiplies = pow(num_multiplies_per_step, num_steps);
// Set parameters needed for all types of parallelism.
int num_threads = 0;
#ifdef _PARALLEL_
# pragma omp parallel
{
if (omp_get_thread_num() == 0) {
num_threads = omp_get_num_threads();
}
}
omp_set_nested(1);
#endif
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_)
# pragma omp parallel
{
mkl_set_num_threads_local(1);
mkl_set_dynamic(0);
}
#endif
#if defined(_PARALLEL_) && (_PARALLEL_ == _DFS_PAR_)
mkl_set_dynamic(0);
#endif
#if defined(_PARALLEL_) && (_PARALLEL_ == _HYBRID_PAR_)
if (num_threads > total_multiplies) {
mkl_set_dynamic(0);
} else {
# pragma omp parallel
{
mkl_set_num_threads_local(1);
mkl_set_dynamic(0);
}
}
#endif
LockAndCounter locker(total_multiplies - (total_multiplies % num_threads));
using FpMilliseconds = std::chrono::duration<float, std::chrono::milliseconds::period>;
auto t1 = std::chrono::high_resolution_clock::now();
#ifdef _PARALLEL_
# pragma omp parallel
{
# pragma omp single
#endif
FastMatmulRecursive(locker, mem_mngr, A, B, C, num_steps, num_steps, 0, x, num_threads, beta);
#ifdef _PARALLEL_
}
#endif
auto t2 = std::chrono::high_resolution_clock::now();
return FpMilliseconds(t2 - t1).count();
}
void TaskManager :: Loop(int thd)
{
/*
static Timer tADD("add entry counter");
static Timer tCASready1("spin-CAS ready tick1");
static Timer tCASready2("spin-CAS ready tick2");
static Timer tCASyield("spin-CAS yield");
static Timer tCAS1("spin-CAS wait");
static Timer texit("exit zone");
static Timer tdec("decrement");
*/
thread_id = thd;
int thds = GetNumThreads();
int mynode = num_nodes * thd/thds;
NodeData & mynode_data = *(nodedata[mynode]);
TaskInfo ti;
ti.nthreads = thds;
ti.thread_nr = thd;
// ti.nnodes = num_nodes;
// ti.node_nr = mynode;
#ifdef USE_NUMA
numa_run_on_node (mynode);
#endif
active_workers++;
workers_on_node[mynode]++;
int jobdone = 0;
#ifdef USE_MKL
auto mkl_max = mkl_get_max_threads();
mkl_set_num_threads_local(1);
#endif
while (!done)
{
if (complete[mynode] > jobdone)
jobdone = complete[mynode];
if (jobnr == jobdone)
{
// RegionTracer t(ti.thread_nr, tCASyield, ti.task_nr);
if(sleep)
this_thread::sleep_for(chrono::microseconds(sleep_usecs));
else
{
#ifdef WIN32
this_thread::yield();
#else // WIN32
sched_yield();
#endif // WIN32
}
continue;
}
{
// RegionTracer t(ti.thread_nr, tADD, ti.task_nr);
// non-atomic fast check ...
