Why parallel matrix multiplication takes so long time? - c++

I create test code where I am computing in parallel one complex matrix.
I am computing on CPU.
I observed that it takes around 3 seconds to finish all the blocks.
Can someone explain why it takes so long time ?
Code
Utils.hpp
#pragma once
#include <chrono>
#include <armadillo>
namespace utils
{
class watch : std::chrono::steady_clock {
time_point start_ = now();
public: auto elapsed_sec() const {return std::chrono::duration<double>(now() - start_).count();}
};
void op_herk(arma::cx_mat && A, arma::cx_mat & C)
{
using blas_int = int;
using T = double;
const char uplo = 'U';
const char trans_A = 'N';
const auto n = blas_int(C.n_cols);
const auto k = blas_int(A.n_cols);
const T local_alpha = T(1);
const T local_beta = T(0);
const blas_int lda = n;
arma::blas::herk<T>( &uplo, &trans_A, &n, &k, &local_alpha, A.mem, &lda, &local_beta, C.memptr(), &n);
arma::herk_helper::inplace_conj_copy_upper_tri_to_lower_tri(C);
}
}
ThreadPoll
#pragma once
#include <boost/thread.hpp>
#include <boost/asio.hpp>
#include <boost/asio/thread_pool.hpp>
class ThreadPool {
public:
explicit ThreadPool(size_t size = boost::thread::hardware_concurrency()) : threadPool(size)
{ }
template<typename F>
void addTask(F &&f)
{
boost::asio::post(threadPool, std::forward<F>(f));
}
void wait()
{
threadPool.wait();
}
~ThreadPool()
{
threadPool.join();
}
private:
boost::asio::thread_pool threadPool;
};
main.cpp
#include <armadillo>
#include "Utils.h"
#include "ThreadPool.h"
int main() {
ThreadPool threadPool;
arma::cx_mat test (256, 30000 , arma::fill::randu);
arma::vec averageTime(30, arma::fill::zeros);
std::vector<arma::cx_mat > results(30);
for(auto &it : results)
it.set_size(256, 256);
{
for(int i = 0; i < 30; ++i)
{
threadPool.addTask([i = i, &results, &averageTime, test = test.submat(arma::span::all, arma::span(0, 20000)), _ = utils::watch() ]() {
utils::op_herk(test, results[i]);
arma::vec r = arma::sort(arma::eig_sym(results[i]), "descent");
std::cout << _.elapsed_sec() << '\n';
averageTime[i] = _.elapsed_sec();
});
}
threadPool.wait();
std::cout << "average " << arma::sum(averageTime)/averageTime.size() <<std::endl;
}
return 0;
}
Parameters :
gcc 9.4
computer : Intel 6 Cores , 12 threads;
armadillo 10.7.3
openblas 0.3.17
CMAKE parameters : set(CMAKE_CXX_FLAGS_RELEASE "${CMAKE_CXX_FLAGS} -msse2 -O3 -mtune=native -flto")
My results :
1.16084
1.16434
1.16571
1.16601
1.17055
1.17118
1.17382
1.17511
1.1767
1.17981
1.18254
1.18537
2.40071
2.40225
2.4025
2.40511
2.40545
2.40565
2.40583
2.40941
2.40972
2.40974
2.41172
2.41291
3.23446
3.23592
3.23734
3.23972
3.24305
3.24484
3.24728
average 2.14871

Related

Why cannot my c++ thread pool accelerate my program?

I tried to implement a c++ thread pool according to some notes made by others, the code is like this:
#include <vector>
#include <queue>
#include <functional>
#include <future>
#include <atomic>
#include <condition_variable>
#include <thread>
#include <mutex>
#include <memory>
#include <glog/logging.h>
#include <iostream>
#include <chrono>
using std::cout;
using std::endl;
class ThreadPool {
public:
ThreadPool(const ThreadPool&) = delete;
ThreadPool(ThreadPool&&) = delete;
ThreadPool& operator=(const ThreadPool&) = delete;
ThreadPool& operator=(ThreadPool&&) = delete;
ThreadPool(uint32_t capacity=std::thread::hardware_concurrency(),
uint32_t n_threads=std::thread::hardware_concurrency()
): capacity(capacity), n_threads(n_threads) {
init(capacity, n_threads);
}
~ThreadPool() noexcept {
shutdown();
}
void init(uint32_t capacity, uint32_t n_threads) {
CHECK_GT(capacity, 0) << "task queue capacity should be greater than 0";
CHECK_GT(n_threads, 0) << "thread pool capacity should be greater than 0";
for (int i{0}; i < n_threads; ++i) {
pool.emplace_back(std::thread([this] {
std::function<void(void)> task;
while (!this->stop) {
{
std::unique_lock<std::mutex> lock(this->q_mutex);
task_q_empty.wait(lock, [&] {return this->stop | !task_q.empty();});
if (this->stop) break;
task = this->task_q.front();
this->task_q.pop();
task_q_full.notify_one();
}
// auto id = std::this_thread::get_id();
// std::cout << "thread id is: " << id << std::endl;
task();
}
}));
}
}
void shutdown() {
stop = true;
task_q_empty.notify_all();
task_q_full.notify_all();
for (auto& thread : pool) {
if (thread.joinable()) {
thread.join();
}
}
}
template<typename F, typename...Args>
auto submit(F&& f, Args&&... args) -> std::future<decltype(f(args...))> {
using res_type = decltype(f(args...));
std::function<res_type(void)> func = std::bind(std::forward<F>(f), std::forward<Args>(args)...);
auto task_ptr = std::make_shared<std::packaged_task<res_type()>>(func);
{
std::unique_lock<std::mutex> lock(q_mutex);
task_q_full.wait(lock, [&] {return this->stop | task_q.size() <= capacity;});
CHECK (this->stop == false) << "should not add task to stopped queue\n";
task_q.emplace([task_ptr]{(*task_ptr)();});
}
task_q_empty.notify_one();
return task_ptr->get_future();
}
private:
std::vector<std::thread> pool;
std::queue<std::function<void(void)>> task_q;
std::condition_variable task_q_full;
std::condition_variable task_q_empty;
std::atomic<bool> stop{false};
std::mutex q_mutex;
uint32_t capacity;
uint32_t n_threads;
};
int add(int a, int b) {return a + b;}
int main() {
auto t1 = std::chrono::steady_clock::now();
int n_threads = 1;
ThreadPool tp;
tp.init(n_threads, 1024);
std::vector<std::future<int>> res;
for (int i{0}; i < 1000000; ++i) {
res.push_back(tp.submit(add, i, i+1));
}
auto t2 = std::chrono::steady_clock::now();
for (auto &el : res) {
el.get();
// cout << el.get() << endl;
}
tp.shutdown();
cout << "processing: "
<< std::chrono::duration<double, std::milli>(t2 - t1).count()
<< endl;
return 0;
}
The problem is that, when I set n_threads=1, the program takes the same length of time as I set n_threads=4. Since my gpu has 72 kernels (from the htop command), I believe the 4 thread would be faster than the 1 thread settings. What is the problem with this implementation of the thread pool please?
