Make Sparse Matrix Multiply Fast - c++

The code is written using C++11. Each Process got tow Matrix Data(Sparse). The test data can be downloaded from enter link description here
Test data contains 2 file : a0 (Sparse Matrix 0) and a1 (Sparse Matrix 1). Each line in file is "i j v", means the sparse matrix Row i, Column j has the value v. i,j,v are all integers.
Use c++11 unordered_map as the sparse matrix's data structure.
unordered_map<int, unordered_map<int, double> > matrix1 ;
matrix1[i][j] = v ; //means at row i column j of matrix1 is value v;
The following code took about 2 minutes. The compile command is g++ -O2 -std=c++11 ./matmult.cpp.
g++ version is 4.8.1, Opensuse 13.1. My computer's info : Intel(R) Core(TM) i5-4200U CPU # 1.60GHz, 4G memory.
#include <iostream>
#include <fstream>
#include <unordered_map>
#include <vector>
#include <thread>
using namespace std;
void load(string fn, unordered_map<int,unordered_map<int, double> > &m) {
ifstream input ;
input.open(fn);
int i, j ; double v;
while (input >> i >> j >> v) {
m[i][j] = v;
}
}
unordered_map<int,unordered_map<int, double> > m1;
unordered_map<int,unordered_map<int, double> > m2;
//vector<vector<int> > keys(BLK_SIZE);
int main() {
load("./a0",m1);
load("./a1",m2);
for (auto r1 : m1) {
for (auto r2 : m2) {
double sim = 0.0 ;
for (auto c1 : r1.second) {
auto f = r2.second.find(c1.first);
if (f != r2.second.end()) {
sim += (f->second) * (c1.second) ;
}
}
}
}
return 0;
}
The code above is too slow. How can I make it run faster? I use multithread.
The new code is following, compile command is g++ -O2 -std=c++11 -pthread ./test.cpp. And it took about 1 minute. I want it to be faster.
How Can I make the task faster? Thank you!
#include <iostream>
#include <fstream>
#include <unordered_map>
#include <vector>
#include <thread>
#define BLK_SIZE 8
using namespace std;
void load(string fn, unordered_map<int,unordered_map<int, double> > &m) {
ifstream input ;
input.open(fn);
int i, j ; double v;
while (input >> i >> j >> v) {
m[i][j] = v;
}
}
unordered_map<int,unordered_map<int, double> > m1;
unordered_map<int,unordered_map<int, double> > m2;
vector<vector<int> > keys(BLK_SIZE);
void thread_sim(int blk_id) {
for (auto row1_id : keys[blk_id]) {
auto r1 = m1[row1_id];
for (auto r2p : m2) {
double sim = 0.0;
for (auto col1 : r1) {
auto f = r2p.second.find(col1.first);
if (f != r2p.second.end()) {
sim += (f->second) * col1.second ;
}
}
}
}
}
int main() {
load("./a0",m1);
load("./a1",m2);
int df = BLK_SIZE - (m1.size() % BLK_SIZE);
int blk_rows = (m1.size() + df) / (BLK_SIZE - 1);
int curr_thread_id = 0;
int index = 0;
for (auto k : m1) {
keys[curr_thread_id].push_back(k.first);
index++;
if (index==blk_rows) {
index = 0;
curr_thread_id++;
}
}
cout << "ok" << endl;
std::thread t[BLK_SIZE];
for (int i = 0 ; i < BLK_SIZE ; ++i){
t[i] = std::thread(thread_sim,i);
}
for (int i = 0; i< BLK_SIZE; ++i)
t[i].join();
return 0 ;
}

Most times when working with sparse matrices one uses more efficient representations than the nested maps you have. Typical choices are Compressed Sparse Row (CSR) or Compressed Sparse Column (CSC). See https://en.wikipedia.org/wiki/Sparse_matrix for details.

You haven't specified the time you expect your example to run in or the platform you hope to run on. These are important design contraints in this example.
There are several areas that I can think of for improving the efficeny of this:-
Improve the way the data is stored
Improve the multithreading
Improve the algorithm
The first point is geared toward the way the system stores the sparse arrays and the interfaces to enable the data to be read. Nested unordered_maps are a good option when speed isn't important but there may be more specific data structures available that are geared toward this problem. At best you may find a library that provides a better way to store the data than nested maps, at worst you may have to come up with something yourself.
The second point refers to the way the multithreading is supported in the language. The original spec for the multithreading system were meant to be platform independant and might miss out handy features some systems might have. Decide what system you want to target and use the OSs threading system. You'll have more control over the way the threading works, possibly reduce the overhead but will lose out on the cross platform support.
The third point will take a bit of work. Is the way you're multiplying the matricies really the most efficent way given the nature of the data. I'm no expert on these things but it is something to consider but it will take a bit of effort.
Lastly, you can always be very specific about the platform you're running on and head into the world of assembly programming. Modern CPUs are complicated beasts. They can sometimes perform operations in parallel. For example, you may be able to do SIMD operations or do parallel integer and floating point operations. Doing this does require a deep understanding of what's going on and there are useful tools to help you out. Intel did have a tool called VTune (it may be something else now) that would analyse code and highlight potential bottlenecks. Ultimately, you'll be wanting to eliminate areas of the algorithm where the CPU is idle waiting for something to happen (like waiting for data from RAM) either by finding something else for the CPU to do or improving the algorithm (or both).
Ultimately, in order to improve the overall speed, you'll need to know what is slowing it down. This generally means knowing how to analyse your code and understand the results. Profilers are the general tool for this but there are platform specific tools available as well.
I know this isn't quite what you want but making code fast is really hard and very time consuming.

Related

Why my inversions of matrices are such slow with LAPACKE in C++ : MAGMA Alternative and set up

I am using LAPACK to inverse a matrix: I did a reference passing, i.e by working on the address. Here below the function with an input matrix and an output matrix referenced by their address.
