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Say I have a 2D array of size h1 x w1
I want to enlarge it (Just like we enlarge an image) by a factor m,n
So that my resulting array if of the size h1*m , w1*n
for example, I have an array arr1[2][2] of size (2, 2)
01 11
Now I enlarged it by a factor (3, 3) so my new array arr2[6][6] becomes
000111
000111
000111
111111
111111
111111
Can you suggest me an algorithm / iterative loop which could generate arr2 by given information ?
I use pointers to arrays in a smart way to index continuous memory as 2d array and a declarator for VLA in a function prototype.
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <stdint.h>
#define ARRAY_SIZE(x) (sizeof(x)/sizeof(x[0]))
#define ERR_ON(expr, msg, ...) \
do{ if(expr) { fprintf(stderr, "%d: error %s failed: " msg "\n", __LINE__, #expr, ##__VA_ARGS__); exit(-1); } }while(0)
/**
* Input: array p with x columns and y rows
* Output: int arr[y * factory][x * factorx]
* newly allocated array created from p resized by a factorx and factory
*/
void *arr2d_getenlarged(size_t x, size_t y, int p[y][x], size_t factorx, size_t factory)
{
const size_t newx = x * factorx;
const size_t newy = y * factory;
int (* const ret)[newx] = malloc(sizeof(*p) * newx * newy);
ERR_ON(ret == NULL, "");
for (size_t i = 0; i < x; ++i) {
for (size_t j = 0; j < y; ++j) {
const int val = p[i][j];
for (size_t m = 0; m < factorx; ++m) {
for (size_t n = 0; n < factory; ++n) {
ret[i * factorx + m][j * factory + n] = val;
}
}
}
}
return ret;
}
void arr2d_print(size_t x, size_t y, int (*arr)[x])
{
printf("--- %p ---\n", (void*)arr);
for (size_t i = 0; i < x; ++i) {
for (size_t j = 0; j < y; ++j) {
printf("[%d,%d]=%d ", i, j, arr[i][j]);
}
printf("\n");
}
}
int main()
{
int (*arr)[2] = malloc(sizeof(*arr) * 2);
ERR_ON(arr == NULL, "");
memcpy(arr, (int[2][2]){{0,1},{1,1}}, sizeof((int[2][2]){0}));
arr2d_print(2, 2, arr);
int (*arr3)[6] = (void*)arr2d_getenlarged(2, 2, &arr[0][0], 3, 3);
arr2d_print(6, 6, arr3);
free(arr);
free(arr3);
printf("Hello World");
return 0;
}
Example output:
--- 0x1203010 ---
[0,0]=0 [0,1]=1
[1,0]=1 [1,1]=1
--- 0x1203030 ---
[0,0]=0 [0,1]=0 [0,2]=0 [0,3]=1 [0,4]=1 [0,5]=1
[1,0]=0 [1,1]=0 [1,2]=0 [1,3]=1 [1,4]=1 [1,5]=1
[2,0]=0 [2,1]=0 [2,2]=0 [2,3]=1 [2,4]=1 [2,5]=1
[3,0]=1 [3,1]=1 [3,2]=1 [3,3]=1 [3,4]=1 [3,5]=1
[4,0]=1 [4,1]=1 [4,2]=1 [4,3]=1 [4,4]=1 [4,5]=1
[5,0]=1 [5,1]=1 [5,2]=1 [5,3]=1 [5,4]=1 [5,5]=1
Hello World
Live version available at onlinegdb.
#include <stdio.h>
#include <stdlib.h>
#define ENLARGEX 3
int src[2][2] = {{0,1},{1,1}};
int main(int argc, const char * argv[]) {
// insert code here...
int **dest;
//int dest[6][6] ={0,};
int i, j;
int sizesrc = sizeof(src)/sizeof(int)/2;
dest = (int **)malloc(sizeof(int*)*sizesrc*ENLARGEX);
for (i = 0; i < sizesrc*ENLARGEX; i++) {
dest[i] = (int *)malloc(sizeof(int)*sizesrc*ENLARGEX);
}
for (i = 0; i < sizesrc*ENLARGEX; i++){
for(j = 0; j < sizesrc*ENLARGEX; j++) {
dest[i][j] = src[i/ENLARGEX][j/ENLARGEX];
printf("%d ", dest[i][j]);
}
printf("\n");
}
for (i = 0; i < sizesrc*ENLARGEX; i++) {
free(dest[i]);
}
free(dest);
return 0;
}
Related
I'm looking to sort a large 3D array along the z-axis.
Example array is X x Y x Z (1000x1000x5)
I'd like to sort along the z-axis so I'd perform 1000x1000 sorts for 5 element along the z-axis.
Edit Update: Tried an attempt to use thrust below. It's functional and I'd store the output back, but this is very slow since I'm sorting 5 elements at a time per (x,y) location:
#include <stdio.h>
#include <stdlib.h>
#include <iostream>
#include <thrust/device_ptr.h>
#include <thrust/sort.h>
#include <thrust/gather.h>
#include <thrust/iterator/counting_iterator.h>
int main(){
int x = 1000, y = 1000, z = 5;
float*** unsorted_cube = new float** [x];
for (int i = 0; i < x; i++)
{
// Allocate memory blocks for
// rows of each 2D array
unsorted_cube[i] = new float* [y];
for (int j = 0; j < y; j++)
{
// Allocate memory blocks for
// columns of each 2D array
unsorted_cube[i][j] = new float[z];
}
}
for (int i = 0; i < x; i++)
{
for (int j = 0; j < y; j++)
{
unsorted_cube[i][j][0] = 4.0f;
unsorted_cube[i][j][1] = 3.0f;
unsorted_cube[i][j][2] = 1.0f;
unsorted_cube[i][j][3] = 5.0f;
unsorted_cube[i][j][4] = 2.0f;
}
}
for (int i = 0; i < 5; i++)
{
printf("unsorted_cube first 5 elements to sort at (0,0): %f\n", unsorted_cube[0][0][i]);
}
float* temp_input;
float* temp_output;
float* raw_ptr;
float raw_ptr_out[5];
cudaMalloc((void**)&raw_ptr, N_Size * sizeof(float));
for (int i = 0; i < x; i++)
{
for (int j = 0; j < y; j++)
{
temp_input[0] = unsorted_cube[i][j][0];
temp_input[1] = unsorted_cube[i][j][1];
temp_input[2] = unsorted_cube[i][j][2];
temp_input[3] = unsorted_cube[i][j][3];
temp_input[4] = unsorted_cube[i][j][4];
cudaMemcpy(raw_ptr, temp_input, 5 * sizeof(float), cudaMemcpyHostToDevice);
thrust::device_ptr<float> dev_ptr = thrust::device_pointer_cast(raw_ptr);
thrust::sort(dev_ptr, dev_ptr + 5);
thrust::host_vector<float> host_vec(5);
thrust::copy(dev_ptr, dev_ptr + 5, raw_ptr_out);
if (i == 0 && j == 0)
{
for (int i = 0; i < 5; i++)
{
temp_output[i] = raw_ptr_out[i];
}
printf("sorted_cube[0,0,0] : %f\n", temp_output[0]);
printf("sorted_cube[0,0,1] : %f\n", temp_output[1]);
printf("sorted_cube[0,0,2] : %f\n", temp_output[2]);
printf("sorted_cube[0,0,3] : %f\n", temp_output[3]);
printf("sorted_cube[0,0,4] : %f\n", temp_output[4]);
}
}
}
}
Assuming that the data is in a format where the values in each xy-plane are consecutive in memory: data[((z * y_length) + y) * x_length + x] (which is be best for coalescing memory accesses on the GPU, as well)
#include <thrust/device_vector.h>
#include <thrust/execution_policy.h>
#include <thrust/for_each.h>
#include <thrust/zip_iterator.h>
void sort_in_z_dir(thrust::device_vector<float> &data,
int x_length, int y_length) { // z_length == 5
auto z_stride = x_length * y_length;
thrust::for_each(
thrust::make_zip_iterator(thrust::make_tuple(
data.begin(),
data.begin() + z_stride,
data.begin() + 2 * z_stride,
data.begin() + 3 * z_stride,
data.begin() + 4 * z_stride)),
thrust::make_zip_iterator(thrust::make_tuple(
data.begin() + z_stride,
data.begin() + 2 * z_stride,
data.begin() + 3 * z_stride,
data.begin() + 4 * z_stride,
data.begin() + 5 * z_stride)),
[] __host__ __device__
(thrust::tuple<float, float, float, float, float> &values) {
float local_data[5] = {thrust::get<0>(values),
thrust::get<1>(values),
thrust::get<2>(values),
thrust::get<3>(values),
thrust::get<4>(values)};
thrust::sort(thrust::seq, local_data, local_data + 5);
thrust::get<0>(values) = local_data[0];
thrust::get<1>(values) = local_data[1];
thrust::get<2>(values) = local_data[2];
thrust::get<3>(values) = local_data[3];
thrust::get<4>(values) = local_data[4];
});
}
This solution is certainly very ugly in terms of hardcoding z_length. One can use some C++ template-"magic" to make z_length into a template parameter, but this seemed to be overkill for this answer about Thrust.