I found few issues:
1) Use ORing instead of the bitwise operation in the both conditional-variable waits:
Replace this - `task_q_empty.wait(lock, [&] {return this->stop | !task_q.empty();});`
By - `task_q_empty.wait(lock, [&] {return this->stop || !task_q.empty();});`
2) Use notify_all() in place of notify_one() in init() and submit().
3) Two condition_variables is unnecessary here, use only task_q_empty.
4) Your use case is not ideal. Switching of the threads may outweigh adding of two integers, it may appear more the threads longer the execution time. Test in optimized mode. Try scenario like this to simulate longer process:
int add(int a, int b) { this_thread::sleep_for(chrono::milliseconds(200)); return a + b; }

Efficiently process each unique permutation of a vector when number of unique elements in vector is much smaller than vector size

In a program I need to apply a function in parallel to each unique permutation of a vector. The size of the vector is around N=15
I already have a function void parallel_for_each_permutation which I can use in combination with a std::set to only process each unique permutation exactly once.
This all works well for the general case. However, in my use case the number of unique elements k per vector is very limited, usually around k=4. This means that I'm currently wasting time constructing the same unique permutation over and over again, just to throw it away because it has already been processed.
Is it possible to process all unique permutations in this special case, without constructing all N! permutations?
Example use-case:
#include <algorithm>
#include <thread>
#include <vector>
#include <mutex>
#include <numeric>
#include <set>
#include <iostream>
template<class Container1, class Container2>
struct Comp{
//compare element-wise less than
bool operator()(const Container1& l, const Container2& r) const{
auto pair = std::mismatch(l.begin(), l.end(), r.begin());
if(pair.first == l.end() && pair.second == r.end())
return false;
return *(pair.first) < *(pair.second);
}
};
template<class Container, class Func>
void parallel_for_each_permutation(const Container& container, int num_threads, Func func){
auto ithPermutation = [](int n, size_t i) -> std::vector<size_t>{
// https://stackoverflow.com/questions/7918806/finding-n-th-permutation-without-computing-others
std::vector<size_t> fact(n);
std::vector<size_t> perm(n);
fact[0] = 1;
for(int k = 1; k < n; k++)
fact[k] = fact[k-1] * k;
for(int k = 0; k < n; k++){
perm[k] = i / fact[n-1-k];
i = i % fact[n-1-k];
}
for(int k = n-1; k > 0; k--){
for(int j = k-1; j >= 0; j--){
if(perm[j] <= perm[k])
perm[k]++;
}
}
return perm;
};
size_t totalNumPermutations = 1;
for(size_t i = 1; i <= container.size(); i++)
totalNumPermutations *= i;
std::vector<std::thread> threads;
for(int threadId = 0; threadId < num_threads; threadId++){
threads.emplace_back([&, threadId](){
const size_t firstPerm = size_t(float(threadId) * totalNumPermutations / num_threads);
const size_t last_excl = std::min(totalNumPermutations, size_t(float(threadId+1) * totalNumPermutations / num_threads));
Container permutation(container);
auto permIndices = ithPermutation(container.size(), firstPerm);
size_t count = firstPerm;
do{
for(int i = 0; i < int(permIndices.size()); i++){
permutation[i] = container[permIndices[i]];
}
func(threadId, permutation);
std::next_permutation(permIndices.begin(), permIndices.end());
++count;
}while(count < last_excl);
});
}
for(auto& thread : threads)
thread.join();
}
template<class Container, class Func>
void parallel_for_each_unique_permutation(const Container& container, Func func){
using Comparator = Comp<Container, Container>;
constexpr int numThreads = 4;
std::set<Container, Comparator> uniqueProcessedPermutations(Comparator{});
std::mutex m;
parallel_for_each_permutation(
container,
numThreads,
[&](int threadId, const auto& permutation){
{
std::lock_guard<std::mutex> lg(m);
if(uniqueProcessedPermutations.count(permutation) > 0){
return;
}else{
uniqueProcessedPermutations.insert(permutation);
}
}
func(permutation);
}
);
}
int main(){
std::vector<int> vector1{1,1,1,1,2,3,2,2,3,3,1};
auto func = [](const auto& vec){return;};
parallel_for_each_unique_permutation(vector1, func);
}
The permutations you have to work with are known in the field of combinatorics as multiset permutations.
They are described for example on The Combinatorial Object Server
with more detailed explanations in this paper by professor Tadao Takaoka.
You have some related Python code and some C++ code in the FXT open source library.
You might consider adding the "multiset" and "combinatorics" tags to your question.
One possibility is to borrow the (header-only) algorithmic code from the FXT library, which provides a simple generator class for those multiset permutations.
Performance level:
Using the FXT algorithm on a test vector of 15 objects, {1,1,1, 2,2,2, 3,3,3,3, 4,4,4,4,4}, one can generate all associated 12,612,600 "permutations" in less than 2 seconds on a plain vanilla Intel x86-64 machine; this is without diagnostics text I/O and without any attempt at optimization.
The algorithm generates exactly those "permutations" that are required, nothing more. So there is no longer a need to generate all 15! "raw" permutations nor to use mutual exclusion to update a shared data structure for filtering purposes.
An adaptor class for generating the permutations:
I will try below to provide code for an adaptor class, which allows your application to use the FXT algorithm while containing the dependency into a single implementation file. That way, the code will hopefully fit better into your application. Think FXT's ulong type and use of raw pointers, versus std::vector<std::size_t> in your code. Besides, FXT is a very extensive library.
