void bitonic_sort_rec(_Iterator begin, _Iterator end, _Compare comp, const mxx::comm& comm, int pbeg, int size, bool dir) {
// get next power of two
int p2 = pow(2, ceil(log(size)/log(2)));
// determine where the two sub-recursions are
int pmid = pbeg + p2/2;
int pend = pbeg + p2;
if (pend > comm.size())
pend = comm.size();
// recursive base-case
if (pend - pbeg <= 1)
return;
// sort the two subsequences, where the first is always a power of 2
if (comm.rank() < pmid) {
// sort descending
bitonic_sort_rec(begin, end, comp, comm, pbeg, p2/2, !dir);
} else {
// sort ascending
bitonic_sort_rec(begin, end, comp, comm, pmid, size - p2/2, dir);
}
// merge bitonic decreasing sequence
bitonic_merge(begin, end, comp, comm, pbeg, pend, dir);
}
void printEdgeListDistribution(Iterator begin, Iterator end, mxx::comm &comm)
{
T localWorkLoad = std::distance(begin, end);
T maxLoad = mxx::reduce(localWorkLoad, 0, mxx::max<T>() , comm);
T minLoad = mxx::reduce(localWorkLoad, 0, mxx::min<T>() , comm);
T meanLoad = mxx::reduce(localWorkLoad, 0, std::plus<T>(), comm)/ comm.size();
auto sep = ",";
LOG_IF(comm.rank() == 0, INFO) << "Distribution of edge list; min-mean-max : " << minLoad << sep << meanLoad << sep << maxLoad;
}
void bitonic_split(_Iterator begin, _Iterator end, _Compare comp, const mxx::comm& comm, int partner, int dir) {
typedef typename std::iterator_traits<_Iterator>::value_type T;
size_t np = std::distance(begin, end);
//std::cout << "[Rank " << comm.rank() << "]: split with partner= " << partner << ", dir=" << dir << std::endl;
std::vector<T> recv_buf(np);
std::vector<T> merge_buf(np);
// send/recv
mxx::datatype dt = mxx::get_datatype<T>();
MPI_Sendrecv(&*begin, np, dt.type(), partner, 0,
&recv_buf[0], np, dt.type(), partner, 0, comm, MPI_STATUS_IGNORE);
// merge in `dir` direction into merge buffer
if ((dir == asc && partner > comm.rank()) || (dir == desc && partner < comm.rank())) {
// forward merge and keep the `np` smaller elements
_Iterator l = begin;
typename std::vector<T>::iterator r = recv_buf.begin();
typename std::vector<T>::iterator o = merge_buf.begin();
for (size_t i = 0; i < np; ++i) {
if (comp(*l, *r)) {
*o = *l;
++o;
++l;
} else {
*o = *r;
++o;
++r;
}
}
} else {
// backward merge and keep the `np` larger elements
_Iterator l = begin+np-1;
typename std::vector<T>::iterator r = recv_buf.begin()+np-1;
typename std::vector<T>::iterator o = merge_buf.begin()+np-1;
for (size_t i = 0; i < np; ++i) {
if (comp(*l, *r)) {
*o = *r;
--o;
--r;
} else {
*o = *l;
--o;
--l;
}
}
}
// copy results into local buffer
std::copy(merge_buf.begin(), merge_buf.end(), begin);
}
void bitonic_merge(_Iterator begin, _Iterator end, _Compare comp, const mxx::comm& comm, int pbeg, int pend, int dir) {
MXX_ASSERT(pbeg <= comm.rank() && comm.rank() < pend);
// get size and terminate at recursive base-case
int size = pend - pbeg;
if (size <= 1)
return;
// get next greater power of 2
int p2 = pow(2, ceil(log(size)/log(2)));
// merge with splits as is done in the power of 2 case
int pmid = pbeg + p2/2;
if (comm.rank() < pmid && comm.rank() + p2/2 < pend) {
// this processor has a partner in the second half
int partner_rank = comm.rank() + p2/2;
bitonic_split(begin, end, comp, comm, partner_rank, dir);
bitonic_merge(begin, end, comp, comm, pbeg, pmid, dir);
} else if (comm.rank() < pmid) {
// this process doesn't have a partner but has to recursively
// participate in the next merge
bitonic_merge(begin, end, comp, comm, pbeg, pmid, dir);
} else { // if (comm.rank() >= pmid)
int partner_rank = comm.rank() - p2/2;
bitonic_split(begin, end, comp, comm, partner_rank, dir);
bitonic_merge(begin, end, comp, comm, pmid, pend, dir);
}
}
void populateEdgeList( std::vector< std::pair<T, T> > &edgeList,
