Parallelisum

Table of Contents

1. Dependence

sudo apt install openmpi-bin
sudo apt install libopenmpi-dev

2. Docker

2.0.1. old note

comands expains
docker images 查看容器
docker pull nginx 1 新增
docker run -d -p 80:80 nginx 2 开始，id， 后台
docker exec -it xxxxxx bash 前台进入，
docker commit xxxxxx newname 生成新容器
docker kill -s KILL xxxxxx 关闭

2.0.2. commands

  • docker pull NAME
  • docker images
  • docker images -a
  • docker run NAME
  • docker run NAME:VERSION
  • docker run -d NAME
  • docker run -p6000:6379 -d redis
  • docker run -p6000:6379 -d –name redis-older redis
  • docker exec -it ID /bin/bash
  • docker exec -it NAME /bin/bash
  • docker ps
  • docker ps -a2
  • docker start ID
  • docker stop ID
  • docker logs ID

2.0.3. discripation

fast delivery
easy deploy and scale
run more workloads
easy management
lightweight image
No guest OS
  • Disadvanage: can not change kernel
  • Less secure than VM
  • Docker Registry hold Docker Images
  • Docker Images create Docker Container(run as instance)
  • Docker Container runs applications
  • the shared levels are readonly, and containers communicate with sockets or Restful API

2.0.4. delete

  • delete docker

docker ps -a // get dockerid or dockername docker stop Did/Dname docker rm Did/Dname

  • delete image docker images // get image id or image name docker rmi Iid/Iname perhaps some none name image should also be rm
  • sudo docker rm $(sudo docker ps -aq)

3. Singularity

3.1. build [sandbox]

build  target source
source can be singularityfile, dockerhubname, online resource,  sandbox simg file, singularity sif file

sudo singularity build singularityfile.sif singularityfile
sudo singularity build singularity.sif docker://dockerhubname


sudo singularity build --sandbox singularityfile.simg singularityfile
sudo singularity build --sandbox singularity.simg docker://dockerhubname

sudo singularity shell  singularityfile.simg

sudo singularity shell --writable singularityfile.simg

sudo singularity shell --bind /home/silin/go:/home/go  -w --nv centos-7.simg

4. C/C++ with OpenMP

4.1. src compile config

C-h v : org-babel-C-compiler change gcc to gcc -fopenmp

4.2. useful libary functions

4.2.1. ompgetthreadnum

int main(int argc, char* argv[])
{
#pragma omp parallel
  {
    printf("omp_get_thread_num:  %d\n",  omp_get_thread_num());
  }
}

omp_get_thread_num:  0
omp_get_thread_num:  5
omp_get_thread_num:  3
omp_get_thread_num:  2
omp_get_thread_num:  7
omp_get_thread_num:  6
omp_get_thread_num:  4
omp_get_thread_num:  1

4.2.2. ompgetnumprocs

int main(int argc, char* argv[])
{
  printf("omp_get_num_procs:  %d\n",  omp_get_num_procs());
  return 0;
}

omp_get_num_procs:  8

4.2.3. ompgetnumthreads

int main(int argc, char* argv[])
{
#pragma omp parallel
  printf("omp_get_num_threads:  %d\n",  omp_get_num_threads());
#pragma omp parallel
#pragma omp master
  {
    printf("omp_get_num_threads:  %d\n",  omp_get_num_threads());
  }
  return 0;
}

omp_get_num_threads:  8
omp_get_num_threads:  8
omp_get_num_threads:  8
omp_get_num_threads:  8
omp_get_num_threads:  8
omp_get_num_threads:  8
omp_get_num_threads:  8
omp_get_num_threads:  8
omp_get_num_threads:  8

4.2.4. ompsetnumthreads

int main()
{
  omp_set_num_threads(4);
  printf("%d\n", omp_get_num_threads( ));
#pragma omp parallel
#pragma omp master
  {
    printf("%d\n", omp_get_num_threads( ));
  }
}


1
4

4.2.5. ompgetwtime

4.2.6. ompgetwtick

4.2.7. ompinitlock

4.2.8. ompgetlock

4.2.9. ompunsetlock

4.2.10. omptestlock

4.2.11. ompdestroylock

4.3. Constructor

parallel
for
parallel for
sections
parallel sections
critical
single
barrier
atomic
master
ordered
threadprivate

4.4. Subconstructor

parivate
firstprivate
lastprivate
reduce
nowait
numthreads
schedule
shared
ordered
copyprivate
copyin
default

4.5. hello world

int main(int argc, char* argv[])
{
#pragma omp parallel
  {
    printf("Hello world from thread %d\n",  omp_get_thread_num());
  }
}

Hello world from thread 0
Hello world from thread 1
Hello world from thread 4
Hello world from thread 3
Hello world from thread 5
Hello world from thread 7
Hello world from thread 6
Hello world from thread 2

4.6. numthreads

int main(int argc, char* argv[])
{
#pragma omp parallel num_threads(6)
  {
    printf("omp_get_num_threads:  %d\n",  omp_get_num_threads());
  }
  return 0;
}

omp_get_num_threads:  6
omp_get_num_threads:  6
omp_get_num_threads:  6
omp_get_num_threads:  6
omp_get_num_threads:  6
omp_get_num_threads:  6

4.7. for

only works in one thread 

int main(int argc, char* argv[])
{
  int j = 0;
#pragma omp  for
  for (j = 0; j < 8; j++){
    printf("j = %d, ThreadID = %d\n", j, omp_get_thread_num());
  }
  return 0;
}

j = 0, ThreadID = 0
j = 1, ThreadID = 0
j = 2, ThreadID = 0
j = 3, ThreadID = 0
j = 4, ThreadID = 0
j = 5, ThreadID = 0
j = 6, ThreadID = 0
j = 7, ThreadID = 0

4.8. ordered

int main(int argc, char* argv[])
{
  int j = 0;
#pragma omp parallel for ordered
  for (j = 0; j < 2; j++){
#pragma omp ordered
    {
      printf("01 ordered j = %d, ThreadID = %d\n", j, omp_get_thread_num());
    }
#pragma omp ordered
    {
      printf("02 ordered j = %d, ThreadID = %d\n", j, omp_get_thread_num());
    }
#pragma omp ordered
    {
      printf("03 ordered j = %d, ThreadID = %d\n", j, omp_get_thread_num());
    }
  }
  return 0;
}

01 ordered j = 0, ThreadID = 0
02 ordered j = 0, ThreadID = 0
03 ordered j = 0, ThreadID = 0
01 ordered j = 1, ThreadID = 1
02 ordered j = 1, ThreadID = 1
03 ordered j = 1, ThreadID = 1