See Convert std::tuple to std::array C++11 and How to convert std::array to std::tuple? for examples on interfacing between arrays and tuples.
The good thing about this solution that up to the sorting algorithm itself it should be pretty much optimal performance-wise. I don't know if thrust::sort is optimized for such small input arrays, but you can replace it by any self written sorting algorithm as I proposed in the comments.
If you want to be able to use different z_length without all this hassle, you might prefer this solution, which sorts in global memory, which is far from optimal, and feels a bit hacky because it uses Thrust pretty much only to launch a kernel. Here you want to have the data ordered the other way around: data[((x * y_length) + y) * z_length + z]
#include <thrust/counting_iterator.h>
#include <thrust/device_vector.h>
#include <thrust/execution_policy.h>
#include <thrust/for_each.h>
void sort_in_z_dir_alternative(thrust::device_vector<float> &data,
int x_length, int y_length, int z_length) {
int n_threads = x_length * y_length;
thrust::for_each(
thrust::make_counting_iterator(0),
thrust::make_counting_iterator(n_threads),
[ddata = thrust::raw_pointer_cast(data.data()), z_length] __host__ __device__ (int idx) {
thrust::sort(thrust::seq,
ddata + z_length * idx,
ddata + z_length * (idx + 1));
});
}
If you are ok with z_length being a template parameter, this might be a solution that combines the best from both worlds (data format like in the first example):
#include <thrust/counting_iterator.h>
#include <thrust/device_vector.h>
#include <thrust/execution_policy.h>
#include <thrust/for_each.h>
template <int z_length>
void sort_in_z_dir_middle_ground(thrust::device_vector<float> &data,
int x_length, int y_length) {
int n_threads = x_length * y_length; // == z_stride
thrust::for_each(
thrust::make_counting_iterator(0),
thrust::make_counting_iterator(n_threads),
[ddata = thrust::raw_pointer_cast(data.data()),
z_length, n_threads] __host__ __device__ (int idx) {
float local_data[z_length];
#pragma unroll
for (int i = 0; i < z_length; ++i) {
local_data[i] = ddata[idx + i * n_threads];
}
thrust::sort(thrust::seq,
local_data,
local_data + z_length);
#pragma unroll
for (int i = 0; i < z_length; ++i) {
ddata[idx + i * n_threads] = local_data[i];
}
});
}
I'm trying to understand how numpy can be so fast, based on my shocking comparison with optimized C/C++ code which is still far from reproducing numpy's speed.
Consider the following example:
Given a 2D array with shape=(N, N) and dtype=float32, which represents a list of N vectors of N dimensions, I am computing the pairwise differences between every pair of vectors. Using numpy broadcasting, this simply writes as:
def pairwise_sub_numpy( X ):
return X - X[:, None, :]
Using timeit I can measure the performance for N=512: it takes 88 ms per call on my laptop.
Now, in C/C++ a naive implementation writes as:
#define X(i, j) _X[(i)*N + (j)]
#define res(i, j, k) _res[((i)*N + (j))*N + (k)]
float* pairwise_sub_naive( const float* _X, int N )
{
float* _res = (float*) aligned_alloc( 32, N*N*N*sizeof(float));
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
for (int k = 0; k < N; k++)
res(i,j,k) = X(i,k) - X(j,k);
}
}
return _res;
}
Compiling using gcc 7.3.0 with -O3 flag, I get 195 ms per call for pairwise_sub_naive(X), which is not too bad given the simplicity of the code, but about 2 times slower than numpy.
Now I start getting serious and add some small optimizations, by indexing the row vectors directly:
float* pairwise_sub_better( const float* _X, int N )
{
float* _res = (float*) aligned_alloc( 32, N*N*N*sizeof(float));
for (int i = 0; i < N; i++) {
const float* xi = & X(i,0);
for (int j = 0; j < N; j++) {
const float* xj = & X(j,0);
float* r = &res(i,j,0);
for (int k = 0; k < N; k++)
r[k] = xi[k] - xj[k];
}
}
return _res;
}
The speed stays the same at 195 ms, which means that the compiler was able to figure that much. Let's now use SIMD vector instructions:
float* pairwise_sub_simd( const float* _X, int N )
{
float* _res = (float*) aligned_alloc( 32, N*N*N*sizeof(float));
// create caches for row vectors which are memory-aligned
float* xi = (float*)aligned_alloc(32, N * sizeof(float));
float* xj = (float*)aligned_alloc(32, N * sizeof(float));
for (int i = 0; i < N; i++) {
memcpy(xi, & X(i,0), N*sizeof(float));
for (int j = 0; j < N; j++) {
memcpy(xj, & X(j,0), N*sizeof(float));
float* r = &res(i,j,0);
for (int k = 0; k < N; k += 256/sizeof(float)) {
const __m256 A = _mm256_load_ps(xi+k);
const __m256 B = _mm256_load_ps(xj+k);
_mm256_store_ps(r+k, _mm256_sub_ps( A, B ));
}
}
}
free(xi);
free(xj);
return _res;
}
This only yields a small boost (178 ms instead of 194 ms per function call).