if ( (mynode_data.participate & 1) == 0) continue;
int oldval = mynode_data.participate += 2;
if ( (oldval & 1) == 0)
{ // job not active, going out again
mynode_data.participate -= 2;
continue;
}
}
if (startup_function) (*startup_function)();
IntRange mytasks = Range(int(ntasks)).Split (mynode, num_nodes);
try
{
while (1)
{
if (mynode_data.start_cnt >= mytasks.Size()) break;
int mytask = mynode_data.start_cnt.fetch_add(1, memory_order_relaxed);
if (mytask >= mytasks.Size()) break;
ti.task_nr = mytasks.First()+mytask;
ti.ntasks = ntasks;
{
RegionTracer t(ti.thread_nr, jobnr, RegionTracer::ID_JOB, ti.task_nr);
(*func)(ti);
}
}
}
catch (Exception e)
{
{
// cout << "got exception in TM" << endl;
lock_guard<mutex> guard(copyex_mutex);
delete ex;
ex = new Exception (e);
mynode_data.start_cnt = mytasks.Size();
}
}
#ifndef __MIC__
atomic_thread_fence (memory_order_release);
#endif // __MIC__
if (cleanup_function) (*cleanup_function)();
jobdone = jobnr;
mynode_data.participate-=2;
{
int oldpart = 1;
if (mynode_data.participate.compare_exchange_strong (oldpart, 0))
{
if (jobdone < jobnr.load())
{ // reopen gate
mynode_data.participate |= 1;
}
else
{
if (mynode != 0)
mynode_data.start_cnt = 0;
complete[mynode] = jobnr.load();
}
}
}
}
#ifdef USE_MKL
mkl_set_num_threads_local(mkl_max);
#endif
workers_on_node[mynode]--;
active_workers--;
}
void FastMatmulRecursive(LockAndCounter& locker, MemoryManager<Scalar>& mem_mngr, Matrix<Scalar>& A, Matrix<Scalar>& B, Matrix<Scalar>& C, int total_steps, int steps_left, int start_index, double x, int num_threads, Scalar beta) {
// Update multipliers
C.UpdateMultiplier(A.multiplier());
C.UpdateMultiplier(B.multiplier());
A.set_multiplier(Scalar(1.0));
B.set_multiplier(Scalar(1.0));
// Base case for recursion
if (steps_left == 0) {
MatMul(A, B, C);
return;
}
Matrix<Scalar> A11 = A.Subblock(2, 2, 1, 1);
Matrix<Scalar> A12 = A.Subblock(2, 2, 1, 2);
Matrix<Scalar> A21 = A.Subblock(2, 2, 2, 1);
Matrix<Scalar> A22 = A.Subblock(2, 2, 2, 2);
Matrix<Scalar> B11 = B.Subblock(2, 2, 1, 1);
Matrix<Scalar> B12 = B.Subblock(2, 2, 1, 2);
Matrix<Scalar> B21 = B.Subblock(2, 2, 2, 1);
Matrix<Scalar> B22 = B.Subblock(2, 2, 2, 2);
Matrix<Scalar> C11 = C.Subblock(2, 2, 1, 1);
Matrix<Scalar> C12 = C.Subblock(2, 2, 1, 2);
Matrix<Scalar> C21 = C.Subblock(2, 2, 2, 1);
Matrix<Scalar> C22 = C.Subblock(2, 2, 2, 2);
// Matrices to store the results of multiplications.
#ifdef _PARALLEL_
Matrix<Scalar> M1(mem_mngr.GetMem(start_index, 1, total_steps - steps_left, M), C11.m(), C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M2(mem_mngr.GetMem(start_index, 2, total_steps - steps_left, M), C11.m(), C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M3(mem_mngr.GetMem(start_index, 3, total_steps - steps_left, M), C11.m(), C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M4(mem_mngr.GetMem(start_index, 4, total_steps - steps_left, M), C11.m(), C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M5(mem_mngr.GetMem(start_index, 5, total_steps - steps_left, M), C11.m(), C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M6(mem_mngr.GetMem(start_index, 6, total_steps - steps_left, M), C11.m(), C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M7(mem_mngr.GetMem(start_index, 7, total_steps - steps_left, M), C11.m(), C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M8(mem_mngr.GetMem(start_index, 8, total_steps - steps_left, M), C11.m(), C11.m(), C11.n(), C.multiplier());
#else