4.9. parallel for

for should work with parallel 

int main(int argc, char* argv[])
{
  int j = 0;
#pragma omp parallel for
  for (j = 0; j < 8; j++){
    printf("j = %d, ThreadID = %d\n", j, omp_get_thread_num());
  }
  return 0;
}

j = 0, ThreadID = 0
j = 1, ThreadID = 1
j = 2, ThreadID = 2
j = 6, ThreadID = 6
j = 5, ThreadID = 5
j = 7, ThreadID = 7
j = 3, ThreadID = 3
j = 4, ThreadID = 4

int main(int argc, char* argv[])
{
  int j = 0;
#pragma omp parallel  for
  for (j = 0; j < 8; j++){
    printf("j = %d, ThreadID = %d\n", j, omp_get_thread_num());
  }
  return 0;
}

j = 7, ThreadID = 7
j = 3, ThreadID = 3
j = 6, ThreadID = 6
j = 2, ThreadID = 2
j = 4, ThreadID = 4
j = 0, ThreadID = 0
j = 1, ThreadID = 1
j = 5, ThreadID = 5

and this can be rewrite as following, for in parallel, but can be multiple for block 

int main(int argc, char* argv[])
{
  int j = 0;
#pragma omp parallel num_threads(4)
  //   #pragma omp parallel  // EQUAL TO   #pragma omp parallel num_threads(8)
  {
#pragma omp  for
    for (j = 0; j <8; j++)
      {
        printf("j = %d, ThreadID = %d\n", j, omp_get_thread_num());
      }
  }
  return 0;
}

j = 0, ThreadID = 0
j = 1, ThreadID = 0
j = 6, ThreadID = 3
j = 7, ThreadID = 3
j = 2, ThreadID = 1
j = 3, ThreadID = 1
j = 4, ThreadID = 2
j = 5, ThreadID = 2

4.10. parallel while

for should work with parallel 

int main(int argc, char* argv[])
{
  int j = 0;
#pragma omp parallel num_threads(8) shared(j)
  while (j < 8){
    printf("j = %d, ThreadID = %d\n", j, omp_get_thread_num());
    j++;
  }
  return 0;
}

j = 0, ThreadID = 0
j = 0, ThreadID = 7
j = 0, ThreadID = 3
j = 2, ThreadID = 3
j = 3, ThreadID = 3
j = 4, ThreadID = 3
j = 5, ThreadID = 3
j = 6, ThreadID = 3
j = 7, ThreadID = 3
j = 0, ThreadID = 6
j = 0, ThreadID = 4
j = 0, ThreadID = 1
j = 0, ThreadID = 5
j = 1, ThreadID = 0
j = 0, ThreadID = 2

4.11. sections and section

void main(int argc, char *argv)
{
#pragma omp parallel sections
  {
#pragma omp section
    printf("section 1 ThreadId = %d\n", omp_get_thread_num());
#pragma omp section
    printf("section 2 ThreadId = %d\n", omp_get_thread_num());
#pragma omp section
    printf("section 3 ThreadId = %d\n", omp_get_thread_num());
#pragma omp section
    printf("section 4 ThreadId = %d\n", omp_get_thread_num());
  }
}

section 4 ThreadId = 0
section 3 ThreadId = 5
section 2 ThreadId = 3
section 1 ThreadId = 6

another form, parallel and sections can also be separated, and with mulitple sections block but each sections are not paralleled, but concatenated 

void main(int argc, char *argv)
{
#pragma omp parallel
  {
#pragma omp sections
    {
#pragma omp section
      printf("section 1 ThreadId = %d\n", omp_get_thread_num());
#pragma omp section
      printf("section 2 ThreadId = %d\n", omp_get_thread_num());
#pragma omp section
      printf("section 3 ThreadId = %d\n", omp_get_thread_num());
    }
#pragma omp sections
    {
#pragma omp section
      printf("section 1 ThreadId = %d\n", omp_get_thread_num());
#pragma omp section
      printf("section 2 ThreadId = %d\n", omp_get_thread_num());
#pragma omp section
      printf("section 3 ThreadId = %d\n", omp_get_thread_num());
    }
  }
}

section 1 ThreadId = 3
section 2 ThreadId = 0
section 3 ThreadId = 4
section 2 ThreadId = 0
section 1 ThreadId = 1
section 3 ThreadId = 6

4.12. master

void main(int argc, char *argv)
{
#pragma omp parallel 
#pragma omp master
  {
    printf("I am the master\n");
  }
}

I am the master

4.13. private

after the block of private for, there are some wired to execute some out of parallelisum 

void main(int argc, char *argv)
{
  int k = 100;
#pragma omp parallel for private(k)
  for ( k=0; k < 8; k++)
    {
      printf("k=%d\n", k);
    }
  printf("kkk = %d\n", k);
#pragma omp parallel sections
  {
#pragma omp section
    printf("kkk = %d\n", k);
  }
}

k=6
k=7
k=3
k=2
k=0
k=4
k=5
k=1
kkk = 100
kkk = 100

4.14. firstprivate

take the vaiable to Parallelisum, but not influence back 

void main(int argc, char *argv)
{
  int k = 100;
#pragma omp parallel for firstprivate(k)
  for (int i=0; i < 8; i++)
    {
      k += i;
      printf("k=%d\n", k);
    }
  printf("k out of parall = %d\n", k);
}

k=103
k=107
k=100
k=104
k=106
k=102
k=105
k=101
k out of parall = 100

4.15. lastprivate

take the vaiable to Parallelisum, and influence back 

void main(int argc, char *argv)
{
  int k = 100;
#pragma omp parallel for firstprivate(k) lastprivate(k)
  for (int i=0; i < 8; i++)
    {
      k += i;
      printf("k=%d\n", k);
    }
  printf("k out of parall = %d\n", k);
}

k=100
k=107
k=106
k=102
k=101
k=105
k=103
k=104
k out of parall = 107

4.16. shared

void main(int argc, char *argv)
{
  int k = 100;
  int i = 1;
#pragma omp parallel for shared(k)
  for ( i=0; i < 8; i++)
    {
      printf("k=%d\n", k);
    }
}

k=100
k=100
k=100
k=100
k=100
k=100
k=100
k=100
k = 100

4.17. reduction

void main(int argc, char *argv)
{
  int sum = 0;
  int i = 0;
#pragma omp parallel for reduction(+:sum)
  for ( i=0; i < 10; i++)
    {
      printf("omp_get_thread_num:  %d\n",  omp_get_thread_num());
      sum += i;
    }
  printf("sum is %d\n", sum);
}

omp_get_thread_num:  0
omp_get_thread_num:  0
omp_get_thread_num:  1
omp_get_thread_num:  1
omp_get_thread_num:  7
omp_get_thread_num:  2
omp_get_thread_num:  5
omp_get_thread_num:  4
omp_get_thread_num:  6
omp_get_thread_num:  3
sum is 45

void main(int argc, char *argv)
{
  int sum = 0;
  int i = 10;
#pragma omp parallel reduction(+:sum)
  {
    printf("omp_get_thread_num:  %d\n",  omp_get_thread_num());
    sum += i;
  }
  printf("sum is %d\n", sum);
}

omp_get_thread_num:  0
omp_get_thread_num:  3
omp_get_thread_num:  4
omp_get_thread_num:  2
omp_get_thread_num:  7
omp_get_thread_num:  6
omp_get_thread_num:  5
omp_get_thread_num:  1
sum is 80