Then I was wondering if a "block-wise" approach, like what is used to optimize dot-products, could be beneficials:
float* pairwise_sub_blocks( const float* _X, int N )
{
float* _res = (float*) aligned_alloc( 32, N*N*N*sizeof(float));
#define B 8
float cache1[B*B], cache2[B*B];
for (int bi = 0; bi < N; bi+=B)
for (int bj = 0; bj < N; bj+=B)
for (int bk = 0; bk < N; bk+=B) {
// load first 8x8 block in the cache
for (int i = 0; i < B; i++)
for (int k = 0; k < B; k++)
cache1[B*i + k] = X(bi+i, bk+k);
// load second 8x8 block in the cache
for (int j = 0; j < B; j++)
for (int k = 0; k < B; k++)
cache2[B*j + k] = X(bj+j, bk+k);
// compute local operations on the caches
for (int i = 0; i < B; i++)
for (int j = 0; j < B; j++)
for (int k = 0; k < B; k++)
res(bi+i,bj+j,bk+k) = cache1[B*i + k] - cache2[B*j + k];
}
return _res;
}
And surprisingly, this is the slowest method so far (258 ms per function call).
To summarize, despite some efforts with some optimized C++ code, I can't come anywhere close the 88 ms / call that numpy achieves effortlessly. Any idea why?
Note: By the way, I am disabling numpy multi-threading and anyway, this kind of operation is not multi-threaded.
Edit: Exact code to benchmark the numpy code:
import numpy as np
def pairwise_sub_numpy( X ):
return X - X[:, None, :]
N = 512
X = np.random.rand(N,N).astype(np.float32)
import timeit
times = timeit.repeat('pairwise_sub_numpy( X )', globals=globals(), number=1, repeat=5)
print(f">> best of 5 = {1000*min(times):.3f} ms")
Full benchmark for C code:
#include <stdio.h>
#include <string.h>
#include <xmmintrin.h> // compile with -mavx -msse4.1
#include <pmmintrin.h>
#include <immintrin.h>
#include <time.h>
#define X(i, j) _x[(i)*N + (j)]
#define res(i, j, k) _res[((i)*N + (j))*N + (k)]
float* pairwise_sub_naive( const float* _x, int N )
{
float* _res = (float*) aligned_alloc( 32, N*N*N*sizeof(float));
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
for (int k = 0; k < N; k++)
res(i,j,k) = X(i,k) - X(j,k);
}
}
return _res;
}
float* pairwise_sub_better( const float* _x, int N )
{
float* _res = (float*) aligned_alloc( 32, N*N*N*sizeof(float));
for (int i = 0; i < N; i++) {
const float* xi = & X(i,0);
for (int j = 0; j < N; j++) {
const float* xj = & X(j,0);
float* r = &res(i,j,0);
for (int k = 0; k < N; k++)
r[k] = xi[k] - xj[k];
}
}
return _res;
}
float* pairwise_sub_simd( const float* _x, int N )
{
float* _res = (float*) aligned_alloc( 32, N*N*N*sizeof(float));
// create caches for row vectors which are memory-aligned
float* xi = (float*)aligned_alloc(32, N * sizeof(float));
float* xj = (float*)aligned_alloc(32, N * sizeof(float));
for (int i = 0; i < N; i++) {
memcpy(xi, & X(i,0), N*sizeof(float));
for (int j = 0; j < N; j++) {
memcpy(xj, & X(j,0), N*sizeof(float));
float* r = &res(i,j,0);
for (int k = 0; k < N; k += 256/sizeof(float)) {
const __m256 A = _mm256_load_ps(xi+k);
const __m256 B = _mm256_load_ps(xj+k);
_mm256_store_ps(r+k, _mm256_sub_ps( A, B ));
}
}
}
free(xi);
free(xj);
return _res;
}
float* pairwise_sub_blocks( const float* _x, int N )
{
float* _res = (float*) aligned_alloc( 32, N*N*N*sizeof(float));
#define B 8
float cache1[B*B], cache2[B*B];
for (int bi = 0; bi < N; bi+=B)
for (int bj = 0; bj < N; bj+=B)
for (int bk = 0; bk < N; bk+=B) {
// load first 8x8 block in the cache
for (int i = 0; i < B; i++)
for (int k = 0; k < B; k++)
cache1[B*i + k] = X(bi+i, bk+k);
// load second 8x8 block in the cache
for (int j = 0; j < B; j++)
for (int k = 0; k < B; k++)
cache2[B*j + k] = X(bj+j, bk+k);
// compute local operations on the caches
for (int i = 0; i < B; i++)
for (int j = 0; j < B; j++)
for (int k = 0; k < B; k++)
res(bi+i,bj+j,bk+k) = cache1[B*i + k] - cache2[B*j + k];
}
return _res;
}
int main()
{
const int N = 512;
float* _x = (float*) malloc( N * N * sizeof(float) );
for( int i = 0; i < N; i++)
for( int j = 0; j < N; j++)
X(i,j) = ((i+j*j+17*i+101) % N) / float(N);
double best = 9e9;
for( int i = 0; i < 5; i++)
{
struct timespec start, stop;
clock_gettime(CLOCK_THREAD_CPUTIME_ID, &start);
//float* res = pairwise_sub_naive( _x, N );
//float* res = pairwise_sub_better( _x, N );
//float* res = pairwise_sub_simd( _x, N );
float* res = pairwise_sub_blocks( _x, N );
clock_gettime(CLOCK_THREAD_CPUTIME_ID, &stop);
double t = (stop.tv_sec - start.tv_sec) * 1e6 + (stop.tv_nsec - start.tv_nsec) / 1e3; // in microseconds
if (t < best) best = t;
free( res );
}
printf("Best of 5 = %f ms\n", best / 1000);
free( _x );
return 0;
}
Compiled using gcc 7.3.0 gcc -Wall -O3 -mavx -msse4.1 -o test_simd test_simd.c
Summary of timings on my machine:
Implementation
Time
numpy
88 ms
C++ naive
194 ms
C++ better
195 ms
C++ SIMD
178 ms
C++ blocked
258 ms
C++ blocked (gcc 8.3.1)
217 ms
As pointed out by some of the comments numpy uses SIMD in its implementation and it does not allocate memory at the point of computation. If I eliminate the memory allocation from your implementation, pre-allocating all the buffers ahead of the computation then I get a better time compared to numpy even with the scaler version(that is the one without any optimizations).
Also in terms of SIMD and why your implementation does not perform much better than the scaler is because your memory access patterns are not ideal for SIMD usage - you do memcopy and you load into SIMD registers from locations that are far apart from each other - e.g. you fill vectors from line 0 and line 511, which might not play well with the cache or with the SIMD prefetcher.
There is also a mistake in how you load the SIMD registers(if I understood correctly what you're trying to compute): a 256 bit SIMD register can load 8 single-precision floating-point numbers 8 * 32 = 256, but in your loop you jump k by "256/sizeof(float)" which is 256/4 = 64; _x and _res are float pointers and the SIMD intrinsics expect also float pointers as arguments so instead of reading all elements from those lines every 8 floats you read them every 64 floats.
The computation can be optimized further by changing the access patterns but also by observing that you repeat some computations: e.g. when iterating with line0 as a base you compute line0 - line1 but at some future time, when iterating with line1 as a base, you need to compute line1 - line0 which is basically -(line0 - line1), that is for each line after line0 a lot of results could be reused from previous computations.
A lot of times SIMD usage or parallelization requires one to change how data is accessed or reasoned about in order to provide meaningful improvements.
Here is what I have done as a first step based on your initial implementation and it is faster than the numpy(don't mind the OpenMP stuff as it's not how its supposed to be done, I just wanted to see how it behaves trying the naive way).
