binary.h
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//make sure that this header file is only loaded once
#ifndef RTS_BINARY_H
#define RTS_BINARY_H
#include "../envi/envi_header.h"
#include "../math/vector.h"
#include <fstream>
#include <sys/stat.h>
#include <cstring>
#include <chrono>
#ifdef _WIN32
#include <Windows.h>
#else
#include <unistd.h>
#endif
namespace stim{
/// This class calculates the optimal setting for independent parameter b (batch size) for
/// minimizing the dependent parameter bps (bytes per second)
class stream_optimizer{
protected:
size_t Bps[2]; //bytes per second for the previous batch
size_t interval_B; //number of bytes processed this interval
size_t interval_ms; //number of milliseconds spent in the current interval
size_t n[2]; //current batch size (in bytes)
size_t h; //spacing used for finite difference calculations
size_t dn; //delta value (in bytes) for setting the batch size (minimum change in batch parameter)
size_t maxn; //maximum value for the batch size
double alpha; //alpha value controls the factor of the gradient that is used to calculate the next point (speed of convergence)
bool sample_step; //calculating the derivative (this class alternates between calculating dBps and B)
bool forward_diff; //evaluate the derivative using forward differences
size_t window_ms; //size of the interval (in milliseconds) integrated to get a reliable bps value
// This function rounds x to the nearest value within dB
size_t round_limit(double n0){
if(n0 < 0) return dn; //if n0 is less than zero, return the lowest possible n
size_t new_n = (size_t)(n0 + 0.5); //now n0 must be positive, so round it to the nearest integer
if(new_n > maxn) new_n = maxn; //limit the returned size of x to within the specified bounds
size_t lowest = new_n / dn;
size_t highest = lowest + dn;
size_t diff[2] = {new_n - lowest, highest - new_n}; //calculate the two differences
if(diff[0] < diff[1])
return lowest;
return highest;
}
public:
//constructor initializes a stream optimizer
stream_optimizer(size_t min_batch_size, size_t max_batch_size, double a = 0.001, double probe_step = 5, size_t window = 2000){
//Bps = 0; //initialize to zero bytes per second processed
Bps[0] = Bps[1] = 0; //initialize the bits per second to 0
interval_B = 0; //zero bytes have been processed at initialization
interval_ms = 0; //no time has been spent on the batch so far
dn = min_batch_size; //set the minimum batch size as the minimum change in batch size
maxn = max_batch_size; //set the maximum batch size
n[0] = max_batch_size; //set B
h = (max_batch_size / min_batch_size) / probe_step * dn;
std::cout<<"h = "<<h<<std::endl;
if(h < dn) h = dn;
alpha = a;
//n[0] = round_limit( (max_batch_size - min_batch_size)/2 );
window_ms = window; //minimum integration interval (for getting a reliable bps measure)
sample_step = true; //the first step is to calculate the derivative
forward_diff = true; //start with the forward difference (since we start at the maximum batch size)
}
size_t update(size_t bytes_processed, size_t ms_spent){
interval_B += bytes_processed; //increment the number of bytes processed
interval_ms += ms_spent; //increment the number of milliseconds spent processing
//if we have sufficient information to evaluate the optimization function at this point
if(interval_ms < window_ms){ //if insufficient time has passed to get a reliable Bps measurement
return n[0];
}
else{ //if we have collected enough information for a reliable Bps estimate
size_t new_Bps = interval_B / interval_ms; //calculate the current Bps
if(Bps[0] == 0){ //if n[0] hasn't been evaluated yet, this is the first step
Bps[0] = new_Bps; //set the initial Bps value
n[1] = n[0] - h; //set the position of the next sample point
std::cout<<"Bps value at n = "<<n[0]<<" is "<<Bps[0]<<" Bps, probing n = "<<n[1]<<std::endl;
return n[1]; //return the probe point
}
else{
Bps[1] = new_Bps; //set the Bps for the current point (n[1])
double Bps_p; //allocate a variable for the derivative
//calculate the derivative
if(n[0] < n[1]){ //if the current point is less than the previous one (probably the most common)
Bps_p = ((double)Bps[1] - (double)Bps[0]) / (double)h; //calculate the derivative using the forward finite difference
}
else{