The issue is that I am obliged to convert the F_matrix into 1D array and I think this is a waste of performances on the runtime level : which way could I find to get rid of this supplementary task which is time consuming I think if I call a lot of times the
function matrix_inverse_lapack.
Below the function concerned :
// Passing Matrixes by Reference
void matrix_inverse_lapack(vector<vector<double>> const &F_matrix, vector<vector<double>> &F_output) {
// Index for loop and arrays
int i, j, ip, idx;
// Size of F_matrix
int N = F_matrix.size();
int *IPIV = new int[N];
// Statement of main array to inverse
double *arr = new double[N*N];
// Output Diagonal block
double *diag = new double[N];
for (i = 0; i<N; i++){
for (j = 0; j<N; j++){
idx = i*N + j;
arr[idx] = F_matrix[i][j];
}
}
// LAPACKE routines
int info1 = LAPACKE_dgetrf(LAPACK_ROW_MAJOR, N, N, arr, N, IPIV);
int info2 = LAPACKE_dgetri(LAPACK_ROW_MAJOR, N, arr, N, IPIV);
for (i = 0; i<N; i++){
for (j = 0; j<N; j++){
idx = i*N + j;
F_output[i][j] = arr[idx];
}
}
delete[] IPIV;
delete[] arr;
}
For example, I call it this way :
vector<vector<double>> CO_CL(lsize*(2*Dim_x+Dim_y), vector<double>(lsize*(2*Dim_x+Dim_y), 0));
... some code
matrix_inverse_lapack(CO_CL, CO_CL);
The performances on inversion are not which are expected, I think this is due to this conversion 2D -> 1D that I described in the function matrix_inverse_lapack.
Update
I was advised to install MAGMA on my MacOS Big Sur 11.3 but I have a lot of difficulties to set up it.
I have a AMD Radeon Pro 5600M graphic card. I have already installed by default Big Sur version all the Framework OpenCL (maybe I am wrong by saying that). Anyone could tell the procedure to follow for the installation of MAGMA. I saw that on a MAGMA software exists on http://magma.maths.usyd.edu.au/magma/ but it is really expensive and doesn't correspond to what I want : I just need all the SDK (headers and libraries) , if possible built with my GPU card. I have already installed all the Intel OpenAPI SDK on my MacOS. Maybe, I could link it to a MAGMA installation.
I saw another link https://icl.utk.edu/magma/software/index.html where MAGMA seems to be public : there is none link with the non-free version above, isn't there ?
First of all let me complain that OP did not provide all necessary data. The program is almost complete, but it is not a minimal, reproducible example. This is important because (a) it wastes time and (b) it hides potentially relevant information, eg. about the matrix initialization. Second, OP did not provide any details on the compilation, which, again may be relevant.
Last, but not least, OP didn't check the status code for possible errors from Lapack functions, and this could also be important for correct interpretation of the results.
Let's start from a minimal reproducible example:
#include <lapacke.h>
#include <vector>
#include <chrono>
#include <iostream>
using Matrix = std::vector<std::vector<double>>;
std::ostream &operator<<(std::ostream &out, Matrix const &v)
{
const auto size = std::min<int>(10, v.size());
for (int i = 0; i < size; i++)
{
for (int j = 0; j < size; j++)
{
out << v[i][j] << "\t";
}
if (size < std::ssize(v)) out << "...";
out << "\n";
}
return out;
}
void matrix_inverse_lapack(Matrix const &F_matrix, Matrix &F_output, std::vector<int> &IPIV_buffer,
std::vector<double> &matrix_buffer)
{
// std::cout << F_matrix << "\n";
auto t0 = std::chrono::steady_clock::now();
const int N = F_matrix.size();
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
auto idx = i * N + j;
matrix_buffer[idx] = F_matrix[i][j];
}
}
auto t1 = std::chrono::steady_clock::now();
// LAPACKE routines
int info1 = LAPACKE_dgetrf(LAPACK_ROW_MAJOR, N, N, matrix_buffer.data(), N, IPIV_buffer.data());
int info2 = LAPACKE_dgetri(LAPACK_ROW_MAJOR, N, matrix_buffer.data(), N, IPIV_buffer.data());
auto t2 = std::chrono::steady_clock::now();
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
auto idx = i * N + j;
F_output[i][j] = matrix_buffer[idx];
}
}
auto t3 = std::chrono::steady_clock::now();
auto whole_fun_time = std::chrono::duration<double>(t3 - t0).count();
auto lapack_time = std::chrono::duration<double>(t2 - t1).count();
// std::cout << F_output << "\n";
std::cout << "status: " << info1 << "\t" << info2 << "\t" << (info1 == 0 && info2 == 0 ? "Success" : "Failure")
<< "\n";
std::cout << "whole function: " << whole_fun_time << "\n";
std::cout << "LAPACKE matrix operations: " << lapack_time << "\n";
std::cout << "conversion: " << (whole_fun_time - lapack_time) / whole_fun_time * 100.0 << "%\n";
}
int main(int argc, const char *argv[])
{
const int M = 5; // numer of test repetitions
const int N = (argc > 1) ? std::stoi(argv[1]) : 10;
std::cout << "Matrix size = " << N << "\n";
std::vector<int> IPIV_buffer(N);
std::vector<double> matrix_buffer(N * N);
// Test matrix_inverse_lapack M times
for (int i = 0; i < M; i++)
{
Matrix CO_CL(N);
for (auto &v : CO_CL) v.resize(N);
int idx = 1;
for (auto &v : CO_CL)
{
for (auto &x : v)
{
x = idx + 1.0 / idx;
idx++;
}
}
matrix_inverse_lapack(CO_CL, CO_CL, IPIV_buffer, matrix_buffer);
}
}
Here, operator<< is an overkill, but may be useful for anyone wanting to verify half-manually that the code works (by uncommenting lines 26 and 58), and ensuring that the code is correct is more important that measuring its performance.