C++
Time scaler version: 55 ms
Time SIMD version: 53 ms
**Time SIMD 2 version: 33 ms**
Time SIMD 3 version: 168 ms
Time OpenMP version: 59 ms
Python numpy
>> best of 5 = 88.794 ms
#include <cstdlib>
#include <xmmintrin.h> // compile with -mavx -msse4.1
#include <pmmintrin.h>
#include <immintrin.h>
#include <numeric>
#include <algorithm>
#include <chrono>
#include <iostream>
#include <cstring>
using namespace std;
float* pairwise_sub_naive (const float* input, float* output, int n)
{
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
for (int k = 0; k < n; k++)
output[(i * n + j) * n + k] = input[i * n + k] - input[j * n + k];
}
}
return output;
}
float* pairwise_sub_simd (const float* input, float* output, int n)
{
for (int i = 0; i < n; i++)
{
const int idxi = i * n;
for (int j = 0; j < n; j++)
{
const int idxj = j * n;
const int outidx = idxi + j;
for (int k = 0; k < n; k += 8)
{
__m256 A = _mm256_load_ps(input + idxi + k);
__m256 B = _mm256_load_ps(input + idxj + k);
_mm256_store_ps(output + outidx * n + k, _mm256_sub_ps( A, B ));
}
}
}
return output;
}
float* pairwise_sub_simd_2 (const float* input, float* output, int n)
{
float* line_buffer = (float*) aligned_alloc(32, n * sizeof(float));
for (int i = 0; i < n; i++)
{
const int idxi = i * n;
for (int j = 0; j < n; j++)
{
const int idxj = j * n;
const int outidx = idxi + j;
for (int k = 0; k < n; k += 8)
{
__m256 A = _mm256_load_ps(input + idxi + k);
__m256 B = _mm256_load_ps(input + idxj + k);
_mm256_store_ps(line_buffer + k, _mm256_sub_ps( A, B ));
}
memcpy(output + outidx * n, line_buffer, n);
}
}
return output;
}
float* pairwise_sub_simd_3 (const float* input, float* output, int n)
{
for (int i = 0; i < n; i++)
{
const int idxi = i * n;
for (int k = 0; k < n; k += 8)
{
__m256 A = _mm256_load_ps(input + idxi + k);
for (int j = 0; j < n; j++)
{
const int idxj = j * n;
const int outidx = (idxi + j) * n;
__m256 B = _mm256_load_ps(input + idxj + k);
_mm256_store_ps(output + outidx + k, _mm256_sub_ps( A, B ));
}
}
}
return output;
}
float* pairwise_sub_openmp (const float* input, float* output, int n)
{
int i, j;
#pragma omp parallel for private(j)
for (i = 0; i < n; i++)
{
for (j = 0; j < n; j++)
{
const int idxi = i * n;
const int idxj = j * n;
const int outidx = idxi + j;
for (int k = 0; k < n; k += 8)
{
__m256 A = _mm256_load_ps(input + idxi + k);
__m256 B = _mm256_load_ps(input + idxj + k);
_mm256_store_ps(output + outidx * n + k, _mm256_sub_ps( A, B ));
}
}
}
/*for (i = 0; i < n; i++)
{
for (j = 0; j < n; j++)
{
for (int k = 0; k < n; k++)
{
output[(i * n + j) * n + k] = input[i * n + k] - input[j * n + k];
}
}
}*/
return output;
}
int main ()
{
constexpr size_t n = 512;
constexpr size_t input_size = n * n;
constexpr size_t output_size = n * n * n;
float* input = (float*) aligned_alloc(32, input_size * sizeof(float));
float* output = (float*) aligned_alloc(32, output_size * sizeof(float));
float* input_simd = (float*) aligned_alloc(32, input_size * sizeof(float));
float* output_simd = (float*) aligned_alloc(32, output_size * sizeof(float));
float* input_par = (float*) aligned_alloc(32, input_size * sizeof(float));
float* output_par = (float*) aligned_alloc(32, output_size * sizeof(float));
iota(input, input + input_size, float(0.0));
fill(output, output + output_size, float(0.0));
iota(input_simd, input_simd + input_size, float(0.0));
fill(output_simd, output_simd + output_size, float(0.0));
iota(input_par, input_par + input_size, float(0.0));
fill(output_par, output_par + output_size, float(0.0));
std::chrono::milliseconds best_scaler{100000};
for (int i = 0; i < 5; ++i)
{
auto start = chrono::high_resolution_clock::now();
pairwise_sub_naive(input, output, n);
auto stop = chrono::high_resolution_clock::now();
auto duration = chrono::duration_cast<chrono::milliseconds>(stop - start);
if (duration < best_scaler)
{
best_scaler = duration;
}
}
cout << "Time scaler version: " << best_scaler.count() << " ms\n";
std::chrono::milliseconds best_simd{100000};
for (int i = 0; i < 5; ++i)
{
auto start = chrono::high_resolution_clock::now();
pairwise_sub_simd(input_simd, output_simd, n);
auto stop = chrono::high_resolution_clock::now();
auto duration = chrono::duration_cast<chrono::milliseconds>(stop - start);
if (duration < best_simd)
{
best_simd = duration;
}
}
cout << "Time SIMD version: " << best_simd.count() << " ms\n";
std::chrono::milliseconds best_simd_2{100000};
for (int i = 0; i < 5; ++i)
{
auto start = chrono::high_resolution_clock::now();
pairwise_sub_simd_2(input_simd, output_simd, n);
auto stop = chrono::high_resolution_clock::now();
auto duration = chrono::duration_cast<chrono::milliseconds>(stop - start);
if (duration < best_simd_2)
{
best_simd_2 = duration;
}
}
cout << "Time SIMD 2 version: " << best_simd_2.count() << " ms\n";
std::chrono::milliseconds best_simd_3{100000};
for (int i = 0; i < 5; ++i)
{
auto start = chrono::high_resolution_clock::now();
pairwise_sub_simd_3(input_simd, output_simd, n);
auto stop = chrono::high_resolution_clock::now();
auto duration = chrono::duration_cast<chrono::milliseconds>(stop - start);
if (duration < best_simd_3)
{
best_simd_3 = duration;
}
}
cout << "Time SIMD 3 version: " << best_simd_3.count() << " ms\n";
std::chrono::milliseconds best_par{100000};
for (int i = 0; i < 5; ++i)
{
auto start = chrono::high_resolution_clock::now();
pairwise_sub_openmp(input_par, output_par, n);
auto stop = chrono::high_resolution_clock::now();
auto duration = chrono::duration_cast<chrono::milliseconds>(stop - start);
if (duration < best_par)
{
best_par = duration;
}
}
cout << "Time OpenMP version: " << best_par.count() << " ms\n";
cout << "Verification\n";
if (equal(output, output + output_size, output_simd))
{
cout << "PASSED\n";
}
else
{
cout << "FAILED\n";
}
return 0;
}
Edit: Small correction as there was a wrong call related to the second version of SIMD implementation.
As you can see now, the second implementation is the fastest as it behaves the best from the point of view of the locality of reference of the cache. Examples 2 and 3 of SIMD implementations are there to illustrate for you how changing memory access patterns to influence the performance of your SIMD optimizations.