Matrix<Scalar> M1(C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M2(C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M3(C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M4(C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M5(C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M6(C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M7(C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M8(C11.m(), C11.n(), C.multiplier());
#endif
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
bool sequential1 = should_launch_task(8, total_steps, steps_left, start_index, 1, num_threads);
bool sequential2 = should_launch_task(8, total_steps, steps_left, start_index, 2, num_threads);
bool sequential3 = should_launch_task(8, total_steps, steps_left, start_index, 3, num_threads);
bool sequential4 = should_launch_task(8, total_steps, steps_left, start_index, 4, num_threads);
bool sequential5 = should_launch_task(8, total_steps, steps_left, start_index, 5, num_threads);
bool sequential6 = should_launch_task(8, total_steps, steps_left, start_index, 6, num_threads);
bool sequential7 = should_launch_task(8, total_steps, steps_left, start_index, 7, num_threads);
bool sequential8 = should_launch_task(8, total_steps, steps_left, start_index, 8, num_threads);
#else
bool sequential1 = false;
bool sequential2 = false;
bool sequential3 = false;
bool sequential4 = false;
bool sequential5 = false;
bool sequential6 = false;
bool sequential7 = false;
bool sequential8 = false;
#endif
// M1 = (1 * A11) * (1 * B11)
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
# pragma omp task if(sequential1) shared(mem_mngr, locker) untied
{
#endif
M1.UpdateMultiplier(Scalar(1));
M1.UpdateMultiplier(Scalar(1));
FastMatmulRecursive(locker, mem_mngr, A11, B11, M1, total_steps, steps_left - 1, (start_index + 1 - 1) * 8, x, num_threads, Scalar(0.0));
#ifndef _PARALLEL_
#endif
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
locker.Decrement();
}
if (should_task_wait(8, total_steps, steps_left, start_index, 1, num_threads)) {
# pragma omp taskwait
# if defined(_PARALLEL_) && (_PARALLEL_ == _HYBRID_PAR_)
SwitchToDFS(locker, num_threads);
# endif
}
#endif
// M2 = (1 * A12) * (1 * B21)
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
# pragma omp task if(sequential2) shared(mem_mngr, locker) untied
{
#endif
M2.UpdateMultiplier(Scalar(1));
M2.UpdateMultiplier(Scalar(1));
FastMatmulRecursive(locker, mem_mngr, A12, B21, M2, total_steps, steps_left - 1, (start_index + 2 - 1) * 8, x, num_threads, Scalar(0.0));
#ifndef _PARALLEL_
#endif
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
locker.Decrement();
}
if (should_task_wait(8, total_steps, steps_left, start_index, 2, num_threads)) {
# pragma omp taskwait
# if defined(_PARALLEL_) && (_PARALLEL_ == _HYBRID_PAR_)
SwitchToDFS(locker, num_threads);
# endif
}
#endif
// M3 = (1 * A11) * (1 * B12)
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
# pragma omp task if(sequential3) shared(mem_mngr, locker) untied
{
#endif
M3.UpdateMultiplier(Scalar(1));
M3.UpdateMultiplier(Scalar(1));
FastMatmulRecursive(locker, mem_mngr, A11, B12, M3, total_steps, steps_left - 1, (start_index + 3 - 1) * 8, x, num_threads, Scalar(0.0));
#ifndef _PARALLEL_
#endif
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
locker.Decrement();
}
if (should_task_wait(8, total_steps, steps_left, start_index, 3, num_threads)) {
# pragma omp taskwait
# if defined(_PARALLEL_) && (_PARALLEL_ == _HYBRID_PAR_)
SwitchToDFS(locker, num_threads);
# endif
}
#endif
// M4 = (1 * A12) * (1 * B22)
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