The code can be compiled with
g++ -std=c++20 -O3 main.cpp -llapacke
The program relies on an external library, lapacke, which needs to be installed, headers + binaries, for the code to compile and run.
My code differs a bit from OP's: it is closer to "modern C++" in that it refrains from using naked pointers; I also added external buffers to matrix_inverse_lapack to suppress continual launching of memory allocator and deallocator, a small improvement that reduces the 2D-1D-2D conversion overhead in a measurable way. I also had to initialize the matrix and find a way to read in OP's mind what the value of N could be. I also added some timer readings for benchmarking. Apart from this, the logic of the code is unchanged.
Now a benchmark carried out on a decent workstation. It lists the percentage of time the conversion takes relative to the total time taken by matrix_inverse_lapack. In other words, I measure the conversion overhead:
N = 10, 3.5%
N = 30, 1.5%
N = 100, 1%
N = 300, 0.5%
N = 1000, 0.35%
N = 3000, 0.1%
The time taken by Lapack nicely scales as N3, as expected (data not shown). The time to invert a matrix is about 16 seconds for N = 3000, and about 5-6 s (5 microseconds) for N = 10.
I assume the overhead of even 3% is completely acceptable. I believe OP uses matrices of size larger then 100, in which case the overhead at or below 1% is certainly acceptable.
So what OP (or anyone having a similar problem) could have done wrong to obtain "unacceptable overhead conversion values"? Here's my short list
Improper compilation
Improper matrix initialization (for tests)
Improper benchmarking
1. Improper compilation
If one forgets to compile in Release mode, one ends up with optimized Lapacke competing with unoptimized conversion. On my machine this peaks at an 33% overhead for N = 20.
2. Improper matrix initialization (for tests)
If one initializes the matrix like this:
for (auto &v : CO_CL)
{
for (auto &x : v)
{
x = idx; // rather than, eg., idx + 1.0/idx
idx++;
}
}
then the matrix is singular, lapack returns quite quickly with the status different from 0. This increases the relative importance of the conversion part. But singular matrices are not what one wants to invert (it's impossible to do).
3. Improper benchmarking
Here's an example of the program output for N = 10:
./a.out 10
Matrix size = 10
status: 0 0 Success
whole function: 0.000127658
LAPACKE matrix operations: 0.000126783
conversion: 0.685425%
status: 0 0 Success
whole function: 1.2497e-05
LAPACKE matrix operations: 1.2095e-05
conversion: 3.21677%
status: 0 0 Success
whole function: 1.0535e-05
LAPACKE matrix operations: 1.0197e-05
conversion: 3.20835%
status: 0 0 Success
whole function: 9.741e-06
LAPACKE matrix operations: 9.422e-06
conversion: 3.27482%
status: 0 0 Success
whole function: 9.939e-06
LAPACKE matrix operations: 9.618e-06
conversion: 3.2297%
One can see that the first call to lapack functions can take 10 times more time than the subsequent calls. This is quite a stable pattern, as if Lapack needed some time for self-initialization. It can affect the measurements for small N badly.
4. What else can be done?
OP apperas to believe that his approach to 2D arrays is good and Lapack is strange and old-fashionable in its packing a 2D array into a 1D array. No. It is Lapack who is right.
If one defines a 2D array as vector<vector<double>>, one obtains one advantage: code simplicity. This comes at a price. Each row of such a matrix is allocated separateley from the others. Thus, a matrix 100 by 100 may be stored in 100 completely different memory blocks. This has a bad impact on the cache (and prefetcher) utilization. Lapck (and other linear algebra packages) enforces compactification of the data in a single, continuous array. This is so to minimize cache and prefetcher misses. If OP had used such an approach from the very beginning, he would probably have gained more than 1-3% that they pay now for the conversion.
This compactification can be achieved in at least three ways.
Write a custom class for a 2D matrix, with the internal data stored in a 1D array and convenient access member funnctions (e.g.: operator ()), or find a library that does just that
Write a custom allocator for std::vector (or find a library). This allocator should allocate the memory from a preallocated 1D vector exactly matching the data storage pattern used by Lapack
Use std::vector<double*> and initailze the pointers with the addresses pointing at the appropriate elements of a preallocated 1D array.
Each of the above solutions forces some changes to the surrounding code, which OP might not want to do. All depends on the code complexity and expected performance gains.
EDIT: Alternative libraries
An alternative approach is to use a library that is known for being a highly optimzed one. Lapack by itself can be regardered as a standard interface with many implementations and it may happen that OP uses an unoptimized one. Which library to choose may depend on the hardware/software platform OP is interested in and may vary in time.
As for now (mid-2021) a decent suggestions are:
Lapack https://www.netlib.org/lapack/
Atlas https://en.wikipedia.org/wiki/Automatically_Tuned_Linear_Algebra_Software http://math-atlas.sourceforge.net/
OpenBlas https://www.openblas.net/
Magma https://developer.nvidia.com/magma
Plasma https://bitbucket.org/icl/plasma/src/main/
If OP uses martices of sizes at least 100, then GPU-oriented MAGMA might be worth trying.
An easier (installation, running) way might with a parallel CPU library, e.g. Plasma. Plsama is Lapack-compliant, it has been being developed by a large team of people, including Jack Dongarra, it also should be rather easy to compile it locally as it is provided with a CMake script.
An example how much a parallel CPU-based, multicore implementation can outperform a single-threaded implementation of the LU-decomposition can be found for example here: https://cse.buffalo.edu/faculty/miller/Courses/CSE633/Tummala-Spring-2014-CSE633.pdf (short answer: 5 to 15 times for matrices of size 1000).

How to get the memory used by a multidimensional vector

I am currently writing some code to create a neural network, and i am trying to make it as optimised as possible. I want to be able to get the amount of memory consumed by a object of type Network, since memory usage is very important in order to avoid cache misses. I tried using sizeof(), however this does not work, since, i assume, that vectors store the values on the heap, so the sizeof() function will just tell me the size of the pointers. Here is my code so far.
