Collection of Generic Parallel Functions: Sorting, Partitioning, Searching,... More...

Classes
class	Mpi_datatype
	An abstract class used for communicating messages using user-defined datatypes. The user must implement the static member function "value()" that returns the MPI_Datatype corresponding to this user-defined datatype. More...

class	Mpi_datatype< bool >
	A template specialization of the abstract class Mpi_datatype. This can be used for communicating messages of type "bool". More...

class	Mpi_datatype< IndexHolder< T > >

class	Mpi_datatype< std::complex< T > >

class	Mpi_pairtype

Functions
template<typename T >
int	Mpi_Isend (T buf, int count, int dest, int tag, MPI_Comm comm, MPI_Request request)

template<typename T >
int	Mpi_Issend (T buf, int count, int dest, int tag, MPI_Comm comm, MPI_Request request)

template<typename T >
int	Mpi_Recv (T buf, int count, int source, int tag, MPI_Comm comm, MPI_Status status)

template<typename T >
int	Mpi_Irecv (T buf, int count, int source, int tag, MPI_Comm comm, MPI_Request request)

template<typename T >
int	Mpi_Gather (T sendBuffer, T recvBuffer, int count, int root, MPI_Comm comm)

template<typename T , typename S >
int	Mpi_Sendrecv (T sendBuf, int sendCount, int dest, int sendTag, S recvBuf, int recvCount, int source, int recvTag, MPI_Comm comm, MPI_Status *status)

template<typename T >
int	Mpi_Bcast (T *buffer, int count, int root, MPI_Comm comm)

template<typename T >
int	Mpi_Scan (T sendbuf, T recvbuf, int count, MPI_Op op, MPI_Comm comm)

template<typename T >
int	Mpi_Reduce (T sendbuf, T recvbuf, int count, MPI_Op op, int root, MPI_Comm comm)

template<typename T >
int	Mpi_Allreduce (T sendbuf, T recvbuf, int count, MPI_Op op, MPI_Comm comm)

template<typename T >
int	Mpi_Alltoall (T sendbuf, T recvbuf, int count, MPI_Comm comm)

template<typename T >
int	Mpi_Allgatherv (T sendbuf, int sendcount, T recvbuf, int recvcounts, int displs, MPI_Comm comm)

template<typename T >
int	Mpi_Allgather (T sendbuf, T recvbuf, int count, MPI_Comm comm)

template<typename T >
int	Mpi_Alltoallv_sparse (T sendbuf, int sendcnts, int sdispls, T recvbuf, int recvcnts, int rdispls, MPI_Comm comm)

template<typename T >
int	Mpi_Alltoallv_dense (T sendbuf, int sendcnts, int sdispls, T recvbuf, int recvcnts, int rdispls, MPI_Comm comm)

template<typename T >
unsigned int	defaultWeight (const T *a)

template<typename T >
int	partitionW (std::vector< T > &vec, unsigned int(getWeight)(const T ), MPI_Comm comm)
	A parallel weighted partitioning function. In our implementation, we do not pose any restriction on the input or the number of processors. This function can be used with an odd number of processors as well. Some processors can pass an empty vector as input. The relative ordering of the elements is preserved. More...

template<typename T >
void	rankSamples (std::vector< T > &arr, std::vector< T > samples, MPI_Comm comm)

template<typename T >
std::vector< T >	Sorted_Sample_Select (std::vector< T > &arr, unsigned int kway, std::vector< unsigned int > &min_idx, std::vector< unsigned int > &max_idx, std::vector< DendroIntL > &splitter_ranks, MPI_Comm comm)

template<typename T >
std::vector< T >	Sorted_approx_Select (std::vector< T > &arr, unsigned int k, MPI_Comm comm)

template<typename T >
std::vector< std::pair< T, DendroIntL > >	Sorted_approx_Select_skewed (std::vector< T > &arr, unsigned int k, MPI_Comm comm)
	new one to handle skewed distributions ... More...

template<typename T >
std::vector< T >	GetRangeMean (std::vector< T > &arr, std::vector< unsigned int > range_min, std::vector< unsigned int > range_max, MPI_Comm comm)

template<typename T >
std::vector< T >	GuessRangeMedian (std::vector< T > &arr, std::vector< unsigned int > range_min, std::vector< unsigned int > range_max, MPI_Comm comm)

template<typename T >
std::vector< T >	Sorted_k_Select (std::vector< T > &arr, std::vector< unsigned int > min_idx, std::vector< unsigned int > max_idx, std::vector< DendroIntL > K, std::vector< T > guess, MPI_Comm comm)
	A parallel k-selection algorithms. More...