4.18. default(shared)

void main(int argc, char *argv)
{
  int k = 100;
  int i = 1;
#pragma omp parallel for default(shared)
  for ( i=0; i < 8; i++)
    {
      printf("k=%d\n", k);
    }
}

k=100
k=100
k=100
k=100
k=100
k=100
k=100
k=100
i=1

4.19. schedule(static)

all iterations will be equally divied to each thread schedule(static, size): size time iterations will be drived each time 

void main(int argc, char *argv)
{
  int i = 0;
#pragma omp parallel for schedule(static)
  for (i = 0; i < 24 ; i++)
    {
      printf("i=%d, thread_id=%d\n", i, omp_get_thread_num());
    }
}

i=0, thread_id=0
i=14, thread_id=7
i=15, thread_id=7
i=2, thread_id=1
i=12, thread_id=6
i=3, thread_id=1
i=18, thread_id=1
i=8, thread_id=4
i=10, thread_id=5
i=19, thread_id=1
i=9, thread_id=4
i=1, thread_id=0
i=11, thread_id=5
i=16, thread_id=0
i=13, thread_id=6
i=4, thread_id=2
i=6, thread_id=3
i=7, thread_id=3
i=22, thread_id=3
i=23, thread_id=3
i=17, thread_id=0
i=5, thread_id=2
i=20, thread_id=2
i=21, thread_id=2

4.20. schedule(dynamic)

all iterations will be dynamically divied to each thread schedule(dynamic, size): size time iterations will be drived each time 

void main(int argc, char *argv)
{
  int i = 0;
#pragma omp parallel for schedule(dynamic)
  for (i = 0; i < 16 ; i++)
    {
      printf("i=%d, thread_id=%d\n", i, omp_get_thread_num());
    }
}

i=7, thread_id=7
i=8, thread_id=7
i=9, thread_id=7
i=10, thread_id=7
i=11, thread_id=7
i=12, thread_id=7
i=13, thread_id=7
i=14, thread_id=7
i=15, thread_id=7
i=0, thread_id=3
i=6, thread_id=1
i=5, thread_id=5
i=1, thread_id=6
i=2, thread_id=2
i=4, thread_id=0
i=3, thread_id=4

4.21. schedule(guided)

void main(int argc, char *argv)
{
  int i = 0;
#pragma omp parallel for schedule(guided)
  for (i = 0; i < 16 ; i++)
    {
      printf("i=%d, thread_id=%d\n", i, omp_get_thread_num());
    }
}

i=8, thread_id=0
i=11, thread_id=7
i=12, thread_id=7
i=13, thread_id=7
i=14, thread_id=7
i=15, thread_id=7
i=6, thread_id=4
i=7, thread_id=4
i=2, thread_id=2
i=3, thread_id=2
i=4, thread_id=6
i=5, thread_id=6
i=9, thread_id=1
i=10, thread_id=5
i=0, thread_id=3
i=1, thread_id=3

5. C/C++ with mpi

sudo apt install libopenmpi-dev

5.1. src compile config

C-h v : org-babel-C-compiler change gcc to mpicc mpirun –use-hwthread-cpus mpirun –host si-u20:8

5.2. MPICOMMWORLD

#include <stdio.h>
#include <stdlib.h>
#include <mpi.h>
int main(int argc, char* argv[])
{
    MPI_Init(&argc, &argv);
    int my_rank;
    MPI_Comm_rank(MPI_COMM_WORLD, &my_rank);
    printf("I am MPI process %d.\n", my_rank);
    MPI_Finalize();
    return EXIT_SUCCESS;
}

I am MPI process 0.

5.3. hello world of processor

#include <mpi.h>
#include <stdio.h>
int main(int argc, char** argv) {
    MPI_Init(NULL, NULL);
    int world_size;
    MPI_Comm_size(MPI_COMM_WORLD, &world_size);
    int world_rank;
    MPI_Comm_rank(MPI_COMM_WORLD, &world_rank);
    char processor_name[MPI_MAX_PROCESSOR_NAME];
    int name_len;
    MPI_Get_processor_name(processor_name, &name_len);
    printf("Hello world from processor %s, rank %d out of %d processors\n",
           processor_name, world_rank, world_size);

    MPI_Finalize();
}

Hello world from processor silin, rank 0 out of 1 processors

5.4. MPICOMMCREAT

#include <stdio.h>
#include <stdlib.h>
#include <mpi.h>

int main(int argc, char* argv[])
{
  MPI_Init(&argc, &argv);
  printf("\n");

  // Check that the application is run with 6 processes.
  int size;
  MPI_Comm_size(MPI_COMM_WORLD, &size);
  if(size != 6)
    {
      printf("Please run this application with 6 MPI processes.\n");
      MPI_Abort(MPI_COMM_WORLD, EXIT_FAILURE);
    }

  // Get my rank in the global communicator
  int my_rank_global;
  MPI_Comm_rank(MPI_COMM_WORLD, &my_rank_global);

  // Get the group or processes of the default communicator
  MPI_Group world_group;
  MPI_Comm_group(MPI_COMM_WORLD, &world_group);

  // Create the new communicator from that group of processes.
  MPI_Comm local_communicator;

  if(my_rank_global == 0 ||
     my_rank_global == 1 ||
     my_rank_global == 2)
    {
      // Keep MPI processes 0, 1, 2 in a group we will call group A.
      int group_a_ranks[3] = {0, 1, 2};
      MPI_Group group_a;
      MPI_Group_incl(world_group, 3, group_a_ranks, &group_a);
      MPI_Comm_create(MPI_COMM_WORLD, group_a, &local_communicator);
    }
  else if(my_rank_global == 3 ||
          my_rank_global == 4)
    {
      // Keep MPI processes 3 and 4 in a group we will call group B.
      int group_b_ranks[2] = {3, 4};
      MPI_Group group_b;
      MPI_Group_incl(world_group, 2, group_b_ranks, &group_b);
      MPI_Comm_create(MPI_COMM_WORLD, group_b, &local_communicator);
    }
  else
    {
      // Only MPI process 5 remains, without a group
      MPI_Comm_create(MPI_COMM_WORLD, MPI_GROUP_EMPTY, &local_communicator);
    }

  // Check if I got into a new communicator (that is, if I was in a group to begin with)
  if(local_communicator == MPI_COMM_NULL)
    {
      // I am not part of the new communicator, I can't participate to that broadcast.
      printf("MPI process %d was not part of any group, thus did not get into a new communicator.\n", my_rank_global);

      // Let's wait all processes before proceeding to the second phase; Cleaner output.
      MPI_Barrier(MPI_COMM_WORLD);
    }
  else
    {
      // Get my rank local to the new communicator
      int my_rank_local;
      MPI_Comm_rank(local_communicator, &my_rank_local);

      printf("MPI process %d in global communicator has now rank %d in new communicator.\n", my_rank_global, my_rank_local);

      // Let's wait all processes before proceeding to the second phase; Cleaner output.
      MPI_Barrier(MPI_COMM_WORLD);

      int size_local_communicator;
      MPI_Comm_size(local_communicator, &size_local_communicator);