#include <iostream>
#include <vector>
#include <random>
#include <chrono>
class Timer
{
private:
std::chrono::time_point<std::chrono::high_resolution_clock> start_time;
public:
Timer(bool auto_start=true)
{
if (auto_start)
{
start();
}
}
void start()
{
start_time = std::chrono::high_resolution_clock::now();
}
float get_duration()
{
std::chrono::duration<float> duration = std::chrono::high_resolution_clock::now() - start_time;
return duration.count();
}
};
class Network
{
public:
std::vector<std::vector<std::vector<float>>> weights;
std::vector<std::vector<std::vector<float>>> deriv_weights;
std::vector<std::vector<float>> biases;
std::vector<std::vector<float>> deriv_biases;
std::vector<std::vector<float>> activations;
std::vector<std::vector<float>> deriv_activations;
};
Network create_network(std::vector<int> layers)
{
Network network;
network.weights.reserve(layers.size() - 1);
int nodes_in_prev_layer = layers[0];
for (unsigned int i = 0; i < layers.size() - 1; ++i)
{
int nodes_in_layer = layers[i + 1];
network.weights.push_back(std::vector<std::vector<float>>());
network.weights[i].reserve(nodes_in_layer);
for (int j = 0; j < nodes_in_layer; ++j)
{
network.weights[i].push_back(std::vector<float>());
network.weights[i][j].reserve(nodes_in_prev_layer);
for (int k = 0; k < nodes_in_prev_layer; ++k)
{
float input_weight = float(std::rand()) / RAND_MAX;
network.weights[i][j].push_back(input_weight);
}
}
nodes_in_prev_layer = nodes_in_layer;
}
return network;
}
int main()
{
Timer timer;
Network network = create_network({784, 800, 16, 10});
std::cout << timer.get_duration() << std::endl;
std::cout << sizeof(network) << std::endl;
std::cin.get();
}
I've recently updated our production neural network code to AVX-512; it's definitely real-world production code. A key part of our optimalisations is that each matrix is not a std::vector, but a 1D AVX-aligned array. Even without AVX alignment, we see a huge benefit in moving to a one-dimensional array backing each matrix. This means the memory access will be fully sequential, which is much faster. The size will then be (rows*cols)*sizeof(float).
We store the bias as the first full row. Commonly that's implemented by prefixing the input with a 1.0 element, but for our AVX code we use the bias as the starting values for the FMA (Fused Multiply-Add) operations. I.e. in pseudo-code result=bias; for(input:inputs) result+=(input*weight). This keeps the input also AVX-aligned.
Since each matrix is used in turn, you can safely have a std::vector<Matrix> layers.
As quote from https://stackoverflow.com/a/17254518/7588455:
Vector stores its elements in an internally-allocated memory array. You can do this:
sizeof(std::vector<int>) + (sizeof(int) * MyVector.size())
This will give you the size of the vector structure itself plus the size of all the ints in it, but it may not include whatever small overhead your memory allocator may impose. I'm not sure there's a platform-independent way to include that.
In your case only the actually internally-allocated memory array matters since you're just accessing these. Also be aware of how you're accessing the memory.
In order to write cache friendly code I highly recommend to read thru this SO post: https://stackoverflow.com/a/16699282/7588455

Doesn't see any significant improvement while using parallel block in OpenMP C++

I am receiving an array of Eigen::MatrixXf and Eigen::Matrix4f in realtime. Both of these arrays are having an equal number of elements. All I am trying to do is just multiply elements of both the arrays together and storing the result in another array at the same index.
Please see the code snippet below-
#define COUNT 4
while (all_ok())
{
Eigen::Matrix4f trans[COUNT];
Eigen::MatrixXf in_data[COUNT];
Eigen::MatrixXf out_data[COUNT];
// at each iteration, new data is filled
// in 'trans' and 'in_data' variables
#pragma omp parallel num_threads(COUNT)
{
#pragma omp for
for (int i = 0; i < COUNT; i++)
out_data[i] = trans[i] * in_clouds[i];
}
}
Please note that COUNT is a constant. The size of trans and in_data is (4 x 4) and (4 x n) respectively, where n is approximately 500,000. In order to parallelize the for loop, I gave OpenMP a try as shown above. However, I don't see any significant improvement in the elapsed time of for loop.
Any suggestions? Any alternatives to perform the same operation, please?
Edit: My idea is to define 4 (=COUNT) threads wherein each of them is taking care of multiplication. In this way, we don't need to create threads every time, I guess!
Works for me using the following self-contained example, that is, I get a x4 speed up when enabling openmp:
#include <iostream>
#include <bench/BenchTimer.h>
using namespace Eigen;
const int COUNT = 4;
EIGEN_DONT_INLINE
void foo(const Matrix4f *trans, const MatrixXf *in_data, MatrixXf *out_data)
{
#pragma omp parallel for num_threads(COUNT)
for (int i = 0; i < COUNT; i++)
out_data[i] = trans[i] * in_data[i];
}
int main()
{
Eigen::Matrix4f trans[COUNT];
Eigen::MatrixXf in_data[COUNT];
Eigen::MatrixXf out_data[COUNT];
int n = 500000;
for (int i = 0; i < COUNT; i++)
{
trans[i].setRandom();
in_data[i].setRandom(4,n);
out_data[i].setRandom(4,n);
}
int tries = 3;
int rep = 1;
BenchTimer t;
BENCH(t, tries, rep, foo(trans, in_data, out_data));
std::cout << " " << t.best(Eigen::REAL_TIMER) << " (" << double(n)*4.*4.*4.*2.e-9/t.best() << " GFlops)\n";
return 0;
}
So 1) make sure you measure the wallclock time and not the CPU time, and 2) make sure that the products is the bottleneck and not filling in_data.