Bps_p = ((double)Bps[0] - (double)Bps[1]) / (double)h; //calculate the derivative using the backward finite difference
}
std::cout<<" probed n = "<<n[1]<<" with "<<Bps[1]<<" Bps, gradient = "<<Bps_p<<" Bps"<<std::endl;
double new_n_precise = n[0] + alpha * Bps_p; //calculate the next point (snap to closest integer)
size_t new_n_nearest = round_limit(new_n_precise); //calculate the next point (given batch parameters)
if(new_n_nearest == n[0]){ //if the newest point is the same as the original point
Bps[0] = Bps[1]; //update the Bps
//if(n[0] == dn) n[1] = n[0] + h; //if we're on the left edge, probe forward
//else n[1] = n[0] - h; //otherwise probe backwards
std::cout<<" staying at n = "<<n[0]<<" for now"<<std::endl;
//return n[1]; //return the probe point
Bps[0] = 0; //reset the Bps for the current point
return n[0]; //return the current point for a re-calculation
}
else{ //if the newest point is different from the original point
n[0] = new_n_nearest; //move to the new point
Bps[0] = 0; //set the Bps to zero (point hasn't been tested)
std::cout<<" moving to n = "<<n[0]<<std::endl;
return n[0]; //return the new point
}
}
}
}
/*// this function updates the optimizer, given the number of bytes processed in an interval and time spent processing
size_t update(size_t bytes_processed, size_t ms_spent){
interval_B += bytes_processed; //increment the number of bytes processed
interval_ms += ms_spent; //increment the number of milliseconds spent processing
//if we have sufficient information to evaluate the optimization function at this point
if(interval_ms >= window_ms){ //if sufficient time has passed to get a reliable Bps measurement
size_t new_Bps = interval_B / interval_ms; //calculate the current Bps
if(sample_step){ //if this is a sample step, collect the information for Bps = f(n0)
Bps = new_Bps; //set the Bps to the evaluated value
n[1] = n[0] - dn; //reduce the batch size by one delta to take a second sample
if(n[1] == 0){ //if the resulting batch size is zero
n[1] = 2*dn; //we're at the left edge: set the new sample point to 2*dn
}
interval_B = interval_ms = 0; //start a new interval at the new sample point
sample_step = false; //next step will calculate the new batch size via optimization
return n[1]; //return the new batch size
}
else{ //if we have sufficient information to evaluate the derivative and optimize
double f = (double)new_Bps; //we have evaluated the function at this location
double fprime;
if(n[1] < n[0] ){ //if the new point is less than the previous point (usually the case)
fprime = (double)(Bps - new_Bps) / (double)dn; //calculate the forward difference
}
else{ //if the new point is larger (only happens at the minimum limit)
fprime = (double)(new_Bps - Bps) / (double)dn; //calculate the backward difference
}
size_t bestn = n[1] - (size_t)(f / fprime); //calculate the best value for B using Newton's method
n[0] = round_limit( (size_t)bestn ); //set the new dependent point
sample_step = true; //the next step will be a sample step
}
}
if(sample_step) return n[0];
return n[1]; //insufficient information, keep the same batch size
}*/
/*size_t update(size_t bytes_processed, size_t ms_spent){
interval_B += bytes_processed; //increment the number of bytes processed
interval_ms += ms_spent; //increment the number of milliseconds spent processing
//if( Bps[0] == 0 ){ //if the left boundary hasn't been processed
//if we have sufficient information to evaluate the optimization function at this point
if(interval_ms >= window_ms){
size_t new_Bps = interval_B / interval_ms; //calculate the current Bps
if(Bps[0] == 0) //if the left interval Bps hasn't been calculated
Bps[0] = interval_B / interval_ms; //that is the interval being processed
else
Bps[1] = interval_B / interval_ms; //otherwise the right interval is being processed
if(Bps[0] != 0 && Bps[1] != 0){ //if both intervals have been processed
}
}*/
size_t update(size_t bytes_processed, size_t ms_spent, size_t& data_rate){
size_t time = update(bytes_processed, ms_spent);
data_rate = Bps[0];
return time;
}
};
/** This class manages the streaming of large multidimensional binary files.
* Generally these are hyperspectral files with 2 spatial and 1 spectral dimension. However, this class supports
* other dimensions via the template parameter D.