To summarize(knowing that I'm far from being complete in my advice) be mindful of your memory access patterns and of the loads and stores to\from the SIMD unit; the SIMD is a different hardware unit inside the processor's core so there is a penalty in shuffling data back and forth, hence when you load a register from memory try to do as many operations as possible with that data and do not be too eager to store it back(of course, in your example that might be all you need to do with the data). Be mindful also that there is a limited number of SIMD registers available and if you load too many then they will "spill", that is they will be stored back to temporary locations in main memory behind the scenes killing all your gains. SIMD optimization, it's a true balance act!
There is some effort to put a cross-platform intrinsics wrapper into the standard(I developed myself a closed source one in my glorious past) and even it's far from being complete, it's worth taking a look at(read the accompanying papers if you're truly interested to learn how SIMD works).
https://github.com/VcDevel/std-simd
This is a complement to the answer posted by #celakev .
I think I finally got to understand what exactly was the issue. The issue was not about allocating the memory in the main function that does the computation.
What was actually taking time is to access new (fresh) memory. I believe that the malloc call returns pages of memory which are virtual, i.e. that does not corresponds to actual physical memory -- until it is explicitly accessed. What actually takes time is the process of allocating physical memory on the fly (which I think is OS-level) when it is accessed in the function code.
Here is a proof. Consider the two following trivial functions:
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
float* just_alloc( size_t N )
{
return (float*) aligned_alloc( 32, sizeof(float)*N );
}
void just_fill( float* _arr, size_t N )
{
for (size_t i = 0; i < N; i++)
_arr[i] = 1;
}
#define Time( code_to_benchmark, cleanup_code ) \
do { \
double best = 9e9; \
for( int i = 0; i < 5; i++) { \
struct timespec start, stop; \
clock_gettime(CLOCK_THREAD_CPUTIME_ID, &start); \
code_to_benchmark; \
clock_gettime(CLOCK_THREAD_CPUTIME_ID, &stop); \
double t = (stop.tv_sec - start.tv_sec) * 1e3 + (stop.tv_nsec - start.tv_nsec) / 1e6; \
printf("Time[%d] = %f ms\n", i, t); \
if (t < best) best = t; \
cleanup_code; \
} \
printf("Best of 5 for '" #code_to_benchmark "' = %f ms\n\n", best); \
} while(0)
int main()
{
const size_t N = 512;
Time( float* arr = just_alloc(N*N*N), free(arr) );
float* arr = just_alloc(N*N*N);
Time( just_fill(arr, N*N*N), ; );
free(arr);
return 0;
}
I get the following timings, which I now detail for each of the calls:
Time[0] = 0.000931 ms
Time[1] = 0.000540 ms
Time[2] = 0.000523 ms
Time[3] = 0.000524 ms
Time[4] = 0.000521 ms
Best of 5 for 'float* arr = just_alloc(N*N*N)' = 0.000521 ms
Time[0] = 189.822237 ms
Time[1] = 45.041083 ms
Time[2] = 46.331428 ms
Time[3] = 44.729433 ms
Time[4] = 42.241279 ms
Best of 5 for 'just_fill(arr, N*N*N)' = 42.241279 ms
As you can see, allocating memory is blazingly fast, but the first time that the memory is accessed, it is 5 times slower than the other times. So, basically the reason that my code was slow was because i was each time reallocating fresh memory that had no physical address yet. (Correct me if I'm wrong but I think that's the gist of it!)
A bit late to the party, but I wanted to add a pairwise method with Eigen, which is supposed to give C++ a high-level algebra manipulation capability and use SIMD under the hood. Just like numpy.
Here is the implementation
#include <iostream>
#include <vector>
#include <chrono>
#include <algorithm>
#include <Eigen/Dense>
auto pairwise_eigen(const Eigen::MatrixXf &input, std::vector<Eigen::MatrixXf> &output) {
for (int k = 0; k < input.cols(); ++k)
output[k] = input
// subtract matrix with repeated k-th column
- input.col(k) * Eigen::RowVectorXf::Ones(input.cols());
}
int main() {
constexpr size_t n = 512;
// allocate input and output
Eigen::MatrixXf input = Eigen::MatrixXf::Random(n, n);
std::vector<Eigen::MatrixXf> output(n);
std::chrono::milliseconds best_eigen{100000};
for (int i = 0; i < 5; ++i) {
auto start = std::chrono::high_resolution_clock::now();
pairwise_eigen(input, output);
auto end = std::chrono::high_resolution_clock::now();
auto duration = std::chrono::duration_cast<std::chrono::milliseconds>(end-start);
if (duration < best_eigen)
best_eigen = duration;
}
std::cout << "Time Eigen version: " << best_eigen.count() << " ms\n";
return 0;
}
The full benchmark tests suggested by #celavek on my system are
Time scaler version: 57 ms
Time SIMD version: 58 ms
Time SIMD 2 version: 40 ms
Time SIMD 3 version: 58 ms
Time OpenMP version: 58 ms
Time Eigen version: 76 ms
Numpy >> best of 5 = 118.489 ms
Whit Eigen there is still a noticeable improvement with respect to Numpy, but not so impressive compared to the "raw" implementations (there is certainly some overhead).
An extra optimization is to allocate the output vector with copies of the input and then subtract directly from each vector entry, simply replacing the following lines
// inside the pairwise method
for (int k = 0; k < input.cols(); ++k)
output[k] -= input.col(k) * Eigen::RowVectorXf::Ones(input.cols());
// at allocation time
std::vector<Eigen::MatrixXf> output(n, input);
This pushes the best of 5 down to 60 ms.
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I have seen a similar question here
However,I could not get an exact answer here, and it is written in 2012.
I am trying to call cublasStatus_t cublasSgbmv(...) function, which is defined in "cublas_v2.h", in a __global__ function. However, I could not use the dynamic parallelism feature. I only have 1 source.cu file. However, I have read that I should compile it in a dynamic way so that it separates device and host functions, then I can link these outputs.
Is there anyone who knows how to do it, or a good source to explain it?
Thanks in advance
edit : if undervoted, please explain the reason at least for me to learn my mistake?
