View source for BETTERRED

= Assignment 1 - Select and Assess =

== Introduction : GPU Benchmarking/Testing using Mandelbrot Sets : Kartik Nagarajan ==


This program generates Mandelbrot sets using CPU's and then saves them to the folder as png's using the freeimage library.

The program is open-source and can be fetched directly from GitHub from https://github.com/sol-prog/Mandelbrot_Set

To compile the program, FreeImage is required to be installed.


=== Compilation Instructions: ===

For Unix based systems:

          g++ -std=c++11 save_image.cpp utils.cpp mandel.cpp -lfreeimage

OSX:

          clang++ -std=c++11 save_image.cpp utils.cpp mandel.cpp -lfreeimage

The program can then be executed by running the compiled binary and it will display the time it took to generate the Mandelbrot set and save the pictures.

=== Observations ===

The program takes a significant amount of time to run as the calculations are being done on the CPU. There are nested loops present within the program that can be parallelized to make the program faster.

The code also has the size of the image and the iterations hard-coded which can be modified to make the program significantly longer to process and make it tough on the GPU's for benchmarking and stability testing by running the process in a loop. The code is relatively straight forward and the parallelization should also be easy to implement and test.


=== Hotspot ===

Hotspot for the program was found in the fractal() function which calls the get_iterations() function that contains 2-nested for loops and a call to escape() which contains a while loop. Profiling the runtime with Instruments on OSX displayed that the fractal() function took up the most amount of runtime and this is the function that will be parallelized using CUDA. Once the function is parallelized, the iterations and size of the image can be increased in order to make the computation relatively stressful on the GPU to get a benchmark or looped in order to do stress testing for GPUs.


=== Profiling Data Screenshots ===

Profile - [https://drive.google.com/open?id=0B2Y_atB3DptbUG5oRWMyUGNQdlU  Profile]

Hotspot Code - [https://drive.google.com/open?id=0B2Y_atB3DptbRlhCUTNyeEFDbEk Hotspot Code]

----

== Introduction : GPU Benchmarking/Testing for NBody : Joshua Kraitberg ==

This program uses Newtonian mechanics and a four-order symplectic Candy-Rozmus integration (a symplectic algorithm guarantees exact conservation of energy and angular momentum). The initial conditions are obtained from JPL Horizons, ahd constants (like masses, gravitational constant) are those recommended by the International Astronomical Union. The program currently does not take into account effects like general relativity, the non-spherical shapes of celestial objects, tidal effects on Earth, etc. It also does not take the 500 asteroids used by JPL Horizons into accound in its model of the Solar System.

[https://github.com/fding/nbody Source]

=== Compilation Instructions: ===

For Unix/Linux based systems:

    g++ -std=c++11 c++/nbody.cpp

=== Observations ===

The program is quite fast for being a single-threaded CPU application.  Almost all the CPU time is spent manipulating data and iterating in vectors.

=== Hotspot ===

Essentially all the time spent running is spent in the doing calculation on vectors.  The dowork function iteratively calls the CRO_step function found in integrators.h file.  The CRO_step function is where most of the vector calculations take place.  A large amount of is also done in the calculate_a function which is used to calulate the acceleration on all the planets.

=== Profiling Data and Screenshots ===

{| class="wikitable mw-collapsible mw-collapsed"
! NBody Hot Functions
|-
| 

<syntaxhighlight lang="cpp">
void dowork(double t){
	int numtimes=int(abs(t/dt));
	dt=t/double(numtimes+1);
	numtimes=numtimes+1;
	for (int i=0;i<numtimes;i++){
		CRO_step(dt,a);
	}
}  

void CRO_step(register double mydt,void (*a)()){
	long double macr_a[4] = {0.5153528374311229364, -0.085782019412973646,0.4415830236164665242, 0.1288461583653841854};
	long double macr_b[4] = {0.1344961992774310892, -0.2248198030794208058, 0.7563200005156682911, 0.3340036032863214255};
	for (int i=0;i<4;i++){
            a();
            for (int j=0;j<ncobjects;j++){
                cobjects[j]->v +=  cobjects[j]->a * mydt*macr_b[i];
                cobjects[j]->pos += cobjects[j]->v  * mydt*macr_a[i]; 
			}
	} //We should really expand the loop for efficiency
}  

void calculate_a(){
	for (int j1=0;j1<ncobjects;j1++){
		cobjects[j1]->a=vect(0,0,0);
	}
	for (int j1=0; j1<ncobjects;j1++){
		for (int j2=j1+1;j2<ncobjects;j2++){
			double m1=cobjects[j1]->m;
			double m2=cobjects[j2]->m;
			vect dist=cobjects[j1]->pos-cobjects[j2]->pos;
			double magd=dist.mag();
			vect base=dist*(1.0/(magd*magd*magd));
			cobjects[j1]->a+=base*(-m2);
			cobjects[j2]->a+=base*m1;
		}
	}
}
</syntaxhighlight>

|}

{| class="wikitable mw-collapsible mw-collapsed"
! NBody Hot Spot Data
|-
| 		     Call graph (explanation follows)


granularity: each sample hit covers 4 byte(s) for 0.16% of 6.18 seconds

index % time    self  children    called     name
                                                 <spontaneous>
[1]     99.7    0.00    6.16                 main [1]
                0.00    6.15       1/1           dowork(double) [3]
                0.00    0.01       1/1           totalL() [14]
                0.00    0.00       1/1           totalE() [16]
                0.00    0.00       1/1           initialize() [17]
                0.00    0.00      28/32712799     vect::operator-(vect const&) [8]
                0.00    0.00      14/118268959     vect::operator*(double const&) [5]
                0.00    0.00      14/5032775     vect::operator=(vect const&) [11]
                0.00    0.00      42/42          std::vector<int, std::allocator<int> >::operator[](unsigned int) [22]
                0.00    0.00      16/16          bool std::operator==<char, std::char_traits<char>, std::allocator<char> >(std::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, char const*) [33]
                0.00    0.00      15/35          std::vector<int, std::allocator<int> >::size() const [23]
                0.00    0.00      14/14          std::vector<int, std::allocator<int> >::push_back(int const&) [39]
                0.00    0.00      14/14          getobj(int) [36]
                0.00    0.00       3/3           std::vector<double, std::allocator<double> >::operator[](unsigned int) [90]
                0.00    0.00       2/2           print_hline() [94]
                0.00    0.00       2/10          std::vector<double, std::allocator<double> >::size() const [45]
                0.00    0.00       1/1           std::ios_base::precision(int) [146]
                0.00    0.00       1/1           std::vector<double, std::allocator<double> >::vector() [142]
                0.00    0.00       1/1           std::vector<int, std::allocator<int> >::vector() [144]
                0.00    0.00       1/1           std::vector<double, std::allocator<double> >::push_back(double const&) [141]
                0.00    0.00       1/1           std::vector<std::string, std::allocator<std::string> >::vector() [135]
                0.00    0.00       1/1           std::vector<std::string, std::allocator<std::string> >::~vector() [136]
                0.00    0.00       1/1           JD(tm*) [103]
                0.00    0.00       1/1           std::vector<double, std::allocator<double> >::push_back(double&&) [140]
                0.00    0.00       1/1           std::vector<int, std::allocator<int> >::~vector() [145]
                0.00    0.00       1/1           std::vector<double, std::allocator<double> >::~vector() [143]
-----------------------------------------------
                0.14    6.01   89870/89870       dowork(double) [3]
[2]     99.6    0.14    6.01   89870         CRO_step(double, void (*)()) [2]
                1.18    4.22  359480/359480      calculate_a() [4]
                0.20    0.29 20130880/118268959     vect::operator*(double const&) [5]
                0.12    0.00 10065440/75490814     vect::operator+=(vect const&) [7]
-----------------------------------------------
                0.00    6.15       1/1           main [1]
[3]     99.6    0.00    6.15       1         dowork(double) [3]
                0.14    6.01   89870/89870       CRO_step(double, void (*)()) [2]
                0.00    0.00       1/1           std::abs(double) [147]
-----------------------------------------------
                1.18    4.22  359480/359480      CRO_step(double, void (*)()) [2]
[4]     87.5    1.18    4.22  359480         calculate_a() [4]
                1.00    1.39 98138040/118268959     vect::operator*(double const&) [5]
                0.78    0.00 65425360/75490814     vect::operator+=(vect const&) [7]
                0.26    0.37 32712680/32712799     vect::operator-(vect const&) [8]
                0.32    0.00 32712680/32712785     vect::mag() [10]
                0.08    0.00 5032720/5032775     vect::operator=(vect const&) [11]
                0.01    0.00 5032720/5032775     vect::vect(double, double, double) [13]
-----------------------------------------------
                0.00    0.00      11/118268959     initialize() [17]
                0.00    0.00      14/118268959     main [1]
                0.00    0.00      14/118268959     totalL() [14]
                0.20    0.29 20130880/118268959     CRO_step(double, void (*)()) [2]
                1.00    1.39 98138040/118268959     calculate_a() [4]
[5]     46.5    1.20    1.67 118268959         vect::operator*(double const&) [5]
                1.67    0.00 118268959/118268959     vect::operator*=(double const&) [6]
-----------------------------------------------
                1.67    0.00 118268959/118268959     vect::operator*(double const&) [5]
[6]     27.1    1.67    0.00 118268959         vect::operator*=(double const&) [6]
-----------------------------------------------
                0.00    0.00      14/75490814     totalL() [14]
                0.12    0.00 10065440/75490814     CRO_step(double, void (*)()) [2]
                0.78    0.00 65425360/75490814     calculate_a() [4]
[7]     14.6    0.91    0.00 75490814         vect::operator+=(vect const&) [7]
-----------------------------------------------
                0.00    0.00      28/32712799     main [1]
                0.00    0.00      91/32712799     totalE() [16]
                0.26    0.37 32712680/32712799     calculate_a() [4]
[8]     10.4    0.27    0.38 32712799         vect::operator-(vect const&) [8]
                0.38    0.00 32712799/32712799     vect::operator-=(vect const&) [9]
-----------------------------------------------
                0.38    0.00 32712799/32712799     vect::operator-(vect const&) [8]
[9]      6.1    0.38    0.00 32712799         vect::operator-=(vect const&) [9]
-----------------------------------------------
                0.00    0.00     105/32712785     totalE() [16]
                0.32    0.00 32712680/32712785     calculate_a() [4]
[10]     5.2    0.32    0.00 32712785         vect::mag() [10]
-----------------------------------------------
                0.00    0.00      14/5032775     main [1]
                0.00    0.00      41/5032775     initialize() [17]
                0.08    0.00 5032720/5032775     calculate_a() [4]
[11]     1.4    0.08    0.00 5032775         vect::operator=(vect const&) [11]
-----------------------------------------------
                                                 <spontaneous>
[12]     0.3    0.02    0.00                 vect::operator+(vect const&) [12]
-----------------------------------------------
                0.00    0.00      14/5032775     cross(vect const&, vect const&) [15]
                0.00    0.00      41/5032775     initialize() [17]
                0.01    0.00 5032720/5032775     calculate_a() [4]
[13]     0.2    0.01    0.00 5032775         vect::vect(double, double, double) [13]
-----------------------------------------------
                0.00    0.01       1/1           main [1]
[14]     0.1    0.00    0.01       1         totalL() [14]
                0.01    0.00      14/14          cross(vect const&, vect const&) [15]
                0.00    0.00      14/118268959     vect::operator*(double const&) [5]
                0.00    0.00      14/75490814     vect::operator+=(vect const&) [7]
                0.00    0.00       1/85          vect::vect() [21]
-----------------------------------------------
                0.01    0.00      14/14          totalL() [14]
[15]     0.1    0.01    0.00      14         cross(vect const&, vect const&) [15]
                0.00    0.00      14/5032775     vect::vect(double, double, double) [13]
|}	

{| class="wikitable mw-collapsible mw-collapsed"
! NBody gprof Complete Data (Warning: long)
|-
| 		     Call graph (explanation follows)