*
* @param T is the data type used to store data to disk (generally float or double)
* @param D is the dimension of the data (default 3)
*/
template< typename T, unsigned int D = 3 >
class binary{
protected:
std::fstream file; //file stream used for reading and writing
std::string name; //file name
unsigned long long R[D]; //resolution
unsigned long long header; //header size (in bytes)
unsigned char* mask; //pointer to a character array: 0 = background, 1 = foreground (or valid data)
double progress; //stores the progress on the current operation (accessible using a thread)
size_t buffer_size; //available memory for processing large files
/// Private initialization function used to set default parameters in the data structure.
void init(){
std::memset(R, 0, sizeof(unsigned long long) * D); //initialize the resolution to zero
header = 0; //initialize the header size to zero
mask = NULL;
progress = 0;
set_buffer(); //set the maximum buffer size to the default
}
/// Private helper function that returns the size of the file on disk using system functions.
long long int get_file_size(){
#ifdef _WIN32
struct _stat64 results;
if(_stat64(name.c_str(), &results) == 0)
return results.st_size;
#else
struct stat results;
if(stat(name.c_str(), &results) == 0)
return results.st_size;
#endif
else return 0;
}
/// Private helper function that tests to make sure that the calculated data size specified by the structure is the same as the data size on disk.
bool test_file_size(){
long long int npts = 1; //initialize the number of data points to 1
for(unsigned int i = 0; i<D; i++) //iterate over each dimension
npts *= R[i]; //compute the total number of data points in the file
long long int datasize = npts * sizeof(T);//multiply the sum by the size of the template parameter
if(datasize + header == get_file_size()) return true; //if the byte size matches the file size, we're golden
else return false; //otherwise return an error
}
/// Private helper function that resets the file pointer to the beginning of the data
void reset(){
file.seekg(header, std::ios_base::beg);
}
/// Private helper file that opens a specified binary file.
/// @param filename is the name of the binary file to stream
bool open_file(std::string filename){
//open the file as binary for reading and writing
file.open(filename.c_str(), std::ios::in | std::ios::out | std::ios::binary);
//if the file isn't open, the user may only have read access
if(!file.is_open()){
std::cout<<"class STIM::BINARY - failed to open file, trying for read only"<<std::endl;
file.open(filename.c_str(), std::ios::in | std::ios::binary);
if(!file.is_open()){
std::cout<<" still unable to load the file"<<std::endl;
return false;
}
}
//if the file is successful
if(file){
name = filename; //set the name
if(test_file_size()) //test the file size
return true;
}
return false;
}
public:
//default constructor
binary(){
init();
}
double get_progress(){
return progress;
}
void reset_progress(){
progress = 0;
}
//specify the maximum fraction of available memory that this class will use for buffering
void set_buffer(double mem_frac = 0.5){ //default to 50%
#ifdef _WIN32
MEMORYSTATUSEX statex;
statex.dwLength = sizeof (statex);
GlobalMemoryStatusEx (&statex);
buffer_size = (size_t)(statex.ullAvailPhys * mem_frac);
#else
size_t pages = sysconf(_SC_PHYS_PAGES);
size_t page_size = sysconf(_SC_PAGE_SIZE);
buffer_size = (size_t)(pages * page_size * mem_frac);
#endif
}
/// Open a binary file for streaming.
/// @param filename is the name of the binary file
/// @param r is a STIM vector specifying the size of the binary file along each dimension
/// @param h is the length (in bytes) of any header file (default zero)
bool open(std::string filename, vec<unsigned long long> r, unsigned long long h = 0){
for(unsigned long long i = 0; i < D; i++) //set the dimensions of the binary file object
R[i] = r[i];
header = h; //save the header size
if(!open_file(filename)) return false; //open the binary file
//reset();
return test_file_size();
}
/// Creates a new binary file for streaming
/// @param filename is the name of the binary file to be created
/// @param r is a STIM vector specifying the size of the file along each dimension
/// @offset specifies how many bytes to offset the file (used to leave room for a header)
bool create(std::string filename, vec<unsigned long long> r, unsigned long long offset = 0){
std::ofstream target(filename.c_str(), std::ios::binary);
//initialize binary file
T p = 0;
for(unsigned long long i =0; i < r[0] * r[1] * r[2]; i++){
target.write((char*)(&p), sizeof(T));
}
for(unsigned long long i = 0; i < D; i++) //set the dimensions of the binary file object
R[i] = r[i];
header = offset; //save the header size
if(!open_file(filename)) return false; //open the binary file
return test_file_size();
}
/// Writes a single page of data to disk. A page consists of a sequence of data of size R[0] * R[1] * ... * R[D-1].