      // The MPI process that got assigned rank 0 in each new communicator will gather all ranks in that communicator and display them
      int global_ranks_in_local_communicator[size_local_communicator];
      MPI_Gather(&my_rank_global,
                 1,
                 MPI_INT,
                 global_ranks_in_local_communicator,
                 1,
                 MPI_INT,
                 0,
                 local_communicator);

      if(my_rank_local == 0)
        {
          printf("MPI processes ");
          for(int i = 0; i < size_local_communicator; i++)
            {
              if(i > 0)
                {
                  printf(" and ");
                }
              printf("%d", global_ranks_in_local_communicator[i]);
            }
          printf(" are in the same new communicator.\n");
        }
    }

  MPI_Finalize();

  return EXIT_SUCCESS;
}


cd ./babel
mpicc -o mpi_comm_create ./mpi_comm_create.c
mpirun --host silin:6 ./mpi_comm_create







MPI process 4 in global communicator has now rank 1 in new communicator.
MPI process 2 in global communicator has now rank 2 in new communicator.
MPI process 0 in global communicator has now rank 0 in new communicator.
MPI process 5 was not part of any group, thus did not get into a new communicator.
MPI process 1 in global communicator has now rank 1 in new communicator.
MPI process 3 in global communicator has now rank 0 in new communicator.
MPI processes 3 and 4 are in the same new communicator.
MPI processes 0 and 1 and 2 are in the same new communicator.

5.5. AllReduce

int main(int argc, char* argv[])
{
    MPI_Init(&argc, &argv);
 
    // Get the size of the communicator
    int size = 0;
    MPI_Comm_size(MPI_COMM_WORLD, &size);
    if(size != 4)
    {
        printf("This application is meant to be run with 4 MPI processes.\n");
        MPI_Abort(MPI_COMM_WORLD, EXIT_FAILURE);
    }
 
    // Get my rank
    int my_rank;
    MPI_Comm_rank(MPI_COMM_WORLD, &my_rank);
 
    // Each MPI process sends its rank to reduction, root MPI process collects the result
    int reduction_result = 0;
    MPI_Allreduce(&my_rank, &reduction_result, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
 
    printf("[MPI Process %d] The sum of all ranks is %d.\n", my_rank, reduction_result);
 
    MPI_Finalize();
 
    return EXIT_SUCCESS;
}

6. Python

6.1. Multi Thread

6.1.1. pure thread start

import threading

def myfunction(a,b):
    print(a*b)

thread1 = threading.Thread(target= myfunction, args=(2,3))
thread2 = threading.Thread(target= myfunction, args=(3,4))
thread1.start()
thread2.start()

6.1.2. thread class

rewrite init and run in class, which inherit class threading.Thread, and start it with start() 

import threading
import time

class myThread(threading.Thread):
    def __init__(self, threadID, name, counter):
        threading.Thread.__init__(self)
        self.threadID = threadID
        self.name = name
        self.counter = counter
    def run(self):
        print("Starting " + self.name)
        self.print_time(self.name, 5, self.counter)
        print("Exiting" + self.name)
    def print_time(self, threadName, counter, delay):
        while counter:
            time.sleep(delay)
            print(f"{threadName}, {time.ctime(time.time())}")
            counter -= 1


thread1 = myThread(1, "threadone", 1)
thread2 = myThread(2, "threadtwo", 2)
thread1.start()
thread2.start()
time.sleep(1)
print("Exiting Main Thread.")


Starting threadone
Starting threadtwo
threadone, Tue Jun  7 23:53:02 2022
Exiting Main Thread.
threadtwo, Tue Jun  7 23:53:03 2022
threadone, Tue Jun  7 23:53:03 2022
threadone, Tue Jun  7 23:53:04 2022
threadtwo, Tue Jun  7 23:53:05 2022
threadone, Tue Jun  7 23:53:05 2022
threadone, Tue Jun  7 23:53:06 2022
Exitingthreadone
threadtwo, Tue Jun  7 23:53:07 2022
threadtwo, Tue Jun  7 23:53:09 2022
threadtwo, Tue Jun  7 23:53:11 2022
Exitingthreadtwo

6.1.3. thread with Lock

import threading
import time

myLock = threading.Lock()
class myThread(threading.Thread):
    def __init__(self, threadID, name, counter):
        threading.Thread.__init__(self)
        self.threadID = threadID
        self.name = name
        self.counter = counter
    def run(self):
        print("Starting " + self.name)
        myLock.acquire()
        self.print_time(self.name, 5, self.counter)
        myLock.release()
        print("Exiting" + self.name)
    def print_time(self, threadName, counter, delay):
        while counter:
            time.sleep(delay)
            print(f"{threadName}, {time.ctime(time.time())}")
            counter -= 1

thread1 = myThread(1, "threadone", 1)
thread2 = myThread(2, "threadtwo", 2)
thread1.start()
thread2.start()
time.sleep(1)
print("Exiting Main Thread.")


Starting threadone
Starting threadtwo
threadone, Tue Jun  7 23:53:58 2022
Exiting Main Thread.
threadone, Tue Jun  7 23:53:59 2022
threadone, Tue Jun  7 23:54:00 2022
threadone, Tue Jun  7 23:54:01 2022
threadone, Tue Jun  7 23:54:02 2022
Exitingthreadone
threadtwo, Tue Jun  7 23:54:04 2022
threadtwo, Tue Jun  7 23:54:06 2022
threadtwo, Tue Jun  7 23:54:08 2022
threadtwo, Tue Jun  7 23:54:10 2022
threadtwo, Tue Jun  7 23:54:12 2022
Exitingthreadtwo

6.2. Multi processing

6.2.1. pure multi process start

import multiprocessing
def myfunction(a,b):
    print(a*b)
process1 = multiprocessing.Process(target=myfunction, args=(2,9))
process2 = multiprocessing.Process(target=myfunction, args=(3,4))
process1.start()
process2.start()

18
12

6.2.2. multi process differ from multi threading

  #+begin_src python :results output :exports both
import multiprocessing
import threading
import random

def myfunction(shared_result, lock=None):
    value = random.randint(1, 10)
    if lock:
        with lock:
            shared_result.append(value)
    else:
        shared_result.append(value)

# Multiprocessing
if __name__ == "__main__":
    with multiprocessing.Manager() as manager:
        result = manager.list()  # Shared list for multiprocessing
        lock = multiprocessing.Lock()

        process1 = multiprocessing.Process(target=myfunction, args=(result, lock))
        process2 = multiprocessing.Process(target=myfunction, args=(result, lock))
        process1.start()
        process2.start()
        process1.join()
        process2.join()
        print("Result of multiprocessing:", list(result))

    # Threading
    result = []  # Normal list for threading
    lock = threading.Lock()

    thread1 = threading.Thread(target=myfunction, args=(result, lock))
    thread2 = threading.Thread(target=myfunction, args=(result, lock))
    thread1.start()
    thread2.start()
    thread1.join()
    thread2.join()
    print("Result of multi-threading:", result)

Result of multiprocessing: [4, 1]
Result of multi-threading: [8, 5]

#+endsrc

6.2.3. Pool

  1. apply
    import multiprocessing as mp
def myfunction(a, b):
    return a*b

pool = mp.Pool(mp.cpu_count())
result = [ pool.apply(myfunction, args=(a, 2)) for a in range(1, 100) ]
pool.close()
print(result)