edit2 :
my specific problem is, I'm using the following code in my Source.cu :
#include <iostream>
#include <vector>
#include <cuda.h>
#include <cstdio>
#include <stdio.h>
#include <device_launch_parameters.h>
#include <stdlib.h> //srand(), rand()
#include <time.h>
#include <builtin_types.h>
#include <cuda_runtime.h>
#include <cublas_v2.h>
#define IDX2C(i ,j , ld ) ((( j )*( ld ))+( i ))
#define HEIGHT 4
#define WIDTH 4
#define V 4
#define KL 2
#define KU 1
#define THREADS_PER_BLOCK 512
#pragma comment(lib, "cublas")
//#pragma comment(lib, "helper_cuda")
using namespace std;
void create_Matrix(int* matrix, int width, int height){
int i, len;
len = height * width;
srand(time(NULL));
for (i = 0; i < len; i++){
matrix[i] = rand() % 10 + 1; //generates number between 1-10
}
}
template <typename T>
void print_vector(T* vector, int len){
for (int i = 0; i < len; i++)
cout << vector[i] << " ";
cout << endl;
}
template <typename T>
void creating_bandedMatrix(T* bandedMatrix, int height, int width, int ku, int kl){
//fill matrix with zeros at the beginning
int i, len;
len = height * width;
for (i = 0; i < len; i++){
bandedMatrix[i] = 0; //generates number between 1-10
}
srand(time(NULL));
//filling banded diagonal
int start, end;
for (int i = 0; i < height; i++){
start = i - kl;
if (start < 0)
start = 0;
end = i + ku + 1;
if (end > width)
end = width;
for (int j = start; j < end; j++){
*(bandedMatrix + (i*width) + j) = (float)(rand() % (10) + 1); //rand() / (T)RAND_MAX;;
}
}
}
template <typename T>
void print_matrix(T* matrix, int width, int height){
int len = width*height;
cout << "asdsffffff" << endl;
for (int i = 0; i < len; i++){
if (!(i%width))
cout << endl;
cout << i << ":" <<matrix[i] << " ";
}
cout << endl;
}
template <typename T>
void computeMatrixVectorMultiplication(T* bandedMatrix, T* vector2){
T row_sum = 0;
T* bandedHostResult = (T*)malloc(WIDTH * sizeof(T));
for (int i = 0; i < HEIGHT; i++){
row_sum = 0;
for (int j = 0; j < WIDTH; j++){
row_sum += (*(bandedMatrix + i*WIDTH + j)) * vector2[j];
}
bandedHostResult[i] = row_sum;
}
//priting the result
cout << "\n\nBanded Host Result...\n";
print_vector(bandedHostResult, WIDTH);
}
template <typename T>
void fillLapackMatrix(T* lapack_matrix, T* bandedMatrix, int kl, int ku, int banded_w, int banded_h, int lapack_w, int lapack_h){
int i, j, lapack_i;
int len = lapack_h * lapack_w;
for (i = 0; i < len; i++){
lapack_matrix[i] = 0; //generates number between 1-10
}
for (i = 0; i < banded_w; i++){
for (j = 0; j < banded_h; j++){
lapack_i = ku + i - j;
*(lapack_matrix + lapack_i*lapack_w + j) = *(bandedMatrix + i*banded_w + j);
//lapack_matrix[lapack_i*lapack_w + j] = bandedMatrix[i*bandedMatrix + j];
}
}
}
__global__ void device_cublasSgbmv(int m,int n,int kl, int ku,float* alpha, float* A, int lda ,float* B,int ldb,float*R, int ldr, float* beta){
int index = blockIdx.x * blockDim.x + threadIdx.x;
cublasHandle_t handle;
cublasCreate(&handle);
cublasOperation_t trans = CUBLAS_OP_N;
float* dev_x;
cudaMalloc((void**)&dev_x,sizeof(float) * n);
if(index < ldr){
cublasSgbmv(handle, trans,m, n, kl, ku, alpha, A, m, B+index*n, 1, beta, R+index*n, 1);
index = 0;
}
}
void fillNormalMatrix(float* B,int h,int w){
for(int i = 0; i < h;i++){
for(int j = 0; j < w;j++){
B[i*w + j] = 1;
}
}
}
int main()
{
cublasStatus_t status;
float *A;
float *x, *y;
float *dev_x, *dev_y;
int incx, incy;
float *dev_A = 0;
float alpha = 1.0f;
float beta = 0.0f;
int matrixSize = WIDTH * HEIGHT;
int i, j;
cublasHandle_t handle;
/* Initialize CUBLAS */
status = cublasCreate(&handle);
if (status != CUBLAS_STATUS_SUCCESS)
{
fprintf(stderr, "!!!! CUBLAS initialization error\n");
return EXIT_FAILURE;
}
//Allocate host memory for the matrices
A = (float *)malloc(matrixSize* sizeof(float));
//Allocate memory for host vectors
x = (float *)malloc(WIDTH * sizeof(float));
y = (float*)malloc(WIDTH * sizeof(float));
// Fill the matrices with test data
creating_bandedMatrix(A, WIDTH, HEIGHT, KU, KL);
cout << "Banded Matrix\n";
print_matrix(A, WIDTH, HEIGHT);
//Fill the vectors with random data
for (i = 0; i < WIDTH; i++){
x[i] = 1;// (float)(rand() % (10) + 1);:
y[i] = (float)(rand() % (10) + 1);
}
cout << "\nvector x...\n";
print_vector(x, WIDTH);
//cout << "\nvector y...\n";
//print_vector(y, WIDTH);
//Allocate device memory for the matrix
if (cudaMalloc((void **)&dev_A, matrixSize * sizeof(float)) != cudaSuccess)
{
fprintf(stderr, "!!!! device memory allocation error (allocate A)\n");
return EXIT_FAILURE;
}
//Allocate device memory for vectors
if (cudaMalloc((void**)&dev_x, WIDTH * sizeof(float)) != cudaSuccess){
fprintf(stderr, "Device Vector Allocation PROBLEM\n");
return EXIT_FAILURE;
}
if (cudaMalloc((void**)&dev_y, WIDTH * sizeof(float)) != cudaSuccess){
fprintf(stderr, "Device Vector Allocation PROBLEM\n");
return EXIT_FAILURE;
}
// Initialize the device vectors with the host vectors
status = cublasSetVector(WIDTH, sizeof(float), x, 1, dev_x, 1);
if (status != CUBLAS_STATUS_SUCCESS)
{
fprintf(stderr, "!!!! device access error (write x vector)\n");
return EXIT_FAILURE;
}
status = cublasSetVector(WIDTH, sizeof(float), y, 1, dev_y, 1);
if (status != CUBLAS_STATUS_SUCCESS)
{
fprintf(stderr, "!!!! device access error (write y vector)\n");
return EXIT_FAILURE;
}
//initialize matrix with lapack format
int lapack_width = WIDTH > HEIGHT ? HEIGHT : WIDTH;
int lapack_height = KL + KU + 1;
int lapackSize = lapack_height * lapack_width;
float* lapack_matrix = (float*)malloc(lapackSize * sizeof(float));
fillLapackMatrix(lapack_matrix, A, KL, KU, WIDTH, HEIGHT, lapack_width, lapack_height);
cout << "\n\nLAPACK MAtrix\n";
print_matrix(lapack_matrix, lapack_width, lapack_height);
//convert to column column matrix
float* col = (float*)malloc(lapackSize * sizeof(float));
for (i = 0; i < WIDTH; i++){
for (j = 0; j < HEIGHT; j++){
col[i + WIDTH*j] = lapack_matrix[WIDTH*i + j];
}
}
cout << "Lapack Column Based Matrix\n";
print_matrix(col,HEIGHT-1,WIDTH);
//status = cublasSetVector(lapackSize, sizeof(float), A, 1, dev_A, 1);
cublasSetMatrix(HEIGHT, WIDTH, sizeof(float), col, HEIGHT, dev_A, HEIGHT);
cublasOperation_t trans = CUBLAS_OP_N;
incy = incx = 1;
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
///////////////////////// Banded Matrix Matrix Multipllicatio ///////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
float* B,*dev_B,*dev_R,*R;
B = (float*)malloc(WIDTH*HEIGHT*sizeof(float));
R = (float*)malloc(WIDTH*HEIGHT*sizeof(float));
fillNormalMatrix(B,WIDTH,HEIGHT);
cudaMalloc((void**)&dev_B,matrixSize*sizeof(*B));
cudaMalloc((void**)&dev_R,matrixSize*sizeof(*R));
cublasSetMatrix(HEIGHT, WIDTH, sizeof(*B), B, HEIGHT, dev_B, HEIGHT);
cout << "Matrix B\n";
print_matrix(B,HEIGHT,WIDTH);
cout << "gfsdf\n";
device_cublasSgbmv<<<1,4>>>(HEIGHT, WIDTH, KL, KU, &alpha, dev_A, WIDTH, dev_B, HEIGHT, dev_R, HEIGHT,&beta);
cout << "after\n";
cublasGetMatrix(HEIGHT,WIDTH, sizeof (*R) ,dev_R ,WIDTH,R,WIDTH);
getchar();
return 0;
}
and compile it like :
nvcc -gencode=arch=compute_35,code=sm_35 -lcublas -lcudadevrt -O3 Source.cu -o Source.o -dc
g++ Source.o -lcublas -lcudart
then, I get the following :
In function `__sti____cudaRegisterAll_48_tmpxft_00001f1e_00000000_6_Source_cpp1_ii_ebe2258a()':
tmpxft_00001f1e_00000000-3_lapack_vector.cudafe1.cpp:(.text.startup+0x575): undefined reference to `__cudaRegisterLinkedBinary_48_tmpxft_00001f1e_00000000_6_Source_cpp1_ii_ebe2258a'
collect2: error: ld returned 1 exit status
You can compile and link the code you have now shown with a single command like this:
nvcc -arch=sm_35 -rdc=true -lcublas -lcublas_device -lcudadevrt -o test Source.cu
You may get some warnings like this:
nvlink warning : SM Arch ('sm_35') not found in '/usr/local/cuda/bin/..//lib64/libcublas_device.a:maxwell_sgemm.asm.o'
nvlink warning : SM Arch ('sm_35') not found in '/usr/local/cuda/bin/..//lib64/libcublas_device.a:maxwell_sm50_sgemm.o'
nvlink warning : SM Arch ('sm_35') not found in '/usr/local/cuda/bin/..//lib64/libcublas_device.a:maxwell_sm50_ssyrk.o'
Those can be safely ignored.