uint64_t chainLength,
uint8_t mode,
const mxx::comm &comm = mxx::comm())
{
mxx::section_timer timer;
//sanity check
assert(mode == LOWTOHIGH_IDS);
//Know the portion of graph to be generated locally
//Lets divide the chainLength value by the number of processes
mxx::partition::block_decomposition<T> part(chainLength, comm.size(), comm.rank());
if(mode == LOWTOHIGH_IDS)
{
//First node (vertex) id on this MPI node
T beginNodeId = part.excl_prefix_size();
T lastNodeId = part.excl_prefix_size() + part.local_size() -1 ;
if(part.local_size() > 0)
{
for(int i = beginNodeId; i < lastNodeId; i++)
{
edgeList.emplace_back(i, i + 1);
edgeList.emplace_back(i + 1, i);
}
//If not last rank, attach edges from last node of this rank to first node of next rank
if(part.prefix_size() < chainLength)
{
edgeList.emplace_back(lastNodeId, lastNodeId+1);
edgeList.emplace_back(lastNodeId+1, lastNodeId);
}
}
}
timer.end_section("graph generation completed");
}
void bitonic_sort(_Iterator begin, _Iterator end, _Compare comp, const mxx::comm& comm) {
size_t np = std::distance(begin, end);
if (!mxx::all_same(np, comm)) {
throw std::runtime_error("bitonic sort only works for the same number of elements on each process.");
}
if (!std::is_sorted(begin, end, comp)) {
// sort local elements first
std::sort(begin, end, comp);
}
// recursively sort via bitonic sort
impl::bitonic_sort_rec(begin, end, comp, comm, 0, comm.size(), impl::asc);
}
void bulk_rmq(const std::size_t n, const std::vector<index_t>& local_els,
std::vector<std::tuple<index_t, index_t, index_t>>& ranges,
const mxx::comm& comm) {
// 3.) bulk-parallel-distributed RMQ for ranges (B2[i-1],B2[i]+1) to get min_lcp[i]
// a.) allgather per processor minimum lcp
// b.) create messages to left-most and right-most processor (i, B2[i])
// c.) on rank==B2[i]: get either left-flank min (i < B2[i])
// or right-flank min (i > B2[i])
// -> in bulk by ordering messages into two groups and sorting by B2[i]
// then linear scan for min starting from left-most/right-most element
// d.) answer with message (i, min(...))
// e.) on rank==i: receive min answer from left-most and right-most
// processor for each range
// -> sort by i
// f.) for each range: get RMQ of intermediary processors
// min(min_p_left, RMQ(p_left+1,p_right-1), min_p_right)
mxx::partition::block_decomposition_buffered<index_t> part(n, comm.size(), comm.rank());
// get size parameters
std::size_t local_size = local_els.size();
std::size_t prefix_size = part.excl_prefix_size();
// create RMQ for local elements
rmq<typename std::vector<index_t>::const_iterator> local_rmq(local_els.begin(), local_els.end());
// get per processor minimum and it's position
auto local_min_it = local_rmq.query(local_els.begin(), local_els.end());
index_t min_pos = (local_min_it - local_els.begin()) + prefix_size;
index_t local_min = *local_min_it;
//assert(local_min == *std::min_element(local_els.begin(), local_els.end()));
std::vector<index_t> proc_mins = mxx::allgather(local_min, comm);
std::vector<index_t> proc_min_pos = mxx::allgather(min_pos, comm);
// create range-minimum-query datastructure for the processor minimums
rmq<typename std::vector<index_t>::iterator> proc_mins_rmq(proc_mins.begin(), proc_mins.end());
// 1.) duplicate vector of triplets
// 2.) (asserting that t[1] < t[2]) send to target processor for t[1]
// 3.) on t[1]: return min and min index of right flank
// 4.) send duplicated to t[2]
// 5.) on t[2]: return min and min index of left flank
// 6.) if (target-p(t[1]) == target-p(t[2])):
// a) target-p(t[1]) participates in twice (2x too much, could later be
// algorithmically optimized away)
// and returns min only from range (t[1],t[2])