    [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 180, 182, 184, 186, 188, 190, 192, 194, 196, 198]
  2. map
    import multiprocessing as mp
def myfunction(a):
    return a*a

pool = mp.Pool(mp.cpu_count())
result =  pool.map(myfunction, [a for a in range(1, 100)]) 
pool.close()
print(result)


    [1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, 2500, 2601, 2704, 2809, 2916, 3025, 3136, 3249, 3364, 3481, 3600, 3721, 3844, 3969, 4096, 4225, 4356, 4489, 4624, 4761, 4900, 5041, 5184, 5329, 5476, 5625, 5776, 5929, 6084, 6241, 6400, 6561, 6724, 6889, 7056, 7225, 7396, 7569, 7744, 7921, 8100, 8281, 8464, 8649, 8836, 9025, 9216, 9409, 9604, 9801]
  3. starmap
    import multiprocessing as mp
def myfunction(a, b):
    return a*b

pool = mp.Pool(mp.cpu_count())
result = pool.starmap(myfunction, [(a, 2) for a in range(1, 100)] ) 
pool.close()
print(result)


    [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 180, 182, 184, 186, 188, 190, 192, 194, 196, 198]
  4. applyasync
    import multiprocessing as mp
def myfunction(a, b):
    return a*b

pool = mp.Pool(mp.cpu_count())
result = [ pool.apply_async(myfunction, args=(a, 2)) for a in range(1, 100)]
result = [r.get() for r in result]
pool.close()
print(result)


    [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 180, 182, 184, 186, 188, 190, 192, 194, 196, 198]
  5. applyasync with callback, must use wait
    import multiprocessing as mp
results = []
def myfunction(a, b):
    return a*b
def collect_result(result):
    global results
    results.append(result)

pool = mp.Pool(mp.cpu_count())
for a in range(1, 100):
    r = pool.apply_async(myfunction, args=(a, 2), callback=collect_result)
    r.wait()
    pool.close()

print(results)

6.2.4. map

import time
import concurrent.futures

def do_something(n):
    print(f"sleeping {n} seconds")
    time.sleep(n)
    return f"Done {n} seconds sleep"


with concurrent.futures.ProcessPoolExecutor() as executor:
    secs = [5,4,3,2,1]
    results = executor.map(do_something, secs)

    for result in results:
        print(result)


sleeping 1 seconds
sleeping 2 seconds
sleeping 3 seconds
sleeping 4 seconds
sleeping 5 seconds
Done 5 seconds sleep
Done 4 seconds sleep
Done 3 seconds sleep
Done 2 seconds sleep
Done 1 seconds sleep

7. Python with mpi

7.1. send & recv

from mpi4py import MPI
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
if rank == 0:
 data = {'a': 1, 'b': 2, 'c':'test string'}
 comm.send(data,dest=1,tag=11)
elif rank == 1:
 data = comm.recv(source=0,tag=11)
 print(data)  

mpirun -n 2 python3 ./babel/mpi_python_example01.py

{'a': 1, 'b': 2, 'c': 'test string'}

7.2. Send & Recv

from mpi4py import MPI
import numpy
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
if rank == 0:
 data = numpy.arange(100, dtype=numpy.float)
 comm.Send(data,dest=1,tag=11)
elif rank == 1:
 data = numpy.empty(100,dtype=numpy.float)
 comm.Recv(data, source=0,tag=11)
 print(data)

mpirun -n 2 python3 ./babel/mpi_python_example02.py

[ 0.  1.  2.  3.  4.  5.  6.  7.  8.  9. 10. 11. 12. 13. 14. 15. 16. 17.
 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35.
 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53.
 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71.
 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89.
 90. 91. 92. 93. 94. 95. 96. 97. 98. 99.]

7.3. Bcast

7.3.1. with map bcast

from mpi4py import MPI
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
if rank == 0:
 data = {'key1' : [7, 2.72, 2+3j], 'key2' : ( 'abc', 'xyz')}
else:
 data = None
data = comm.bcast(data, root=0)
print(data)  

mpirun -n 3 python3 ./babel/mpi_python_example03.py

{'key1': [7, 2.72, (2+3j)], 'key2': ('abc', 'xyz')}
{'key1': [7, 2.72, (2+3j)], 'key2': ('abc', 'xyz')}
{'key1': [7, 2.72, (2+3j)], 'key2': ('abc', 'xyz')}

7.3.2. with array Bcast

from mpi4py import MPI
import numpy as np
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
if rank == 0:
 data = np.arange(100, dtype='i')
else:
 data = np.empty(100, dtype='i')
comm.Bcast(data, root=0)
for i in range(100):
 assert data[i] == i


mpirun -n 3 python3 ./babel/mpi_python_example07.py

7.4. scatter

7.4.1. with number

from mpi4py import MPI
comm = MPI.COMM_WORLD
size = comm.Get_size()
rank = comm.Get_rank()
if rank == 0:
 data = [(i+1)**2 for i in range(size)]
else:
 data = None
data = comm.scatter(data, root=0)
assert data == (rank+1)**2


mpirun -n 4 python3 ./babel/mpi_python_example04.py

7.4.2. with array

from mpi4py import MPI
import numpy as np
comm = MPI.COMM_WORLD
size = comm.Get_size()
rank = comm.Get_rank()
sendbuf = None
if rank == 0:
 sendbuf = np.empty([size, 100], dtype='i')
 sendbuf.T[:,:] = range(size)
recvbuf = np.empty(100, dtype='i')
comm.Scatter(sendbuf, recvbuf, root=0)
assert np.allclose(recvbuf, rank)  

mpirun --host si-u20:6 python3 ./babel/mpi_python_example08.py

7.5. Gather

7.5.1. with number gather

from mpi4py import MPI
comm = MPI.COMM_WORLD
size = comm.Get_size()
rank = comm.Get_rank()
data = (rank+1)**2
data = comm.gather(data, root=0)
if rank == 0:
 for i in range(size):
  assert data[i] == (i+1)**2
else:
 assert data is None


mpirun --host si-u20:8 python3 ./babel/mpi_python_example05.py

8
8
8
8
8
8
8
8

7.5.2. with array Gather

from mpi4py import MPI
import numpy as np
comm = MPI.COMM_WORLD
size = comm.Get_size()
rank = comm.Get_rank()
sendbuf = np.zeros(100, dtype='i') + rank
recvbuf = None
if rank == 0:
 recvbuf = np.empty([size, 100], dtype='i')
comm.Gather(sendbuf, recvbuf, root=0)
if rank == 0:
 for i in range(size):
  assert np.allclose(recvbuf[i,:], i)

mpirun -n 4 python3 ./babel/mpi_python_example09.py

7.6. Dynamic Process Management

from mpi4py import MPI
import numpy
import sys
comm = MPI.COMM_SELF.Spawn(sys.executable,
                           args=['./mpi_python_example_server.py'],
                           maxprocs=2)
N = numpy.array(100, 'i')
comm.Bcast([N, MPI.INT], root=MPI.ROOT)
PI = numpy.array(0.0, 'd')
comm.Reduce(None, [PI, MPI.DOUBLE],
            op=MPI.SUM, root=MPI.ROOT)
print(PI)
comm.Disconnect()