/// @param p is a pointer to the data to be written
/// @param page is the page number (index of the highest-numbered dimension)
bool write_page( T * p, unsigned long long page){
if(p == NULL){
std::cout<<"ERROR: unable to write into file, empty pointer"<<std::endl;
exit(1);
}
file.seekg(R[1] * R[0] * page * sizeof(T) + header, std::ios::beg); //seek to the desired location on disk
file.write((char *)p, R[0] * R[1] * sizeof(T)); //write binary data
return true;
}
/// Reads a page from disk. A page consists of a sequence of data of size R[0] * R[1] * ... * R[D-1].
/// @param p is a pointer to pre-allocated memory equal to the page size
/// @param page is the index of the page
bool read_page( T * p, unsigned long long page, bool PROGRESS = false){
if(PROGRESS) progress = 0;
if (page >= R[2]){ //make sure the bank number is right
std::cout<<"ERROR: page out of range"<<std::endl;
return false;
}
file.seekg(R[1] * R[0] * page * sizeof(T) + header, std::ios::beg); //write into memory from the binary file
file.read((char *)p, R[0] * R[1] * sizeof(T));
if(PROGRESS) progress = 100;
return true;
}
///Reads a line Z (slowest dimension) for a given XY value
/// @param p is a pointer to pre-allocated memory equal to the line size R[2]
/// @param x is the x coordinate
/// @param y is the y coordinate
void read_line_2( T* p, size_t n, bool PROGRESS = false){
unsigned long long i;
if(PROGRESS) progress = 0;
if ( n > R[0] * R[1]){ //make sure the sample and line number is right
std::cout<<"ERROR: sample or line out of range in "<<__FILE__<<" (line "<<__LINE__<<")"<<std::endl;
exit(1);
}
file.seekg(n * sizeof(T), std::ios::beg); //point to the certain sample and line
for (i = 0; i < R[2]; i++){ //for each band
file.read((char *)(p + i), sizeof(T));
file.seekg((R[1] * R[0] - 1) * sizeof(T), std::ios::cur); //go to the next band
if(PROGRESS) progress = (double)i / (double)R[2] * 100;
}
if(PROGRESS) progress = 100;
}
void read_line_2( T * p, unsigned long long x, unsigned long long y, bool PROGRESS = false){
read_line_2(p, y * R[0] + x, PROGRESS);
/*unsigned long long i;
if(PROGRESS) progress = 0;
if ( x >= R[0] || y >= R[1]){ //make sure the sample and line number is right
std::cout<<"ERROR: sample or line out of range"<<std::endl;
return false;
}
file.seekg((x + y * R[0]) * sizeof(T), std::ios::beg); //point to the certain sample and line
for (i = 0; i < R[2]; i++)
{
file.read((char *)(p + i), sizeof(T));
file.seekg((R[1] * R[0] - 1) * sizeof(T), std::ios::cur); //go to the next band
if(PROGRESS) progress = (double)i / (double)R[2] * 100;
}
if(PROGRESS) progress = 100;
return true;*/
}
///Reads a line X (fastest dimension) for a given YZ value
/// @param p is a pointer to pre-allocated memory equal to the line size R[2]
/// @param x is the y coordinate
/// @param y is the z coordinate
bool read_line_0(T * p, unsigned long long y, unsigned long long z, bool PROGRESS = false){
//test to make sure the specified value is within range
if( y >= R[1] || z >= R[2] ){
std::cout<<"ERROR: sample ("<<y<<", "<<z<<") out of range in "<<__FILE__<<" (line "<<__LINE__<<")"<<std::endl;
return false;
}
file.seekg((z * R[0] * R[1] + y * R[0]) * sizeof(T), std::ios::beg); //seek to the start of the line
file.read((char *)p, sizeof(T) * R[0]); //read the line
if(PROGRESS) progress = 100;
return true;
}
///Reads a line Y (second fastest dimension) for a given XZ value
/// @param p is a pointer to pre-allocated memory equal to the line size R[2]
/// @param x is the y coordinate
/// @param z is the z coordinate
bool read_line_1(T * p, unsigned long long x, unsigned long long z, bool PROGRESS = false){
if(PROGRESS) progress = 0;