Finally, for maximal performance don't forget to enable AVX/FMA (e.g., with -march=native), and of course make sure to benchmark with compiler's optimization ON.
For the record, on my computer the above example takes 0.25s without openmp, and 0.065s with.
You need to specify -fopenmp during compilation and linking. But you will quickly hit the limit, where RAM access is stopping further speeding up. You really should have a look at vector intrinsics. Dependent on you CPU you could accelerate your operations to the size of your register divided by the size of your variable (float = 4). So if your processor supports say AVX, you'd be dealing with 8 floats at a time. If you need some inspiration, you're welcome to steal code from my medical image reconstruction library here:
https://github.com/kvahed/codeare/blob/master/src/matrix/SIMDTraits.hpp
The code does the whole shebang for float/double real and complex.

Auto Parallelization with VS

I am trying to understand how the auto-parallelization works to speed up the execution of a program I am writing. I have created a simpler example:
#include <iostream>
#include <vector>
#include <chrono>
using namespace std;
using namespace std::chrono;
class matrix
{
public:
matrix(int size, double value)
{
A.resize(size, vector<double>(size, value));
B.resize(size, vector<double>(size, value));
};
void prodScal(double valore)
{
for (int m = 0; m < A.size(); m++)
for (int n = 0; n < A.size(); n++)
{
B[m][n] = A[m][n] * valore;
};
};
double elemento(int riga, int column) { return B[riga][column]; }
protected:
vector<vector<double>> A, B;
};
void main()
{
matrix* M;
M = new matrix(1000, 174.9);
high_resolution_clock::time_point t1 = high_resolution_clock::now();
#pragma loop(hint_parallel(4))
for (int i = 0; i < 1000; i++)
M->prodScal(567.3);
high_resolution_clock::time_point t2 = high_resolution_clock::now();
auto duration = duration_cast<milliseconds>(t2 - t1).count();
cout << "execution time [ms]: " << duration << endl;
}
When I try to compile this code using cl main.cpp /O2 /Qpar /Qpar-report:2, I get the following message:
c:\users\utente\documents\visual studio 2017\projects\parallel\parallel\main.cpp(39) : info C5012: ciclo non parallelizzato a causa del motivo '500'
c:\users\utente\documents\visual studio 2017\projects\parallel\parallel\main.cpp(39) : info C5012: ciclo non parallelizzato a causa del motivo '500'
c:\users\utente\documents\visual studio 2017\projects\parallel\parallel\main.cpp(38) : info C5012: ciclo non parallelizzato a causa del motivo '1000'
Can you help me with the correct way to parallelize this loop?
Thanks.
Auto-parallelisation efforts ( or Beliefs? ) are a rather dual-edge sword :
A machine can "guess" an intent only to a certain degree ( and can give-up, whenever such intent was not clear to a pre-wired set of transformation strategies ), so rather do not expect any bright tricks on a large scale of different approaches possible. Marketing people will beat all their drums and blow all their whistles to sell auto-"thinking"-PRODUCTs, but the reality is different. Even the best of the bests admit, that best performance comes from instruction-level profiling and sometimes they even avoid superscalar pipelined processor-knit tricks, so as to gain the last few nanoseconds, lost in parallelised-code performance at the very last level of CPU uop instruction flow. So, better never expect such expertise to happen just by using a #pragma code-section in a belief, the "machine"-will-invent a smartest way ahead.
So, test it ( always and thoroughly ):
An attempt to "parallelise" an outermost for(){...} is not the best step to start with. Both performance-wise and resources-wise. Let's tackle the case from a different side, the calculation itself:
#include <iostream> // https://stackoverflow.com/questions/48033769/auto-parallelization-with-vs
#include <vector>
#include <chrono> // g++ FLAGS.ADD: -std=c++11
#include <omp.h> // g++ FLAGS.ADD: -fopenmp -lm
#define OMP_NUM_OF_THREADS 4
using namespace std;
using namespace std::chrono;
class matrix {
public:
matrix( int size, double value ) {
A.resize( size, vector<double>( size, value ) );
B.resize( size, vector<double>( size, value ) );
}
void prodScal( double aScalarVALORE ) {
// #pragma loop( hint_parallel(4) ) // matrix_(hint_parallel(4)).cpp:18:0: warning: ignoring #pragma loop [-Wunknown-pragmas]
#pragma omp parallel num_threads( OMP_NUM_OF_THREADS ) // _____ YET, AGNOSTIC TO ANY BETTER CACHE-LINE RE-USE POLICY
for ( unsigned int m = 0; m < A.size(); m++ )
for ( unsigned int n = 0; n < A.size(); n++ )
B[m][n] = A[m][n] * aScalarVALORE;
}
double elemento( int riga, int column ) { return B[riga][column]; }
protected:
vector<vector<double>> A, B;
};
int main() { // matrix_(hint_parallel(4)).cpp:31:11: error: ‘::main’ must return ‘int’
matrix* M;
M = new matrix( 1000, 174.9 );
high_resolution_clock::time_point t1 = high_resolution_clock::now();
// *******************
// DEFINITELY NOT HERE
// *******************
// #pragma loop(hint_parallel(4)) // JUST A TEST EXECUTION, NOT ANY PARALLELISATION BENEFIT FOR A PROCESS-PER-SE PERFORMANCE
for ( int i = 0; i < 1000; i++ )
M->prodScal( 567.3 );
high_resolution_clock::time_point t2 = high_resolution_clock::now();
auto duration = duration_cast<milliseconds>( t2 - t1 ).count();
cout << "execution time [ms]: " << duration << endl;
/*
* execution time [ms]: 21601
------------------
(program exited with code: 0)
* */
return 0;
}
Once having a working code, the performance tweaking, to gain max, is the next hurdle.
A better stepping through a for(){...} can dramatically improve the sum of costs of all the MEM-fetches ( paying ~ +100 [ns] for each non-cached reference ) v/s CACHE-re-use ( paying just ~ +1.5 [ns] for any cache-re-use ).