# pragma omp task if(sequential4) shared(mem_mngr, locker) untied
{
#endif
M4.UpdateMultiplier(Scalar(1));
M4.UpdateMultiplier(Scalar(1));
FastMatmulRecursive(locker, mem_mngr, A12, B22, M4, total_steps, steps_left - 1, (start_index + 4 - 1) * 8, x, num_threads, Scalar(0.0));
#ifndef _PARALLEL_
#endif
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
locker.Decrement();
}
if (should_task_wait(8, total_steps, steps_left, start_index, 4, num_threads)) {
# pragma omp taskwait
# if defined(_PARALLEL_) && (_PARALLEL_ == _HYBRID_PAR_)
SwitchToDFS(locker, num_threads);
# endif
}
#endif
// M5 = (1 * A21) * (1 * B11)
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
# pragma omp task if(sequential5) shared(mem_mngr, locker) untied
{
#endif
M5.UpdateMultiplier(Scalar(1));
M5.UpdateMultiplier(Scalar(1));
FastMatmulRecursive(locker, mem_mngr, A21, B11, M5, total_steps, steps_left - 1, (start_index + 5 - 1) * 8, x, num_threads, Scalar(0.0));
#ifndef _PARALLEL_
#endif
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
locker.Decrement();
}
if (should_task_wait(8, total_steps, steps_left, start_index, 5, num_threads)) {
# pragma omp taskwait
# if defined(_PARALLEL_) && (_PARALLEL_ == _HYBRID_PAR_)
SwitchToDFS(locker, num_threads);
# endif
}
#endif
// M6 = (1 * A22) * (1 * B21)
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
# pragma omp task if(sequential6) shared(mem_mngr, locker) untied
{
#endif
M6.UpdateMultiplier(Scalar(1));
M6.UpdateMultiplier(Scalar(1));
FastMatmulRecursive(locker, mem_mngr, A22, B21, M6, total_steps, steps_left - 1, (start_index + 6 - 1) * 8, x, num_threads, Scalar(0.0));
#ifndef _PARALLEL_
#endif
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
locker.Decrement();
}
if (should_task_wait(8, total_steps, steps_left, start_index, 6, num_threads)) {
# pragma omp taskwait
# if defined(_PARALLEL_) && (_PARALLEL_ == _HYBRID_PAR_)
SwitchToDFS(locker, num_threads);
# endif
}
#endif
// M7 = (1 * A21) * (1 * B12)
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
# pragma omp task if(sequential7) shared(mem_mngr, locker) untied
{
#endif
M7.UpdateMultiplier(Scalar(1));
M7.UpdateMultiplier(Scalar(1));
FastMatmulRecursive(locker, mem_mngr, A21, B12, M7, total_steps, steps_left - 1, (start_index + 7 - 1) * 8, x, num_threads, Scalar(0.0));
#ifndef _PARALLEL_
#endif
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
locker.Decrement();
}
if (should_task_wait(8, total_steps, steps_left, start_index, 7, num_threads)) {
# pragma omp taskwait
# if defined(_PARALLEL_) && (_PARALLEL_ == _HYBRID_PAR_)
SwitchToDFS(locker, num_threads);
# endif
}
#endif
// M8 = (1 * A22) * (1 * B22)
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
# pragma omp task if(sequential8) shared(mem_mngr, locker) untied
{
#endif
M8.UpdateMultiplier(Scalar(1));
M8.UpdateMultiplier(Scalar(1));
FastMatmulRecursive(locker, mem_mngr, A22, B22, M8, total_steps, steps_left - 1, (start_index + 8 - 1) * 8, x, num_threads, Scalar(0.0));
#ifndef _PARALLEL_
#endif
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
locker.Decrement();
}
if (should_task_wait(8, total_steps, steps_left, start_index, 8, num_threads)) {
# pragma omp taskwait
}
#endif
M_Add1(M1, M2, C11, x, false, beta);
M_Add2(M3, M4, C12, x, false, beta);
M_Add3(M5, M6, C21, x, false, beta);
M_Add4(M7, M8, C22, x, false, beta);
// Handle edge cases with dynamic peeling
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
if (total_steps == steps_left) {
mkl_set_num_threads_local(num_threads);
mkl_set_dynamic(0);
}
#endif
DynamicPeeling(A, B, C, 2, 2, 2, beta);
}