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Closed 8 years ago.
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I want to write a SHA1-Function in CUDA, but when I execute the function, I get wrong results out of the function. When I run the same function on the CPU, I get correct results. My SHA-Function looks like:
__device__ void SHA1_CUDA(uint8_t input_string[], int slen, uint32_t Hash_ptr[])
{
printf("Input string is %s, input len is %d\n", input_string, slen);
uint32_t K[80];
uint32_t A,B,C,D,E,TEMP;
int r,k,ln,t,l,i,j;
Hash_ptr[0]=0x67452301;
Hash_ptr[1]=0xefcdab89;
Hash_ptr[2]=0x98badcfe;
Hash_ptr[3]=0x10325476;
Hash_ptr[4]=0xc3d2e1f0;
ln=slen;
r = (int)((ln+1)/64);
if (((ln+1) % 64) > 56)
{
r=r+1;
}
// initialize Constants
for(t=0; t<80; t++)
{
if (t<20)
{
K[t] = 0x5a827999;
}
if ((t>19)&(t<40))
{
K[t] = 0x6ED9EBA1;
}
if ((t>39)&(t<60))
{
K[t] = 0x8F1BBCDC;
}
if (t>59)
{
K[t] = 0xca62c1d6;
}
}
for(l=0; l <= r; l++)
{
uint32_t W[80]={0};
//Initialize Text
for (i=0; i<16; i++)
{
for(j=0; j<4; j++)
{
if (4*i+j <= ln)
{
k = input_string[64*l+4*i+j];
}
else
{
k =0;
}
if (k<0)
{
k = k +256;
}
if (4*i+j == ln)
{
k = 0x80;
}
// W[i]= W[i] + k*(uint32_t)pow(256,(double)3-j);
W[i]= W[i] + k*expo_d[3-j];
}
}
if ((W[14]==0)&(W[15]==0))
{
W[15]=8*slen;
}
// Hash Cycle
for (t = 16; t <80; t++)
{
W[t] = Rol(W[t-3]^W[t-8]^W[t-14]^W[t-16],1);
}
A = Hash_ptr[0];
B = Hash_ptr[1];
C = Hash_ptr[2];
D = Hash_ptr[3];
E = Hash_ptr[4];
for(t = 0; t < 80; t++)
{
TEMP = (Rol(A,5) + f(B,C,D,t) + E + W[t] + K[t]);
E = D;
D = C;
C = Rol(B,30);
B = A;
A = TEMP;
}
Hash_ptr[0] = Hash_ptr[0] + A;
Hash_ptr[1] = Hash_ptr[1] + B;
Hash_ptr[2] = Hash_ptr[2] + C;
Hash_ptr[3] = Hash_ptr[3] + D;
Hash_ptr[4] = Hash_ptr[4] + E;
ln = ln - 64;
}
}
(host function is analogous, only with __host__ instead of __device__).
My kernel function is
__global__ void test_sha(uint8_t pw[], int* pw_len, uint32_t H[])
{
SHA1_CUDA(pw, *pw_len, H);
}
and I'm calling it like
printf("\nTesting SHA\n");
uint32_t * H_h = (uint32_t*)malloc(sizeof(uint32_t)*5);
memset(H_h, 0, sizeof(uint32_t) * 5);
uint32_t * H_d;
cudaMalloc(&H_d, sizeof(uint32_t)*5);
cudaMemcpy(H_d, H_h, 5*sizeof(uint32_t), cudaMemcpyHostToDevice);
test_sha<<<1, 1>>>(Pass_d, Pass_len_d, H_d);
cudaMemcpy(H_h, H_d, 5*sizeof(uint32_t), cudaMemcpyDeviceToHost);
cudaFree(H_d);
for(int i = 0; i < 5; i++)
printf("%x ", H_h[i]);
printf("\n\n");
printf("Comparing to CPU: \n");
SHA1_CUDA_h(Pass_h, Pass_len, H_h);
for(int i = 0; i < 5; i++)
printf("%x ", H_h[i]);
printf("\n\n");
free(H_h);
So, my printf-function in the SHA-function tells me that everything has been transferred correctly, but nevertheless I get wrong results...
Where is my mistake?
Problem solved, the ROL-function Rol_CUDA I was using in my function returned bad values, thus no one except me could solve the problem.
For everyone who wants to use this function: In line 51 on pastebin, there should be a 32-y, and not a -y. With this correction everything works.
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I'm optimizing the function, I try every way and even sse, and modified code to return from different position to see the calculate timespan but finally I found most of the time spends on the bool judgement. Even I replace all code in the if statement with a simple add operation in it, it still cost 6000ms.
My platform is gcc 4.7.1 e5506 cpu. Its input 'a' and 'b' is a 1000size int array, and 'asize', 'bsize' are corresponding array size. MATCH_MASK = 16383, I run the function 100000 times to statistics a timespan. Is there any good idea to the problem. Thank you!
if (aoffsets[i] && boffsets[i]) // this line costs most time
Code:
uint16_t aoffsets[DOUBLE_MATCH_MASK] = {0}; // important! or it will only be right on the first time
uint16_t* boffsets = aoffsets + MATCH_MASK;
uint8_t* seen = (uint8_t *)aoffsets;
auto fn_init_offsets = [](const int32_t* x, int n_size, uint16_t offsets[])->void
{
for (int i = 0; i < n_size; ++i)
offsets[MATCH_STRIP(x[i])] = i;
};
fn_init_offsets(a, asize, aoffsets);
fn_init_offsets(b, bsize, boffsets);
uint8_t topcount = 0;
int topoffset = 0;
{
std::vector<uint8_t> count_vec(asize + bsize + 1, 0); // it's the fastest way already, very near to tls
uint8_t* counts = &(count_vec[0]);
//return aoffsets[0]; // cost 1375 ms
for (int i = 0; i < MATCH_MASK; ++i)
{
if (aoffsets[i] && boffsets[i]) // this line costs most time
{
//++affsets[i]; // for test
int offset = (aoffsets[i] -= boffsets[i]);
if ((-n_maxoffset <= offset && offset <= n_maxoffset))
{
offset += bsize;
uint8_t n_cur_count = ++counts[offset];
if (n_cur_count > topcount)
{
topcount = n_cur_count;
topoffset = offset;
}
}
}
}
}
return aoffsets[0]; // cost 6000ms
First, memset(count_vec,0, N); of a memaligned buffer wins over std::vector by 30%.