granularity: each sample hit covers 4 byte(s) for 0.16% of 6.18 seconds

index % time    self  children    called     name
                                                 <spontaneous>
[1]     99.7    0.00    6.16                 main [1]
                0.00    6.15       1/1           dowork(double) [3]
                0.00    0.01       1/1           totalL() [14]
                0.00    0.00       1/1           totalE() [16]
                0.00    0.00       1/1           initialize() [17]
                0.00    0.00      28/32712799     vect::operator-(vect const&) [8]
                0.00    0.00      14/118268959     vect::operator*(double const&) [5]
                0.00    0.00      14/5032775     vect::operator=(vect const&) [11]
                0.00    0.00      42/42          std::vector<int, std::allocator<int> >::operator[](unsigned int) [22]
                0.00    0.00      16/16          bool std::operator==<char, std::char_traits<char>, std::allocator<char> >(std::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, char const*) [33]
                0.00    0.00      15/35          std::vector<int, std::allocator<int> >::size() const [23]
                0.00    0.00      14/14          std::vector<int, std::allocator<int> >::push_back(int const&) [39]
                0.00    0.00      14/14          getobj(int) [36]
                0.00    0.00       3/3           std::vector<double, std::allocator<double> >::operator[](unsigned int) [90]
                0.00    0.00       2/2           print_hline() [94]
                0.00    0.00       2/10          std::vector<double, std::allocator<double> >::size() const [45]
                0.00    0.00       1/1           std::ios_base::precision(int) [146]
                0.00    0.00       1/1           std::vector<double, std::allocator<double> >::vector() [142]
                0.00    0.00       1/1           std::vector<int, std::allocator<int> >::vector() [144]
                0.00    0.00       1/1           std::vector<double, std::allocator<double> >::push_back(double const&) [141]
                0.00    0.00       1/1           std::vector<std::string, std::allocator<std::string> >::vector() [135]
                0.00    0.00       1/1           std::vector<std::string, std::allocator<std::string> >::~vector() [136]
                0.00    0.00       1/1           JD(tm*) [103]
                0.00    0.00       1/1           std::vector<double, std::allocator<double> >::push_back(double&&) [140]
                0.00    0.00       1/1           std::vector<int, std::allocator<int> >::~vector() [145]
                0.00    0.00       1/1           std::vector<double, std::allocator<double> >::~vector() [143]
-----------------------------------------------
                0.14    6.01   89870/89870       dowork(double) [3]
[2]     99.6    0.14    6.01   89870         CRO_step(double, void (*)()) [2]
                1.18    4.22  359480/359480      calculate_a() [4]
                0.20    0.29 20130880/118268959     vect::operator*(double const&) [5]
                0.12    0.00 10065440/75490814     vect::operator+=(vect const&) [7]
-----------------------------------------------
                0.00    6.15       1/1           main [1]
[3]     99.6    0.00    6.15       1         dowork(double) [3]
                0.14    6.01   89870/89870       CRO_step(double, void (*)()) [2]
                0.00    0.00       1/1           std::abs(double) [147]
-----------------------------------------------
                1.18    4.22  359480/359480      CRO_step(double, void (*)()) [2]
[4]     87.5    1.18    4.22  359480         calculate_a() [4]
                1.00    1.39 98138040/118268959     vect::operator*(double const&) [5]
                0.78    0.00 65425360/75490814     vect::operator+=(vect const&) [7]
                0.26    0.37 32712680/32712799     vect::operator-(vect const&) [8]
                0.32    0.00 32712680/32712785     vect::mag() [10]
                0.08    0.00 5032720/5032775     vect::operator=(vect const&) [11]
                0.01    0.00 5032720/5032775     vect::vect(double, double, double) [13]
-----------------------------------------------
                0.00    0.00      11/118268959     initialize() [17]
                0.00    0.00      14/118268959     main [1]
                0.00    0.00      14/118268959     totalL() [14]
                0.20    0.29 20130880/118268959     CRO_step(double, void (*)()) [2]
                1.00    1.39 98138040/118268959     calculate_a() [4]
[5]     46.5    1.20    1.67 118268959         vect::operator*(double const&) [5]
                1.67    0.00 118268959/118268959     vect::operator*=(double const&) [6]
-----------------------------------------------
                1.67    0.00 118268959/118268959     vect::operator*(double const&) [5]
[6]     27.1    1.67    0.00 118268959         vect::operator*=(double const&) [6]
-----------------------------------------------
                0.00    0.00      14/75490814     totalL() [14]
                0.12    0.00 10065440/75490814     CRO_step(double, void (*)()) [2]
                0.78    0.00 65425360/75490814     calculate_a() [4]
[7]     14.6    0.91    0.00 75490814         vect::operator+=(vect const&) [7]
-----------------------------------------------
                0.00    0.00      28/32712799     main [1]
                0.00    0.00      91/32712799     totalE() [16]
                0.26    0.37 32712680/32712799     calculate_a() [4]
[8]     10.4    0.27    0.38 32712799         vect::operator-(vect const&) [8]
                0.38    0.00 32712799/32712799     vect::operator-=(vect const&) [9]
-----------------------------------------------
                0.38    0.00 32712799/32712799     vect::operator-(vect const&) [8]
[9]      6.1    0.38    0.00 32712799         vect::operator-=(vect const&) [9]
-----------------------------------------------
                0.00    0.00     105/32712785     totalE() [16]
                0.32    0.00 32712680/32712785     calculate_a() [4]
[10]     5.2    0.32    0.00 32712785         vect::mag() [10]
-----------------------------------------------
                0.00    0.00      14/5032775     main [1]
                0.00    0.00      41/5032775     initialize() [17]
                0.08    0.00 5032720/5032775     calculate_a() [4]
[11]     1.4    0.08    0.00 5032775         vect::operator=(vect const&) [11]
-----------------------------------------------
                                                 <spontaneous>
[12]     0.3    0.02    0.00                 vect::operator+(vect const&) [12]
-----------------------------------------------
                0.00    0.00      14/5032775     cross(vect const&, vect const&) [15]
                0.00    0.00      41/5032775     initialize() [17]
                0.01    0.00 5032720/5032775     calculate_a() [4]
[13]     0.2    0.01    0.00 5032775         vect::vect(double, double, double) [13]
-----------------------------------------------
                0.00    0.01       1/1           main [1]
[14]     0.1    0.00    0.01       1         totalL() [14]
                0.01    0.00      14/14          cross(vect const&, vect const&) [15]
                0.00    0.00      14/118268959     vect::operator*(double const&) [5]
                0.00    0.00      14/75490814     vect::operator+=(vect const&) [7]
                0.00    0.00       1/85          vect::vect() [21]
-----------------------------------------------
                0.01    0.00      14/14          totalL() [14]
[15]     0.1    0.01    0.00      14         cross(vect const&, vect const&) [15]
                0.00    0.00      14/5032775     vect::vect(double, double, double) [13]
-----------------------------------------------
                0.00    0.00       1/1           main [1]
[16]     0.0    0.00    0.00       1         totalE() [16]
                0.00    0.00      91/32712799     vect::operator-(vect const&) [8]
                0.00    0.00     105/32712785     vect::mag() [10]
                0.00    0.00      14/14          __gnu_cxx::__promote_2<__gnu_cxx::__enable_if<(std::__is_arithmetic<double>::__value)&&(std::__is_arithmetic<int>::__value), double>::__type, int>::__type std::pow<double, int>(double, int) [40]
-----------------------------------------------
                0.00    0.00       1/1           main [1]
[17]     0.0    0.00    0.00       1         initialize() [17]
                0.00    0.00      41/5032775     vect::operator=(vect const&) [11]
                0.00    0.00      11/118268959     vect::operator*(double const&) [5]
                0.00    0.00      41/5032775     vect::vect(double, double, double) [13]
-----------------------------------------------
                0.00    0.00       1/85          totalL() [14]
                0.00    0.00      84/85          cobject::cobject() [37]
[21]     0.0    0.00    0.00      85         vect::vect() [21]
-----------------------------------------------
                0.00    0.00      42/42          main [1]
[22]     0.0    0.00    0.00      42         std::vector<int, std::allocator<int> >::operator[](unsigned int) [22]
-----------------------------------------------
                0.00    0.00      15/35          main [1]
                0.00    0.00      20/35          std::vector<int, std::allocator<int> >::_M_check_len(unsigned int, char const*) const [71]
[23]     0.0    0.00    0.00      35         std::vector<int, std::allocator<int> >::size() const [23]
-----------------------------------------------
                0.00    0.00      30/30          std::_Niter_base<int*>::iterator_type std::__niter_base<int*>(int*) [25]
[24]     0.0    0.00    0.00      30         std::_Iter_base<int*, false>::_S_base(int*) [24]
-----------------------------------------------
                0.00    0.00      30/30          int* std::__copy_move_a2<true, int*, int*>(int*, int*, int*) [50]
[25]     0.0    0.00    0.00      30         std::_Niter_base<int*>::iterator_type std::__niter_base<int*>(int*) [25]
                0.00    0.00      30/30          std::_Iter_base<int*, false>::_S_base(int*) [24]
-----------------------------------------------
                0.00    0.00      10/20          void std::vector<int, std::allocator<int> >::_M_insert_aux<int const&>(__gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >, int const&&&) [73]
                0.00    0.00      10/20          __gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >::difference_type __gnu_cxx::operator-<int*, std::vector<int, std::allocator<int> > >(__gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > > const&, __gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > > const&) [70]
[26]     0.0    0.00    0.00      20         __gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >::base() const [26]
-----------------------------------------------
                0.00    0.00      20/20          std::_Iter_base<std::move_iterator<int*>, true>::_S_base(std::move_iterator<int*>) [28]
[27]     0.0    0.00    0.00      20         std::move_iterator<int*>::base() const [27]
-----------------------------------------------
                0.00    0.00      20/20          std::_Miter_base<std::move_iterator<int*> >::iterator_type std::__miter_base<std::move_iterator<int*> >(std::move_iterator<int*>) [30]
[28]     0.0    0.00    0.00      20         std::_Iter_base<std::move_iterator<int*>, true>::_S_base(std::move_iterator<int*>) [28]
                0.00    0.00      20/20          std::move_iterator<int*>::base() const [27]
-----------------------------------------------
                0.00    0.00      20/20          std::move_iterator<int*> std::make_move_iterator<int*>(int* const&) [31]
[29]     0.0    0.00    0.00      20         std::move_iterator<int*>::move_iterator(int*) [29]
-----------------------------------------------
                0.00    0.00      20/20          int* std::copy<std::move_iterator<int*>, int*>(std::move_iterator<int*>, std::move_iterator<int*>, int*) [54]
[30]     0.0    0.00    0.00      20         std::_Miter_base<std::move_iterator<int*> >::iterator_type std::__miter_base<std::move_iterator<int*> >(std::move_iterator<int*>) [30]
                0.00    0.00      20/20          std::_Iter_base<std::move_iterator<int*>, true>::_S_base(std::move_iterator<int*>) [28]
-----------------------------------------------
                0.00    0.00      20/20          int* std::__uninitialized_move_a<int*, int*, std::allocator<int> >(int*, int*, int*, std::allocator<int>&) [53]
[31]     0.0    0.00    0.00      20         std::move_iterator<int*> std::make_move_iterator<int*>(int* const&) [31]
                0.00    0.00      20/20          std::move_iterator<int*>::move_iterator(int*) [29]
-----------------------------------------------
                0.00    0.00       1/16          std::vector<int, std::allocator<int> >::~vector() [145]
                0.00    0.00      15/16          void std::vector<int, std::allocator<int> >::_M_insert_aux<int const&>(__gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >, int const&&&) [73]
[32]     0.0    0.00    0.00      16         std::_Vector_base<int, std::allocator<int> >::_M_get_Tp_allocator() [32]
-----------------------------------------------
                0.00    0.00      16/16          main [1]
[33]     0.0    0.00    0.00      16         bool std::operator==<char, std::char_traits<char>, std::allocator<char> >(std::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, char const*) [33]
-----------------------------------------------
                0.00    0.00       1/16          __gnu_cxx::new_allocator<double>::construct(double*, double const&) [108]
                0.00    0.00       1/16          void __gnu_cxx::new_allocator<double>::construct<double>(double*, double&&) [109]
                0.00    0.00      14/16          __gnu_cxx::new_allocator<int>::construct(int*, int const&) [38]
[34]     0.0    0.00    0.00      16         operator new(unsigned int, void*) [34]
-----------------------------------------------
                0.00    0.00       5/15          __gnu_cxx::new_allocator<int>::allocate(unsigned int, void const*) [69]
                0.00    0.00      10/15          std::vector<int, std::allocator<int> >::max_size() const [46]
[35]     0.0    0.00    0.00      15         __gnu_cxx::new_allocator<int>::max_size() const [35]
-----------------------------------------------
                0.00    0.00      14/14          main [1]
[36]     0.0    0.00    0.00      14         getobj(int) [36]
-----------------------------------------------
                0.00    0.00      14/14          __static_initialization_and_destruction_0(int, int) [105]
[37]     0.0    0.00    0.00      14         cobject::cobject() [37]
                0.00    0.00      84/85          vect::vect() [21]
-----------------------------------------------
                0.00    0.00       5/14          void std::vector<int, std::allocator<int> >::_M_insert_aux<int const&>(__gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >, int const&&&) [73]
                0.00    0.00       9/14          std::vector<int, std::allocator<int> >::push_back(int const&) [39]
[38]     0.0    0.00    0.00      14         __gnu_cxx::new_allocator<int>::construct(int*, int const&) [38]
                0.00    0.00      14/16          operator new(unsigned int, void*) [34]
-----------------------------------------------
                0.00    0.00      14/14          main [1]
[39]     0.0    0.00    0.00      14         std::vector<int, std::allocator<int> >::push_back(int const&) [39]
                0.00    0.00       9/14          __gnu_cxx::new_allocator<int>::construct(int*, int const&) [38]
                0.00    0.00       5/5           std::vector<int, std::allocator<int> >::end() [74]
                0.00    0.00       5/5           void std::vector<int, std::allocator<int> >::_M_insert_aux<int const&>(__gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >, int const&&&) [73]
-----------------------------------------------
                0.00    0.00      14/14          totalE() [16]
[40]     0.0    0.00    0.00      14         __gnu_cxx::__promote_2<__gnu_cxx::__enable_if<(std::__is_arithmetic<double>::__value)&&(std::__is_arithmetic<int>::__value), double>::__type, int>::__type std::pow<double, int>(double, int) [40]
-----------------------------------------------
                0.00    0.00      12/12          std::_Niter_base<double*>::iterator_type std::__niter_base<double*>(double*) [42]
[41]     0.0    0.00    0.00      12         std::_Iter_base<double*, false>::_S_base(double*) [41]
-----------------------------------------------
                0.00    0.00      12/12          double* std::__copy_move_a2<true, double*, double*>(double*, double*, double*) [83]
[42]     0.0    0.00    0.00      12         std::_Niter_base<double*>::iterator_type std::__niter_base<double*>(double*) [42]
                0.00    0.00      12/12          std::_Iter_base<double*, false>::_S_base(double*) [41]
-----------------------------------------------
                0.00    0.00       5/10          std::vector<int, std::allocator<int> >::end() [74]
                0.00    0.00       5/10          std::vector<int, std::allocator<int> >::begin() [75]
[43]     0.0    0.00    0.00      10         __gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >::__normal_iterator(int* const&) [43]
-----------------------------------------------
                0.00    0.00      10/10          std::vector<int, std::allocator<int> >::max_size() const [46]
[44]     0.0    0.00    0.00      10         std::_Vector_base<int, std::allocator<int> >::_M_get_Tp_allocator() const [44]
-----------------------------------------------
                0.00    0.00       2/10          main [1]
                0.00    0.00       8/10          std::vector<double, std::allocator<double> >::_M_check_len(unsigned int, char const*) const [98]
[45]     0.0    0.00    0.00      10         std::vector<double, std::allocator<double> >::size() const [45]
-----------------------------------------------
                0.00    0.00      10/10          std::vector<int, std::allocator<int> >::_M_check_len(unsigned int, char const*) const [71]
[46]     0.0    0.00    0.00      10         std::vector<int, std::allocator<int> >::max_size() const [46]
                0.00    0.00      10/10          std::_Vector_base<int, std::allocator<int> >::_M_get_Tp_allocator() const [44]
                0.00    0.00      10/15          __gnu_cxx::new_allocator<int>::max_size() const [35]
-----------------------------------------------
                0.00    0.00      10/10          int* std::__copy_move_a<true, int*, int*>(int*, int*, int*) [49]
[47]     0.0    0.00    0.00      10         int* std::__copy_move<true, true, std::random_access_iterator_tag>::__copy_m<int>(int const*, int const*, int*) [47]
-----------------------------------------------
                0.00    0.00      10/10          int* std::uninitialized_copy<std::move_iterator<int*>, int*>(std::move_iterator<int*>, std::move_iterator<int*>, int*) [51]
[48]     0.0    0.00    0.00      10         int* std::__uninitialized_copy<true>::__uninit_copy<std::move_iterator<int*>, int*>(std::move_iterator<int*>, std::move_iterator<int*>, int*) [48]
                0.00    0.00      10/10          int* std::copy<std::move_iterator<int*>, int*>(std::move_iterator<int*>, std::move_iterator<int*>, int*) [54]
-----------------------------------------------
                0.00    0.00      10/10          int* std::__copy_move_a2<true, int*, int*>(int*, int*, int*) [50]
[49]     0.0    0.00    0.00      10         int* std::__copy_move_a<true, int*, int*>(int*, int*, int*) [49]
                0.00    0.00      10/10          int* std::__copy_move<true, true, std::random_access_iterator_tag>::__copy_m<int>(int const*, int const*, int*) [47]
-----------------------------------------------
                0.00    0.00      10/10          int* std::copy<std::move_iterator<int*>, int*>(std::move_iterator<int*>, std::move_iterator<int*>, int*) [54]
[50]     0.0    0.00    0.00      10         int* std::__copy_move_a2<true, int*, int*>(int*, int*, int*) [50]
                0.00    0.00      30/30          std::_Niter_base<int*>::iterator_type std::__niter_base<int*>(int*) [25]
                0.00    0.00      10/10          int* std::__copy_move_a<true, int*, int*>(int*, int*, int*) [49]
-----------------------------------------------
                0.00    0.00      10/10          int* std::__uninitialized_copy_a<std::move_iterator<int*>, int*, int>(std::move_iterator<int*>, std::move_iterator<int*>, int*, std::allocator<int>&) [52]
[51]     0.0    0.00    0.00      10         int* std::uninitialized_copy<std::move_iterator<int*>, int*>(std::move_iterator<int*>, std::move_iterator<int*>, int*) [51]
                0.00    0.00      10/10          int* std::__uninitialized_copy<true>::__uninit_copy<std::move_iterator<int*>, int*>(std::move_iterator<int*>, std::move_iterator<int*>, int*) [48]
-----------------------------------------------
                0.00    0.00      10/10          int* std::__uninitialized_move_a<int*, int*, std::allocator<int> >(int*, int*, int*, std::allocator<int>&) [53]
[52]     0.0    0.00    0.00      10         int* std::__uninitialized_copy_a<std::move_iterator<int*>, int*, int>(std::move_iterator<int*>, std::move_iterator<int*>, int*, std::allocator<int>&) [52]
                0.00    0.00      10/10          int* std::uninitialized_copy<std::move_iterator<int*>, int*>(std::move_iterator<int*>, std::move_iterator<int*>, int*) [51]
-----------------------------------------------
                0.00    0.00      10/10          void std::vector<int, std::allocator<int> >::_M_insert_aux<int const&>(__gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >, int const&&&) [73]
[53]     0.0    0.00    0.00      10         int* std::__uninitialized_move_a<int*, int*, std::allocator<int> >(int*, int*, int*, std::allocator<int>&) [53]
                0.00    0.00      20/20          std::move_iterator<int*> std::make_move_iterator<int*>(int* const&) [31]
                0.00    0.00      10/10          int* std::__uninitialized_copy_a<std::move_iterator<int*>, int*, int>(std::move_iterator<int*>, std::move_iterator<int*>, int*, std::allocator<int>&) [52]
-----------------------------------------------
                0.00    0.00      10/10          int* std::__uninitialized_copy<true>::__uninit_copy<std::move_iterator<int*>, int*>(std::move_iterator<int*>, std::move_iterator<int*>, int*) [48]
[54]     0.0    0.00    0.00      10         int* std::copy<std::move_iterator<int*>, int*>(std::move_iterator<int*>, std::move_iterator<int*>, int*) [54]
                0.00    0.00      20/20          std::_Miter_base<std::move_iterator<int*> >::iterator_type std::__miter_base<std::move_iterator<int*> >(std::move_iterator<int*>) [30]
                0.00    0.00      10/10          int* std::__copy_move_a2<true, int*, int*>(int*, int*, int*) [50]
-----------------------------------------------
                0.00    0.00       2/8           void std::vector<double, std::allocator<double> >::_M_insert_aux<double const&>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double const&&&) [138]
                0.00    0.00       2/8           void std::vector<double, std::allocator<double> >::_M_insert_aux<double>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double&&) [139]
                0.00    0.00       4/8           __gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >::difference_type __gnu_cxx::operator-<double*, std::vector<double, std::allocator<double> > >(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > > const&, __gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > > const&) [97]