Header file for the "adaptor" class:
// File: MSetPermGen.h
#ifndef MSET_PERM_GEN_H
#define MSET_PERM_GEN_H
#include <iostream>
#include <vector>
class MSetPermGenImpl; // from algorithmic backend
using IntVec = std::vector<int>;
using SizeVec = std::vector<std::size_t>;
// Generator class for multiset permutations:
class MSetPermGen {
public:
MSetPermGen(const IntVec& vec);
std::size_t getCycleLength() const;
bool forward(size_t incr);
bool next();
const SizeVec& getPermIndices() const;
const IntVec& getItems() const;
const IntVec& getItemValues() const;
private:
std::size_t cycleLength_;
MSetPermGenImpl* genImpl_; // implementation generator
IntVec itemValues_; // only once each
IntVec items_; // copy of ctor argument
SizeVec freqs_; // repetition counts
SizeVec state_; // array of indices in 0..n-1
};
#endif
The class constructor takes exactly the argument type provided in your main program. Of course, the key method is next(). You can also move the automaton by several steps at once using the forward(incr)method.
Example client program:
// File: test_main.cpp
#include <cassert>
#include "MSetPermGen.h"
using std::cout;
using std::cerr;
using std::endl;
// utility functions:
std::vector<int> getMSPermutation(const MSetPermGen& mspg)
{
std::vector<int> res;
auto indices = mspg.getPermIndices(); // always between 0 and n-1
auto values = mspg.getItemValues(); // whatever the user put in
std::size_t n = indices.size();
assert( n == items.size() );
res.reserve(n);
for (std::size_t i=0; i < n; i++) {
auto xi = indices[i];
res.push_back(values[xi]);
}
return res;
}
void printPermutation(const std::vector<int>& p, std::ostream& fh)
{
std::size_t n = p.size();
for (size_t i=0; i < n; i++)
fh << p[i] << " ";
fh << '\n';
}
int main(int argc, const char* argv[])
{
std::vector<int> vec0{1,1, 2,2,2}; // N=5
std::vector<int> vec1{1,1, 1,1, 2, 3, 2,2, 3,3, 1}; // N=11
std::vector<int> vec2{1,1,1, 2,2,2, 3,3,3,3, 4,4,4,4,4}; // N=15
MSetPermGen pg0{vec0};
MSetPermGen pg1{vec1};
MSetPermGen pg2{vec2};
auto pg = &pg0; // choice of 0, 1, 2 for sizing
auto cl = pg->getCycleLength();
auto permA = getMSPermutation(*pg);
printPermutation(permA, cout);
for (std::size_t pi=0; pi < (cl-1); pi++) {
pg->next();
auto permB = getMSPermutation(*pg);
printPermutation(permB, cout);
}
return EXIT_SUCCESS;
}
Text output from the above small program:
1 1 2 2 2
1 2 1 2 2
1 2 2 1 2
1 2 2 2 1
2 1 1 2 2
2 1 2 1 2
2 1 2 2 1
2 2 1 1 2
2 2 1 2 1
2 2 2 1 1
You get only 10 items from vector {1,1, 2,2,2}, because 5! / (2! * 3!) = 120/(2*6) = 10.
The implementation file for the adaptor class, MSetPermGen.cpp, consists of two parts. The first part is FXT code with minimal adaptations. The second part is the MSetPermGen class proper.
First part of implementation file:
// File: MSetPermGen.cpp - part 1 of 2 - FXT code
// -------------- Beginning of header-only FXT combinatorics code -----------
// This file is part of the FXT library.
// Copyright (C) 2010, 2012, 2014 Joerg Arndt
// License: GNU General Public License version 3 or later,
// see the file COPYING.txt in the main directory.
//-- https://www.jjj.de/fxt/
//-- https://fossies.org/dox/fxt-2018.07.03/mset-perm-lex_8h_source.html
#include <cstddef>
using ulong = std::size_t;
inline void swap2(ulong& xa, ulong& xb)
{
ulong save_xb = xb;
xb = xa;
xa = save_xb;
}
class mset_perm_lex
// Multiset permutations in lexicographic order, iterative algorithm.
{
public:
ulong k_; // number of different sorts of objects
ulong *r_; // number of elements '0' in r[0], '1' in r[1], ..., 'k-1' in r[k-1]
ulong n_; // number of objects
ulong *ms_; // multiset data in ms[0], ..., ms[n-1], sentinels at [-1] and [-2]
private: // have pointer data
mset_perm_lex(const mset_perm_lex&); // forbidden
mset_perm_lex & operator = (const mset_perm_lex&); // forbidden
public:
explicit mset_perm_lex(const ulong *r, ulong k)
{
k_ = k;
r_ = new ulong[k];
for (ulong j=0; j<k_; ++j) r_[j] = r[j]; // get buckets
n_ = 0;
for (ulong j=0; j<k_; ++j) n_ += r_[j];
ms_ = new ulong[n_+2];
ms_[0] = 0; ms_[1] = 1; // sentinels: ms[0] < ms[1]
ms_ += 2; // nota bene
first();
}
void first()
{
for (ulong j=0, i=0; j<k_; ++j)
for (ulong h=r_[j]; h!=0; --h, ++i)
ms_[i] = j;
}
~mset_perm_lex()
{
ms_ -= 2;
delete [] ms_;
delete [] r_;
}
const ulong * data() const { return ms_; }
ulong next()
// Return position of leftmost change,
// return n with last permutation.
{
// find rightmost pair with ms[i] < ms[i+1]:
const ulong n1 = n_ - 1;
ulong i = n1;
do { --i; } while ( ms_[i] >= ms_[i+1] ); // can read sentinel
if ( (long)i < 0 ) return n_; // last sequence is falling seq.
// find rightmost element ms[j] less than ms[i]:
ulong j = n1;
while ( ms_[i] >= ms_[j] ) { --j; }
swap2(ms_[i], ms_[j]);
// Here the elements ms[i+1], ..., ms[n-1] are a falling sequence.