from mpi4py import MPI
import numpy
comm = MPI.Comm.Get_parent()
size = comm.Get_size()
rank = comm.Get_rank()
N = numpy.array(0, dtype='i')
comm.Bcast([N, MPI.INT], root=0)
h = 1.0 / N; s = 0.0
for i in range(rank, N, size):
 x = h * (i + 0.5)
 s += 4.0 / (1.0 + x**2)
PI = numpy.array(s * h, dtype='d')
comm.Reduce([PI, MPI.DOUBLE], None, op=MPI.SUM, root=0)
comm.Disconnect()


mpirun --host si-u20:4 python3 ./babel/mpi_python_example_client.py

8. Go

8.1. go chan

package main
import (
        "fmt"
        "time"
)
func main() {
        var times int
        go func() {
                for {
                }
        }()
        go func() {
                for {
                }
        }()
        go func() {
                for {
                }
        }()
        go func() {
                for {
                }
        }()
        go func() {
                for {
                }
        }()
        for times = 0; times <= 10; times++ {
                fmt.Println("tick", times)
                time.Sleep(time.Second)
        }
}


package main
import (
        "fmt"
        "time"
)
func main() {
        ch1 := make(chan int)
        go func (ch chan int){
                for{
                        select {
                        case <- ch:
                                fmt.Println("get it")
                        default:
                                fmt.Println("still not")
                        }
                }
        }(ch1)

        time.Sleep(time.Second)
        ch1 <- 2;
}

9. Go with mpi

9.1. cpuNum

package main
import (
        "fmt"
        "runtime"
)

func main() {
        cpuNum := runtime.NumCPU()
        fmt.Println("cpu number is :", cpuNum)
        runtime.GOMAXPROCS(cpuNum)
}

cpu number is : 8

go build ./babel/go_mpi_cpuNum.go && ./babel/go_mpi_cpuNum

cpu number is : 8

9.2. IsOn

package main

import (
        "fmt"
        mpi "github.com/sbromberger/gompi"
)
func main() {
        ison := mpi.IsOn()
        if ison {
                fmt.Println("ison is on")
        } else {
                fmt.Println("ison is  not on")
        }
        mpi.Start(true)
        ison = mpi.IsOn()
        if ison {
                fmt.Println("ison is on")
        } else {
                fmt.Println("ison is  not on ")
        }
        mpi.Stop()
}

cd babel
go mod tidy
go build ./go_mpi_ison.go && ./go_mpi_ison

ison is  not on
ison is on

9.3. WorldRank

package main

import (
        "fmt"
        mpi "github.com/sbromberger/gompi"
)
func main() {
        mpi.Start(true)
        rank := mpi.WorldRank()
        fmt.Println("rank is", rank)
        mpi.Stop()
}

cd babel
go mod tidy
go build ./go_mpi_WorldRank.go && mpirun --use-hwthread-cpus ./go_mpi_WorldRank

rank is 0
rank is 1
rank is 2
rank is 3
rank is 5
rank is 7
rank is 6
rank is 4

9.4. WorldSize

package main

import (
        "fmt"
        mpi "github.com/sbromberger/gompi"
)
func main() {
        mpi.Start(true)
        size := mpi.WorldSize()
        fmt.Println("rank is", size)
        mpi.Stop()
}

cd babel
go mod tidy
go build ./go_mpi_WorldSize.go && mpirun --use-hwthread-cpus ./go_mpi_WorldSize

rank is 8
rank is 8
rank is 8
rank is 8
rank is 8
rank is 8
rank is 8
rank is 8

9.5. NewCommunicator

package main

import (
        "fmt"
        mpi "github.com/sbromberger/gompi"
)
func main() {
        mpi.Start(true)
        var ranks []int
        newComm := mpi.NewCommunicator(ranks)
        fmt.Println("newComm.Size() is :", newComm.Size())
        fmt.Println("newComm.Rank() is :", newComm.Rank())
        mpi.Stop()
}

cd babel
go mod tidy
go build ./go_mpi_NewCommunicator.go && mpirun --use-hwthread-cpus ./go_mpi_NewCommunicator

newComm.Size() is : 8
newComm.Rank() is : 1
newComm.Size() is : 8
newComm.Rank() is : 7
newComm.Size() is : 8
newComm.Rank() is : 2
newComm.Size() is : 8
newComm.Size() is : 8
newComm.Rank() is : 0
newComm.Rank() is : 4
newComm.Size() is : 8
newComm.Rank() is : 3
newComm.Size() is : 8
newComm.Rank() is : 5
newComm.Size() is : 8
newComm.Rank() is : 6

package main

import (
        "fmt"
        mpi "github.com/sbromberger/gompi"
)
func main() {
        mpi.Start(true)
        var ranks []int = []int{0,1,2,3}
        newComm := mpi.NewCommunicator(ranks)
        fmt.Println("newComm.Size() is :", newComm.Size())
        fmt.Println("newComm.Rank() is :", newComm.Rank())
        mpi.Stop()
}

cd babel
go build ./go_mpi_NewCommunicator_withranks.go && mpirun --host si-u20:4 ./go_mpi_NewCommunicator_withranks

newComm.Size() is : 4
newComm.Rank() is : 0
newComm.Size() is : 4
newComm.Rank() is : 1
newComm.Size() is : 4
newComm.Rank() is : 2
newComm.Size() is : 4
newComm.Rank() is : 3

9.6. SendInt32 && RecvInt32

package main
import (
        "fmt"
        mpi "github.com/sbromberger/gompi"
)
func main() {
        mpi.Start(true)
        fmt.Println()
        var ranks []int 
        newComm := mpi.NewCommunicator(ranks)
        if newComm.Rank() == 0 {
                var data int32 = 60
                newComm.SendInt32(data, 1, 10)
        }
        if newComm.Rank() == 1 {
                data, _ := newComm.RecvInt32(0, 10)
                fmt.Println(data)
        }
        mpi.Stop()
}

cd babel
go mod tidy
go build ./go_mpi_SendInt32.go
mpirun --use-hwthread-cpus ./go_mpi_SendInt32







60

9.7. SendInt32s && RecvInt32s

package main

import (
        "fmt"

        mpi "github.com/sbromberger/gompi"
)
func main() {
        mpi.Start(true)
        fmt.Println()
        var ranks []int 
        newComm := mpi.NewCommunicator(ranks)
        if newComm.Rank() == 0 {
                var data []uint32 = []uint32{1, 2, 3, 4}
                newComm.SendUInt32s(data, 1, 10)
        }
        if newComm.Rank() == 1 {
                data, _ := newComm.RecvInt32s(0, 10)
                fmt.Println(data)
        }
        mpi.Stop()
}

cd babel
go mod tidy
go build ./go_mpi_SendUInt32s.go
mpirun --host si:6 ./go_mpi_SendUInt32s







[1 2 3 4]