[55]     0.0    0.00    0.00       8         __gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >::base() const [55]
-----------------------------------------------
                0.00    0.00       8/8           std::_Iter_base<std::move_iterator<double*>, true>::_S_base(std::move_iterator<double*>) [57]
[56]     0.0    0.00    0.00       8         std::move_iterator<double*>::base() const [56]
-----------------------------------------------
                0.00    0.00       8/8           std::_Miter_base<std::move_iterator<double*> >::iterator_type std::__miter_base<std::move_iterator<double*> >(std::move_iterator<double*>) [59]
[57]     0.0    0.00    0.00       8         std::_Iter_base<std::move_iterator<double*>, true>::_S_base(std::move_iterator<double*>) [57]
                0.00    0.00       8/8           std::move_iterator<double*>::base() const [56]
-----------------------------------------------
                0.00    0.00       8/8           std::move_iterator<double*> std::make_move_iterator<double*>(double* const&) [60]
[58]     0.0    0.00    0.00       8         std::move_iterator<double*>::move_iterator(double*) [58]
-----------------------------------------------
                0.00    0.00       8/8           double* std::copy<std::move_iterator<double*>, double*>(std::move_iterator<double*>, std::move_iterator<double*>, double*) [87]
[59]     0.0    0.00    0.00       8         std::_Miter_base<std::move_iterator<double*> >::iterator_type std::__miter_base<std::move_iterator<double*> >(std::move_iterator<double*>) [59]
                0.00    0.00       8/8           std::_Iter_base<std::move_iterator<double*>, true>::_S_base(std::move_iterator<double*>) [57]
-----------------------------------------------
                0.00    0.00       8/8           double* std::__uninitialized_move_a<double*, double*, std::allocator<double> >(double*, double*, double*, std::allocator<double>&) [86]
[60]     0.0    0.00    0.00       8         std::move_iterator<double*> std::make_move_iterator<double*>(double* const&) [60]
                0.00    0.00       8/8           std::move_iterator<double*>::move_iterator(double*) [58]
-----------------------------------------------
                0.00    0.00       1/7           std::vector<double, std::allocator<double> >::~vector() [143]
                0.00    0.00       3/7           void std::vector<double, std::allocator<double> >::_M_insert_aux<double const&>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double const&&&) [138]
                0.00    0.00       3/7           void std::vector<double, std::allocator<double> >::_M_insert_aux<double>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double&&) [139]
[61]     0.0    0.00    0.00       7         std::_Vector_base<double, std::allocator<double> >::_M_get_Tp_allocator() [61]
-----------------------------------------------
                0.00    0.00       2/7           std::vector<double, std::allocator<double> >::_M_check_len(unsigned int, char const*) const [98]
                0.00    0.00       5/7           std::vector<int, std::allocator<int> >::_M_check_len(unsigned int, char const*) const [71]
[62]     0.0    0.00    0.00       7         unsigned int const& std::max<unsigned int>(unsigned int const&, unsigned int const&) [62]
-----------------------------------------------
                0.00    0.00       2/6           __gnu_cxx::new_allocator<double>::allocate(unsigned int, void const*) [96]
                0.00    0.00       4/6           std::vector<double, std::allocator<double> >::max_size() const [79]
[63]     0.0    0.00    0.00       6         __gnu_cxx::new_allocator<double>::max_size() const [63]
-----------------------------------------------
                0.00    0.00       6/6           void std::_Destroy<int*>(int*, int*) [66]
[64]     0.0    0.00    0.00       6         void std::_Destroy_aux<true>::__destroy<int*>(int*, int*) [64]
-----------------------------------------------
                0.00    0.00       1/6           std::_Vector_base<int, std::allocator<int> >::~_Vector_base() [134]
                0.00    0.00       5/6           void std::vector<int, std::allocator<int> >::_M_insert_aux<int const&>(__gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >, int const&&&) [73]
[65]     0.0    0.00    0.00       6         std::_Vector_base<int, std::allocator<int> >::_M_deallocate(int*, unsigned int) [65]
                0.00    0.00       5/5           __gnu_cxx::new_allocator<int>::deallocate(int*, unsigned int) [68]
-----------------------------------------------
                0.00    0.00       6/6           void std::_Destroy<int*, int>(int*, int*, std::allocator<int>&) [67]
[66]     0.0    0.00    0.00       6         void std::_Destroy<int*>(int*, int*) [66]
                0.00    0.00       6/6           void std::_Destroy_aux<true>::__destroy<int*>(int*, int*) [64]
-----------------------------------------------
                0.00    0.00       1/6           std::vector<int, std::allocator<int> >::~vector() [145]
                0.00    0.00       5/6           void std::vector<int, std::allocator<int> >::_M_insert_aux<int const&>(__gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >, int const&&&) [73]
[67]     0.0    0.00    0.00       6         void std::_Destroy<int*, int>(int*, int*, std::allocator<int>&) [67]
                0.00    0.00       6/6           void std::_Destroy<int*>(int*, int*) [66]
-----------------------------------------------
                0.00    0.00       5/5           std::_Vector_base<int, std::allocator<int> >::_M_deallocate(int*, unsigned int) [65]
[68]     0.0    0.00    0.00       5         __gnu_cxx::new_allocator<int>::deallocate(int*, unsigned int) [68]
-----------------------------------------------
                0.00    0.00       5/5           std::_Vector_base<int, std::allocator<int> >::_M_allocate(unsigned int) [72]
[69]     0.0    0.00    0.00       5         __gnu_cxx::new_allocator<int>::allocate(unsigned int, void const*) [69]
                0.00    0.00       5/15          __gnu_cxx::new_allocator<int>::max_size() const [35]
-----------------------------------------------
                0.00    0.00       5/5           void std::vector<int, std::allocator<int> >::_M_insert_aux<int const&>(__gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >, int const&&&) [73]
[70]     0.0    0.00    0.00       5         __gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >::difference_type __gnu_cxx::operator-<int*, std::vector<int, std::allocator<int> > >(__gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > > const&, __gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > > const&) [70]
                0.00    0.00      10/20          __gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >::base() const [26]
-----------------------------------------------
                0.00    0.00       5/5           void std::vector<int, std::allocator<int> >::_M_insert_aux<int const&>(__gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >, int const&&&) [73]
[71]     0.0    0.00    0.00       5         std::vector<int, std::allocator<int> >::_M_check_len(unsigned int, char const*) const [71]
                0.00    0.00      20/35          std::vector<int, std::allocator<int> >::size() const [23]
                0.00    0.00      10/10          std::vector<int, std::allocator<int> >::max_size() const [46]
                0.00    0.00       5/7           unsigned int const& std::max<unsigned int>(unsigned int const&, unsigned int const&) [62]
-----------------------------------------------
                0.00    0.00       5/5           void std::vector<int, std::allocator<int> >::_M_insert_aux<int const&>(__gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >, int const&&&) [73]
[72]     0.0    0.00    0.00       5         std::_Vector_base<int, std::allocator<int> >::_M_allocate(unsigned int) [72]
                0.00    0.00       5/5           __gnu_cxx::new_allocator<int>::allocate(unsigned int, void const*) [69]
-----------------------------------------------
                0.00    0.00       5/5           std::vector<int, std::allocator<int> >::push_back(int const&) [39]
[73]     0.0    0.00    0.00       5         void std::vector<int, std::allocator<int> >::_M_insert_aux<int const&>(__gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >, int const&&&) [73]
                0.00    0.00      15/16          std::_Vector_base<int, std::allocator<int> >::_M_get_Tp_allocator() [32]
                0.00    0.00      10/20          __gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >::base() const [26]
                0.00    0.00      10/10          int* std::__uninitialized_move_a<int*, int*, std::allocator<int> >(int*, int*, int*, std::allocator<int>&) [53]
                0.00    0.00       5/5           std::vector<int, std::allocator<int> >::_M_check_len(unsigned int, char const*) const [71]
                0.00    0.00       5/5           std::vector<int, std::allocator<int> >::begin() [75]
                0.00    0.00       5/5           __gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >::difference_type __gnu_cxx::operator-<int*, std::vector<int, std::allocator<int> > >(__gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > > const&, __gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > > const&) [70]
                0.00    0.00       5/5           std::_Vector_base<int, std::allocator<int> >::_M_allocate(unsigned int) [72]
                0.00    0.00       5/5           int const&&& std::forward<int const&>(std::remove_reference<int const&>::type&) [76]
                0.00    0.00       5/14          __gnu_cxx::new_allocator<int>::construct(int*, int const&) [38]
                0.00    0.00       5/6           void std::_Destroy<int*, int>(int*, int*, std::allocator<int>&) [67]
                0.00    0.00       5/6           std::_Vector_base<int, std::allocator<int> >::_M_deallocate(int*, unsigned int) [65]
-----------------------------------------------
                0.00    0.00       5/5           std::vector<int, std::allocator<int> >::push_back(int const&) [39]
[74]     0.0    0.00    0.00       5         std::vector<int, std::allocator<int> >::end() [74]
                0.00    0.00       5/10          __gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >::__normal_iterator(int* const&) [43]
-----------------------------------------------
                0.00    0.00       5/5           void std::vector<int, std::allocator<int> >::_M_insert_aux<int const&>(__gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >, int const&&&) [73]
[75]     0.0    0.00    0.00       5         std::vector<int, std::allocator<int> >::begin() [75]
                0.00    0.00       5/10          __gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >::__normal_iterator(int* const&) [43]
-----------------------------------------------
                0.00    0.00       5/5           void std::vector<int, std::allocator<int> >::_M_insert_aux<int const&>(__gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >, int const&&&) [73]
[76]     0.0    0.00    0.00       5         int const&&& std::forward<int const&>(std::remove_reference<int const&>::type&) [76]
-----------------------------------------------
                0.00    0.00       2/4           std::vector<double, std::allocator<double> >::end() [100]
                0.00    0.00       2/4           std::vector<double, std::allocator<double> >::begin() [101]
[77]     0.0    0.00    0.00       4         __gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >::__normal_iterator(double* const&) [77]
-----------------------------------------------
                0.00    0.00       4/4           std::vector<double, std::allocator<double> >::max_size() const [79]
[78]     0.0    0.00    0.00       4         std::_Vector_base<double, std::allocator<double> >::_M_get_Tp_allocator() const [78]
-----------------------------------------------
                0.00    0.00       4/4           std::vector<double, std::allocator<double> >::_M_check_len(unsigned int, char const*) const [98]
[79]     0.0    0.00    0.00       4         std::vector<double, std::allocator<double> >::max_size() const [79]
                0.00    0.00       4/4           std::_Vector_base<double, std::allocator<double> >::_M_get_Tp_allocator() const [78]
                0.00    0.00       4/6           __gnu_cxx::new_allocator<double>::max_size() const [63]
-----------------------------------------------
                0.00    0.00       4/4           double* std::__copy_move_a<true, double*, double*>(double*, double*, double*) [82]
[80]     0.0    0.00    0.00       4         double* std::__copy_move<true, true, std::random_access_iterator_tag>::__copy_m<double>(double const*, double const*, double*) [80]
-----------------------------------------------
                0.00    0.00       4/4           double* std::uninitialized_copy<std::move_iterator<double*>, double*>(std::move_iterator<double*>, std::move_iterator<double*>, double*) [84]
[81]     0.0    0.00    0.00       4         double* std::__uninitialized_copy<true>::__uninit_copy<std::move_iterator<double*>, double*>(std::move_iterator<double*>, std::move_iterator<double*>, double*) [81]
                0.00    0.00       4/4           double* std::copy<std::move_iterator<double*>, double*>(std::move_iterator<double*>, std::move_iterator<double*>, double*) [87]
-----------------------------------------------
                0.00    0.00       4/4           double* std::__copy_move_a2<true, double*, double*>(double*, double*, double*) [83]
[82]     0.0    0.00    0.00       4         double* std::__copy_move_a<true, double*, double*>(double*, double*, double*) [82]
                0.00    0.00       4/4           double* std::__copy_move<true, true, std::random_access_iterator_tag>::__copy_m<double>(double const*, double const*, double*) [80]
-----------------------------------------------
                0.00    0.00       4/4           double* std::copy<std::move_iterator<double*>, double*>(std::move_iterator<double*>, std::move_iterator<double*>, double*) [87]
[83]     0.0    0.00    0.00       4         double* std::__copy_move_a2<true, double*, double*>(double*, double*, double*) [83]
                0.00    0.00      12/12          std::_Niter_base<double*>::iterator_type std::__niter_base<double*>(double*) [42]
                0.00    0.00       4/4           double* std::__copy_move_a<true, double*, double*>(double*, double*, double*) [82]
-----------------------------------------------
                0.00    0.00       4/4           double* std::__uninitialized_copy_a<std::move_iterator<double*>, double*, double>(std::move_iterator<double*>, std::move_iterator<double*>, double*, std::allocator<double>&) [85]
[84]     0.0    0.00    0.00       4         double* std::uninitialized_copy<std::move_iterator<double*>, double*>(std::move_iterator<double*>, std::move_iterator<double*>, double*) [84]
                0.00    0.00       4/4           double* std::__uninitialized_copy<true>::__uninit_copy<std::move_iterator<double*>, double*>(std::move_iterator<double*>, std::move_iterator<double*>, double*) [81]
-----------------------------------------------
                0.00    0.00       4/4           double* std::__uninitialized_move_a<double*, double*, std::allocator<double> >(double*, double*, double*, std::allocator<double>&) [86]
[85]     0.0    0.00    0.00       4         double* std::__uninitialized_copy_a<std::move_iterator<double*>, double*, double>(std::move_iterator<double*>, std::move_iterator<double*>, double*, std::allocator<double>&) [85]
                0.00    0.00       4/4           double* std::uninitialized_copy<std::move_iterator<double*>, double*>(std::move_iterator<double*>, std::move_iterator<double*>, double*) [84]
-----------------------------------------------
                0.00    0.00       2/4           void std::vector<double, std::allocator<double> >::_M_insert_aux<double const&>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double const&&&) [138]
                0.00    0.00       2/4           void std::vector<double, std::allocator<double> >::_M_insert_aux<double>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double&&) [139]
[86]     0.0    0.00    0.00       4         double* std::__uninitialized_move_a<double*, double*, std::allocator<double> >(double*, double*, double*, std::allocator<double>&) [86]
                0.00    0.00       8/8           std::move_iterator<double*> std::make_move_iterator<double*>(double* const&) [60]
                0.00    0.00       4/4           double* std::__uninitialized_copy_a<std::move_iterator<double*>, double*, double>(std::move_iterator<double*>, std::move_iterator<double*>, double*, std::allocator<double>&) [85]
-----------------------------------------------
                0.00    0.00       4/4           double* std::__uninitialized_copy<true>::__uninit_copy<std::move_iterator<double*>, double*>(std::move_iterator<double*>, std::move_iterator<double*>, double*) [81]
[87]     0.0    0.00    0.00       4         double* std::copy<std::move_iterator<double*>, double*>(std::move_iterator<double*>, std::move_iterator<double*>, double*) [87]
                0.00    0.00       8/8           std::_Miter_base<std::move_iterator<double*> >::iterator_type std::__miter_base<std::move_iterator<double*> >(std::move_iterator<double*>) [59]
                0.00    0.00       4/4           double* std::__copy_move_a2<true, double*, double*>(double*, double*, double*) [83]
-----------------------------------------------
                0.00    0.00       3/3           void std::_Destroy<double*>(double*, double*) [92]
[88]     0.0    0.00    0.00       3         void std::_Destroy_aux<true>::__destroy<double*>(double*, double*) [88]
-----------------------------------------------
                0.00    0.00       1/3           std::_Vector_base<double, std::allocator<double> >::~_Vector_base() [130]
                0.00    0.00       1/3           void std::vector<double, std::allocator<double> >::_M_insert_aux<double const&>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double const&&&) [138]
                0.00    0.00       1/3           void std::vector<double, std::allocator<double> >::_M_insert_aux<double>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double&&) [139]
[89]     0.0    0.00    0.00       3         std::_Vector_base<double, std::allocator<double> >::_M_deallocate(double*, unsigned int) [89]
                0.00    0.00       2/2           __gnu_cxx::new_allocator<double>::deallocate(double*, unsigned int) [95]
-----------------------------------------------
                0.00    0.00       3/3           main [1]
[90]     0.0    0.00    0.00       3         std::vector<double, std::allocator<double> >::operator[](unsigned int) [90]
-----------------------------------------------
                0.00    0.00       1/3           void std::vector<double, std::allocator<double> >::emplace_back<double>(double&&) [137]
                0.00    0.00       1/3           void __gnu_cxx::new_allocator<double>::construct<double>(double*, double&&) [109]
                0.00    0.00       1/3           void std::vector<double, std::allocator<double> >::_M_insert_aux<double>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double&&) [139]
[91]     0.0    0.00    0.00       3         double&& std::forward<double>(std::remove_reference<double>::type&) [91]
-----------------------------------------------
                0.00    0.00       3/3           void std::_Destroy<double*, double>(double*, double*, std::allocator<double>&) [93]
[92]     0.0    0.00    0.00       3         void std::_Destroy<double*>(double*, double*) [92]
                0.00    0.00       3/3           void std::_Destroy_aux<true>::__destroy<double*>(double*, double*) [88]
-----------------------------------------------
                0.00    0.00       1/3           std::vector<double, std::allocator<double> >::~vector() [143]
                0.00    0.00       1/3           void std::vector<double, std::allocator<double> >::_M_insert_aux<double const&>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double const&&&) [138]
                0.00    0.00       1/3           void std::vector<double, std::allocator<double> >::_M_insert_aux<double>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double&&) [139]
[93]     0.0    0.00    0.00       3         void std::_Destroy<double*, double>(double*, double*, std::allocator<double>&) [93]
                0.00    0.00       3/3           void std::_Destroy<double*>(double*, double*) [92]
-----------------------------------------------
                0.00    0.00       2/2           main [1]
[94]     0.0    0.00    0.00       2         print_hline() [94]
-----------------------------------------------
                0.00    0.00       2/2           std::_Vector_base<double, std::allocator<double> >::_M_deallocate(double*, unsigned int) [89]
[95]     0.0    0.00    0.00       2         __gnu_cxx::new_allocator<double>::deallocate(double*, unsigned int) [95]
-----------------------------------------------
                0.00    0.00       2/2           std::_Vector_base<double, std::allocator<double> >::_M_allocate(unsigned int) [99]
[96]     0.0    0.00    0.00       2         __gnu_cxx::new_allocator<double>::allocate(unsigned int, void const*) [96]
                0.00    0.00       2/6           __gnu_cxx::new_allocator<double>::max_size() const [63]
-----------------------------------------------
                0.00    0.00       1/2           void std::vector<double, std::allocator<double> >::_M_insert_aux<double const&>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double const&&&) [138]
                0.00    0.00       1/2           void std::vector<double, std::allocator<double> >::_M_insert_aux<double>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double&&) [139]
[97]     0.0    0.00    0.00       2         __gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >::difference_type __gnu_cxx::operator-<double*, std::vector<double, std::allocator<double> > >(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > > const&, __gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > > const&) [97]
                0.00    0.00       4/8           __gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >::base() const [55]
-----------------------------------------------
                0.00    0.00       1/2           void std::vector<double, std::allocator<double> >::_M_insert_aux<double const&>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double const&&&) [138]
                0.00    0.00       1/2           void std::vector<double, std::allocator<double> >::_M_insert_aux<double>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double&&) [139]
[98]     0.0    0.00    0.00       2         std::vector<double, std::allocator<double> >::_M_check_len(unsigned int, char const*) const [98]
                0.00    0.00       8/10          std::vector<double, std::allocator<double> >::size() const [45]
                0.00    0.00       4/4           std::vector<double, std::allocator<double> >::max_size() const [79]
                0.00    0.00       2/7           unsigned int const& std::max<unsigned int>(unsigned int const&, unsigned int const&) [62]
-----------------------------------------------
                0.00    0.00       1/2           void std::vector<double, std::allocator<double> >::_M_insert_aux<double const&>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double const&&&) [138]
                0.00    0.00       1/2           void std::vector<double, std::allocator<double> >::_M_insert_aux<double>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double&&) [139]
[99]     0.0    0.00    0.00       2         std::_Vector_base<double, std::allocator<double> >::_M_allocate(unsigned int) [99]