template<typename T >
int	HyperQuickSort (std::vector< T > &in, std::vector< T > &out, MPI_Comm comm)
	A parallel hyper quick sort implementation. More...

template<typename T >
int	HyperQuickSort_kway (std::vector< T > &in, std::vector< T > &out, MPI_Comm comm)

template<typename T >
int	HyperQuickSort_cav (std::vector< T > &in, std::vector< T > &out, MPI_Comm comm)

template<typename T >
int	HyperQuickSort (std::vector< T > &arr, MPI_Comm comm)

template<typename T >
int	HyperQuickSort_kway (std::vector< T > &in, MPI_Comm comm)

template<typename T >
int	HyperQuickSort_cav (std::vector< T > &in, MPI_Comm comm)

template<typename T >
int	sampleSort (std::vector< T > &in, std::vector< T > &out, MPI_Comm comm)
	A parallel sample sort implementation. In our implementation, we do not pose any restriction on the input or the number of processors. This function can be used with an odd number of processors as well. Some processors can pass an empty vector as input. If the total number of elements in the vector (globally) is fewer than 10*p^2, where p is the number of processors, then we will use bitonic sort instead of sample sort to sort the vector. We use a paralle bitonic sort to sort the samples in the sample sort algorithm. Hence, the complexity of the algorithm is O(n/p log n/p) + O(p log p). Here, n is the global length of the vector and p is the number of processors. More...

template<typename T >
int	sampleSort (std::vector< T > &in, MPI_Comm comm)

int	splitComm2way (bool iAmEmpty, MPI_Comm *new_comm, MPI_Comm orig_comm)
	Splits a communication group into two, one containing processors that passed a value of 'false' for the parameter 'iAmEmpty' and the another containing processors that passed a value of 'true' for the parameter. Both the groups are sorted in the ascending order of their ranks in the old comm. More...

int	splitComm2way (const bool isEmptyList, MPI_Comm new_comm, MPI_Comm orig_comm)
	Splits a communication group into two depending on the values in isEmptyList. Both the groups are sorted in the ascending order of their ranks in the old comm. All processors must call this function with the same 'isEmptyList' array. More...

int	splitCommUsingSplittingRank (int splittingRank, MPI_Comm *new_comm, MPI_Comm orig_comm)

unsigned int	splitCommBinary (MPI_Comm orig_comm, MPI_Comm *new_comm)
	Splits a communication group into two, the first having a power of 2 number of processors and the other having the remainder. The first group is sorted in the ascending order of their ranks in the old comm and the second group is sorted in the descending order of their ranks in the old comm. More...

unsigned int	splitCommBinaryNoFlip (MPI_Comm orig_comm, MPI_Comm *new_comm)
	Splits a communication group into two, the first having a power of 2 number of processors and the other having the remainder. Both the groups are sorted in the ascending order of their ranks in the old comm. More...

template<typename T >
void	MergeLists (std::vector< T > &listA, std::vector< T > &listB, int KEEP_WHAT)
	Merges lists A, and B, retaining either the low or the High in list A. More...

template<typename T >
void	MergeSplit (std::vector< T > &local_list, int which_keys, int partner, MPI_Comm comm)
	The main operation in the parallel bitonic sort algorithm. This implements the compare-split operation. More...

template<typename T >
void	Par_bitonic_sort_incr (std::vector< T > &local_list, int proc_set_size, MPI_Comm comm)

template<typename T >
void	Par_bitonic_sort_decr (std::vector< T > &local_list, int proc_set_size, MPI_Comm comm)

template<typename T >
void	Par_bitonic_merge_incr (std::vector< T > &local_list, int proc_set_size, MPI_Comm comm)

template<typename T >
void	bitonicSort_binary (std::vector< T > &in, MPI_Comm comm)
	An implementation of parallel bitonic sort that expects the number of processors to be a power of 2. However, unlike most implementations, we do not expect the length of the vector (neither locally nor globally) to be a power of 2 or even. Moreover, each processor can call this with a different number of elements. However, we do expect that 'in' atleast has 1 element on each processor. More...