// Reverse order to the right:
ulong r = n1;
ulong s = i + 1;
while ( r > s ) { swap2(ms_[r], ms_[s]); --r; ++s; }
return i;
}
};
// -------------- End of header-only FXT combinatorics code -----------
Second part of the class implementation file:
// Second part of file MSetPermGen.cpp: non-FXT code
#include <cassert>
#include <tuple>
#include <map>
#include <iostream>
#include <cstdio>
#include "MSetPermGen.h"
using std::cout;
using std::cerr;
using std::endl;
class MSetPermGenImpl { // wrapper class
public:
MSetPermGenImpl(const SizeVec& freqs) : fg(freqs.data(), freqs.size())
{}
private:
mset_perm_lex fg;
friend class MSetPermGen;
};
static std::size_t fact(size_t n)
{
std::size_t f = 1;
for (std::size_t i = 1; i <= n; i++)
f = f*i;
return f;
}
MSetPermGen::MSetPermGen(const IntVec& vec) : items_(vec)
{
std::map<int,int> ma;
for (int i: vec) {
ma[i]++;
}
int item, freq;
for (const auto& p : ma) {
std::tie(item, freq) = p;
itemValues_.push_back(item);
freqs_.push_back(freq);
}
cycleLength_ = fact(items_.size());
for (auto i: freqs_)
cycleLength_ /= fact(i);
// create FXT-level generator:
genImpl_ = new MSetPermGenImpl(freqs_);
for (std::size_t i=0; i < items_.size(); i++)
state_.push_back(genImpl_->fg.ms_[i]);
}
std::size_t MSetPermGen::getCycleLength() const
{
return cycleLength_;
}
bool MSetPermGen::forward(size_t incr)
{
std::size_t n = items_.size();
std::size_t rc = 0;
// move forward state by brute force, could be improved:
for (std::size_t i=0; i < incr; i++)
rc = genImpl_->fg.next();
for (std::size_t j=0; j < n; j++)
state_[j] = genImpl_->fg.ms_[j];
return (rc != n);
}
bool MSetPermGen::next()
{
return forward(1);
}
const SizeVec& MSetPermGen::getPermIndices() const
{
return (this->state_);
}
const IntVec& MSetPermGen::getItems() const
{
return (this->items_);
}
const IntVec& MSetPermGen::getItemValues() const
{
return (this->itemValues_);
}
Adapting the parallel application:
Regarding your multithreaded application, given that generating the "permutations" is cheap, you can afford to create one generator object per thread.
Before launching the actual computation, you forward each generator to its appropriate initial position, that is at step thread_id * (cycleLength / num_threads).
I have tried to adapt your code to this MSetPermGen class along these lines. See code below.
With 3 threads, an input vector {1,1,1, 2,2,2, 3,3,3,3, 4,4,4,4,4} of size 15 (giving 12,612,600 permutations) and all diagnostics enabled, your modified parallel program runs in less than 10 seconds; less than 2 seconds with all diagnostics switched off.
Modified parallel program:
#include <algorithm>
#include <thread>
#include <vector>
#include <atomic>
#include <mutex>
#include <numeric>
#include <set>
#include <iostream>
#include <fstream>
#include <sstream>
#include <cstdlib>
#include "MSetPermGen.h"
using std::cout;
using std::endl;
// debug and instrumentation:
static std::atomic<size_t> permCounter;
static bool doManagePermCounter = true;
static bool doThreadLogfiles = true;
static bool doLogfileHeaders = true;
template<class Container, class Func>
void parallel_for_each_permutation(const Container& container, int numThreads, Func mfunc) {
MSetPermGen gen0(container);
std::size_t totalNumPermutations = gen0.getCycleLength();
std::size_t permShare = totalNumPermutations / numThreads;
if ((totalNumPermutations % numThreads) != 0)
permShare++;
std::cout << "totalNumPermutations: " << totalNumPermutations << std::endl;
std::vector<std::thread> threads;
for (int threadId = 0; threadId < numThreads; threadId++) {
threads.emplace_back([&, threadId]() {
// generate some per-thread logfile name
std::ostringstream fnss;
fnss << "thrlog_" << threadId << ".txt";
std::string fileName = fnss.str();
std::ofstream fh(fileName);
MSetPermGen thrGen(container);
const std::size_t firstPerm = permShare * threadId;
thrGen.forward(firstPerm);
const std::size_t last_excl = std::min(totalNumPermutations,
(threadId+1) * permShare);
if (doLogfileHeaders) {
fh << "MSG threadId: " << threadId << '\n';
fh << "MSG firstPerm: " << firstPerm << '\n';
fh << "MSG lastExcl : " << last_excl << '\n';
}
Container permutation(container);
auto values = thrGen.getItemValues();
auto permIndices = thrGen.getPermIndices();
auto nsz = permIndices.size();
std::size_t count = firstPerm;
do {
for (std::size_t i = 0; i < nsz; i++) {
permutation[i] = values[permIndices[i]];
}
mfunc(threadId, permutation);
if (doThreadLogfiles) {
for (std::size_t i = 0; i < nsz; i++)
fh << permutation[i] << ' ';
fh << '\n';
}
thrGen.next();
permIndices = thrGen.getPermIndices();
++count;
if (doManagePermCounter) {
permCounter++;
}
} while (count < last_excl);
fh.close();
});
}
for(auto& thread : threads)
thread.join();
}
template<class Container, class Func>
void parallel_for_each_unique_permutation(const Container& container, Func func) {
constexpr int numThreads = 3;
parallel_for_each_permutation(
container,
numThreads,
[&](int threadId, const auto& permutation){
// no longer need any mutual exclusion
func(permutation);
}
);
}
int main()
{
std::vector<int> vector1{1,1,1,1,2,3,2,2,3,3,1}; // N=11
std::vector<int> vector0{1,1, 2,2,2}; // N=5
std::vector<int> vector2{1,1,1, 2,2,2, 3,3,3,3, 4,4,4,4,4}; // N=15
auto func = [](const auto& vec) { return; };
permCounter.store(0);
parallel_for_each_unique_permutation(vector2, func);
auto finalPermCounter = permCounter.load();
cout << "FinalPermCounter = " << finalPermCounter << endl;
}

How to get the future value?

In using packaged_task, I collected all the futures in a vector. After that, I push back the future values with get(). However, I got the wrong answer. Can anyone help? Thank you very much.