//test to make sure the specified value is within range
if( x >= R[0] || z >= R[2] ){
std::cout<<"ERROR: sample or line out of range in "<<__FILE__<<" (line "<<__LINE__<<")"<<std::endl;
return false;
}
file.seekg((z * R[0] * R[1] + x) * sizeof(T), std::ios::beg); //seek to the start of the line
for (unsigned long long i = 0; i < R[1]; i++){ //for each pixel in the line
file.read((char *)(p + i), sizeof(T)); //read the pixel
file.seekg((R[0] - 1) * sizeof(T), std::ios::cur); //seek to the next pixel in the line
if(PROGRESS) progress = (double)i / (double)R[1] * 100;
}
if(PROGRESS) progress = 100;
return true;
}
/// Reads a plane given a coordinate along the 0-axis (YZ plane)
/// @param p is a pointer to pre-allocated memory of size R[1] * R[2] * sizeof(T)
/// @param n is the 0-axis coordinate used to retrieve the plane
bool read_plane_0(T* p, unsigned long long n, bool PROGRESS = false){
if(PROGRESS) progress = 0;
if (n >= R[0]){ //make sure the number is within the possible range
std::cout<<"ERROR: sample or line out of range in "<<__FILE__<<" (line "<<__LINE__<<")"<<std::endl;
return false;
}
unsigned long long jump = (R[0] - 1) * sizeof(T); //number of bytes to skip between samples
//seek to the start of the plane
file.seekg(n * sizeof(T), std::ios::beg);
unsigned long long N = R[1] * R[2];
for(unsigned long long i = 0; i<N; i++){
file.read((char*)(p+i), sizeof(T));
file.seekg(jump, std::ios::cur);
if(PROGRESS) progress = (double)(i+1) / N * 100;
}
return true;
}
/// Reads a plane given a coordinate along the 1-axis (XZ plane)
/// @param p is a pointer to pre-allocated memory of size R[0] * R[2] * sizeof(T)
/// @param n is the 1-axis coordinate used to retrieve the plane
bool read_plane_1(T* p, unsigned long long n, bool PROGRESS = false){
if(PROGRESS) progress = 0;
unsigned long long L = R[0] * sizeof(T); //caculate the number of bytes in a sample line
unsigned long long jump = R[0] * (R[1] - 1) * sizeof(T);
if (n >= R[1]){ //make sure the bank number is right
std::cout<<"ERROR read_plane_1: page out of range"<<std::endl;
return false;
}
file.seekg(R[0] * n * sizeof(T), std::ios::beg);
for (unsigned long long i = 0; i < R[2]; i++){
if(PROGRESS) progress = (double)i / R[2] * 100;
file.read((char *)(p + i * R[0]), L);
file.seekg( jump, std::ios::cur);
std::cout<<i<<" ";
}
if(PROGRESS) progress = 100;
return true;
}
/// Reads a plane given a coordinate along the 2-axis (XY plane)
/// @param p is a pointer to pre-allocated memory of size R[0] * R[1] * sizeof(T)
/// @param n is the 2-axis coordinate used to retrieve the plane
bool read_plane_2(T* p, unsigned long long n, bool PROGRESS = false){
return read_page(p, n, PROGRESS);
}
/// Reads a single pixel, treating the entire data set as a linear array
/// @param p is a pointer to pre-allocated memory of size sizeof(T)
/// @param i is the index to the pixel using linear indexing
bool read_pixel(T* p, unsigned long long i){
if(i >= R[0] * R[1] * R[2]){
std::cout<<"ERROR read_pixel: n is out of range"<<std::endl;
return false;
}
file.seekg(i * sizeof(T), std::ios::cur);
file.read((char*)p, sizeof(T));
}
/// Reads a single pixel, given an x, y, z coordinate
/// @param p is a pointer to pre-allocated memory of size sizeof(T)
/// @param x is the x (0) axis coordinate
/// @param y is the y (1) axis coordinate
/// @param z is the z (2) axis coordinate
bool read_pixel(T* p, unsigned long long x, unsigned long long y, unsigned long long z){
if(x < 0 || x >= R[0] || y < 0 || y >= R[1] || z < 0 || z > R[2]){
std::cout<<"ERROR read_pixel: (x,y,z) is out of range"<<std::endl;
return false;
}
unsigned long long i = z * R[0] * R[1] + y * R[0] + z;