                0.00    0.00       2/2           __gnu_cxx::new_allocator<double>::allocate(unsigned int, void const*) [96]
-----------------------------------------------
                0.00    0.00       1/2           std::vector<double, std::allocator<double> >::push_back(double const&) [141]
                0.00    0.00       1/2           void std::vector<double, std::allocator<double> >::emplace_back<double>(double&&) [137]
[100]    0.0    0.00    0.00       2         std::vector<double, std::allocator<double> >::end() [100]
                0.00    0.00       2/4           __gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >::__normal_iterator(double* const&) [77]
-----------------------------------------------
                0.00    0.00       1/2           void std::vector<double, std::allocator<double> >::_M_insert_aux<double const&>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double const&&&) [138]
                0.00    0.00       1/2           void std::vector<double, std::allocator<double> >::_M_insert_aux<double>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double&&) [139]
[101]    0.0    0.00    0.00       2         std::vector<double, std::allocator<double> >::begin() [101]
                0.00    0.00       2/4           __gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >::__normal_iterator(double* const&) [77]
-----------------------------------------------
                0.00    0.00       1/1           __do_global_ctors_aux [302]
[102]    0.0    0.00    0.00       1         _GLOBAL__sub_I__Z2TTd [102]
                0.00    0.00       1/1           __static_initialization_and_destruction_0(int, int) [105]
-----------------------------------------------
                0.00    0.00       1/1           main [1]
[103]    0.0    0.00    0.00       1         JD(tm*) [103]
-----------------------------------------------
                0.00    0.00       1/1           __static_initialization_and_destruction_0(int, int) [105]
[104]    0.0    0.00    0.00       1         TT(double) [104]
-----------------------------------------------
                0.00    0.00       1/1           _GLOBAL__sub_I__Z2TTd [102]
[105]    0.0    0.00    0.00       1         __static_initialization_and_destruction_0(int, int) [105]
                0.00    0.00      14/14          cobject::cobject() [37]
                0.00    0.00       1/1           TT(double) [104]
-----------------------------------------------
                0.00    0.00       1/1           std::allocator<std::string>::allocator() [114]
[106]    0.0    0.00    0.00       1         __gnu_cxx::new_allocator<std::string>::new_allocator() [106]
-----------------------------------------------
                0.00    0.00       1/1           std::allocator<std::string>::~allocator() [115]
[107]    0.0    0.00    0.00       1         __gnu_cxx::new_allocator<std::string>::~new_allocator() [107]
-----------------------------------------------
                0.00    0.00       1/1           void std::vector<double, std::allocator<double> >::_M_insert_aux<double const&>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double const&&&) [138]
[108]    0.0    0.00    0.00       1         __gnu_cxx::new_allocator<double>::construct(double*, double const&) [108]
                0.00    0.00       1/16          operator new(unsigned int, void*) [34]
-----------------------------------------------
                0.00    0.00       1/1           void std::vector<double, std::allocator<double> >::_M_insert_aux<double>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double&&) [139]
[109]    0.0    0.00    0.00       1         void __gnu_cxx::new_allocator<double>::construct<double>(double*, double&&) [109]
                0.00    0.00       1/3           double&& std::forward<double>(std::remove_reference<double>::type&) [91]
                0.00    0.00       1/16          operator new(unsigned int, void*) [34]
-----------------------------------------------
                0.00    0.00       1/1           std::allocator<double>::allocator() [116]
[110]    0.0    0.00    0.00       1         __gnu_cxx::new_allocator<double>::new_allocator() [110]
-----------------------------------------------
                0.00    0.00       1/1           std::allocator<double>::~allocator() [117]
[111]    0.0    0.00    0.00       1         __gnu_cxx::new_allocator<double>::~new_allocator() [111]
-----------------------------------------------
                0.00    0.00       1/1           std::allocator<int>::allocator() [118]
[112]    0.0    0.00    0.00       1         __gnu_cxx::new_allocator<int>::new_allocator() [112]
-----------------------------------------------
                0.00    0.00       1/1           std::allocator<int>::~allocator() [119]
[113]    0.0    0.00    0.00       1         __gnu_cxx::new_allocator<int>::~new_allocator() [113]
-----------------------------------------------
                0.00    0.00       1/1           std::_Vector_base<std::string, std::allocator<std::string> >::_Vector_impl::_Vector_impl() [121]
[114]    0.0    0.00    0.00       1         std::allocator<std::string>::allocator() [114]
                0.00    0.00       1/1           __gnu_cxx::new_allocator<std::string>::new_allocator() [106]
-----------------------------------------------
                0.00    0.00       1/1           std::_Vector_base<std::string, std::allocator<std::string> >::_Vector_impl::~_Vector_impl() [122]
[115]    0.0    0.00    0.00       1         std::allocator<std::string>::~allocator() [115]
                0.00    0.00       1/1           __gnu_cxx::new_allocator<std::string>::~new_allocator() [107]
-----------------------------------------------
                0.00    0.00       1/1           std::_Vector_base<double, std::allocator<double> >::_Vector_impl::_Vector_impl() [127]
[116]    0.0    0.00    0.00       1         std::allocator<double>::allocator() [116]
                0.00    0.00       1/1           __gnu_cxx::new_allocator<double>::new_allocator() [110]
-----------------------------------------------
                0.00    0.00       1/1           std::_Vector_base<double, std::allocator<double> >::_Vector_impl::~_Vector_impl() [128]
[117]    0.0    0.00    0.00       1         std::allocator<double>::~allocator() [117]
                0.00    0.00       1/1           __gnu_cxx::new_allocator<double>::~new_allocator() [111]
-----------------------------------------------
                0.00    0.00       1/1           std::_Vector_base<int, std::allocator<int> >::_Vector_impl::_Vector_impl() [131]
[118]    0.0    0.00    0.00       1         std::allocator<int>::allocator() [118]
                0.00    0.00       1/1           __gnu_cxx::new_allocator<int>::new_allocator() [112]
-----------------------------------------------
                0.00    0.00       1/1           std::_Vector_base<int, std::allocator<int> >::_Vector_impl::~_Vector_impl() [132]
[119]    0.0    0.00    0.00       1         std::allocator<int>::~allocator() [119]
                0.00    0.00       1/1           __gnu_cxx::new_allocator<int>::~new_allocator() [113]
-----------------------------------------------
                0.00    0.00       1/1           void std::_Destroy<std::string*>(std::string*, std::string*) [150]
[120]    0.0    0.00    0.00       1         void std::_Destroy_aux<false>::__destroy<std::string*>(std::string*, std::string*) [120]
-----------------------------------------------
                0.00    0.00       1/1           std::_Vector_base<std::string, std::allocator<std::string> >::_Vector_base() [125]
[121]    0.0    0.00    0.00       1         std::_Vector_base<std::string, std::allocator<std::string> >::_Vector_impl::_Vector_impl() [121]
                0.00    0.00       1/1           std::allocator<std::string>::allocator() [114]
-----------------------------------------------
                0.00    0.00       1/1           std::_Vector_base<std::string, std::allocator<std::string> >::~_Vector_base() [126]
[122]    0.0    0.00    0.00       1         std::_Vector_base<std::string, std::allocator<std::string> >::_Vector_impl::~_Vector_impl() [122]
                0.00    0.00       1/1           std::allocator<std::string>::~allocator() [115]
-----------------------------------------------
                0.00    0.00       1/1           std::_Vector_base<std::string, std::allocator<std::string> >::~_Vector_base() [126]
[123]    0.0    0.00    0.00       1         std::_Vector_base<std::string, std::allocator<std::string> >::_M_deallocate(std::string*, unsigned int) [123]
-----------------------------------------------
                0.00    0.00       1/1           std::vector<std::string, std::allocator<std::string> >::~vector() [136]
[124]    0.0    0.00    0.00       1         std::_Vector_base<std::string, std::allocator<std::string> >::_M_get_Tp_allocator() [124]
-----------------------------------------------
                0.00    0.00       1/1           std::vector<std::string, std::allocator<std::string> >::vector() [135]
[125]    0.0    0.00    0.00       1         std::_Vector_base<std::string, std::allocator<std::string> >::_Vector_base() [125]
                0.00    0.00       1/1           std::_Vector_base<std::string, std::allocator<std::string> >::_Vector_impl::_Vector_impl() [121]
-----------------------------------------------
                0.00    0.00       1/1           std::vector<std::string, std::allocator<std::string> >::~vector() [136]
[126]    0.0    0.00    0.00       1         std::_Vector_base<std::string, std::allocator<std::string> >::~_Vector_base() [126]
                0.00    0.00       1/1           std::_Vector_base<std::string, std::allocator<std::string> >::_M_deallocate(std::string*, unsigned int) [123]
                0.00    0.00       1/1           std::_Vector_base<std::string, std::allocator<std::string> >::_Vector_impl::~_Vector_impl() [122]
-----------------------------------------------
                0.00    0.00       1/1           std::_Vector_base<double, std::allocator<double> >::_Vector_base() [129]
[127]    0.0    0.00    0.00       1         std::_Vector_base<double, std::allocator<double> >::_Vector_impl::_Vector_impl() [127]
                0.00    0.00       1/1           std::allocator<double>::allocator() [116]
-----------------------------------------------
                0.00    0.00       1/1           std::_Vector_base<double, std::allocator<double> >::~_Vector_base() [130]
[128]    0.0    0.00    0.00       1         std::_Vector_base<double, std::allocator<double> >::_Vector_impl::~_Vector_impl() [128]
                0.00    0.00       1/1           std::allocator<double>::~allocator() [117]
-----------------------------------------------
                0.00    0.00       1/1           std::vector<double, std::allocator<double> >::vector() [142]
[129]    0.0    0.00    0.00       1         std::_Vector_base<double, std::allocator<double> >::_Vector_base() [129]
                0.00    0.00       1/1           std::_Vector_base<double, std::allocator<double> >::_Vector_impl::_Vector_impl() [127]
-----------------------------------------------
                0.00    0.00       1/1           std::vector<double, std::allocator<double> >::~vector() [143]
[130]    0.0    0.00    0.00       1         std::_Vector_base<double, std::allocator<double> >::~_Vector_base() [130]
                0.00    0.00       1/3           std::_Vector_base<double, std::allocator<double> >::_M_deallocate(double*, unsigned int) [89]
                0.00    0.00       1/1           std::_Vector_base<double, std::allocator<double> >::_Vector_impl::~_Vector_impl() [128]
-----------------------------------------------
                0.00    0.00       1/1           std::_Vector_base<int, std::allocator<int> >::_Vector_base() [133]
[131]    0.0    0.00    0.00       1         std::_Vector_base<int, std::allocator<int> >::_Vector_impl::_Vector_impl() [131]
                0.00    0.00       1/1           std::allocator<int>::allocator() [118]
-----------------------------------------------
                0.00    0.00       1/1           std::_Vector_base<int, std::allocator<int> >::~_Vector_base() [134]
[132]    0.0    0.00    0.00       1         std::_Vector_base<int, std::allocator<int> >::_Vector_impl::~_Vector_impl() [132]
                0.00    0.00       1/1           std::allocator<int>::~allocator() [119]
-----------------------------------------------
                0.00    0.00       1/1           std::vector<int, std::allocator<int> >::vector() [144]
[133]    0.0    0.00    0.00       1         std::_Vector_base<int, std::allocator<int> >::_Vector_base() [133]
                0.00    0.00       1/1           std::_Vector_base<int, std::allocator<int> >::_Vector_impl::_Vector_impl() [131]
-----------------------------------------------
                0.00    0.00       1/1           std::vector<int, std::allocator<int> >::~vector() [145]
[134]    0.0    0.00    0.00       1         std::_Vector_base<int, std::allocator<int> >::~_Vector_base() [134]
                0.00    0.00       1/6           std::_Vector_base<int, std::allocator<int> >::_M_deallocate(int*, unsigned int) [65]
                0.00    0.00       1/1           std::_Vector_base<int, std::allocator<int> >::_Vector_impl::~_Vector_impl() [132]
-----------------------------------------------
                0.00    0.00       1/1           main [1]
[135]    0.0    0.00    0.00       1         std::vector<std::string, std::allocator<std::string> >::vector() [135]
                0.00    0.00       1/1           std::_Vector_base<std::string, std::allocator<std::string> >::_Vector_base() [125]
-----------------------------------------------
                0.00    0.00       1/1           main [1]
[136]    0.0    0.00    0.00       1         std::vector<std::string, std::allocator<std::string> >::~vector() [136]
                0.00    0.00       1/1           std::_Vector_base<std::string, std::allocator<std::string> >::_M_get_Tp_allocator() [124]
                0.00    0.00       1/1           void std::_Destroy<std::string*, std::string>(std::string*, std::string*, std::allocator<std::string>&) [151]
                0.00    0.00       1/1           std::_Vector_base<std::string, std::allocator<std::string> >::~_Vector_base() [126]
-----------------------------------------------
                0.00    0.00       1/1           std::vector<double, std::allocator<double> >::push_back(double&&) [140]
[137]    0.0    0.00    0.00       1         void std::vector<double, std::allocator<double> >::emplace_back<double>(double&&) [137]
                0.00    0.00       1/3           double&& std::forward<double>(std::remove_reference<double>::type&) [91]
                0.00    0.00       1/2           std::vector<double, std::allocator<double> >::end() [100]
                0.00    0.00       1/1           void std::vector<double, std::allocator<double> >::_M_insert_aux<double>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double&&) [139]
-----------------------------------------------
                0.00    0.00       1/1           std::vector<double, std::allocator<double> >::push_back(double const&) [141]
[138]    0.0    0.00    0.00       1         void std::vector<double, std::allocator<double> >::_M_insert_aux<double const&>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double const&&&) [138]
                0.00    0.00       3/7           std::_Vector_base<double, std::allocator<double> >::_M_get_Tp_allocator() [61]
                0.00    0.00       2/8           __gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >::base() const [55]
                0.00    0.00       2/4           double* std::__uninitialized_move_a<double*, double*, std::allocator<double> >(double*, double*, double*, std::allocator<double>&) [86]
                0.00    0.00       1/2           std::vector<double, std::allocator<double> >::_M_check_len(unsigned int, char const*) const [98]
                0.00    0.00       1/2           std::vector<double, std::allocator<double> >::begin() [101]
                0.00    0.00       1/2           __gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >::difference_type __gnu_cxx::operator-<double*, std::vector<double, std::allocator<double> > >(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > > const&, __gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > > const&) [97]
                0.00    0.00       1/2           std::_Vector_base<double, std::allocator<double> >::_M_allocate(unsigned int) [99]
                0.00    0.00       1/1           double const&&& std::forward<double const&>(std::remove_reference<double const&>::type&) [149]
                0.00    0.00       1/1           __gnu_cxx::new_allocator<double>::construct(double*, double const&) [108]
                0.00    0.00       1/3           void std::_Destroy<double*, double>(double*, double*, std::allocator<double>&) [93]
                0.00    0.00       1/3           std::_Vector_base<double, std::allocator<double> >::_M_deallocate(double*, unsigned int) [89]
-----------------------------------------------
                0.00    0.00       1/1           void std::vector<double, std::allocator<double> >::emplace_back<double>(double&&) [137]
[139]    0.0    0.00    0.00       1         void std::vector<double, std::allocator<double> >::_M_insert_aux<double>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double&&) [139]
                0.00    0.00       3/7           std::_Vector_base<double, std::allocator<double> >::_M_get_Tp_allocator() [61]
                0.00    0.00       2/8           __gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >::base() const [55]
                0.00    0.00       2/4           double* std::__uninitialized_move_a<double*, double*, std::allocator<double> >(double*, double*, double*, std::allocator<double>&) [86]
                0.00    0.00       1/2           std::vector<double, std::allocator<double> >::_M_check_len(unsigned int, char const*) const [98]
                0.00    0.00       1/2           std::vector<double, std::allocator<double> >::begin() [101]
                0.00    0.00       1/2           __gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >::difference_type __gnu_cxx::operator-<double*, std::vector<double, std::allocator<double> > >(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > > const&, __gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > > const&) [97]
                0.00    0.00       1/2           std::_Vector_base<double, std::allocator<double> >::_M_allocate(unsigned int) [99]
                0.00    0.00       1/3           double&& std::forward<double>(std::remove_reference<double>::type&) [91]
                0.00    0.00       1/1           void __gnu_cxx::new_allocator<double>::construct<double>(double*, double&&) [109]
                0.00    0.00       1/3           void std::_Destroy<double*, double>(double*, double*, std::allocator<double>&) [93]
                0.00    0.00       1/3           std::_Vector_base<double, std::allocator<double> >::_M_deallocate(double*, unsigned int) [89]
-----------------------------------------------
                0.00    0.00       1/1           main [1]
[140]    0.0    0.00    0.00       1         std::vector<double, std::allocator<double> >::push_back(double&&) [140]
                0.00    0.00       1/1           std::remove_reference<double&>::type&& std::move<double&>(double&&&) [148]
                0.00    0.00       1/1           void std::vector<double, std::allocator<double> >::emplace_back<double>(double&&) [137]
-----------------------------------------------
                0.00    0.00       1/1           main [1]
[141]    0.0    0.00    0.00       1         std::vector<double, std::allocator<double> >::push_back(double const&) [141]
                0.00    0.00       1/2           std::vector<double, std::allocator<double> >::end() [100]
                0.00    0.00       1/1           void std::vector<double, std::allocator<double> >::_M_insert_aux<double const&>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double const&&&) [138]
-----------------------------------------------
                0.00    0.00       1/1           main [1]
[142]    0.0    0.00    0.00       1         std::vector<double, std::allocator<double> >::vector() [142]
                0.00    0.00       1/1           std::_Vector_base<double, std::allocator<double> >::_Vector_base() [129]
-----------------------------------------------
                0.00    0.00       1/1           main [1]
[143]    0.0    0.00    0.00       1         std::vector<double, std::allocator<double> >::~vector() [143]
                0.00    0.00       1/7           std::_Vector_base<double, std::allocator<double> >::_M_get_Tp_allocator() [61]
                0.00    0.00       1/3           void std::_Destroy<double*, double>(double*, double*, std::allocator<double>&) [93]
                0.00    0.00       1/1           std::_Vector_base<double, std::allocator<double> >::~_Vector_base() [130]
-----------------------------------------------
                0.00    0.00       1/1           main [1]
[144]    0.0    0.00    0.00       1         std::vector<int, std::allocator<int> >::vector() [144]
                0.00    0.00       1/1           std::_Vector_base<int, std::allocator<int> >::_Vector_base() [133]
-----------------------------------------------
                0.00    0.00       1/1           main [1]
[145]    0.0    0.00    0.00       1         std::vector<int, std::allocator<int> >::~vector() [145]
                0.00    0.00       1/16          std::_Vector_base<int, std::allocator<int> >::_M_get_Tp_allocator() [32]
                0.00    0.00       1/6           void std::_Destroy<int*, int>(int*, int*, std::allocator<int>&) [67]
                0.00    0.00       1/1           std::_Vector_base<int, std::allocator<int> >::~_Vector_base() [134]
-----------------------------------------------
                0.00    0.00       1/1           main [1]
[146]    0.0    0.00    0.00       1         std::ios_base::precision(int) [146]
-----------------------------------------------
                0.00    0.00       1/1           dowork(double) [3]
[147]    0.0    0.00    0.00       1         std::abs(double) [147]
-----------------------------------------------
                0.00    0.00       1/1           std::vector<double, std::allocator<double> >::push_back(double&&) [140]
[148]    0.0    0.00    0.00       1         std::remove_reference<double&>::type&& std::move<double&>(double&&&) [148]
-----------------------------------------------
                0.00    0.00       1/1           void std::vector<double, std::allocator<double> >::_M_insert_aux<double const&>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double const&&&) [138]
[149]    0.0    0.00    0.00       1         double const&&& std::forward<double const&>(std::remove_reference<double const&>::type&) [149]
-----------------------------------------------
                0.00    0.00       1/1           void std::_Destroy<std::string*, std::string>(std::string*, std::string*, std::allocator<std::string>&) [151]
[150]    0.0    0.00    0.00       1         void std::_Destroy<std::string*>(std::string*, std::string*) [150]
                0.00    0.00       1/1           void std::_Destroy_aux<false>::__destroy<std::string*>(std::string*, std::string*) [120]
-----------------------------------------------
                0.00    0.00       1/1           std::vector<std::string, std::allocator<std::string> >::~vector() [136]
[151]    0.0    0.00    0.00       1         void std::_Destroy<std::string*, std::string>(std::string*, std::string*, std::allocator<std::string>&) [151]
                0.00    0.00       1/1           void std::_Destroy<std::string*>(std::string*, std::string*) [150]
-----------------------------------------------