#define BOOST_THREAD_PROVIDES_FUTURE
#include <boost/thread/future.hpp>
#include <vector>
#include <iostream>
using namespace std;
vector<int> subFun(int n) {
vector<int> a{ 2 * n, 3 * n };
return a;
}
int main() {
vector<boost::future<vector<int>>> g;
vector<vector<int>> x(10, vector<int>(2));
int i;
for (i = 0; i < 10; i++) {
boost::packaged_task<vector<int>> task{ boost::bind(&subFun, i) };
g.push_back(task.get_future());
boost::thread t{ std::move(task) };
}
for (auto& m : g) {
x.push_back(m.get());
}
cout << x[3][0] << endl;//should be 6, now is 0
return 0;
}
The realest issue is that you push_back into x, but you already had it initialized here:
vector<vector<int>> x(10, vector<int>(2));
So, you just add 10 more elements, instead of putting the result at indices 0..9. I'd suggest not pre-filling, like #patrick's answer, or instead filling the designated slot:
#define BOOST_THREAD_PROVIDES_FUTURE
#include <boost/thread/future.hpp>
#include <vector>
#include <iostream>
using namespace std;
void subFun(int n, vector<int>& into) {
into = { 2 * n, 3 * n };
}
int main() {
vector<boost::future<void>> futures;
vector<vector<int>> x(10, vector<int>(2));
for (size_t i = 0; i < x.size(); i++) {
boost::packaged_task<void> task{ boost::bind(&subFun, i, std::ref(x[i])) };
futures.push_back(task.get_future());
boost::thread(std::move(task)).detach();
}
for (auto& f : futures)
f.wait();
cout << x[3][0] << endl;
}
Of course you can be more complex:
#define BOOST_THREAD_PROVIDES_FUTURE
#include <boost/thread/future.hpp>
#include <vector>
#include <iostream>
struct TaskResult {
int index;
std::vector<int> data;
};
TaskResult subFun(int n) {
return { n, { 2 * n, 3 * n } };
}
int main() {
std::vector<boost::future<TaskResult>> futures;
std::vector<std::vector<int>> x(10, std::vector<int>(2));
for (size_t i = 0; i < x.size(); i++) {
boost::packaged_task<TaskResult> task{ boost::bind(&subFun, i) };
futures.push_back(task.get_future());
boost::thread(std::move(task)).detach();
}
for (auto& f : futures) {
auto r = f.get();
x[r.index] = r.data;
}
std::cout << x[3][0] << std::endl;
}
After much tinkering, I found this program works without abort traps (which I'm surprised you weren't getting):
#include <future>
#include <thread>
#include <functional>
#include <vector>
#include <iostream>
std::vector<int> subFun(int n) {
std::vector<int> a { 2 * n, 3 * n };
return a;
}
int main() {
std::vector<std::future<std::vector<int>>> g;
std::vector<std::vector<int>> x;
int i;
for (i = 0; i < 10; i++) {
std::packaged_task<std::vector<int>(int)> task{ subFun };
g.push_back(task.get_future());
std::thread { std::move(task), i }.detach();
}
for (auto& m : g) {
m.wait();
x.push_back(m.get());
}
std::cout << x[3][0] << std::endl; // is now 6
return 0;
}
Convert to boost as necessary. This answer was extremely helpful in finding a couple of key issues.

Increasing allocation performance for strings

I ported a Java GC test program to C++ (see the code below) as well as Python. The Java and Python performance is much greater than C++ and I was thinking this was due to all the calls to new that have to be done to create the strings each time. I've tried using Boost's fast_pool_allocator but that actually worsened performance from 700ms to 1200ms. Am I using the allocator wrong, or is there something else I should be doing?
EDIT: Compiled with g++ -O3 -march=native --std=c++11 garbage.cpp -lboost_system. g++ is version 4.8.1
One iteration takes in Python is about 300ms and with Java about 50ms. std::allocator gives about 700ms and boost::fast_pool_allocator gives about 1200ms.
#include <string>
#include <vector>
#include <chrono>
#include <list>
#include <iostream>
#include <boost/pool/pool_alloc.hpp>
#include <memory>
//#include <gc/gc_allocator.h>
using namespace std;
#include <sstream>
typedef boost::fast_pool_allocator<char> c_allocator;
//typedef std::allocator<char> c_allocator;
typedef basic_string<char, char_traits<char>, c_allocator> pool_string;
namespace patch {
template <typename T> pool_string to_string(const T& in) {
std::basic_stringstream<char, char_traits<char>, c_allocator> stm;
stm << in;
return stm.str();
}
}
#include "mytime.hpp"
class Garbage {
public:
vector<pool_string> outer;
vector<pool_string> old;
const int nThreads = 1;
//static auto time = chrono::high_resolution_clock();
void go() {
// outer.resize(1000000);
//old.reserve(1000000);
auto tt = mytime::msecs();
for (int i = 0; i < 10; ++i) {
if (i % 100 == 0) {
cout << "DOING AN OLD" << endl;
doOld();
tt = mytime::msecs();
}
for (int j = 0; j < 1000000/nThreads; ++j)
outer.push_back(patch::to_string(j));
outer.clear();
auto t = mytime::msecs();
cout << (t - tt) << endl;
tt = t;
}
}
void doOld() {
old.clear();
for (int i = 0; i < 1000000/nThreads; ++i)
old.push_back(patch::to_string(i));
}
};
int main() {
Garbage().go();
}
The problem is you're using a new string stream each time to convert an integer.
Fix it:
namespace patch {
template <typename T> pool_string to_string(const T& in) {
return boost::lexical_cast<pool_string>(in);
}
}
Now the timings are:
DOING AN OLD
0.175462
0.0670085
0.0669926
0.0687969
0.0692518
0.0669318
0.0669196
0.0669187
0.0668962
0.0669185
real 0m0.801s
user 0m0.784s
sys 0m0.016s
See it Live On Coliru
Full code for reference:
#include <boost/pool/pool_alloc.hpp>
#include <chrono>
#include <iostream>
#include <list>
#include <memory>
#include <sstream>
#include <string>
#include <vector>
#include <boost/lexical_cast.hpp>
//#include <gc/gc_allocator.h>
using string = std::string;
namespace patch {
template <typename T> string to_string(const T& in) {
return boost::lexical_cast<string>(in);
}
}
class Timer
{
typedef std::chrono::high_resolution_clock clock;
clock::time_point _start;
public:
Timer() { reset(); }
void reset() { _start = now(); }
double elapsed()
{
using namespace std::chrono;
auto e = now() - _start;
return duration_cast<nanoseconds>(e).count()*1.0e-9;
}
clock::time_point now()
{
return clock::now();
}
};
class Garbage {
public:
std::vector<string> outer;
std::vector<string> old;
const int nThreads = 1;
void go() {
outer.resize(1000000);
//old.reserve(1000000);
Timer timer;
for (int i = 0; i < 10; ++i) {
if (i % 100 == 0) {
std::cout << "DOING AN OLD" << std::endl;
doOld();
}
for (int j = 0; j < 1000000/nThreads; ++j)
outer.push_back(patch::to_string(j));
outer.clear();
std::cout << timer.elapsed() << std::endl;
timer.reset();
}
}
void doOld() {
old.clear();
for (int i = 0; i < 1000000/nThreads; ++i)
old.push_back(patch::to_string(i));
}
};
int main() {
Garbage().go();
}
Since I don't use boost on my machine, I simplified the code to use standard C++11 to_string (thus accidentally "fixing" the problem sehe found), and got this:
#include <string>
#include <vector>
#include <chrono>
#include <list>
#include <iostream>
#include <memory>
//#include <gc/gc_allocator.h>
#include <sstream>
using namespace std;
class Timer
{
typedef std::chrono::high_resolution_clock clock;
clock::time_point _start;
public:
Timer() { reset(); }
void reset() { _start = now(); }
double elapsed()
{
using namespace std::chrono;
auto e = now() - _start;
return duration_cast<nanoseconds>(e).count()*1.0e-9;
}
clock::time_point now()
{
return clock::now();
}
};
class Garbage {
public:
vector<string> outer;
vector<string> old;
const int nThreads = 1;
Timer timer;
void go() {
// outer.resize(1000000);
//old.reserve(1000000);
for (int i = 0; i < 10; ++i) {
if (i % 100 == 0) {
cout << "DOING AN OLD" << endl;
doOld();
}
for (int j = 0; j < 1000000/nThreads; ++j)
outer.push_back(to_string(j));
outer.clear();
cout << timer.elapsed() << endl;
timer.reset();
}
}
void doOld() {
old.clear();
for (int i = 0; i < 1000000/nThreads; ++i)
old.push_back(to_string(i));
}
};
int main() {
Garbage().go();
}
Compiling with:
$ g++ -O3 -std=c++11 gc.cpp
$ ./a.out
DOING AN OLD
0.414637
0.189082
0.189143
0.186336
0.184449
0.18504
0.186302
0.186055
0.183123
0.186835
clang 3.5 build with source from Friday 18th of April 2014 gives similar results with the same compiler options.