template<typename T >
void	bitonicSort (std::vector< T > &in, MPI_Comm comm)
	An implementation of parallel bitonic sort that does not expect the number of processors to be a power of 2. In fact, the number of processors can even be odd. Moreover, we do not even expect the length of the vector (neither locally nor globally) to be a power of 2 or even. Moreover, each processor can call this with a different number of elements. However, we do expect that 'in' atleast has 1 element on each processor. This recursively calls the function bitonicSort_binary, followed by a special parallel merge. More...

int	AdjustCommunicationPattern (std::vector< int > &send_sizes, std::vector< int > &send_partners, std::vector< int > &recv_sizes, std::vector< int > &recv_partners, MPI_Comm comm)

Detailed Description

Collection of Generic Parallel Functions: Sorting, Partitioning, Searching,...

Author: Hari Sundar hsund.nosp@m.ar@g.nosp@m.mail..nosp@m.com

Function Documentation

◆ AdjustCommunicationPattern()

int par::AdjustCommunicationPattern	(	std::vector< int > &	send_sizes,
		std::vector< int > &	send_partners,
		std::vector< int > &	recv_sizes,
		std::vector< int > &	recv_partners,
		MPI_Comm	comm
	)

Definition at line 279 of file parUtils.cpp.

◆ bitonicSort()

template<typename T >

void par::bitonicSort	(	std::vector< T > &	in,
		MPI_Comm	comm
	)

An implementation of parallel bitonic sort that does not expect the number of processors to be a power of 2. In fact, the number of processors can even be odd. Moreover, we do not even expect the length of the vector (neither locally nor globally) to be a power of 2 or even. Moreover, each processor can call this with a different number of elements. However, we do expect that 'in' atleast has 1 element on each processor. This recursively calls the function bitonicSort_binary, followed by a special parallel merge.

Parameters

in	the vector to be sorted

Author: Hari Sundar

See also: bitonicSort_binary

◆ bitonicSort_binary()

template<typename T >

void par::bitonicSort_binary	(	std::vector< T > &	in,
		MPI_Comm	comm
	)

An implementation of parallel bitonic sort that expects the number of processors to be a power of 2. However, unlike most implementations, we do not expect the length of the vector (neither locally nor globally) to be a power of 2 or even. Moreover, each processor can call this with a different number of elements. However, we do expect that 'in' atleast has 1 element on each processor.

Parameters

in	the vector to be sorted

Author: Hari Sundar

◆ defaultWeight()

template<typename T >

unsigned int par::defaultWeight ( const T * a )

◆ GetRangeMean()

template<typename T >

std::vector<T> par::GetRangeMean	(	std::vector< T > &	arr,
		std::vector< unsigned int >	range_min,
		std::vector< unsigned int >	range_max,
		MPI_Comm	comm
	)

◆ GuessRangeMedian()

template<typename T >

std::vector<T> par::GuessRangeMedian	(	std::vector< T > &	arr,
		std::vector< unsigned int >	range_min,
		std::vector< unsigned int >	range_max,
		MPI_Comm	comm
	)

◆ HyperQuickSort() [1/2]

template<typename T >

int par::HyperQuickSort	(	std::vector< T > &	in,
		std::vector< T > &	out,
		MPI_Comm	comm
	)

A parallel hyper quick sort implementation.

Author: Dhairya Malhotra

Parameters

in	the input vector
out	the output vector
comm	the communicator

◆ HyperQuickSort() [2/2]

template<typename T >

int par::HyperQuickSort	(	std::vector< T > &	arr,
		MPI_Comm	comm
	)

◆ HyperQuickSort_cav() [1/2]

template<typename T >

int par::HyperQuickSort_cav	(	std::vector< T > &	in,
		std::vector< T > &	out,
		MPI_Comm	comm
	)

◆ HyperQuickSort_cav() [2/2]

template<typename T >

int par::HyperQuickSort_cav	(	std::vector< T > &	in,
		MPI_Comm	comm
	)

◆ HyperQuickSort_kway() [1/2]

template<typename T >

int par::HyperQuickSort_kway	(	std::vector< T > &	in,
		std::vector< T > &	out,
		MPI_Comm	comm
	)

◆ HyperQuickSort_kway() [2/2]

template<typename T >

int par::HyperQuickSort_kway	(	std::vector< T > &	in,
		MPI_Comm	comm
	)

◆ MergeLists()

template<typename T >

void par::MergeLists	(	std::vector< T > &	listA,
		std::vector< T > &	listB,
		int	KEEP_WHAT
	)

Merges lists A, and B, retaining either the low or the High in list A.