 This table describes the call tree of the program, and was sorted by
 the total amount of time spent in each function and its children.

 Each entry in this table consists of several lines.  The line with the
 index number at the left hand margin lists the current function.
 The lines above it list the functions that called this function,
 and the lines below it list the functions this one called.
 This line lists:
     index	A unique number given to each element of the table.
		Index numbers are sorted numerically.
		The index number is printed next to every function name so
		it is easier to look up where the function in the table.

     % time	This is the percentage of the `total' time that was spent
		in this function and its children.  Note that due to
		different viewpoints, functions excluded by options, etc,
		these numbers will NOT add up to 100%.

     self	This is the total amount of time spent in this function.

     children	This is the total amount of time propagated into this
		function by its children.

     called	This is the number of times the function was called.
		If the function called itself recursively, the number
		only includes non-recursive calls, and is followed by
		a `+' and the number of recursive calls.

     name	The name of the current function.  The index number is
		printed after it.  If the function is a member of a
		cycle, the cycle number is printed between the
		function's name and the index number.


 For the function's parents, the fields have the following meanings:

     self	This is the amount of time that was propagated directly
		from the function into this parent.

     children	This is the amount of time that was propagated from
		the function's children into this parent.

     called	This is the number of times this parent called the
		function `/' the total number of times the function
		was called.  Recursive calls to the function are not
		included in the number after the `/'.

     name	This is the name of the parent.  The parent's index
		number is printed after it.  If the parent is a
		member of a cycle, the cycle number is printed between
		the name and the index number.

 If the parents of the function cannot be determined, the word
 `<spontaneous>' is printed in the `name' field, and all the other
 fields are blank.

 For the function's children, the fields have the following meanings:

     self	This is the amount of time that was propagated directly
		from the child into the function.

     children	This is the amount of time that was propagated from the
		child's children to the function.

     called	This is the number of times the function called
		this child `/' the total number of times the child
		was called.  Recursive calls by the child are not
		listed in the number after the `/'.

     name	This is the name of the child.  The child's index
		number is printed after it.  If the child is a
		member of a cycle, the cycle number is printed
		between the name and the index number.

 If there are any cycles (circles) in the call graph, there is an
 entry for the cycle-as-a-whole.  This entry shows who called the
 cycle (as parents) and the members of the cycle (as children.)
 The `+' recursive calls entry shows the number of function calls that
 were internal to the cycle, and the calls entry for each member shows,
 for that member, how many times it was called from other members of
 the cycle.

�
Index by function name

 [102] _GLOBAL__sub_I__Z2TTd (nbody.cpp) [98] std::vector<double, std::allocator<double> >::_M_check_len(unsigned int, char const*) const [139] void std::vector<double, std::allocator<double> >::_M_insert_aux<double>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double&&)
  [17] initialize()           [45] std::vector<double, std::allocator<double> >::size() const [100] std::vector<double, std::allocator<double> >::end()
   [4] calculate_a()          [79] std::vector<double, std::allocator<double> >::max_size() const [101] std::vector<double, std::allocator<double> >::begin()
  [94] print_hline()          [71] std::vector<int, std::allocator<int> >::_M_check_len(unsigned int, char const*) const [140] std::vector<double, std::allocator<double> >::push_back(double&&)
 [103] JD(tm*)                [23] std::vector<int, std::allocator<int> >::size() const [141] std::vector<double, std::allocator<double> >::push_back(double const&)
 [104] TT(double)             [46] std::vector<int, std::allocator<int> >::max_size() const [142] std::vector<double, std::allocator<double> >::vector()
 [105] __static_initialization_and_destruction_0(int, int) (nbody.cpp) [114] std::allocator<std::string>::allocator() [143] std::vector<double, std::allocator<double> >::~vector()
  [15] cross(vect const&, vect const&) [115] std::allocator<std::string>::~allocator() [90] std::vector<double, std::allocator<double> >::operator[](unsigned int)
   [3] dowork(double)        [116] std::allocator<double>::allocator() [73] void std::vector<int, std::allocator<int> >::_M_insert_aux<int const&>(__gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >, int const&&&)
  [36] getobj(int)           [117] std::allocator<double>::~allocator() [74] std::vector<int, std::allocator<int> >::end()
  [16] totalE()              [118] std::allocator<int>::allocator() [75] std::vector<int, std::allocator<int> >::begin()
  [14] totalL()              [119] std::allocator<int>::~allocator() [39] std::vector<int, std::allocator<int> >::push_back(int const&)
   [2] CRO_step(double, void (*)()) [41] std::_Iter_base<double*, false>::_S_base(double*) [144] std::vector<int, std::allocator<int> >::vector()
  [10] vect::mag()            [24] std::_Iter_base<int*, false>::_S_base(int*) [145] std::vector<int, std::allocator<int> >::~vector()
  [13] vect::vect(double, double, double) [57] std::_Iter_base<std::move_iterator<double*>, true>::_S_base(std::move_iterator<double*>) [22] std::vector<int, std::allocator<int> >::operator[](unsigned int)
  [21] vect::vect()           [28] std::_Iter_base<std::move_iterator<int*>, true>::_S_base(std::move_iterator<int*>) [146] std::ios_base::precision(int)
  [11] vect::operator=(vect const&) [80] double* std::__copy_move<true, true, std::random_access_iterator_tag>::__copy_m<double>(double const*, double const*, double*) [59] std::_Miter_base<std::move_iterator<double*> >::iterator_type std::__miter_base<std::move_iterator<double*> >(std::move_iterator<double*>)
   [9] vect::operator-=(vect const&) [47] int* std::__copy_move<true, true, std::random_access_iterator_tag>::__copy_m<int>(int const*, int const*, int*) [30] std::_Miter_base<std::move_iterator<int*> >::iterator_type std::__miter_base<std::move_iterator<int*> >(std::move_iterator<int*>)
   [6] vect::operator*=(double const&) [120] void std::_Destroy_aux<false>::__destroy<std::string*>(std::string*, std::string*) [42] std::_Niter_base<double*>::iterator_type std::__niter_base<double*>(double*)
   [8] vect::operator-(vect const&) [88] void std::_Destroy_aux<true>::__destroy<double*>(double*, double*) [25] std::_Niter_base<int*>::iterator_type std::__niter_base<int*>(int*)
   [5] vect::operator*(double const&) [64] void std::_Destroy_aux<true>::__destroy<int*>(int*, int*) [82] double* std::__copy_move_a<true, double*, double*>(double*, double*, double*)
   [7] vect::operator+=(vect const&) [121] std::_Vector_base<std::string, std::allocator<std::string> >::_Vector_impl::_Vector_impl() [49] int* std::__copy_move_a<true, int*, int*>(int*, int*, int*)
  [12] vect::operator+(vect const&) [122] std::_Vector_base<std::string, std::allocator<std::string> >::_Vector_impl::~_Vector_impl() [83] double* std::__copy_move_a2<true, double*, double*>(double*, double*, double*)
  [37] cobject::cobject()    [123] std::_Vector_base<std::string, std::allocator<std::string> >::_M_deallocate(std::string*, unsigned int) [50] int* std::__copy_move_a2<true, int*, int*>(int*, int*, int*)
 [106] __gnu_cxx::new_allocator<std::string>::new_allocator() [124] std::_Vector_base<std::string, std::allocator<std::string> >::_M_get_Tp_allocator() [60] std::move_iterator<double*> std::make_move_iterator<double*>(double* const&)
 [107] __gnu_cxx::new_allocator<std::string>::~new_allocator() [125] std::_Vector_base<std::string, std::allocator<std::string> >::_Vector_base() [31] std::move_iterator<int*> std::make_move_iterator<int*>(int* const&)
  [95] __gnu_cxx::new_allocator<double>::deallocate(double*, unsigned int) [126] std::_Vector_base<std::string, std::allocator<std::string> >::~_Vector_base() [84] double* std::uninitialized_copy<std::move_iterator<double*>, double*>(std::move_iterator<double*>, std::move_iterator<double*>, double*)
  [96] __gnu_cxx::new_allocator<double>::allocate(unsigned int, void const*) [99] std::_Vector_base<double, std::allocator<double> >::_M_allocate(unsigned int) [51] int* std::uninitialized_copy<std::move_iterator<int*>, int*>(std::move_iterator<int*>, std::move_iterator<int*>, int*)
 [108] __gnu_cxx::new_allocator<double>::construct(double*, double const&) [127] std::_Vector_base<double, std::allocator<double> >::_Vector_impl::_Vector_impl() [85] double* std::__uninitialized_copy_a<std::move_iterator<double*>, double*, double>(std::move_iterator<double*>, std::move_iterator<double*>, double*, std::allocator<double>&)
 [109] void __gnu_cxx::new_allocator<double>::construct<double>(double*, double&&) [128] std::_Vector_base<double, std::allocator<double> >::_Vector_impl::~_Vector_impl() [52] int* std::__uninitialized_copy_a<std::move_iterator<int*>, int*, int>(std::move_iterator<int*>, std::move_iterator<int*>, int*, std::allocator<int>&)
 [110] __gnu_cxx::new_allocator<double>::new_allocator() [89] std::_Vector_base<double, std::allocator<double> >::_M_deallocate(double*, unsigned int) [86] double* std::__uninitialized_move_a<double*, double*, std::allocator<double> >(double*, double*, double*, std::allocator<double>&)
 [111] __gnu_cxx::new_allocator<double>::~new_allocator() [61] std::_Vector_base<double, std::allocator<double> >::_M_get_Tp_allocator() [53] int* std::__uninitialized_move_a<int*, int*, std::allocator<int> >(int*, int*, int*, std::allocator<int>&)
  [68] __gnu_cxx::new_allocator<int>::deallocate(int*, unsigned int) [129] std::_Vector_base<double, std::allocator<double> >::_Vector_base() [147] std::abs(double)
  [69] __gnu_cxx::new_allocator<int>::allocate(unsigned int, void const*) [130] std::_Vector_base<double, std::allocator<double> >::~_Vector_base() [62] unsigned int const& std::max<unsigned int>(unsigned int const&, unsigned int const&)
  [38] __gnu_cxx::new_allocator<int>::construct(int*, int const&) [72] std::_Vector_base<int, std::allocator<int> >::_M_allocate(unsigned int) [40] __gnu_cxx::__promote_2<__gnu_cxx::__enable_if<(std::__is_arithmetic<double>::__value)&&(std::__is_arithmetic<int>::__value), double>::__type, int>::__type std::pow<double, int>(double, int)
 [112] __gnu_cxx::new_allocator<int>::new_allocator() [131] std::_Vector_base<int, std::allocator<int> >::_Vector_impl::_Vector_impl() [87] double* std::copy<std::move_iterator<double*>, double*>(std::move_iterator<double*>, std::move_iterator<double*>, double*)
 [113] __gnu_cxx::new_allocator<int>::~new_allocator() [132] std::_Vector_base<int, std::allocator<int> >::_Vector_impl::~_Vector_impl() [54] int* std::copy<std::move_iterator<int*>, int*>(std::move_iterator<int*>, std::move_iterator<int*>, int*)
  [77] __gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >::__normal_iterator(double* const&) [65] std::_Vector_base<int, std::allocator<int> >::_M_deallocate(int*, unsigned int) [148] std::remove_reference<double&>::type&& std::move<double&>(double&&&)
  [43] __gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >::__normal_iterator(int* const&) [32] std::_Vector_base<int, std::allocator<int> >::_M_get_Tp_allocator() [149] double const&&& std::forward<double const&>(std::remove_reference<double const&>::type&)
  [97] __gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >::difference_type __gnu_cxx::operator-<double*, std::vector<double, std::allocator<double> > >(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > > const&, __gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > > const&) [133] std::_Vector_base<int, std::allocator<int> >::_Vector_base() [76] int const&&& std::forward<int const&>(std::remove_reference<int const&>::type&)
  [70] __gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >::difference_type __gnu_cxx::operator-<int*, std::vector<int, std::allocator<int> > >(__gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > > const&, __gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > > const&) [134] std::_Vector_base<int, std::allocator<int> >::~_Vector_base() [91] double&& std::forward<double>(std::remove_reference<double>::type&)
  [63] __gnu_cxx::new_allocator<double>::max_size() const [58] std::move_iterator<double*>::move_iterator(double*) [150] void std::_Destroy<std::string*>(std::string*, std::string*)
  [35] __gnu_cxx::new_allocator<int>::max_size() const [29] std::move_iterator<int*>::move_iterator(int*) [151] void std::_Destroy<std::string*, std::string>(std::string*, std::string*, std::allocator<std::string>&)
  [55] __gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >::base() const [81] double* std::__uninitialized_copy<true>::__uninit_copy<std::move_iterator<double*>, double*>(std::move_iterator<double*>, std::move_iterator<double*>, double*) [92] void std::_Destroy<double*>(double*, double*)
  [26] __gnu_cxx::__normal_iterator<int*, std::vector<int, std::allocator<int> > >::base() const [48] int* std::__uninitialized_copy<true>::__uninit_copy<std::move_iterator<int*>, int*>(std::move_iterator<int*>, std::move_iterator<int*>, int*) [93] void std::_Destroy<double*, double>(double*, double*, std::allocator<double>&)
  [78] std::_Vector_base<double, std::allocator<double> >::_M_get_Tp_allocator() const [135] std::vector<std::string, std::allocator<std::string> >::vector() [66] void std::_Destroy<int*>(int*, int*)
  [44] std::_Vector_base<int, std::allocator<int> >::_M_get_Tp_allocator() const [136] std::vector<std::string, std::allocator<std::string> >::~vector() [67] void std::_Destroy<int*, int>(int*, int*, std::allocator<int>&)
  [56] std::move_iterator<double*>::base() const [137] void std::vector<double, std::allocator<double> >::emplace_back<double>(double&&) [33] bool std::operator==<char, std::char_traits<char>, std::allocator<char> >(std::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, char const*)
  [27] std::move_iterator<int*>::base() const [138] void std::vector<double, std::allocator<double> >::_M_insert_aux<double const&>(__gnu_cxx::__normal_iterator<double*, std::vector<double, std::allocator<double> > >, double const&&&) [34] operator new(unsigned int, void*)

|}

----
== Introduction : GPU Benchmarking/Gaussian Blur Filter : Colin Paul ==
[[Image:Cinque_terre.jpg|860px]][[Image:Cinque_terre_BLURRED.jpg|860px]]
[[Image:F2RiP.gif|500px|thumb|alt=convolution pattern]]
[[Image:Img16.png|500px|thumb|alt=Plot of frequency response of the 2D Gaussian]]
===What is Gaussian blurring?===