// 7.) on i: sort both by i, then pairwise iterate through and get target-p
// for both min indeces. if there are p's in between: use proc_min_rmq
// to get value and index of min p, then get global min index of that
// processor (needs to be gotten as well during the allgather)
// TODO: maybe template value type as different type than index_type
// (right now has to be identical, which suffices for LCP)
std::vector<std::tuple<index_t, index_t, index_t> > ranges_right(ranges);
// first communication
mxx::all2all_func(
ranges,
[&](const std::tuple<index_t, index_t, index_t>& x) {
return part.target_processor(std::get<1>(x));
}, comm);
// find mins from start to right border locally
for (auto it = ranges.begin(); it != ranges.end(); ++it)
{
assert(std::get<1>(*it) < std::get<2>(*it));
auto range_begin = local_els.begin() + (std::get<1>(*it) - prefix_size);
auto range_end = local_els.end();
if (std::get<2>(*it) < prefix_size + local_size)
{
range_end = local_els.begin() + (std::get<2>(*it) - prefix_size);
}
auto range_min = local_rmq.query(range_begin, range_end);
std::get<1>(*it) = (range_min - local_els.begin()) + prefix_size;
std::get<2>(*it) = *range_min;
}
// send results back to originator
mxx::all2all_func(
ranges,
[&](const std::tuple<index_t, index_t, index_t>& x) {
return part.target_processor(std::get<0>(x));
}, comm);
// second communication
mxx::all2all_func(
ranges_right,
[&](const std::tuple<index_t, index_t, index_t>& x) {
return part.target_processor(std::get<2>(x)-1);
}, comm);
// find mins from start to right border locally
for (auto it = ranges_right.begin(); it != ranges_right.end(); ++it)
{
assert(std::get<1>(*it) < std::get<2>(*it));
auto range_end = local_els.begin() + (std::get<2>(*it) - prefix_size);
auto range_begin = local_els.begin();
if (std::get<1>(*it) >= prefix_size)
{
range_begin = local_els.begin() + (std::get<1>(*it) - prefix_size);
}
auto range_min = local_rmq.query(range_begin, range_end);
std::get<1>(*it) = (range_min - local_els.begin()) + prefix_size;
std::get<2>(*it) = *range_min;
}
// send results back to originator
mxx::all2all_func(
ranges_right,
[&](const std::tuple<index_t, index_t, index_t>& x) {
return part.target_processor(std::get<0>(x));
}, comm);
// get total min and save into ranges
assert(ranges.size() == ranges_right.size());
// sort both by target index
std::sort(ranges.begin(), ranges.end(),
[](const std::tuple<index_t, index_t, index_t>& x,
const std::tuple<index_t, index_t, index_t>& y) {
return std::get<0>(x) < std::get<0>(y);
});
std::sort(ranges_right.begin(), ranges_right.end(),
[](const std::tuple<index_t, index_t, index_t>& x,
const std::tuple<index_t, index_t, index_t>& y) {
return std::get<0>(x) < std::get<0>(y);
});
// iterate through both results (left and right)
// and get overall minimum
for (std::size_t i=0; i < ranges.size(); ++i)
{
assert(std::get<0>(ranges[i]) == std::get<0>(ranges_right[i]));
std::size_t left_min_idx = std::get<1>(ranges[i]);
std::size_t right_min_idx = std::get<1>(ranges_right[i]);
// get min of both ranges
if (std::get<2>(ranges[i]) > std::get<2>(ranges_right[i]))
{
ranges[i] = ranges_right[i];
}
// if the answer is different
if (left_min_idx != right_min_idx)
{
int p_left = part.target_processor(left_min_idx);
int p_right = part.target_processor(right_min_idx);
// get minimum of both elements
if (p_left + 1 < p_right)
{
// get min from per process min RMQ
auto p_min_it =
proc_mins_rmq.query(proc_mins.begin() + p_left + 1,
proc_mins.begin() + p_right);
index_t p_min = *p_min_it;
// if smaller, save as overall minimum
if (p_min < std::get<2>(ranges[i]))
{
std::get<1>(ranges[i]) = proc_min_pos[p_min_it - proc_mins.begin()];
std::get<2>(ranges[i]) = p_min;
}
}
}
}
}