Author: Hari Sundar

Parameters

listA	Input list, and where the output is stored.
listB	Second input list.
KEEP_WHAT	determines whether to retain the High or the low values from A and B. One of KEEP_HIGH or KEEP_LOW.

Merging the two lists when their sizes are not the same is a bit involved. The major condition that needs to be used is that all elements that are less than max(min(A), min(B)) are retained by the KEEP_LOW processor, and similarly all elements that are larger larger than min(max(A), max(B)) are retained by the KEEP_HIGH processor.

The reason for this is that, on the Keep_Low side,

max(min(A), min(B)) > min(A) > max(A-)

and similarly on the Keep_high side,

min(max(A), max(B)) < max(A) < min(A+)

which guarantees that the merged lists remain bitonic.

◆ MergeSplit()

template<typename T >

void par::MergeSplit	(	std::vector< T > &	local_list,
		int	which_keys,
		int	partner,
		MPI_Comm	comm
	)

The main operation in the parallel bitonic sort algorithm. This implements the compare-split operation.

Author: Hari Sundar

Parameters

which_keys	is one of KEEP_HIGH or KEEP_LOW
partner	is the processor with which to Merge and Split.
local_list	the input vector
comm	the communicator

◆ Mpi_Allgather()

template<typename T >

int par::Mpi_Allgather	(	T *	sendbuf,
		T *	recvbuf,
		int	count,
		MPI_Comm	comm
	)

◆ Mpi_Allgatherv()

template<typename T >

int par::Mpi_Allgatherv	(	T *	sendbuf,
		int	sendcount,
		T *	recvbuf,
		int *	recvcounts,
		int *	displs,
		MPI_Comm	comm
	)

◆ Mpi_Allreduce()

template<typename T >

int par::Mpi_Allreduce	(	T *	sendbuf,
		T *	recvbuf,
		int	count,
		MPI_Op	op,
		MPI_Comm	comm
	)

◆ Mpi_Alltoall()

template<typename T >

int par::Mpi_Alltoall	(	T *	sendbuf,
		T *	recvbuf,
		int	count,
		MPI_Comm	comm
	)

◆ Mpi_Alltoallv_dense()

template<typename T >

int par::Mpi_Alltoallv_dense	(	T *	sendbuf,
		int *	sendcnts,
		int *	sdispls,
		T *	recvbuf,
		int *	recvcnts,
		int *	rdispls,
		MPI_Comm	comm
	)

◆ Mpi_Alltoallv_sparse()

template<typename T >

int par::Mpi_Alltoallv_sparse	(	T *	sendbuf,
		int *	sendcnts,
		int *	sdispls,
		T *	recvbuf,
		int *	recvcnts,
		int *	rdispls,
		MPI_Comm	comm
	)

◆ Mpi_Bcast()

template<typename T >

int par::Mpi_Bcast	(	T *	buffer,
		int	count,
		int	root,
		MPI_Comm	comm
	)

◆ Mpi_Gather()

template<typename T >

int par::Mpi_Gather	(	T *	sendBuffer,
		T *	recvBuffer,
		int	count,
		int	root,
		MPI_Comm	comm
	)

◆ Mpi_Irecv()

template<typename T >

int par::Mpi_Irecv	(	T *	buf,
		int	count,
		int	source,
		int	tag,
		MPI_Comm	comm,
		MPI_Request *	request
	)

◆ Mpi_Isend()

template<typename T >

int par::Mpi_Isend	(	T *	buf,
		int	count,
		int	dest,
		int	tag,
		MPI_Comm	comm,
		MPI_Request *	request
	)

◆ Mpi_Issend()

template<typename T >

int par::Mpi_Issend	(	T *	buf,
		int	count,
		int	dest,
		int	tag,
		MPI_Comm	comm,
		MPI_Request *	request
	)

◆ Mpi_Recv()

template<typename T >

int par::Mpi_Recv	(	T *	buf,
		int	count,
		int	source,
		int	tag,
		MPI_Comm	comm,
		MPI_Status *	status
	)

◆ Mpi_Reduce()

template<typename T >

int par::Mpi_Reduce	(	T *	sendbuf,
		T *	recvbuf,
		int	count,
		MPI_Op	op,
		int	root,
		MPI_Comm	comm
	)