It depends on the global size of the matrices, on the L3, L2 and L1 cache-sizes and on the cache-lines lengths / associativity, not to mention an additional performance skew(s) if the code is to be run on a virtual device.
The static sizing and an approximate NUMA-topology could be depicted using lstopo ( lscpu in an absence of the smart hwloc service ).
Here, you can read the cache capacities, that can hold the matrix cells for any potential speedup from a smart re-use ( obeying the cache-line striding of the for(){...} indexes ).
Best performance could be gained from tuning the for()-loop stepping, best near the CPU-hardware available ILP-level ( using another degree of parallelism possible from CPU Instruction-Level-Parallelism, permitted for co-executed micro-instruction chains ( ref. Intel CPU publications on these details ) and best tested on the target platform ( cross-compilation would fail to allow such optimisation without performance benchmarks on the target CPU-architecture, best on the target platform in-vivo ).
Details are way beyond the limited scope of this media format here, on StackOverflow, but definitely if interested in performance tuning, you will find both sources and your own experimentation hands-on experience will govern your further steps. To just somehow sense the powers, 've made a large-matrix linear algebra project to finish a few [TB] matrix processing from ~ 126 hours down to a few minutes ( not counting the loading phase, to get the matrix data into the RAM ), right by the very careful parallel code-design, so indeed worth doing the design "right".
For even higher performance, one will have to also avoid O/S from evicting the expensively pre-fetched data, so even more efforts are needed for ultimate performance, than just to rely on an automated "auto-parallelisation"-toy.
Epilogue:
If still in doubts, if that were indeed possible, why would HPC centers still take care for and nourish the HPC-experts for designing ultimately performant code, if the "auto-parallelisation"-toys would do it better or at least the same as these expert nerdy geeks?? They would not, if they indeed could.

How fast is D compared to C++?

I like some features of D, but would be interested if they come with a
runtime penalty?
To compare, I implemented a simple program that computes scalar products of many short vectors both in C++ and in D. The result is surprising:
D: 18.9 s [see below for final runtime]
C++: 3.8 s
Is C++ really almost five times as fast or did I make a mistake in the D
program?
I compiled C++ with g++ -O3 (gcc-snapshot 2011-02-19) and D with dmd -O (dmd 2.052) on a moderate recent linux desktop. The results are reproducible over several runs and standard deviations negligible.
Here the C++ program:
#include <iostream>
#include <random>
#include <chrono>
#include <string>
#include <vector>
#include <array>
typedef std::chrono::duration<long, std::ratio<1, 1000>> millisecs;
template <typename _T>
long time_since(std::chrono::time_point<_T>& time) {
long tm = std::chrono::duration_cast<millisecs>( std::chrono::system_clock::now() - time).count();
time = std::chrono::system_clock::now();
return tm;
}
const long N = 20000;
const int size = 10;
typedef int value_type;
typedef long long result_type;
typedef std::vector<value_type> vector_t;
typedef typename vector_t::size_type size_type;
inline value_type scalar_product(const vector_t& x, const vector_t& y) {
value_type res = 0;
size_type siz = x.size();
for (size_type i = 0; i < siz; ++i)
res += x[i] * y[i];
return res;
}
int main() {
auto tm_before = std::chrono::system_clock::now();
// 1. allocate and fill randomly many short vectors
vector_t* xs = new vector_t [N];
for (int i = 0; i < N; ++i) {
xs[i] = vector_t(size);
}
std::cerr << "allocation: " << time_since(tm_before) << " ms" << std::endl;
std::mt19937 rnd_engine;
std::uniform_int_distribution<value_type> runif_gen(-1000, 1000);
for (int i = 0; i < N; ++i)
for (int j = 0; j < size; ++j)
xs[i][j] = runif_gen(rnd_engine);
std::cerr << "random generation: " << time_since(tm_before) << " ms" << std::endl;
// 2. compute all pairwise scalar products:
time_since(tm_before);
result_type avg = 0;
for (int i = 0; i < N; ++i)
for (int j = 0; j < N; ++j)
avg += scalar_product(xs[i], xs[j]);
avg = avg / N*N;
auto time = time_since(tm_before);
std::cout << "result: " << avg << std::endl;
std::cout << "time: " << time << " ms" << std::endl;
}
And here the D version:
import std.stdio;
import std.datetime;
import std.random;
const long N = 20000;
const int size = 10;
alias int value_type;
alias long result_type;
alias value_type[] vector_t;
alias uint size_type;
value_type scalar_product(const ref vector_t x, const ref vector_t y) {
value_type res = 0;
size_type siz = x.length;
for (size_type i = 0; i < siz; ++i)
res += x[i] * y[i];
return res;
}
int main() {
auto tm_before = Clock.currTime();
// 1. allocate and fill randomly many short vectors
vector_t[] xs;
xs.length = N;
for (int i = 0; i < N; ++i) {
xs[i].length = size;
}
writefln("allocation: %i ", (Clock.currTime() - tm_before));
tm_before = Clock.currTime();
for (int i = 0; i < N; ++i)
for (int j = 0; j < size; ++j)
xs[i][j] = uniform(-1000, 1000);
writefln("random: %i ", (Clock.currTime() - tm_before));
tm_before = Clock.currTime();
// 2. compute all pairwise scalar products:
result_type avg = cast(result_type) 0;
for (int i = 0; i < N; ++i)
for (int j = 0; j < N; ++j)
avg += scalar_product(xs[i], xs[j]);
avg = avg / N*N;
writefln("result: %d", avg);
auto time = Clock.currTime() - tm_before;
writefln("scalar products: %i ", time);
return 0;
}
To enable all optimizations and disable all safety checks, compile your D program with the following DMD flags:
-O -inline -release -noboundscheck
EDIT: I've tried your programs with g++, dmd and gdc. dmd does lag behind, but gdc achieves performance very close to g++. The commandline I used was gdmd -O -release -inline (gdmd is a wrapper around gdc which accepts dmd options).