My processor is a AMD Phenom(tm) II X4 965, running at 3.6GHz (if I remember right).

How to optimize an indirect radix sort? (a.k.a. how to optimize unpredictable memory access patterns)

I've written an indirect radix sort algorithm in C++ (by indirect, I mean it returns the indices of the items):
#include <algorithm>
#include <iterator>
#include <vector>
template<class It1, class It2>
void radix_ipass(
It1 begin, It1 const end,
It2 const a, size_t const i,
std::vector<std::vector<size_t> > &buckets)
{
size_t ncleared = 0;
for (It1 j = begin; j != end; ++j)
{
size_t const k = a[*j][i];
while (k >= ncleared && ncleared < buckets.size())
{ buckets[ncleared++].clear(); }
if (k >= buckets.size())
{
buckets.resize(k + 1);
ncleared = buckets.size();
}
buckets[k].push_back(size_t());
using std::swap; swap(buckets[k].back(), *j);
}
for (std::vector<std::vector<size_t> >::iterator
j = buckets.begin(); j != buckets.begin() + ncleared; j->clear(), ++j)
{
begin = std::swap_ranges(j->begin(), j->end(), begin);
}
}
template<class It, class It2>
void radix_isort(It const begin, It const end, It2 const items)
{
for (ptrdiff_t i = 0; i != end - begin; ++i) { items[i] = i; }
size_t smax = 0;
for (It i = begin; i != end; ++i)
{
size_t const n = i->size();
smax = n > smax ? n : smax;
}
std::vector<std::vector<size_t> > buckets;
for (size_t i = 0; i != smax; ++i)
{
radix_ipass(
items, items + (end - begin),
begin, smax - i - 1, buckets);
}
}
It seems to perform around 40% faster than std::sort when I test it with the following code (3920 ms compared to 6530 ms):
#include <functional>
template<class Key>
struct key_comp : public Key
{
explicit key_comp(Key const &key = Key()) : Key(key) { }
template<class T>
bool operator()(T const &a, T const &b) const
{ return this->Key::operator()(a) < this->Key::operator()(b); }
};
template<class Key>
key_comp<Key> make_key_comp(Key const &key) { return key_comp<Key>(key); }
template<class T1, class T2>
struct add : public std::binary_function<T1, T2, T1>
{ T1 operator()(T1 a, T2 const &b) const { return a += b; } };
template<class F>
struct deref : public F
{
deref(F const &f) : F(f) { }
typename std::iterator_traits<
typename F::result_type
>::value_type const
&operator()(typename F::argument_type const &a) const
{ return *this->F::operator()(a); }
};
template<class T> deref<T> make_deref(T const &t) { return deref<T>(t); }
size_t xorshf96(void) // random number generator
{
static size_t x = 123456789, y = 362436069, z = 521288629;
x ^= x << 16;
x ^= x >> 5;
x ^= x << 1;
size_t t = x;
x = y;
y = z;
z = t ^ x ^ y;
return z;
}
#include <stdio.h>
#include <time.h>
#include <array>
int main(void)
{
typedef std::vector<std::array<size_t, 3> > Items;
Items items(1 << 24);
std::vector<size_t> ranks(items.size() * 2);
for (size_t i = 0; i != items.size(); i++)
{
ranks[i] = i;
for (size_t j = 0; j != items[i].size(); j++)
{ items[i][j] = xorshf96() & 0xFFF; }
}
clock_t const start = clock();
if (1) { radix_isort(items.begin(), items.end(), ranks.begin()); }
else // STL sorting
{
std::sort(
ranks.begin(),
ranks.begin() + items.size(),
make_key_comp(make_deref(std::bind1st(
add<Items::const_iterator, ptrdiff_t>(),
items.begin()))));
}
printf("%u ms\n",
(unsigned)((clock() - start) * 1000 / CLOCKS_PER_SEC),
std::min(ranks.begin(), ranks.end()));
return 0;
}
Hmm, I guess that's the best I can do, I thought.
But after lots of banging my head against the wall, I realized that prefetching in the beginning of radix_ipass can help cut down the result to 1440 ms (!):
#include <xmmintrin.h>
...
for (It1 j = begin; j != end; ++j)
{
#if defined(_MM_TRANSPOSE4_PS) // should be defined if xmmintrin.h is included
enum { N = 8 };
if (end - j > N)
{ _mm_prefetch((char const *)(&a[j[N]][i]), _MM_HINT_T0); }
#endif
...
}
Clearly, the bottleneck is the memory bandwidth---the access pattern is unpredictable.
So now my question is: what else can I do to make it even faster on similar amounts of data?
Or is there not much room left for improvement?
(I'm hoping to avoid compromising the readability of the code if possible, so if the readability is harmed, the improvement should be significant.)
Using a more compact data structure that combines ranks and values can boost the performance of std::sort by a factor 2-3. Essentially, the sort now runs on a vector<pair<Value,Rank>>. The Value data type, std::array<integer_type, 3> has been replaced for this by a more compact pair<uint32_t, uint8_t> data structure. Only half a byte of it is unused, and the < comparison can by done in two steps, first using a presumably efficient comparison of uint32_ts (it's not clear if the loop used by std::array<..>::operator< can be optimized to a similarly fast code, but the replacement of std::array<integer_type,3> by this data structure yielded another performance boost).