At a high level, Gaussian blurring works just like [https://en.wikipedia.org/wiki/Box_blur box blurring] in that there is a weight per pixel and that for each pixel, you apply the weights to that pixel and it’s neighbors to come up<br/>
with the final value for the blurred pixel. It uses a convolution pattern which is a linear stencil that applies fixed weights to the elements of a neighborhood in the combination operation.

With true Gaussian blurring however, the function that defines the weights for each pixel technically never reaches zero, but gets smaller and smaller over distance. In theory, this makes a<br/>
Gaussian kernel infinitely large. In practice though, you can choose a cut-off point and set the bounds.

====The parameters to a Gaussian blur are:====

*Sigma (&sigma;) – This defines how much blur there is. A larger number is a higher amount of blur.
*Radius – The size of the kernel in pixels. The appropriate pixel size can be calculated for a specific sigma, but more information on that lower down.

Just like box blur, a Gaussian blur is separable which means that you can either apply a 2D convolution kernel, or you can apply a 1D convolution kernel on each axis. Doing a single 2D convolution<br/>
means more calculations, but you only need one buffer to put the results into. Doing two 1D convolutions (one on each axis), ends up being fewer calculations, but requires two buffers to put the results<br/>
into (one intermediate buffer to hold the first axis results).

Here is a 3 pixel 1D Gaussian Kernel for a sigma of 1.0:


[[Image:1dkernel.png|250px]]

<br/>This kernel is useful for a two pass algorithm: First, perform a horizontal blur with the weights below and then perform a vertical blur on the resulting image (or vice versa).<br/>

Below is a 3×3 pixel 2D Gaussian Kernel also with a sigma of 1.0. Note that this can be calculated as an outer product (tensor product) of 1D kernels:


[[Image:2dkernel.png|250px]]

<br/>These weights below be used directly in a single pass blur algorithm: n<sup>2</sup> samples per pixel.<br/>

An interesting property of Gaussian blurs is that you can apply multiple smaller blurs and it will come up with the result as if you did a larger Blur. Unfortunately it’s more <br/>
calculations doing multiple smaller blurs so is not usually worth while.

If you apply multiple blurs, the equivalent blur is the square root of the sum of the squares of the blur. Taking wikipedia’s [https://en.wikipedia.org/wiki/Gaussian_blur example], if you applied a blur with radius 6 and a blur<br/>
with a radius of 8, you’d end up with the equivelant of a radius 10 blur. This is because &radic; ( 6<sup>2</sup> + 8<sup>2</sup> ) = 10

[[Image:Kernalweightperpixel.PNG|500px|thumb|alt=2D Gaussian]]

====Calculating The Kernel====

There are a couple ways to calculate a Gaussian kernel.

Pascal’s triangle approaches the Gaussian bell curve as the row number reaches infinity. Pascal’s triangle also represents the numbers that each term<br/>
is calculated by after expanding binomials (x + y)<sup>N</sup>. So technically, you could use a row from Pascal’s triangle as a 1D kernel and normalize the result, but it isn’t the most accurate.

A better way is to use the Gaussian function which is this: e<sup>-x<sup>2</sup>/(2 * &sigma;<sup>2</sup>)</sup>

Where the sigma is your blur amount and x ranges across your values from the negative to the positive. For instance, if your kernel was 5 values, it would range from -2 to +2.

An even better way would be to integrate the Gaussian function instead of just taking point samples. Refer to the two graphs on the right.<br/>
The graphs plot the continuous distribution function and the discrete kernel approximation. One thing to look out for are the tails of the distribution vs. kernel support:<br/>
For the current configuration, we have 13.36% of the curve’s area outside the discrete kernel. Note that the weights are renormalized such that the sum of all weights is one. Or in other words:<br/>
the probability mass outside the discrete kernel is redistributed evenly to all pixels within the kernel. The weights are calculated by numerical integration of the continuous gaussian distribution<br/>
over each discrete kernel tap.

Make sure to normalize the result so that the weights add up to 1. This makes sure that your blurring doesn’t make the image get brighter (greater than 1) or dimmer (less than 1).

====Calculating The Kernel Size====

Given a sigma value, you can calculate the size of the kernel you need by using this formula:1 + 2 &radic; ( -2&sigma;<sup>2</sup> ln 0.0005 )

That formula makes a Kernel large enough such that it cuts off when the value in the kernel is less than 0.5%. You can adjust the number in there to higher or lower depending on your desires for<br/>
speed versus quality.

===Running the program===
====Code====
{| class="wikitable mw-collapsible mw-collapsed"
! Windows [https://goo.gl/aAUr6m source]- Gassusan Blur Filter Main (Visual Studio)
|-
|
<syntaxhighlight lang="cpp">
#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <array>
#include <vector>
#include <functional>
#include <windows.h>  // for bitmap headers.

const float c_pi = 3.14159265359f;

struct SImageData
{
  SImageData()
    : m_width(0)
    , m_height(0)
  { }

  long m_width;
  long m_height;
  long m_pitch;
  std::vector<uint8_t> m_pixels;
};

void WaitForEnter()
{
  char c;
  std::cout << "Press Enter key to exit ... ";
  std::cin.get(c);
}

bool LoadImage(const char *fileName, SImageData& imageData)
{
  // open the file if we can
  FILE *file;
  file = fopen(fileName, "rb");
  if (!file)
    return false;

  // read the headers if we can
  BITMAPFILEHEADER header;
  BITMAPINFOHEADER infoHeader;
  if (fread(&header, sizeof(header), 1, file) != 1 ||
    fread(&infoHeader, sizeof(infoHeader), 1, file) != 1 ||
    header.bfType != 0x4D42 || infoHeader.biBitCount != 24)
  {
    fclose(file);
    return false;
  }

  // read in our pixel data if we can. Note that it's in BGR order, and width is padded to the next power of 4
  imageData.m_pixels.resize(infoHeader.biSizeImage);
  fseek(file, header.bfOffBits, SEEK_SET);
  if (fread(&imageData.m_pixels[0], imageData.m_pixels.size(), 1, file) != 1)
  {
    fclose(file);
    return false;
  }

  imageData.m_width = infoHeader.biWidth;
  imageData.m_height = infoHeader.biHeight;

  imageData.m_pitch = imageData.m_width * 3;
  if (imageData.m_pitch & 3)
  {
    imageData.m_pitch &= ~3;
    imageData.m_pitch += 4;
  }

  fclose(file);
  return true;
}

bool SaveImage(const char *fileName, const SImageData &image)
{
  // open the file if we can
  FILE *file;
  file = fopen(fileName, "wb");
  if (!file)
    return false;

  // make the header info
  BITMAPFILEHEADER header;
  BITMAPINFOHEADER infoHeader;

  header.bfType = 0x4D42;
  header.bfReserved1 = 0;
  header.bfReserved2 = 0;
  header.bfOffBits = 54;

  infoHeader.biSize = 40;
  infoHeader.biWidth = image.m_width;
  infoHeader.biHeight = image.m_height;
  infoHeader.biPlanes = 1;
  infoHeader.biBitCount = 24;
  infoHeader.biCompression = 0;
  infoHeader.biSizeImage = image.m_pixels.size();
  infoHeader.biXPelsPerMeter = 0;
  infoHeader.biYPelsPerMeter = 0;
  infoHeader.biClrUsed = 0;
  infoHeader.biClrImportant = 0;

  header.bfSize = infoHeader.biSizeImage + header.bfOffBits;

  // write the data and close the file
  fwrite(&header, sizeof(header), 1, file);
  fwrite(&infoHeader, sizeof(infoHeader), 1, file);
  fwrite(&image.m_pixels[0], infoHeader.biSizeImage, 1, file);
  fclose(file);
  return true;
}

int PixelsNeededForSigma(float sigma)
{
  // returns the number of pixels needed to represent a gaussian kernal that has values
  // down to the threshold amount.  A gaussian function technically has values everywhere
  // on the image, but the threshold lets us cut it off where the pixels contribute to
  // only small amounts that aren't as noticeable.
  const float c_threshold = 0.005f; // 0.5%
  return int(floor(1.0f + 2.0f * sqrtf(-2.0f * sigma * sigma * log(c_threshold)))) + 1;
}

float Gaussian(float sigma, float x)
{
  return expf(-(x*x) / (2.0f * sigma*sigma));
}

float GaussianSimpsonIntegration(float sigma, float a, float b)
{
  return
    ((b - a) / 6.0f) *
    (Gaussian(sigma, a) + 4.0f * Gaussian(sigma, (a + b) / 2.0f) + Gaussian(sigma, b));
}

std::vector<float> GaussianKernelIntegrals(float sigma, int taps)
{
  std::vector<float> ret;
  float total = 0.0f;
  for (int i = 0; i < taps; ++i)
  {
    float x = float(i) - float(taps / 2);
    float value = GaussianSimpsonIntegration(sigma, x - 0.5f, x + 0.5f);
    ret.push_back(value);
    total += value;
  }
  // normalize it
  for (unsigned int i = 0; i < ret.size(); ++i)
  {
    ret[i] /= total;
  }
  return ret;
}

const uint8_t* GetPixelOrBlack(const SImageData& image, int x, int y)
{
  static const uint8_t black[3] = { 0, 0, 0 };
  if (x < 0 || x >= image.m_width ||
    y < 0 || y >= image.m_height)
  {
    return black;
  }

  return &image.m_pixels[(y * image.m_pitch) + x * 3];
}

void BlurImage(const SImageData& srcImage, SImageData &destImage, float xblursigma, float yblursigma, unsigned int xblursize, unsigned int yblursize)
{
  // allocate space for copying the image for destImage and tmpImage
  destImage.m_width = srcImage.m_width;
  destImage.m_height = srcImage.m_height;
  destImage.m_pitch = srcImage.m_pitch;
  destImage.m_pixels.resize(destImage.m_height * destImage.m_pitch);

  SImageData tmpImage;
  tmpImage.m_width = srcImage.m_width;
  tmpImage.m_height = srcImage.m_height;
  tmpImage.m_pitch = srcImage.m_pitch;
  tmpImage.m_pixels.resize(tmpImage.m_height * tmpImage.m_pitch);

  // horizontal blur from srcImage into tmpImage
  {
    auto row = GaussianKernelIntegrals(xblursigma, xblursize);

    int startOffset = -1 * int(row.size() / 2);

    for (int y = 0; y < tmpImage.m_height; ++y)
    {
      for (int x = 0; x < tmpImage.m_width; ++x)
      {
        std::array<float, 3> blurredPixel = { { 0.0f, 0.0f, 0.0f } };
        for (unsigned int i = 0; i < row.size(); ++i)
        {
          const uint8_t *pixel = GetPixelOrBlack(srcImage, x + startOffset + i, y);
          blurredPixel[0] += float(pixel[0]) * row[i];
          blurredPixel[1] += float(pixel[1]) * row[i];
          blurredPixel[2] += float(pixel[2]) * row[i];
        }

        uint8_t *destPixel = &tmpImage.m_pixels[y * tmpImage.m_pitch + x * 3];

        destPixel[0] = uint8_t(blurredPixel[0]);
        destPixel[1] = uint8_t(blurredPixel[1]);
        destPixel[2] = uint8_t(blurredPixel[2]);
      }
    }
  }

  // vertical blur from tmpImage into destImage
  {
    auto row = GaussianKernelIntegrals(yblursigma, yblursize);

    int startOffset = -1 * int(row.size() / 2);

    for (int y = 0; y < destImage.m_height; ++y)
    {
      for (int x = 0; x < destImage.m_width; ++x)
      {
        std::array<float, 3> blurredPixel = { { 0.0f, 0.0f, 0.0f } };
        for (unsigned int i = 0; i < row.size(); ++i)
        {
          const uint8_t *pixel = GetPixelOrBlack(tmpImage, x, y + startOffset + i);
          blurredPixel[0] += float(pixel[0]) * row[i];
          blurredPixel[1] += float(pixel[1]) * row[i];
          blurredPixel[2] += float(pixel[2]) * row[i];
        }

        uint8_t *destPixel = &destImage.m_pixels[y * destImage.m_pitch + x * 3];

        destPixel[0] = uint8_t(blurredPixel[0]);
        destPixel[1] = uint8_t(blurredPixel[1]);
        destPixel[2] = uint8_t(blurredPixel[2]);
      }
    }
  }
}

int main(int argc, char **argv)
{
  float xblursigma, yblursigma;

  bool showUsage = argc < 5 ||
    (sscanf(argv[3], "%f", &xblursigma) != 1) ||
    (sscanf(argv[4], "%f", &yblursigma) != 1);

  char *srcFileName = argv[1];
  char *destFileName = argv[2];

  if (showUsage)
  {
    printf("Usage: <source> <dest> <xblur> <yblur>\nBlur values are sigma\n\n");
    WaitForEnter();
    return 1;
  }

  // calculate pixel sizes, and make sure they are odd 
  int xblursize = PixelsNeededForSigma(xblursigma) | 1;
  int yblursize = PixelsNeededForSigma(yblursigma) | 1;

  printf("Attempting to blur a 24 bit image.\n");
  printf("  Source=%s\n  Dest=%s\n  blur=[%0.1f, %0.1f] px=[%d,%d]\n\n", srcFileName, destFileName, xblursigma, yblursigma, xblursize, yblursize);

  SImageData srcImage;
  if (LoadImage(srcFileName, srcImage))
  {
    printf("%s loaded\n", srcFileName);
    SImageData destImage;
    BlurImage(srcImage, destImage, xblursigma, yblursigma, xblursize, yblursize);
    if (SaveImage(destFileName, destImage))
      printf("Blurred image saved as %s\n", destFileName);
    else
    {
      printf("Could not save blurred image as %s\n", destFileName);
      WaitForEnter();
      return 1;
    }
  }
  else
  {
    printf("could not read 24 bit bmp file %s\n\n", srcFileName);
    WaitForEnter();
    return 1;
  }
  return 0;
}
</syntaxhighlight>

|}

Ported to Linux:

{| class="wikitable mw-collapsible mw-collapsed"
! Linux source - Gassusan Blur Filter Main (Command Line)
|-
|
<syntaxhighlight lang="cpp">
#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <math.h>
#include <array>
#include <vector>
#include <functional>
#include "windows.h"  // for bitmap headers.