◆ Mpi_Scan()

template<typename T >

int par::Mpi_Scan	(	T *	sendbuf,
		T *	recvbuf,
		int	count,
		MPI_Op	op,
		MPI_Comm	comm
	)

◆ Mpi_Sendrecv()

template<typename T , typename S >

int par::Mpi_Sendrecv	(	T *	sendBuf,
		int	sendCount,
		int	dest,
		int	sendTag,
		S *	recvBuf,
		int	recvCount,
		int	source,
		int	recvTag,
		MPI_Comm	comm,
		MPI_Status *	status
	)

◆ Par_bitonic_merge_incr()

template<typename T >

void par::Par_bitonic_merge_incr	(	std::vector< T > &	local_list,
		int	proc_set_size,
		MPI_Comm	comm
	)

Author: Hari Sundar

◆ Par_bitonic_sort_decr()

template<typename T >

void par::Par_bitonic_sort_decr	(	std::vector< T > &	local_list,
		int	proc_set_size,
		MPI_Comm	comm
	)

Author: Hari Sundar

◆ Par_bitonic_sort_incr()

template<typename T >

void par::Par_bitonic_sort_incr	(	std::vector< T > &	local_list,
		int	proc_set_size,
		MPI_Comm	comm
	)

Author: Hari Sundar

◆ partitionW()

template<typename T >

int par::partitionW	(	std::vector< T > &	vec,
		unsigned int()(const T )	getWeight,
		MPI_Comm	comm
	)

A parallel weighted partitioning function. In our implementation, we do not pose any restriction on the input or the number of processors. This function can be used with an odd number of processors as well. Some processors can pass an empty vector as input. The relative ordering of the elements is preserved.

Author: Hari Sundar; Rahul Sampath

Parameters

vec	the input vector
getWeight	function pointer to compute the weight of each element. If you pass NULL, then every element will get a weight equal to 1.
comm	the communicator

◆ rankSamples()

template<typename T >

void par::rankSamples	(	std::vector< T > &	arr,
		std::vector< T >	samples,
		MPI_Comm	comm
	)

◆ sampleSort() [1/2]

template<typename T >

int par::sampleSort	(	std::vector< T > &	in,
		std::vector< T > &	out,
		MPI_Comm	comm
	)

A parallel sample sort implementation. In our implementation, we do not pose any restriction on the input or the number of processors. This function can be used with an odd number of processors as well. Some processors can pass an empty vector as input. If the total number of elements in the vector (globally) is fewer than 10*p^2, where p is the number of processors, then we will use bitonic sort instead of sample sort to sort the vector. We use a paralle bitonic sort to sort the samples in the sample sort algorithm. Hence, the complexity of the algorithm is O(n/p log n/p) + O(p log p). Here, n is the global length of the vector and p is the number of processors.

Author: Hari Sundar

Parameters

in	the input vector
out	the output vector
comm	the communicator

◆ sampleSort() [2/2]

template<typename T >

int par::sampleSort	(	std::vector< T > &	in,
		MPI_Comm	comm
	)

◆ Sorted_approx_Select()

template<typename T >

std::vector<T> par::Sorted_approx_Select	(	std::vector< T > &	arr,
		unsigned int	k,
		MPI_Comm	comm
	)

◆ Sorted_approx_Select_skewed()

template<typename T >

std::vector<std::pair<T, DendroIntL> > par::Sorted_approx_Select_skewed	(	std::vector< T > &	arr,
		unsigned int	k,
		MPI_Comm	comm
	)

new one to handle skewed distributions ...

◆ Sorted_k_Select()

template<typename T >

std::vector<T> par::Sorted_k_Select	(	std::vector< T > &	arr,
		std::vector< unsigned int >	min_idx,
		std::vector< unsigned int >	max_idx,
		std::vector< DendroIntL >	K,
		std::vector< T >	guess,
		MPI_Comm	comm
	)

A parallel k-selection algorithms.

Author: Hari Sundar

Date: 2013-01-10

Parameters

arr	arr from which samples are to be selected
k	number of samples
isSorted	if false, arr is locally sorted first.

Returns: list of k keys.