9.8. SendString && RecvString

package main

import (
        "fmt"

        mpi "github.com/sbromberger/gompi"
)
func main() {
        mpi.Start(true)
        fmt.Println()
        var ranks []int
        newComm := mpi.NewCommunicator(ranks)
        if newComm.Rank() == 0 {
                str1 := "str11"
                newComm.SendString("nihao", 1, 11)
                newComm.SendString(str1, 1, 10)
        }
        // better with differ tags, but with the same tags works here also
        if newComm.Rank() == 1 {
                nihao, _ := newComm.RecvString(0, 11)
                str1, _ := newComm.RecvString(0, 10)
                fmt.Println(nihao)
                fmt.Println(str1)
        }
        mpi.Stop()
}


cd babel
go mod tidy
go build ./go_mpi_SendString.go
mpirun -n 2 ./go_mpi_SendString



nihao
str11

9.9. ReduceInt32s

package main

import (
        "fmt"

        mpi "github.com/sbromberger/gompi"
)
func main() {
        mpi.Start(true)
        fmt.Println()
        var ranks []int
        newComm := mpi.NewCommunicator(ranks)
        var dest []int32 = []int32{0, 0, 0, 0}
        var send []int32 = []int32{7, 2, 3, 4}
        newComm.ReduceInt32s(dest, send, mpi.OpSum, 0)
        if newComm.Rank() == 0 {
                fmt.Println(dest)
        }
        mpi.Stop()
}

cd babel
go mod tidy
go build ./go_mpi_ReduceInt32s.go
mpirun -n 4 ./go_mpi_ReduceInt32s





[28 8 12 16]

9.10. AllreduceInt64s

package main
import (
        "fmt"
        mpi "github.com/sbromberger/gompi"
)
func main() {
        mpi.Start(true)
        var ranks []int
        newComm := mpi.NewCommunicator(ranks)
        var dest []int64 = []int64{0, 0}
        var send []int64 = []int64{20 * int64(newComm.Rank()), 2}
        newComm.AllreduceInt64s(dest, send, mpi.OpSum, 0)
        if newComm.Rank() == 0 {
                fmt.Println(dest)
        }
        mpi.Stop()
}

cd babel
go mod tidy
go build ./go_mpi_AllreduceInt64s.go
mpirun -n 4 ./go_mpi_AllreduceInt64s


[120 8]

9.11. BcastInt64s

package main
import (
        "fmt"
        mpi "github.com/sbromberger/gompi"
)

func main() {
        mpi.Start(true)
        var ranks []int
        newComm := mpi.NewCommunicator(ranks)
        var send []int64 = []int64{10 + int64(newComm.Rank())}
        fmt.Printf("process %v now has original value of %v from main process  \n", newComm.Rank(), send)
        newComm.BcastInt64s(send, 0)
        if newComm.Rank() != 0 {
           fmt.Printf("process %v now has bordcasted value of %v from main process  \n", newComm.Rank(), send)
        }
        mpi.Stop()
}


cd babel
go mod tidy
go build ./go_mpi_BcastInt64s.go
mpirun -n 4 ./go_mpi_BcastInt64s

process 3 now has original value of [13] from main process  
process 1 now has original value of [11] from main process  
process 0 now has original value of [10] from main process  
process 2 now has original value of [12] from main process  
process 1 now has bordcasted value of [10] from main process  
process 2 now has bordcasted value of [10] from main process  
process 3 now has bordcasted value of [10] from main process

9.12. distributed-client

package main

import (
        "fmt"
        "math/rand"
        "time"

        mpi "github.com/sbromberger/gompi"
)

func main(){
        mpi.Start(true)
        var ranks []int
        newComm := mpi.NewCommunicator(ranks)
        fmt.Println("rank is ", newComm.Rank())
        start := []float64{0, 0, 0}
        ends := []float64{0, 0, 0}
        newComm.BcastFloat64s(start, 0)

        if newComm.Rank() != 0 {
                for { 
                        for i, x := range start {
                                start[i] = x+float64(rand.Intn(10))
                        }
                        time.Sleep(time.Second)
                        fmt.Printf("process %v now has value of %v from main process \n", newComm.Rank(), start)
                        newComm.SendFloat64s(start, 0, newComm.Rank())
                        start, _ = newComm.RecvFloat64s(0, newComm.Rank())
                }
        }

        if newComm.Rank() == 0 {
                go func (){
                        for { 
                                start, _ := newComm.RecvFloat64s(1, 1)
                                for i, _ := range start {
                                        start[i] = start[i] * ends[i]
                                }
                                newComm.SendFloat64s(start, 1, 1)
                        }
                }()

                go func (){
                        for { 
                                start, _ := newComm.RecvFloat64s(2, 2)
                                for i, _ := range start {
                                        start[i] = start[i] * ends[i]
                                }
                                newComm.SendFloat64s(start, 2, 2)
                        }
                }()

                go func (){
                        for { 
                                start, _ := newComm.RecvFloat64s(3, 3)
                                for i, _ := range start {
                                        start[i] = start[i] * ends[i]
                                }
                                newComm.SendFloat64s(start, 3, 3)
                        }
                }()
        }
        mpi.Stop()
}



cd babel
go mod tidy
go build ./go_mpi_distributed-client.go
mpirun -n 4 ./go_mpi_distributed-client

9.13. Distributed learning server client

package main

import (
        "fmt"
        "sync"
        "time"

        mpi "github.com/sbromberger/gompi"
)

func mainn(){
        mpi.Start(true)
        var ranks []int
        newComm := mpi.NewCommunicator(ranks)

        start := []float64{float64(newComm.Rank()), float64(newComm.Rank()), float64(newComm.Rank())}
        //	ends := []float64{0, 0, 0}
        var m sync.Mutex
        ch1 := make(chan []float64, 3)
        ch2 := make(chan []float64, 3)
        ch3 := make(chan []float64, 3)
        fmt.Printf("Orignal: %v now has value of %v from main process \n", newComm.Rank(), start)

        newComm.BcastFloat64s(start, 0)

        if newComm.Rank() == 0 {
                go func (ch0 chan []float64){
                        for { 
                                start, _ := newComm.RecvFloat64s(1, 1)
                                ch0 <- start
                        }
                }(ch1)

                go func (ch0 chan []float64){
                        for { 
                                start, _ := newComm.RecvFloat64s(2, 2)
                                ch0 <- start;
                        }
                }(ch2)

                go func (ch0 chan []float64){
                        for { 
                                start, _ := newComm.RecvFloat64s(3, 3)
                                ch0 <- start;
                        }
                }(ch3)
        }

        func (newComm *mpi.Communicator ) {
                for {
                        select {
                        case <- ch1:
                                m.Lock()
                                data := <- ch1
                                for i, _ := range start {
                                        start[i] = start[i] * data[i]
                                }
                                m.Unlock()
                                newComm.BcastFloat64s(start, 0)
                                fmt.Printf("From process %v now has value of %v from main process \n", data, start)
                        case <- ch2:
                                m.Lock()
                                data := <- ch2
                                for i, _ := range start {
                                        start[i] = start[i] * data[i]
                                }
                                m.Unlock()
                                newComm.BcastFloat64s(start, 0)
                                fmt.Printf("From process %v now has value of %v from main process \n", data, start)
                        case <- ch3:
                                m.Lock()
                                data := <- ch3
                                for i, _ := range start {
                                        start[i] = start[i] * data[i]
                                }
                                m.Unlock()
                                newComm.BcastFloat64s(start, 0)
                                fmt.Printf("From process %v now has value of %v from main process \n", data, start)
                                default:
                        }
                }
        }(newComm)