/* uncomment the line below if you want to run grpof */
//#define RUN_GPROF

const float c_pi = 3.14159265359f;

struct SImageData
{
  SImageData()
    : m_width(0)
    , m_height(0)
  { }

  long m_width;
  long m_height;
  long m_pitch;
  std::vector<uint8_t> m_pixels;
};

void WaitForEnter()
{
  char c;
  std::cout << "Press Enter key to exit ... ";
  std::cin.get(c);
}

bool LoadImage(const char *fileName, SImageData& imageData)
{
  // open the file if we can
  FILE *file;
  file = fopen(fileName, "rb");
  if (!file)
    return false;

  // read the headers if we can
  BITMAPFILEHEADER header;
  BITMAPINFOHEADER infoHeader;
  if (fread(&header, sizeof(header), 1, file) != 1 ||
    fread(&infoHeader, sizeof(infoHeader), 1, file) != 1 ||
    header.bfType != 0x4D42 || infoHeader.biBitCount != 24)
  {
    fclose(file);
    return false;
  }

  // read in our pixel data if we can. Note that it's in BGR order, and width is padded to the next power of 4
  imageData.m_pixels.resize(infoHeader.biSizeImage);
  fseek(file, header.bfOffBits, SEEK_SET);
  if (fread(&imageData.m_pixels[0], imageData.m_pixels.size(), 1, file) != 1)
  {
    fclose(file);
    return false;
  }

  imageData.m_width = infoHeader.biWidth;
  imageData.m_height = infoHeader.biHeight;

  imageData.m_pitch = imageData.m_width * 3;
  if (imageData.m_pitch & 3)
  {
    imageData.m_pitch &= ~3;
    imageData.m_pitch += 4;
  }

  fclose(file);
  return true;
}

bool SaveImage(const char *fileName, const SImageData &image)
{
  // open the file if we can
  FILE *file;
  file = fopen(fileName, "wb");
  if (!file)
    return false;

  // make the header info
  BITMAPFILEHEADER header;
  BITMAPINFOHEADER infoHeader;

  header.bfType = 0x4D42;
  header.bfReserved1 = 0;
  header.bfReserved2 = 0;
  header.bfOffBits = 54;

  infoHeader.biSize = 40;
  infoHeader.biWidth = image.m_width;
  infoHeader.biHeight = image.m_height;
  infoHeader.biPlanes = 1;
  infoHeader.biBitCount = 24;
  infoHeader.biCompression = 0;
  infoHeader.biSizeImage = image.m_pixels.size();
  infoHeader.biXPelsPerMeter = 0;
  infoHeader.biYPelsPerMeter = 0;
  infoHeader.biClrUsed = 0;
  infoHeader.biClrImportant = 0;

  header.bfSize = infoHeader.biSizeImage + header.bfOffBits;

  // write the data and close the file
  fwrite(&header, sizeof(header), 1, file);
  fwrite(&infoHeader, sizeof(infoHeader), 1, file);
  fwrite(&image.m_pixels[0], infoHeader.biSizeImage, 1, file);
  fclose(file);
  return true;
}

int PixelsNeededForSigma(float sigma)
{
  // returns the number of pixels needed to represent a gaussian kernal that has values
  // down to the threshold amount.  A gaussian function technically has values everywhere
  // on the image, but the threshold lets us cut it off where the pixels contribute to
  // only small amounts that aren't as noticeable.
  const float c_threshold = 0.005f; // 0.5%
  return int(floor(1.0f + 2.0f * sqrtf(-2.0f * sigma * sigma * log(c_threshold)))) + 1;
}

float Gaussian(float sigma, float x)
{
  return expf(-(x*x) / (2.0f * sigma*sigma));
}

float GaussianSimpsonIntegration(float sigma, float a, float b)
{
  return
    ((b - a) / 6.0f) *
    (Gaussian(sigma, a) + 4.0f * Gaussian(sigma, (a + b) / 2.0f) + Gaussian(sigma, b));
}

std::vector<float> GaussianKernelIntegrals(float sigma, int taps)
{
  std::vector<float> ret;
  float total = 0.0f;
  for (int i = 0; i < taps; ++i)
  {
    float x = float(i) - float(taps / 2);
    float value = GaussianSimpsonIntegration(sigma, x - 0.5f, x + 0.5f);
    ret.push_back(value);
    total += value;
  }
  // normalize it
  for (unsigned int i = 0; i < ret.size(); ++i)
  {
    ret[i] /= total;
  }
  return ret;
}

const uint8_t* GetPixelOrBlack(const SImageData& image, int x, int y)
{
  static const uint8_t black[3] = { 0, 0, 0 };
  if (x < 0 || x >= image.m_width ||
    y < 0 || y >= image.m_height)
  {
    return black;
  }

  return &image.m_pixels[(y * image.m_pitch) + x * 3];
}

void BlurImage(const SImageData& srcImage, SImageData &destImage, float xblursigma, float yblursigma, unsigned int xblursize, unsigned int yblursize)
{
  // allocate space for copying the image for destImage and tmpImage
  destImage.m_width = srcImage.m_width;
  destImage.m_height = srcImage.m_height;
  destImage.m_pitch = srcImage.m_pitch;
  destImage.m_pixels.resize(destImage.m_height * destImage.m_pitch);

  SImageData tmpImage;
  tmpImage.m_width = srcImage.m_width;
  tmpImage.m_height = srcImage.m_height;
  tmpImage.m_pitch = srcImage.m_pitch;
  tmpImage.m_pixels.resize(tmpImage.m_height * tmpImage.m_pitch);

  // horizontal blur from srcImage into tmpImage
  {
    auto row = GaussianKernelIntegrals(xblursigma, xblursize);

    int startOffset = -1 * int(row.size() / 2);

    for (int y = 0; y < tmpImage.m_height; ++y)
    {
      for (int x = 0; x < tmpImage.m_width; ++x)
      {
        std::array<float, 3> blurredPixel = { { 0.0f, 0.0f, 0.0f } };
        for (unsigned int i = 0; i < row.size(); ++i)
        {
          const uint8_t *pixel = GetPixelOrBlack(srcImage, x + startOffset + i, y);
          blurredPixel[0] += float(pixel[0]) * row[i];
          blurredPixel[1] += float(pixel[1]) * row[i];
          blurredPixel[2] += float(pixel[2]) * row[i];
        }

        uint8_t *destPixel = &tmpImage.m_pixels[y * tmpImage.m_pitch + x * 3];

        destPixel[0] = uint8_t(blurredPixel[0]);
        destPixel[1] = uint8_t(blurredPixel[1]);
        destPixel[2] = uint8_t(blurredPixel[2]);
      }
    }
  }

  // vertical blur from tmpImage into destImage
  {
    auto row = GaussianKernelIntegrals(yblursigma, yblursize);

    int startOffset = -1 * int(row.size() / 2);

    for (int y = 0; y < destImage.m_height; ++y)
    {
      for (int x = 0; x < destImage.m_width; ++x)
      {
        std::array<float, 3> blurredPixel = { { 0.0f, 0.0f, 0.0f } };
        for (unsigned int i = 0; i < row.size(); ++i)
        {
          const uint8_t *pixel = GetPixelOrBlack(tmpImage, x, y + startOffset + i);
          blurredPixel[0] += float(pixel[0]) * row[i];
          blurredPixel[1] += float(pixel[1]) * row[i];
          blurredPixel[2] += float(pixel[2]) * row[i];
        }

        uint8_t *destPixel = &destImage.m_pixels[y * destImage.m_pitch + x * 3];

        destPixel[0] = uint8_t(blurredPixel[0]);
        destPixel[1] = uint8_t(blurredPixel[1]);
        destPixel[2] = uint8_t(blurredPixel[2]);
      }
    }
  }
}

int main(int argc, char **argv)
{

#ifdef RUN_GPROF

  float xblursigma = 3.0f, yblursigma = 3.0f;

  bool showUsage = false;

  const char *srcFileName = "cinque_terre.bmp";
  const char *destFileName = "cinque_terre_BLURRED.bmp";

#else

  float xblursigma, yblursigma;

  bool showUsage = argc < 5 ||
    (sscanf(argv[3], "%f", &xblursigma) != 1) ||
    (sscanf(argv[4], "%f", &yblursigma) != 1);

  char *srcFileName = argv[1];
  char *destFileName = argv[2];

#endif /* RUN_GROF */

  if (showUsage)
  {
    printf("Usage: <source> <dest> <xblur> <yblur>\nBlur values are sigma\n\n");
    WaitForEnter();
    return 1;
  }

  // calculate pixel sizes, and make sure they are odd
  int xblursize = PixelsNeededForSigma(xblursigma) | 1;
  int yblursize = PixelsNeededForSigma(yblursigma) | 1;

  printf("Attempting to blur a 24 bit image.\n");
  printf("  Source=%s\n  Dest=%s\n  blur=[%0.1f, %0.1f] px=[%d,%d]\n\n", srcFileName, destFileName, xblursigma, yblursigma, xblursize, yblursize);

  SImageData srcImage;
  if (LoadImage(srcFileName, srcImage))
  {
    printf("%s loaded\n", srcFileName);
    SImageData destImage;
    BlurImage(srcImage, destImage, xblursigma, yblursigma, xblursize, yblursize);
    if (SaveImage(destFileName, destImage))
      printf("Blurred image saved as %s\n", destFileName);
    else
    {
      printf("Could not save blurred image as %s\n", destFileName);
      WaitForEnter();
      return 1;
    }
  }
  else
  {
    printf("could not read 24 bit bmp file %s\n\n", srcFileName);
    WaitForEnter();
    return 1;
  }
  return 0;
}
</syntaxhighlight>

|}

{| class="wikitable mw-collapsible mw-collapsed"
! Linux source - Gassusan Blur Filter Header (Linux cannot use Windows API, replicated the required structs. Ref: MSDN [https://msdn.microsoft.com/en-us/library/windows/desktop/dd183374(v=vs.85).aspx 1][https://msdn.microsoft.com/en-us/library/windows/desktop/dd183376(v=vs.85).aspx 2])
|-
|
<syntaxhighlight lang="cpp">
#pragma once

// for Linux platform, please make sure the size of data type is correct for BMP spec.
// if you use this on Windows or other platforms, please pay attention to this.
typedef int LONG;
typedef unsigned char BYTE;
typedef unsigned int DWORD;
typedef unsigned short WORD;

// __attribute__((packed)) on non-Intel architecture may cause some unexpected errors!

typedef struct tagBITMAPFILEHEADER
{
    WORD    bfType;             // 2  /* File type */
    DWORD   bfSize;             // 4  /* File size in bytes */
    WORD    bfReserved1;        // 2
    WORD    bfReserved2;        // 2
    DWORD   bfOffBits;          // 4 /* Offset to image data, bytes */
} __attribute__((packed)) BITMAPFILEHEADER;

typedef struct tagBITMAPINFOHEADER
{
    DWORD    biSize;            // 4 /* Header size in bytes */
    LONG     biWidth;           // 4 /* Width of image */
    LONG     biHeight;          // 4 /* Height of image */
    WORD     biPlanes;          // 2 /* Number of colour planes */
    WORD     biBitCount;        // 2 /* Bits per pixel */
    DWORD    biCompression;     // 4 /* Compression type */
    DWORD    biSizeImage;       // 4 /* Image size in bytes */
    LONG     biXPelsPerMeter;   // 4
    LONG     biYPelsPerMeter;   // 4 /* Pixels per meter */
    DWORD    biClrUsed;         // 4 /* Number of colours */
    DWORD    biClrImportant;    // 4 /* Important colours */
} __attribute__((packed)) BITMAPINFOHEADER;
</syntaxhighlight>

|}

====Windows====
To compile and run the program:
# Set-up an empty Visual C++ - Visual Studio project.
# Save [http://matrix.senecac.on.ca/~cpaul12/cinque_terre.bmp this] image and place it in your projects directory.
# Copy the Windows version of the main source code above and paste it into a [your chosen file name].cpp file.
# Go into you Debug properties of your project.
# Add four (4) values into the Debugging -> Command Arguments (outlined below)
# Run in Release x64
The command line arguments are structured as follows:
 [input image filename].bmp [output image filename].bmp [x - sigma value] [y - sigmea value] => cinque_terre.bmp cinque_terre_BLURRED.bmp 3.0 3.0

====Linux====
To compile and run the program:
# Navigate to the directory you want to run the program in.
# Save [http://matrix.senecac.on.ca/~cpaul12/cinque_terre.bmp this] image and place it directory you will be running the program from. 
# Copy the Linux version of the main source code above and paste it into a [your chosen file name].cpp file.
# Copy the Linux version of the header source code above and paste it into a file named windows.h.
Compile the binaries using the following command:
 g++ -O2 -std=c++0x -Wall -pedantic [your chosen file name].cpp -o gblur
The command line arguments are structured as follows:
 [input image filename].bmp [output image filename].bmp [x - sigma value] [y - sigmea value]
Run the compiled program with the required arguments
 ./gblur cinque_terre.bmp cinque_terre_BLURRED.bmp 3.0 3.0

====Mac OS X====
To compile and run the program:
# Navigate to the directory you want to run the program in.
# Save [http://matrix.senecac.on.ca/~cpaul12/cinque_terre.bmp this] image and place it directory you will be running the program from. 
# Copy the Linux version of the main source code above and paste it into a [your chosen file name].cpp file.
# Copy the Linux version of the header source code above and paste it into a file named windows.h.
Compile the binaries using the following command:
 clang++ -O2 -std=c++0x -Wall -pedantic [your chosen file name].cpp -o gblur
The command line arguments are structured as follows:
 [input image filename].bmp [output image filename].bmp [x - sigma value] [y - sigmea value]
Run the compiled program with the required arguments
 ./gblur cinque_terre.bmp cinque_terre_BLURRED.bmp 3.0 3.0

===Analysis===

 Flat profile:
 
 Each sample counts as 0.01 seconds.
   %   cumulative   self              self     total
  time   seconds   seconds    calls  ns/call  ns/call  name
  61.38      3.37     3.37                             BlurImage(SImageData const&, SImageData&, float, float, unsigned int, unsigned int)
  38.62      5.49     2.12 172032000    12.32    12.32  GetPixelOrBlack(SImageData const&, int, int)
   0.00      5.49     0.00      126     0.00     0.00  Gaussian(float, float)
   0.00      5.49     0.00       42     0.00     0.00  GaussianSimpsonIntegration(float, float, float)
   0.00      5.49     0.00       12     0.00     0.00  void std::vector<float, std::allocator<float> >::_M_insert_aux<float const&>(__gnu_cxx::__normal_iterator<float*, std::vector<float, std::allocator<float> > >, float const&&&)
   0.00      5.49     0.00        3     0.00     0.00  std::vector<unsigned char, std::allocator<unsigned char> >::_M_default_append(unsigned int)
   0.00      5.49     0.00        2     0.00     0.00  GaussianKernelIntegrals(float, int)
   0.00      5.49     0.00        1     0.00     0.00  _GLOBAL__sub_I__Z12WaitForEnterv

 Call graph:
 
 
 granularity: each sample hit covers 4 byte(s) for 0.18% of 5.49 seconds
 
 index % time    self  children    called     name
                                                 <spontaneous>
 [1]    100.0    3.37    2.12                 BlurImage(SImageData const&, SImageData&, float, float, unsigned int, unsigned int) [1]
                 2.12    0.00 172032000/172032000     GetPixelOrBlack(SImageData const&, int, int) [2]
                 0.00    0.00       2/2           GaussianKernelIntegrals(float, int) [11]
                 0.00    0.00       2/3           std::vector<unsigned char, std::allocator<unsigned char> >::_M_default_append(unsigned int) [10]
 -----------------------------------------------
                 2.12    0.00 172032000/172032000     BlurImage(SImageData const&, SImageData&, float, float, unsigned int, unsigned int) [1]
 [2]     38.6    2.12    0.00 172032000         GetPixelOrBlack(SImageData const&, int, int) [2]
 -----------------------------------------------
                 0.00    0.00     126/126         GaussianSimpsonIntegration(float, float, float) [8]
 [7]      0.0    0.00    0.00     126         Gaussian(float, float) [7]
 -----------------------------------------------
                 0.00    0.00      42/42          GaussianKernelIntegrals(float, int) [11]
 [8]      0.0    0.00    0.00      42         GaussianSimpsonIntegration(float, float, float) [8]
                 0.00    0.00     126/126         Gaussian(float, float) [7]
 -----------------------------------------------
                 0.00    0.00      12/12          GaussianKernelIntegrals(float, int) [11]
 [9]      0.0    0.00    0.00      12         void std::vector<float, std::allocator<float> >::_M_insert_aux<float const&>(__gnu_cxx::__normal_iterator<float*, std::vector<float, std::allocator<float> > >, float const&&&) [9]
 -----------------------------------------------
                 0.00    0.00       1/3           LoadImage(char const*, SImageData&) [15]
                 0.00    0.00       2/3           BlurImage(SImageData const&, SImageData&, float, float, unsigned int, unsigned int) [1]
 [10]     0.0    0.00    0.00       3         std::vector<unsigned char, std::allocator<unsigned char> >::_M_default_append(unsigned int) [10]
 -----------------------------------------------
                 0.00    0.00       2/2           BlurImage(SImageData const&, SImageData&, float, float, unsigned int, unsigned int) [1]
 [11]     0.0    0.00    0.00       2         GaussianKernelIntegrals(float, int) [11]
                 0.00    0.00      42/42          GaussianSimpsonIntegration(float, float, float) [8]
                 0.00    0.00      12/12          void std::vector<float, std::allocator<float> >::_M_insert_aux<float const&>(__gnu_cxx::__normal_iterator<float*, std::vector<float, std::allocator<float> > >, float const&&&) [9]
 -----------------------------------------------
                 0.00    0.00       1/1           __do_global_ctors_aux [18]
 [12]     0.0    0.00    0.00       1         _GLOBAL__sub_I__Z12WaitForEnterv [12]
 -----------------------------------------------
 
 Index by function name
 
   [12] _GLOBAL__sub_I__Z12WaitForEnterv (gaussian.cpp) [8] GaussianSimpsonIntegration(float, float, float) [9] void std::vector<float, std::allocator<float> >::_M_insert_aux<float const&>(__gnu_cxx::__normal_iterator<float*, std::vector<float, std::allocator<float> > >, float const&&&)
    [2] GetPixelOrBlack(SImageData const&, int, int) [7] Gaussian(float, float) [10] std::vector<unsigned char, std::allocator<unsigned char> >::_M_default_append(unsigned int)
   [11] GaussianKernelIntegrals(float, int) [1] BlurImage(SImageData const&, SImageData&, float, float, unsigned int, unsigned int)

=== Observations ===

The program does not take a long time to run, but run-time depends on the values of sigma (&sigma;) and the kernel block size. If you specify larger values for these parameters the runtime increases<br/>
significantly. The code is straight forward and parallelization should be easy to implement.