You can try to use the branchless expression (aoffsets[i] * boffsets[i]) and calculate some of not-to-be-used expressions simultaneously: offset = aoffset[i]-boffset[i]; offset+bsize; offset+n_maxoffset;.
Depending on the typical range of offset, one could be tempted to calculate the min/max of (offset+bsize) to restrict the needed memset(count_vec) at the next iteration: no need to clear already zero values.
As pointed by philipp, it's good to interleave the operations -- then again, one can read both aoffset[i] and boffset[i] simultaneously from uint32_t aboffset[N]; with some clever bit masking (that generates change mask for: aoffset[i], aoffset[i+1]) one could possibly handle 2 sets in parallel using 64-bit simulated SIMD in pure c (up to the histogram accumulation part).
You can increase the speed of your program by reducing the cache misses: aoffsets[i] and boffsets[i] are relatively far away from each other in memory. By placing them next to each other, you speed up the program significantly. On my machine (e5400 cpu, VS2012) the execution time is reduced from 3.0 seconds to 2.3 seconds:
#include <vector>
#include <windows.h>
#include <iostream>
typedef unsigned short uint16_t;
typedef int int32_t;
typedef unsigned int uint32_t;
typedef unsigned char uint8_t;
#define MATCH_MASK 16383
#define DOUBLE_MATCH_MASK (MATCH_MASK*2)
static const int MATCH_BITS = 14;
static const int MATCH_LEFT = (32 - MATCH_BITS);
#define MATCH_STRIP(x) ((uint32_t)(x) >> MATCH_LEFT)
static const int n_maxoffset = 1000;
uint16_t test(int32_t* a, int asize, int32_t* b, int bsize)
{
uint16_t offsets[DOUBLE_MATCH_MASK] = {0};
auto fn_init_offsets = [](const int32_t* x, int n_size, uint16_t offsets[])->void
{
for (int i = 0; i < n_size; ++i)
offsets[MATCH_STRIP(x[i])*2 /*important. leave space for other offsets*/] = i;
};
fn_init_offsets(a, asize, offsets);
fn_init_offsets(b, bsize, offsets+1);
uint8_t topcount = 0;
int topoffset = 0;
{
std::vector<uint8_t> count_vec(asize + bsize + 1, 0);
uint8_t* counts = &(count_vec[0]);
for (int i = 0; i < MATCH_MASK; i+=2)
{
if (offsets[i] && offsets[i+1])
{
int offset = (offsets[i] - offsets[i+1]); //NOTE: I removed
if ((-n_maxoffset <= offset && offset <= n_maxoffset))
{
offset += bsize;
uint8_t n_cur_count = ++counts[offset];
if (n_cur_count > topcount)
{
topcount = n_cur_count;
topoffset = offset;
}
}
}
}
}
return offsets[0];
}
int main(int argc, char* argv[])
{
const int sizes = 1000;
int32_t* a = new int32_t[sizes];
int32_t* b = new int32_t[sizes];
for (int i=0;i<sizes;i++)
{
a[i] = rand()*rand();
b[i] = rand()*rand();
}
//Variablen
LONGLONG g_Frequency, g_CurentCount, g_LastCount;
QueryPerformanceFrequency((LARGE_INTEGER*)&g_Frequency);
QueryPerformanceCounter((LARGE_INTEGER*)&g_CurentCount);
int sum = 0;
for (int i=0;i<100000;i++)
{
sum += test(a,sizes,b,sizes);
}
QueryPerformanceCounter((LARGE_INTEGER*)&g_LastCount);
double dTimeDiff = (((double)(g_LastCount-g_CurentCount))/((double)g_Frequency));
std::cout << "Result: " << sum << std::endl <<"time: " << dTimeDiff << std::endl;
delete[] a;
delete[] b;
return 0;
}
compared to your version of test().
#include <vector>
#include <windows.h>
#include <iostream>
typedef unsigned short uint16_t;
typedef int int32_t;
typedef unsigned int uint32_t;
typedef unsigned char uint8_t;
#define MATCH_MASK 16383
#define DOUBLE_MATCH_MASK (MATCH_MASK*2)
static const int MATCH_BITS = 14;
static const int MATCH_LEFT = (32 - MATCH_BITS);
#define MATCH_STRIP(x) ((uint32_t)(x) >> MATCH_LEFT)
static const int n_maxoffset = 1000;
uint16_t test(int32_t* a, int asize, int32_t* b, int bsize)
{
uint16_t aoffsets[DOUBLE_MATCH_MASK] = {0}; // important! or it will only be right on the first time
uint16_t* boffsets = aoffsets + MATCH_MASK;
auto fn_init_offsets = [](const int32_t* x, int n_size, uint16_t offsets[])->void
{
for (int i = 0; i < n_size; ++i)
offsets[MATCH_STRIP(x[i])] = i;
};
fn_init_offsets(a, asize, aoffsets);
fn_init_offsets(b, bsize, boffsets);
uint8_t topcount = 0;
int topoffset = 0;
{
std::vector<uint8_t> count_vec(asize + bsize + 1, 0);
uint8_t* counts = &(count_vec[0]);
for (int i = 0; i < MATCH_MASK; ++i)
{
if (aoffsets[i] && boffsets[i])
{
int offset = (aoffsets[i] - boffsets[i]); //NOTE: I removed the -= because otherwise offset would always be positive!
if ((-n_maxoffset <= offset && offset <= n_maxoffset))
{
offset += bsize;
uint8_t n_cur_count = ++counts[offset];
if (n_cur_count > topcount)
{
topcount = n_cur_count;
topoffset = offset;
}
}
}
}
}
return aoffsets[0];
}
int main(int argc, char* argv[])
{
const int sizes = 1000;
int32_t* a = new int32_t[sizes];
int32_t* b = new int32_t[sizes];
for (int i=0;i<sizes;i++)
{
a[i] = rand()*rand();
b[i] = rand()*rand();
}
LONGLONG g_Frequency, g_CurentCount, g_LastCount;
QueryPerformanceFrequency((LARGE_INTEGER*)&g_Frequency);
QueryPerformanceCounter((LARGE_INTEGER*)&g_CurentCount);
int sum = 0;
for (int i=0;i<100000;i++)
{
sum += test(a,sizes,b,sizes);
}
QueryPerformanceCounter((LARGE_INTEGER*)&g_LastCount);
double dTimeDiff = (((double)(g_LastCount-g_CurentCount))/((double)g_Frequency));
std::cout << "Result: " << sum << std::endl <<"time: " << dTimeDiff << std::endl;
delete[] a;
delete[] b;
return 0;
}