return read_pixel(p, i);
}
/// Reads a block specified by an (x, y, z) position and size using the largest possible contiguous reads
size_t read(T* dest, size_t x, size_t y, size_t z, size_t sx, size_t sy, size_t sz){
auto t0 = std::chrono::high_resolution_clock::now();
size_t size_bytes = sx * sy * sz * sizeof(T); //size of the block to read in bytes
size_t start = z * R[0] * R[1] + y * R[0] + x; //calculate the start postion
size_t start_bytes = start * sizeof(T); //start position in bytes
file.seekg(start * sizeof(T), std::ios::beg); //seek to the start position
if(sx == R[0] && sy == R[1]){ //if sx and sy result in a contiguous volume along z
file.read((char*)dest, size_bytes); //read the block in one pass
}
else if(sx == R[0]){ //if sx is contiguous, read each z-axis slice can be read in one pass
size_t jump_bytes = (R[1] - sy) * R[0] * sizeof(T); //jump between each slice
size_t slice_bytes = sx * sy * sizeof(T); //size of the slice to be read
for(size_t zi = 0; zi < sz; zi++){ //for each z-axis slice
file.read((char*)dest, slice_bytes); //read the slice
dest += sx * sy; //move the destination pointer to the next slice
file.seekg(jump_bytes, std::ios::cur); //skip to the next slice in the file
}
}
else{
//in this case, x is not contiguous so the volume must be read line-by-line
size_t jump_x_bytes = (R[0] - sx) * sizeof(T); //number of bytes skipped in the x direction
size_t jump_y_bytes = (R[1] - sy) * R[0] * sizeof(T) + jump_x_bytes; //number of bytes skipped between slices
size_t line_bytes = sx * sizeof(T); //size of the line to be read
size_t zi, yi;
for(zi = 0; zi < sz; zi++){ //for each slice
file.read((char*)dest, line_bytes); //read the first line
for(yi = 1; yi < sy; yi++){ //read each additional line
dest += sx; //move the pointer in the destination block to the next line
file.seekg(jump_x_bytes, std::ios::cur); //skip to the next line in the file
file.read((char*)dest, line_bytes); //read the line to the destination block
}
file.seekg(jump_y_bytes, std::ios::cur); //skip to the beginning of the next slice
}
}
auto t1 = std::chrono::high_resolution_clock::now();
return std::chrono::duration_cast<std::chrono::milliseconds>(t1-t0).count();
}
// permutes a block of data from the current interleave to the interleave specified (re-arranged dimensions to the order specified by [d0, d1, d2])
size_t permute(T* dest, T* src, size_t sx, size_t sy, size_t sz, size_t d0, size_t d1, size_t d2){
auto t0 = std::chrono::high_resolution_clock::now();
size_t d[3] = {d0, d1, d2};
size_t s[3] = {sx, sy, sz};
size_t p[3];// = {x, y, z};
if(d[0] == 0 && d[1] == 1 && d[2] == 2){
//this isn't actually a permute - just copy the data
memcpy(dest, src, sizeof(T) * sx * sy * sz);
}
else if(d[0] == 0){ //the individual lines are contiguous, so you can memcpy line-by-line
size_t y, z;
size_t src_idx, dest_idx;
size_t x_bytes = sizeof(T) * sx;
for(z = 0; z < sz; z++){
p[2] = z;
for(y = 0; y < sy; y++){
p[1] = y;
src_idx = z * sx * sy + y * sx;
dest_idx = p[d[2]] * s[d[0]] * s[d[1]] + p[d[1]] * s[d[0]];
memcpy(dest + dest_idx, src + src_idx, x_bytes);
}
}
}
else{ //loop through every damn point
size_t x, y, z;
size_t src_idx, dest_idx;
size_t src_z, src_y;
for(z = 0; z < sz; z++){
p[2] = z;
src_z = z * sx * sy;
for(y = 0; y < sy; y++){
p[1] = y;
src_y = src_z + y * sx;
for(x = 0; x < sx; x++){
p[0] = x;
src_idx = src_y + x;
dest_idx = p[d[2]] * s[d[0]] * s[d[1]] + p[d[1]] * s[d[0]] + p[d[0]];
dest[dest_idx] = src[src_idx];
}
}
}
}
auto t1 = std::chrono::high_resolution_clock::now();
return std::chrono::duration_cast<std::chrono::milliseconds>(t1-t0).count();
}
};
}
#endif