===Hotspot===
{| class="wikitable mw-collapsible mw-collapsed"
! Culptit - BlurImage( ... )
|-
|
<syntaxhighlight lang="cpp">
void BlurImage(const SImageData& srcImage, SImageData &destImage, float xblursigma, float yblursigma, unsigned int xblursize, unsigned int yblursize)
{

  // ...

  {
    auto row = GaussianKernelIntegrals(xblursigma, xblursize);

    // ...

    for (int y = 0; y < tmpImage.m_height; ++y)
    {
      for (int x = 0; x < tmpImage.m_width; ++x)
      {

        // ...

        for (unsigned int i = 0; i < row.size(); ++i)
        {
          const uint8_t *pixel = GetPixelOrBlack(srcImage, x + startOffset + i, y);

          // ...

        }

        // ...

      }
    }
  }

  {
    auto row = GaussianKernelIntegrals(yblursigma, yblursize);

    // ...

    for (int y = 0; y < destImage.m_height; ++y)
    {
      for (int x = 0; x < destImage.m_width; ++x)
      {

        // ...

        for (unsigned int i = 0; i < row.size(); ++i)
        {
          const uint8_t *pixel = GetPixelOrBlack(tmpImage, x, y + startOffset + i);

          // ...

        }

        // ...

      }
    }
  }
}
</syntaxhighlight>

|}
According to the Flat profile, 61.38% of the time is spent in the BlurImage function. This function contains a set of triply-nested for-loops which equates to a run-time of T(n) is O(n<sup>3</sup>).<br/>
Referring to the Call graph we can see more supporting evidence that this application spends nearly all of its execution time in the BlurImage function. Therefore this function is the prime candidate<br/>
for parallelization using CUDA. The sigma (&sigma;) and the kernel size can be increased in order to make the computation stressful on the GPU to get a significant benchmark.

= Assignment 2 - Parallelize =

{| class="wikitable mw-collapsible mw-collapsed"
! Unoptimized - BlurImage( ... )
|-
|
<syntaxhighlight lang="cpp">
#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <array>
#include <vector>
#include <functional>
#include <windows.h>  // for bitmap headers.
#include <algorithm>
#include <chrono>

#include <cuda_runtime.h>
// to remove intellisense highlighting
#include <device_launch_parameters.h>
#include <device_functions.h>

//#ifdef __CUDACC__
//#if __CUDACC_VER_MAJOR__ == 1
//const int ntpb = 512;
//#else
//const int ntpb = 1024;
//#endif
//#endif
const int ntpb = 1024;
const int STREAMS = 32;

void check(cudaError_t error) {
	if (error != cudaSuccess) {
		throw std::exception(cudaGetErrorString(error));
	}
}

struct SImageData
{
	SImageData()
		: m_width(0)
		, m_height(0)
	{ }

	long m_width;
	long m_height;
	long m_pitch;
	std::vector<uint8_t> m_pixels;
};

void WaitForEnter()
{
	char c;
	std::cout << "Press Enter key to exit ... ";
	std::cin.get(c);
}

bool LoadImage(const char *fileName, SImageData& imageData)
{
	// open the file if we can
	FILE *file;
	file = fopen(fileName, "rb");
	if (!file)
		return false;

	// read the headers if we can
	BITMAPFILEHEADER header;
	BITMAPINFOHEADER infoHeader;
	if (fread(&header, sizeof(header), 1, file) != 1 ||
		fread(&infoHeader, sizeof(infoHeader), 1, file) != 1 ||
		header.bfType != 0x4D42 || infoHeader.biBitCount != 24)
	{
		fclose(file);
		return false;
	}

	// read in our pixel data if we can. Note that it's in BGR order, and width is padded to the next power of 4
	imageData.m_pixels.resize(infoHeader.biSizeImage);
	fseek(file, header.bfOffBits, SEEK_SET);
	if (fread(&imageData.m_pixels[0], imageData.m_pixels.size(), 1, file) != 1)
	{
		fclose(file);
		return false;
	}

	imageData.m_width = infoHeader.biWidth;
	imageData.m_height = infoHeader.biHeight;

	imageData.m_pitch = imageData.m_width * 3;
	if (imageData.m_pitch & 3)
	{
		imageData.m_pitch &= ~3;
		imageData.m_pitch += 4;
	}

	fclose(file);
	return true;
}

bool SaveImage(const char *fileName, const SImageData &image)
{
	// open the file if we can
	FILE *file;
	file = fopen(fileName, "wb");
	if (!file)
		return false;

	// make the header info
	BITMAPFILEHEADER header;
	BITMAPINFOHEADER infoHeader;

	header.bfType = 0x4D42;
	header.bfReserved1 = 0;
	header.bfReserved2 = 0;
	header.bfOffBits = 54;

	infoHeader.biSize = 40;
	infoHeader.biWidth = image.m_width;
	infoHeader.biHeight = image.m_height;
	infoHeader.biPlanes = 1;
	infoHeader.biBitCount = 24;
	infoHeader.biCompression = 0;
	infoHeader.biSizeImage = image.m_pixels.size();
	infoHeader.biXPelsPerMeter = 0;
	infoHeader.biYPelsPerMeter = 0;
	infoHeader.biClrUsed = 0;
	infoHeader.biClrImportant = 0;

	header.bfSize = infoHeader.biSizeImage + header.bfOffBits;

	// write the data and close the file
	fwrite(&header, sizeof(header), 1, file);
	fwrite(&infoHeader, sizeof(infoHeader), 1, file);
	fwrite(&image.m_pixels[0], infoHeader.biSizeImage, 1, file);
	fclose(file);
	return true;
}

int PixelsNeededForSigma(float sigma)
{
	// returns the number of pixels needed to represent a gaussian kernal that has values
	// down to the threshold amount.  A gaussian function technically has values everywhere
	// on the image, but the threshold lets us cut it off where the pixels contribute to
	// only small amounts that aren't as noticeable.
	const float c_threshold = 0.005f; // 0.5%
	return int(floor(1.0f + 2.0f * sqrtf(-2.0f * sigma * sigma * log(c_threshold)))) + 1;
}

float Gaussian(float sigma, float x)
{
	return expf(-(x*x) / (2.0f * sigma*sigma));
}

float GaussianSimpsonIntegration(float sigma, float a, float b)
{
	return
		((b - a) / 6.0f) *
		(Gaussian(sigma, a) + 4.0f * Gaussian(sigma, (a + b) / 2.0f) + Gaussian(sigma, b));
}

std::vector<float> GaussianKernelIntegrals(float sigma, int taps)
{
	std::vector<float> ret;
	float total = 0.0f;
	for (int i = 0; i < taps; ++i)
	{
		float x = float(i) - float(taps / 2);
		float value = GaussianSimpsonIntegration(sigma, x - 0.5f, x + 0.5f);
		ret.push_back(value);
		total += value;
	}
	// normalize it
	for (unsigned int i = 0; i < ret.size(); ++i)
	{
		ret[i] /= total;
	}
	return ret;
}

struct BGRPixel {
	float b;
	float g;
	float r;
};

__global__ void blur_kernel(BGRPixel* imageIn, BGRPixel* imageOut, float* blur, int n_blur, int x, int start, int jump) {
	int idx = blockDim.x*blockIdx.x + threadIdx.x;	// Location on the row

	if (idx < x) {
		int id = start + idx;
		int bstart = id - (n_blur / 2)*jump;

		BGRPixel pixel{ 0.0f, 0.0f, 0.0f };

		for (int i = 0; i < n_blur; ++i) {
			int bid = bstart + i*jump;
			float iblur = blur[i];

			pixel.b += imageIn[bid].b * iblur;
			pixel.g += imageIn[bid].g * iblur;
			pixel.r += imageIn[bid].r * iblur;
		}

		imageOut[id].b = pixel.b;
		imageOut[id].g = pixel.g;
		imageOut[id].r = pixel.r;
	}
}

void BlurImage(const SImageData& srcImage, SImageData &destImage, float xblursigma, float yblursigma, unsigned int xblursize, unsigned int yblursize)
{
	int xImage = srcImage.m_width;							// Width of image
	int yImage = srcImage.m_height;							// Height of image
	int imageSize = xImage*yImage;

	int xPadded = xImage + (xblursize - 1);					// Width including padding
	int yPadded = yImage + (yblursize - 1);					// Height including padding
	int paddedSize = xPadded*yPadded;

	int xPad = xblursize / 2;								// Number of padding columns on each side
	int yPad = yblursize / 2;
	int padOffset = xPadded*yPad + xPad;							// Offset to first pixel in padded image

	float* pinnedImage = nullptr;
	BGRPixel* d_padded1 = nullptr;
	BGRPixel* d_padded2 = nullptr;

	float*	d_xblur = nullptr;					// XBlur integrals
	int		n_xblur;							// N

	float*	d_yblur = nullptr;					// YBlur integrals
	int		n_yblur;							// N

	// Allocate memory for host and device
	check(cudaHostAlloc((void**)&pinnedImage, 3 * imageSize * sizeof(float), 0));
	check(cudaMalloc((void**)&d_padded1, paddedSize * sizeof(BGRPixel)));
	check(cudaMalloc((void**)&d_padded2, paddedSize * sizeof(BGRPixel)));

	// Copy image to pinned memory
	for (int i = 0; i < 3 * imageSize; ++i) {
		pinnedImage[i] = (float)srcImage.m_pixels[i];
	}

	// Allocate and assign intergrals
	{
		auto row_blur = GaussianKernelIntegrals(xblursigma, xblursize);
		auto col_blur = GaussianKernelIntegrals(yblursigma, yblursize);

		// ROW
		n_xblur = row_blur.size();
		check(cudaMalloc((void**)&d_xblur, n_xblur * sizeof(float)));
		check(cudaMemcpy(d_xblur, row_blur.data(), n_xblur * sizeof(float), cudaMemcpyHostToDevice));

		// COLUMN
		n_yblur = col_blur.size();
		check(cudaMalloc((void**)&d_yblur, n_yblur * sizeof(float)));
		check(cudaMemcpy(d_yblur, col_blur.data(), n_yblur * sizeof(float), cudaMemcpyHostToDevice));
	}


	cudaStream_t stream[STREAMS];

	int nblks = (xImage + (ntpb - 1)) / ntpb;

	for (int i = 0; i < STREAMS; ++i) {
		check(cudaStreamCreate(&stream[i]));
	}

	for (int i = 0; i < yImage;) {
		for (int j = 0; j < STREAMS && i < yImage; ++j, ++i) {
			cudaMemcpyAsync(d_padded1 + padOffset + i*xPadded, pinnedImage + (3 * i*xImage), 3 * xImage * sizeof(float), cudaMemcpyHostToDevice, stream[j]);
		}
	}

	for (int i = 0; i < yImage;) {
		for (int j = 0; j < STREAMS && i < yImage; ++j, ++i) {
			blur_kernel << <nblks, ntpb, 0, stream[j] >> > (d_padded1, d_padded2, d_xblur, n_xblur, xImage, padOffset + i*xPadded, 1);
		}
	}

	for (int i = 0; i < yImage;) {
		for (int j = 0; j < STREAMS && i < yImage; ++j, ++i) {
			blur_kernel << <nblks, ntpb, 0, stream[j] >> > (d_padded2, d_padded1, d_yblur, n_yblur, xImage, padOffset + i*xPadded, xPadded);
		}
	}

	for (int i = 0; i < yImage;) {
		for (int j = 0; j < STREAMS && i < yImage; ++j, ++i) {
			check(cudaMemcpyAsync(pinnedImage + (3 * i*xImage), d_padded1 + padOffset + i*xPadded, xImage * sizeof(BGRPixel), cudaMemcpyDeviceToHost, stream[j]));
		}
	}

	for (int i = 0; i < STREAMS; ++i) {
		check(cudaStreamSynchronize(stream[i]));
		check(cudaStreamDestroy(stream[i]));
	}

	destImage.m_width = srcImage.m_width;
	destImage.m_height = srcImage.m_height;
	destImage.m_pitch = srcImage.m_pitch;
	destImage.m_pixels.resize(srcImage.m_pixels.size());

	for (int i = 0; i < 3 * imageSize; i++) {
		destImage.m_pixels[i] = (uint8_t)pinnedImage[i];
	};

	check(cudaFree(d_xblur));
	check(cudaFree(d_yblur));

	check(cudaFreeHost(pinnedImage));
	check(cudaFree(d_padded1));
	check(cudaFree(d_padded2));

	check(cudaDeviceReset());
}

int main(int argc, char **argv)
{
	float xblursigma, yblursigma;

	bool showUsage = argc < 5 ||
		(sscanf(argv[3], "%f", &xblursigma) != 1) ||
		(sscanf(argv[4], "%f", &yblursigma) != 1);

	char *srcFileName = argv[1];
	char *destFileName = argv[2];

	if (showUsage)
	{
		printf("Usage: <source> <dest> <xblur> <yblur>\nBlur values are sigma\n\n");
		WaitForEnter();
		return 1;
	}

	// calculate pixel sizes, and make sure they are odd 
	int xblursize = PixelsNeededForSigma(xblursigma) | 1;
	int yblursize = PixelsNeededForSigma(yblursigma) | 1;

	printf("Attempting to blur a 24 bit image.\n");
	printf("  Source=%s\n  Dest=%s\n  blur=[%0.1f, %0.1f] px=[%d,%d]\n\n", srcFileName, destFileName, xblursigma, yblursigma, xblursize, yblursize);

	SImageData srcImage;
	if (LoadImage(srcFileName, srcImage))
	{
		printf("%s loaded\n", srcFileName);
		SImageData destImage;

		auto t1 = std::chrono::high_resolution_clock::now();
		BlurImage(srcImage, destImage, xblursigma, yblursigma, xblursize, yblursize);
		auto t2 = std::chrono::high_resolution_clock::now();

		std::cout << "BlurImage time: " << std::chrono::duration_cast<std::chrono::microseconds>(t2 - t1).count() << "us" << std::endl;


		if (SaveImage(destFileName, destImage))
			printf("Blurred image saved as %s\n", destFileName);
		else
		{
			printf("Could not save blurred image as %s\n", destFileName);
			WaitForEnter();
			return 1;
		}
	}
	else
	{
		printf("could not read 24 bit bmp file %s\n\n", srcFileName);
		WaitForEnter();
		return 1;
	}
	return 0;
}
</syntaxhighlight>

|}

== Objectives ==
The main objective was to not change the main function.  This objective was met, although code had to be added for profiling.
 
== Steps ==
=== Host Memory Management ===
In the original program a bmp is loaded into an vector of uint8_t.  This is not ideal for CUDA, therefore an array of pinned memory was allocated.  This array contains the same amount of elements but stores them as a structure, "BGRPixel" which is three contiguous floats.  The vector is then transferred over to pinned memory.  
=== Device Memory Management ===
To get a blurred pixel the surrounding pixels must be sampled, in some cases this means sampling pixels outside the bounds of the image.  In the original, a simple if check was used to determine if the pixel was outside the bounds or the image, if it was a black pixel was returned instead.  This if statement most likely would have caused massive thread divergence in a kernel, therefore the images created in device memory featured additional padding of black pixels to compensate for this.  Two such images were created, one to perform horizontal blur and one to perform vertical blur.  Other small device arrays were also needed to store the Gaussian integrals that are used to produce the blurring effect.
=== Host to Device ===
To copy the pinned image to the device an array of streams was used to asynchronously copy each row of the image over.  Doing so allowed the rows to be easily copied over while avoiding infringing on the extra padding pixels.
=== Kernels ===
First one image is blurred horizontally.  One image is used as a reference while the other is written to.  Kernels are also executed using the streams, so that each stream will blur a single row at a time.  After the horizontal blur is finished the vertical blur is launched in the same manner, except that the previously written to image is used as a reference while the previous reference is now written to.  The two blur are able to use the same kernel due to the fact that the pixel sampling technique works by iterating through pixels because of this the step size can be changed to sample across the row or down the column. 
=== Device to Host ===
After that is done the image is copied back using the streams in the same way it was copied over.

== Results ==
[[File:uvso2.png]]
[[File:usession.png]]
[[File:ktimes.png]]

== Output Images ==
[http://imgur.com/a/CtMOc Image Gallery]

= Assignment 3 - Optimize =