Still, it doesn't get as efficient as the radix sort. (Maybe you could tweak a custom QuickSort with prefetches?)
Besides that additional sorting method, I've replaced the xorshf96 by a mt19937, because I know how to provide a seed for the latter ;)
The seed and the number of values can be changed via two command-line arguments: first the seed, then the count.
Compiled with g++ 4.9.0 20131022, using -std=c++11 -march=native -O3, for a 64-bit linux
Sample runs; important note running on a Core2Duo processor U9400 (old & slow!)
item count: 16000000
using std::sort
duration: 12260 ms
result sorted: true
seed: 5648
item count: 16000000
using std::sort
duration: 12230 ms
result sorted: true
seed: 5648
item count: 16000000
using std::sort
duration: 12230 ms
result sorted: true
seed: 5648
item count: 16000000
using std::sort with a packed data structure
duration: 4290 ms
result sorted: true
seed: 5648
item count: 16000000
using std::sort with a packed data structure
duration: 4270 ms
result sorted: true
seed: 5648
item count: 16000000
using std::sort with a packed data structure
duration: 4280 ms
result sorted: true
item count: 16000000
using radix sort
duration: 3790 ms
result sorted: true
seed: 5648
item count: 16000000
using radix sort
duration: 3820 ms
result sorted: true
seed: 5648
item count: 16000000
using radix sort
duration: 3780 ms
result sorted: true
New or changed code:
template<class It>
struct fun_obj
{
It beg;
bool operator()(ptrdiff_t lhs, ptrdiff_t rhs)
{
return beg[lhs] < beg[rhs];
}
};
template<class It>
fun_obj<It> make_fun_obj(It beg)
{
return fun_obj<It>{beg};
}
struct uint32p8_t
{
uint32_t m32;
uint8_t m8;
uint32p8_t(std::array<uint16_t, 3> const& a)
: m32( a[0]<<(32-3*4) | a[1]<<(32-2*3*4) | (a[2]&0xF00)>>8)
, m8( a[2]&0xFF )
{
}
operator std::array<size_t, 3>() const
{
return {{m32&0xFFF00000 >> (32-3*4), m32&0x000FFF0 >> (32-2*3*4),
(m32&0xF)<<8 | m8}};
}
friend bool operator<(uint32p8_t const& lhs, uint32p8_t const& rhs)
{
if(lhs.m32 < rhs.m32) return true;
if(lhs.m32 > rhs.m32) return false;
return lhs.m8 < rhs.m8;
}
};
#include <stdio.h>
#include <time.h>
#include <array>
#include <iostream>
#include <iomanip>
#include <utility>
#include <algorithm>
#include <cstdlib>
#include <iomanip>
#include <random>
int main(int argc, char* argv[])
{
std::cout.sync_with_stdio(false);
constexpr auto items_count_default = 2<<22;
constexpr auto seed_default = 42;
uint32_t const seed = argc > 1 ? std::atoll(argv[1]) : seed_default;
std::cout << "seed: " << seed << "\n";
size_t const items_count = argc > 2 ? std::atoll(argv[2])
: items_count_default;
std::cout << "item count: " << items_count << "\n";
using Items_array_value_t =
#ifdef RADIX_SORT
size_t
#elif defined(STDSORT)
uint16_t
#elif defined(STDSORT_PACKED)
uint16_t
#endif
;
typedef std::vector<std::array<Items_array_value_t, 3> > Items;
Items items(items_count);
auto const ranks_count =
#ifdef RADIX_SORT
items.size() * 2
#elif defined(STDSORT)
items.size()
#elif defined(STDSORT_PACKED)
items.size()
#endif
;
//auto prng = xorshf96;
std::mt19937 gen(seed);
std::uniform_int_distribution<> dist;
auto prng = [&dist, &gen]{return dist(gen);};
std::vector<size_t> ranks(ranks_count);
for (size_t i = 0; i != items.size(); i++)
{
ranks[i] = i;
for (size_t j = 0; j != items[i].size(); j++)
{ items[i][j] = prng() & 0xFFF; }
}
std::cout << "using ";
clock_t const start = clock();
#ifdef RADIX_SORT
std::cout << "radix sort\n";
radix_isort(items.begin(), items.end(), ranks.begin());
#elif defined(STDSORT)
std::cout << "std::sort\n";
std::sort(ranks.begin(), ranks.begin() + items.size(),
make_fun_obj(items.cbegin())
//make_key_comp(make_deref(std::bind1st(
// add<Items::const_iterator, ptrdiff_t>(),
// items.begin())))
);
#elif defined(STDSORT_PACKED)
std::cout << "std::sort with a packed data structure\n";
using Items_ranks = std::vector< std::pair<uint32p8_t,
decltype(ranks)::value_type> >;
Items_ranks items_ranks;
size_t i = 0;
for(auto iI = items.cbegin(); iI != items.cend(); ++iI, ++i)
{
items_ranks.emplace_back(*iI, i);
}
std::sort(begin(items_ranks), end(items_ranks),
[](Items_ranks::value_type const& lhs,
Items_ranks::value_type const& rhs)
{ return lhs.first < rhs.first; }
);
std::transform(items_ranks.cbegin(), items_ranks.cend(), begin(ranks),
[](Items_ranks::value_type const& e) { return e.second; }
);
#endif
auto const duration = (clock() - start) / (CLOCKS_PER_SEC / 1000);
bool const sorted = std::is_sorted(ranks.begin(), ranks.begin() + items.size(),
make_fun_obj(items.cbegin()));
std::cout << "duration: " << duration << " ms\n"
<< "result sorted: " << std::boolalpha << sorted << "\n";
return 0;
}
Full code:
#include <algorithm>
#include <iterator>
#include <vector>
#include <cstddef>
using std::size_t;
using std::ptrdiff_t;
#include <xmmintrin.h>
template<class It1, class It2>
void radix_ipass(
It1 begin, It1 const end,
It2 const a, size_t const i,
std::vector<std::vector<size_t> > &buckets)
{
size_t ncleared = 0;
for (It1 j = begin; j != end; ++j)
{
#if defined(_MM_TRANSPOSE4_PS)
constexpr auto N = 8;
if(end - j > N)
{ _mm_prefetch((char const *)(&a[j[N]][i]), _MM_HINT_T0); }
#else
#error SS intrinsic not found