Looking at the assembler listing, it looks like neither dmd nor gdc inlined scalar_product, but g++/gdc did emit MMX instructions, so they might be auto-vectorizing the loop.
One big thing that slows D down is a subpar garbage collection implementation. Benchmarks that don't heavily stress the GC will show very similar performance to C and C++ code compiled with the same compiler backend. Benchmarks that do heavily stress the GC will show that D performs abysmally. Rest assured, though, this is a single (albeit severe) quality-of-implementation issue, not a baked-in guarantee of slowness. Also, D gives you the ability to opt out of GC and tune memory management in performance-critical bits, while still using it in the less performance-critical 95% of your code.
I've put some effort into improving GC performance lately and the results have been rather dramatic, at least on synthetic benchmarks. Hopefully these changes will be integrated into one of the next few releases and will mitigate the issue.
This is a very instructive thread, thanks for all the work to the OP and helpers.
One note - this test is not assessing the general question of abstraction/feature penalty or even that of backend quality. It focuses on virtually one optimization (loop optimization). I think it's fair to say that gcc's backend is somewhat more refined than dmd's, but it would be a mistake to assume that the gap between them is as large for all tasks.
Definitely seems like a quality-of-implementation issue.
I ran some tests with the OP's code and made some changes. I actually got D going faster for LDC/clang++, operating on the assumption that arrays must be allocated dynamically (xs and associated scalars). See below for some numbers.
Questions for the OP
Is it intentional that the same seed be used for each iteration of C++, while not so for D?
Setup
I have tweaked the original D source (dubbed scalar.d) to make it portable between platforms. This only involved changing the type of the numbers used to access and modify the size of arrays.
After this, I made the following changes:
Used uninitializedArray to avoid default inits for scalars in xs (probably made the biggest difference). This is important because D normally default-inits everything silently, which C++ does not.
Factored out printing code and replaced writefln with writeln
Changed imports to be selective
Used pow operator (^^) instead of manual multiplication for final step of calculating average
Removed the size_type and replaced appropriately with the new index_type alias
...thus resulting in scalar2.cpp (pastebin):
import std.stdio : writeln;
import std.datetime : Clock, Duration;
import std.array : uninitializedArray;
import std.random : uniform;
alias result_type = long;
alias value_type = int;
alias vector_t = value_type[];
alias index_type = typeof(vector_t.init.length);// Make index integrals portable - Linux is ulong, Win8.1 is uint
immutable long N = 20000;
immutable int size = 10;
// Replaced for loops with appropriate foreach versions
value_type scalar_product(in ref vector_t x, in ref vector_t y) { // "in" is the same as "const" here
value_type res = 0;
for(index_type i = 0; i < size; ++i)
res += x[i] * y[i];
return res;
}
int main() {
auto tm_before = Clock.currTime;
auto countElapsed(in string taskName) { // Factor out printing code
writeln(taskName, ": ", Clock.currTime - tm_before);
tm_before = Clock.currTime;
}
// 1. allocate and fill randomly many short vectors
vector_t[] xs = uninitializedArray!(vector_t[])(N);// Avoid default inits of inner arrays
for(index_type i = 0; i < N; ++i)
xs[i] = uninitializedArray!(vector_t)(size);// Avoid more default inits of values
countElapsed("allocation");
for(index_type i = 0; i < N; ++i)
for(index_type j = 0; j < size; ++j)
xs[i][j] = uniform(-1000, 1000);
countElapsed("random");
// 2. compute all pairwise scalar products:
result_type avg = 0;
for(index_type i = 0; i < N; ++i)
for(index_type j = 0; j < N; ++j)
avg += scalar_product(xs[i], xs[j]);
avg /= N ^^ 2;// Replace manual multiplication with pow operator
writeln("result: ", avg);
countElapsed("scalar products");
return 0;
}
After testing scalar2.d (which prioritized optimization for speed), out of curiousity I replaced the loops in main with foreach equivalents, and called it scalar3.d (pastebin):
import std.stdio : writeln;
import std.datetime : Clock, Duration;
import std.array : uninitializedArray;
import std.random : uniform;
alias result_type = long;
alias value_type = int;
alias vector_t = value_type[];
alias index_type = typeof(vector_t.init.length);// Make index integrals portable - Linux is ulong, Win8.1 is uint
immutable long N = 20000;
immutable int size = 10;
// Replaced for loops with appropriate foreach versions
value_type scalar_product(in ref vector_t x, in ref vector_t y) { // "in" is the same as "const" here
value_type res = 0;
for(index_type i = 0; i < size; ++i)
res += x[i] * y[i];
return res;
}
int main() {
auto tm_before = Clock.currTime;
auto countElapsed(in string taskName) { // Factor out printing code
writeln(taskName, ": ", Clock.currTime - tm_before);
tm_before = Clock.currTime;
}
// 1. allocate and fill randomly many short vectors
vector_t[] xs = uninitializedArray!(vector_t[])(N);// Avoid default inits of inner arrays
foreach(ref x; xs)
x = uninitializedArray!(vector_t)(size);// Avoid more default inits of values
countElapsed("allocation");
foreach(ref x; xs)
foreach(ref val; x)
val = uniform(-1000, 1000);
countElapsed("random");
// 2. compute all pairwise scalar products:
result_type avg = 0;
foreach(const ref x; xs)
foreach(const ref y; xs)
avg += scalar_product(x, y);
avg /= N ^^ 2;// Replace manual multiplication with pow operator
writeln("result: ", avg);
countElapsed("scalar products");
return 0;
}
I compiled each of these tests using an LLVM-based compiler, since LDC seems to be the best option for D compilation in terms of performance. On my x86_64 Arch Linux installation I used the following packages:
clang 3.6.0-3
ldc 1:0.15.1-4
dtools 2.067.0-2
I used the following commands to compile each:
C++: clang++ scalar.cpp -o"scalar.cpp.exe" -std=c++11 -O3
D: rdmd --compiler=ldc2 -O3 -boundscheck=off <sourcefile>
Results
The results (screenshot of raw console output) of each version of the source as follows:
scalar.cpp (original C++):
allocation: 2 ms
random generation: 12 ms
result: 29248300000
time: 2582 ms
C++ sets the standard at 2582 ms.