◆ Sorted_Sample_Select()

template<typename T >

std::vector<T> par::Sorted_Sample_Select	(	std::vector< T > &	arr,
		unsigned int	kway,
		std::vector< unsigned int > &	min_idx,
		std::vector< unsigned int > &	max_idx,
		std::vector< DendroIntL > &	splitter_ranks,
		MPI_Comm	comm
	)

◆ splitComm2way() [1/2]

int par::splitComm2way	(	bool	iAmEmpty,
		MPI_Comm *	new_comm,
		MPI_Comm	orig_comm
	)

Splits a communication group into two, one containing processors that passed a value of 'false' for the parameter 'iAmEmpty' and the another containing processors that passed a value of 'true' for the parameter. Both the groups are sorted in the ascending order of their ranks in the old comm.

Author: Rahul Sampath

Parameters

iAmEmpty	Some flag to determine which group the calling processor will be combined into.
orig_comm	The comm group that needs to be split.
new_comm	The new comm group.

Definition at line 120 of file parUtils.cpp.

◆ splitComm2way() [2/2]

int par::splitComm2way	(	const bool *	isEmptyList,
		MPI_Comm *	new_comm,
		MPI_Comm	orig_comm
	)

Splits a communication group into two depending on the values in isEmptyList. Both the groups are sorted in the ascending order of their ranks in the old comm. All processors must call this function with the same 'isEmptyList' array.

Author: Rahul Sampath

Parameters

isEmptyList	flags (of length equal to the number of processors) to determine whether each processor is active or not.
orig_comm	The comm group that needs to be split.
new_comm	The new comm group.

Definition at line 225 of file parUtils.cpp.

◆ splitCommBinary()

unsigned int par::splitCommBinary	(	MPI_Comm	orig_comm,
		MPI_Comm *	new_comm
	)

Splits a communication group into two, the first having a power of 2 number of processors and the other having the remainder. The first group is sorted in the ascending order of their ranks in the old comm and the second group is sorted in the descending order of their ranks in the old comm.

Author: Hari Sundar

Parameters

orig_comm	The comm group that needs to be split.
new_comm	The new comm group.

Definition at line 21 of file parUtils.cpp.

◆ splitCommBinaryNoFlip()

unsigned int par::splitCommBinaryNoFlip	(	MPI_Comm	orig_comm,
		MPI_Comm *	new_comm
	)

Splits a communication group into two, the first having a power of 2 number of processors and the other having the remainder. Both the groups are sorted in the ascending order of their ranks in the old comm.

Author: Hari Sundar

Parameters

orig_comm	The comm group that needs to be split.
new_comm	The new comm group.

Definition at line 70 of file parUtils.cpp.

◆ splitCommUsingSplittingRank()

int par::splitCommUsingSplittingRank	(	int	splittingRank,
		MPI_Comm *	new_comm,
		MPI_Comm	orig_comm
	)

Definition at line 180 of file parUtils.cpp.

Classes

Functions

Detailed Description

Function Documentation

◆ AdjustCommunicationPattern()

◆ bitonicSort()

◆ bitonicSort_binary()

◆ defaultWeight()

◆ GetRangeMean()

◆ GuessRangeMedian()

◆ HyperQuickSort() [1/2]

◆ HyperQuickSort() [2/2]

◆ HyperQuickSort_cav() [1/2]

◆ HyperQuickSort_cav() [2/2]

◆ HyperQuickSort_kway() [1/2]

◆ HyperQuickSort_kway() [2/2]

◆ MergeLists()

◆ MergeSplit()

◆ Mpi_Allgather()

◆ Mpi_Allgatherv()

◆ Mpi_Allreduce()

◆ Mpi_Alltoall()

◆ Mpi_Alltoallv_dense()

◆ Mpi_Alltoallv_sparse()

◆ Mpi_Bcast()

◆ Mpi_Gather()

◆ Mpi_Irecv()

◆ Mpi_Isend()

◆ Mpi_Issend()

◆ Mpi_Recv()

◆ Mpi_Reduce()

◆ Mpi_Scan()

◆ Mpi_Sendrecv()

◆ Par_bitonic_merge_incr()

◆ Par_bitonic_sort_decr()

◆ Par_bitonic_sort_incr()

◆ partitionW()

◆ rankSamples()

◆ sampleSort() [1/2]

◆ sampleSort() [2/2]

◆ Sorted_approx_Select()

◆ Sorted_approx_Select_skewed()

◆ Sorted_k_Select()

◆ Sorted_Sample_Select()

◆ splitComm2way() [1/2]

◆ splitComm2way() [2/2]

◆ splitCommBinary()

◆ splitCommBinaryNoFlip()

◆ splitCommUsingSplittingRank()