#endif
size_t const k = a[*j][i];
while (k >= ncleared && ncleared < buckets.size())
{ buckets[ncleared++].clear(); }
if (k >= buckets.size())
{
buckets.resize(k + 1);
ncleared = buckets.size();
}
buckets[k].push_back(size_t());
using std::swap; swap(buckets[k].back(), *j);
}
for (std::vector<std::vector<size_t> >::iterator
j = buckets.begin(); j != buckets.begin() + ncleared; j->clear(), ++j)
{
begin = std::swap_ranges(j->begin(), j->end(), begin);
}
}
template<class It, class It2>
void radix_isort(It const begin, It const end, It2 const items)
{
for (ptrdiff_t i = 0; i != end - begin; ++i) { items[i] = i; }
size_t smax = 0;
for (It i = begin; i != end; ++i)
{
size_t const n = i->size();
smax = n > smax ? n : smax;
}
std::vector<std::vector<size_t> > buckets;
for (size_t i = 0; i != smax; ++i)
{
radix_ipass(
items, items + (end - begin),
begin, smax - i - 1, buckets);
}
}
#include <functional>
template<class Key>
struct key_comp : public Key
{
explicit key_comp(Key const &key = Key()) : Key(key) { }
template<class T>
bool operator()(T const &a, T const &b) const
{ return this->Key::operator()(a) < this->Key::operator()(b); }
};
template<class Key>
key_comp<Key> make_key_comp(Key const &key) { return key_comp<Key>(key); }
template<class T1, class T2>
struct add : public std::binary_function<T1, T2, T1>
{ T1 operator()(T1 a, T2 const &b) const { return a += b; } };
template<class F>
struct deref : public F
{
deref(F const &f) : F(f) { }
typename std::iterator_traits<
typename F::result_type
>::value_type const
&operator()(typename F::argument_type const &a) const
{ return *this->F::operator()(a); }
};
template<class T> deref<T> make_deref(T const &t) { return deref<T>(t); }
size_t xorshf96(void) // random number generator
{
static size_t x = 123456789, y = 362436069, z = 521288629;
x ^= x << 16;
x ^= x >> 5;
x ^= x << 1;
size_t t = x;
x = y;
y = z;
z = t ^ x ^ y;
return z;
}
template<class It>
struct fun_obj
{
It beg;
bool operator()(ptrdiff_t lhs, ptrdiff_t rhs)
{
return beg[lhs] < beg[rhs];
}
};
template<class It>
fun_obj<It> make_fun_obj(It beg)
{
return fun_obj<It>{beg};
}
struct uint32p8_t
{
uint32_t m32;
uint8_t m8;
uint32p8_t(std::array<uint16_t, 3> const& a)
: m32( a[0]<<(32-3*4) | a[1]<<(32-2*3*4) | (a[2]&0xF00)>>8)
, m8( a[2]&0xFF )
{
}
operator std::array<size_t, 3>() const
{
return {{m32&0xFFF00000 >> (32-3*4), m32&0x000FFF0 >> (32-2*3*4),
(m32&0xF)<<8 | m8}};
}
friend bool operator<(uint32p8_t const& lhs, uint32p8_t const& rhs)
{
if(lhs.m32 < rhs.m32) return true;
if(lhs.m32 > rhs.m32) return false;
return lhs.m8 < rhs.m8;
}
};
#include <stdio.h>
#include <time.h>
#include <array>
#include <iostream>
#include <iomanip>
#include <utility>
#include <algorithm>
#include <cstdlib>
#include <iomanip>
#include <random>
int main(int argc, char* argv[])
{
std::cout.sync_with_stdio(false);
constexpr auto items_count_default = 2<<22;
constexpr auto seed_default = 42;
uint32_t const seed = argc > 1 ? std::atoll(argv[1]) : seed_default;
std::cout << "seed: " << seed << "\n";
size_t const items_count = argc > 2 ? std::atoll(argv[2]) : items_count_default;
std::cout << "item count: " << items_count << "\n";
using Items_array_value_t =
#ifdef RADIX_SORT
size_t
#elif defined(STDSORT)
uint16_t
#elif defined(STDSORT_PACKED)
uint16_t
#endif
;
typedef std::vector<std::array<Items_array_value_t, 3> > Items;
Items items(items_count);
auto const ranks_count =
#ifdef RADIX_SORT
items.size() * 2
#elif defined(STDSORT)
items.size()
#elif defined(STDSORT_PACKED)
items.size()
#endif
;
//auto prng = xorshf96;
std::mt19937 gen(seed);
std::uniform_int_distribution<> dist;
auto prng = [&dist, &gen]{return dist(gen);};
std::vector<size_t> ranks(ranks_count);
for (size_t i = 0; i != items.size(); i++)
{
ranks[i] = i;
for (size_t j = 0; j != items[i].size(); j++)
{ items[i][j] = prng() & 0xFFF; }
}
std::cout << "using ";
clock_t const start = clock();
#ifdef RADIX_SORT
std::cout << "radix sort\n";
radix_isort(items.begin(), items.end(), ranks.begin());
#elif defined(STDSORT)
std::cout << "std::sort\n";
std::sort(ranks.begin(), ranks.begin() + items.size(),
make_fun_obj(items.cbegin())
//make_key_comp(make_deref(std::bind1st(
// add<Items::const_iterator, ptrdiff_t>(),
// items.begin())))
);
#elif defined(STDSORT_PACKED)
std::cout << "std::sort with a packed data structure\n";
using Items_ranks = std::vector< std::pair<uint32p8_t,
decltype(ranks)::value_type> >;
Items_ranks items_ranks;
size_t i = 0;
for(auto iI = items.cbegin(); iI != items.cend(); ++iI, ++i)
{
items_ranks.emplace_back(*iI, i);
}
std::sort(begin(items_ranks), end(items_ranks),
[](Items_ranks::value_type const& lhs,
Items_ranks::value_type const& rhs)
{ return lhs.first < rhs.first; }
);
std::transform(items_ranks.cbegin(), items_ranks.cend(), begin(ranks),
[](Items_ranks::value_type const& e) { return e.second; }
);
#endif
auto const duration = (clock() - start) / (CLOCKS_PER_SEC / 1000);
bool const sorted = std::is_sorted(ranks.begin(), ranks.begin() + items.size(),
make_fun_obj(items.cbegin()));
std::cout << "duration: " << duration << " ms\n"
<< "result sorted: " << std::boolalpha << sorted << "\n";
return 0;
}