scalar.d (modified OP source):
allocation: 5 ms, 293 μs, and 5 hnsecs
random: 10 ms, 866 μs, and 4 hnsecs
result: 53237080000
scalar products: 2 secs, 956 ms, 513 μs, and 7 hnsecs
This ran for ~2957 ms. Slower than the C++ implementation, but not too much.
scalar2.d (index/length type change and uninitializedArray optimization):
allocation: 2 ms, 464 μs, and 2 hnsecs
random: 5 ms, 792 μs, and 6 hnsecs
result: 59
scalar products: 1 sec, 859 ms, 942 μs, and 9 hnsecs
In other words, ~1860 ms. So far this is in the lead.
scalar3.d (foreaches):
allocation: 2 ms, 911 μs, and 3 hnsecs
random: 7 ms, 567 μs, and 8 hnsecs
result: 189
scalar products: 2 secs, 182 ms, and 366 μs
~2182 ms is slower than scalar2.d, but faster than the C++ version.
Conclusion
With the correct optimizations, the D implementation actually went faster than its equivalent C++ implementation using the LLVM-based compilers available. The current gap between D and C++ for most applications seems only to be based on limitations of current implementations.
dmd is the reference implementation of the language and thus most work is put into the frontend to fix bugs rather than optimizing the backend.
"in" is faster in your case cause you are using dynamic arrays which are reference types. With ref you introduce another level of indirection (which is normally used to alter the array itself and not only the contents).
Vectors are usually implemented with structs where const ref makes perfect sense. See smallptD vs. smallpt for a real-world example featuring loads of vector operations and randomness.
Note that 64-Bit can also make a difference. I once missed that on x64 gcc compiles 64-Bit code while dmd still defaults to 32 (will change when the 64-Bit codegen matures). There was a remarkable speedup with "dmd -m64 ...".
Whether C++ or D is faster is likely to be highly dependent on what you're doing. I would think that when comparing well-written C++ to well-written D code, they would generally either be of similar speed, or C++ would be faster, but what the particular compiler manages to optimize could have a big effect completely aside from the language itself.
However, there are a few cases where D stands a good chance of beating C++ for speed. The main one which comes to mind would be string processing. Thanks to D's array slicing capabalities, strings (and arrays in general) can be processed much faster than you can readily do in C++. For D1, Tango's XML processor is extremely fast, thanks primarily to D's array slicing capabilities (and hopefully D2 will have a similarly fast XML parser once the one that's currently being worked on for Phobos has been completed). So, ultimately whether D or C++ is going to be faster is going to be very dependent on what you're doing.
Now, I am suprised that you're seeing such a difference in speed in this particular case, but it is the sort of thing that I would expect to improve as dmd improves. Using gdc might yield better results and would likely be a closer comparison of the language itself (rather than the backend) given that it's gcc-based. But it wouldn't surprise me at all if there are a number of things which could be done to speed up the code that dmd generates. I don't think that there's much question that gcc is more mature than dmd at this point. And code optimizations are one of the prime fruits of code maturity.
Ultimately, what matters is how well dmd performs for your particular application, but I do agree that it would definitely be nice to know how well C++ and D compare in general. In theory, they should be pretty much the same, but it really depends on the implementation. I think that a comprehensive set of benchmarks would be required to really test how well the two presently compare however.
You can write C code is D so as far as which is faster, it will depend on a lot of things:
What compiler you use
What feature you use
how aggressively you optimize
Differences in the first aren't fair to drag in. The second might give C++ an advantage as it, if anything, has fewer heavy features. The third is the fun one: D code in some ways is easier to optimize because in general it is easier to understand. Also it has the ability to do a large degree of generative programing allowing things like verbose and repetitive but fast code to be written in a shorter forms.
Seems like a quality of implementation issue. For example, here's what I've been testing with:
import std.datetime, std.stdio, std.random;
version = ManualInline;
immutable N = 20000;
immutable Size = 10;
alias int value_type;
alias long result_type;
alias value_type[] vector_type;
result_type scalar_product(in vector_type x, in vector_type y)
in
{
assert(x.length == y.length);
}
body
{
result_type result = 0;
foreach(i; 0 .. x.length)
result += x[i] * y[i];
return result;
}
void main()
{
auto startTime = Clock.currTime();
// 1. allocate vectors
vector_type[] vectors = new vector_type[N];
foreach(ref vec; vectors)
vec = new value_type[Size];
auto time = Clock.currTime() - startTime;
writefln("allocation: %s ", time);
startTime = Clock.currTime();
// 2. randomize vectors
foreach(ref vec; vectors)
foreach(ref e; vec)
e = uniform(-1000, 1000);
time = Clock.currTime() - startTime;
writefln("random: %s ", time);
startTime = Clock.currTime();
// 3. compute all pairwise scalar products
result_type avg = 0;
foreach(vecA; vectors)
foreach(vecB; vectors)
{
version(ManualInline)
{
result_type result = 0;
foreach(i; 0 .. vecA.length)
result += vecA[i] * vecB[i];
avg += result;
}
else
{
avg += scalar_product(vecA, vecB);
}
}
avg = avg / (N * N);
time = Clock.currTime() - startTime;
writefln("scalar products: %s ", time);
writefln("result: %s", avg);
}
With ManualInline defined I get 28 seconds, but without I get 32. So the compiler isn't even inlining this simple function, which I think it's clear it should be.
(My command line is dmd -O -noboundscheck -inline -release ....)