        if newComm.Rank() != 0 {
                for {
                        time.Sleep(time.Second*2)
                        fmt.Printf("PROCESS: %v now has value of %v from main process \n", newComm.Rank(), start)
                        for i, x := range start {
                                start[i] = x+1
                        }
                        newComm.SendFloat64s(start, 0, newComm.Rank())
                }
        }

        mpi.Stop()
}

9.14. Distributed learning server client one to one

package main

import (
        "fmt"
        "time"

        mpi "github.com/sbromberger/gompi"
)


func main(){
        mpi.Start(true)
        var ranks []int
        newComm := mpi.NewCommunicator(ranks)
        ch0 := make(chan int)

        start := []float64{float64(newComm.Rank()), float64(newComm.Rank()), float64(newComm.Rank())}
        fmt.Printf("Orignal: %v now has value of %v from main process \n", newComm.Rank(), start)

        go func (newComm *mpi.Communicator, ch0 chan int) {
                time.Sleep(time.Second*1)
                for {
                        select {
                        case data := <- ch0:
                                for i, _ := range start {
                                        start[i] = start[i] * float64(data)
                                }
                                fmt.Printf("From server: %v now has value of %v from main process \n", newComm.Rank(), start)
                                newComm.BcastFloat64s(start, 0)
                        case <-	time.After(time.Minute):
                                fmt.Println("Time out")
                        }
                }
        }(newComm, ch0)

        if newComm.Rank() == 0 {
                go func (ch0 chan int ){
                        for {
                                newComm.RecvFloat64s(1, 1)
                                ch0 <- 1;
                        }
                }(ch0)
        }

        if newComm.Rank() == 1 {
                for {
                        time.Sleep(time.Second*2)
                        for i, _ := range start {
                                start[i] = start[i] + 2
                        }
                        fmt.Printf("From client: %v now has value of %v from main process \n", newComm.Rank(), start)
                        newComm.SendFloat64s(start, 0, newComm.Rank())
                }
        }

        time.Sleep(time.Minute)
        mpi.Stop()
}

10. GPGPU

10.1. get variables

#include <stdio.h>
#include <cuda.h>
#include <assert.h>
#include <cuda_runtime.h>
#include <curand_kernel.h>
#define N 32
__global__ void add(
                    int *dthreadIdx_x,
                    int *dthreadIdx_y,
                    int *dthreadIdx_z,
                    int *dblockIdx_x,
                    int *dblockIdx_y,
                    int *dblockIdx_z,
                    int *dblockDim_x,
                    int *dblockDim_y,
                    int *dblockDim_z,
                    int *dgridDim_x,
                    int *dgridDim_y,
                    int *dgridDim_z){
  *dthreadIdx_x = threadIdx.x;
  *dthreadIdx_y = threadIdx.y;
  *dthreadIdx_z = threadIdx.z;
  *dblockIdx_x = blockIdx.x;
  *dblockIdx_y = blockIdx.y;
  *dblockIdx_z = blockIdx.z;
  *dblockDim_x = blockDim.x;
  *dblockDim_y = blockDim.y;
  *dblockDim_z = blockDim.z;
  *dgridDim_x = gridDim.x;
  *dgridDim_y = gridDim.y;
  *dgridDim_z = gridDim.z;
}
int main()
{
  int threadIdx_x = 0;
  int threadIdx_y = 0;
  int threadIdx_z = 0;
  int blockIdx_x = 0;
  int blockIdx_y = 0;
  int blockIdx_z = 0;
  int blockDim_x = 0;
  int blockDim_y = 0;
  int blockDim_z = 0;
  int gridDim_x = 0;
  int gridDim_y = 0;
  int gridDim_z = 0;

  int *dthreadIdx_x;
  int *dthreadIdx_y;
  int *dthreadIdx_z;
  int *dblockIdx_x;
  int *dblockIdx_y;
  int *dblockIdx_z;
  int *dblockDim_x;
  int *dblockDim_y;
  int *dblockDim_z;
  int *dgridDim_x;
  int *dgridDim_y;
  int *dgridDim_z;

  cudaMalloc((void **)&dthreadIdx_x, sizeof(int));
  cudaMalloc((void **)&dthreadIdx_y, sizeof(int));
  cudaMalloc((void **)&dthreadIdx_z, sizeof(int));
  cudaMalloc((void **)&dblockIdx_x, sizeof(int));
  cudaMalloc((void **)&dblockIdx_y, sizeof(int));
  cudaMalloc((void **)&dblockIdx_z, sizeof(int));
  cudaMalloc((void **)&dblockDim_x, sizeof(int));
  cudaMalloc((void **)&dblockDim_y, sizeof(int));
  cudaMalloc((void **)&dblockDim_z, sizeof(int));
  cudaMalloc((void **)&dgridDim_x, sizeof(int));
  cudaMalloc((void **)&dgridDim_y, sizeof(int));
  cudaMalloc((void **)&dgridDim_z, sizeof(int));

  dim3 BlockPerGrid(1, 1, 1);
  dim3 ThreadsPerBlock(N, N, 1);
  add <<< BlockPerGrid, ThreadsPerBlock >>>(
                                            dthreadIdx_x,
                                            dthreadIdx_y,
                                            dthreadIdx_z,
                                            dblockIdx_x,
                                            dblockIdx_y,
                                            dblockIdx_z,
                                            dblockDim_x,
                                            dblockDim_y,
                                            dblockDim_z,
                                            dgridDim_x,
                                            dgridDim_y,
                                            dgridDim_z
                                            );
  cudaMemcpy(&threadIdx_x,dthreadIdx_x, sizeof(int), cudaMemcpyDeviceToHost);
  printf("threadIdx_x is %d \n", threadIdx_x);
  cudaMemcpy(&threadIdx_y,dthreadIdx_y, sizeof(int), cudaMemcpyDeviceToHost);
  printf("threadIdx_y is %d \n", threadIdx_y);
  cudaMemcpy(&threadIdx_z,dthreadIdx_z, sizeof(int), cudaMemcpyDeviceToHost);
  printf("threadIdx_z is %d \n", threadIdx_z);

  cudaMemcpy(&blockIdx_x, dblockIdx_x, sizeof(int), cudaMemcpyDeviceToHost);
  printf("blockIdx_x is %d \n", blockIdx_x);
  cudaMemcpy(&blockIdx_y, dblockIdx_y, sizeof(int), cudaMemcpyDeviceToHost);
  printf("blockIdx_y is %d \n", blockIdx_y);
  cudaMemcpy(&blockIdx_z, dblockIdx_z, sizeof(int), cudaMemcpyDeviceToHost);
  printf("blockIdx_z is %d \n", blockIdx_z);


  cudaMemcpy(&blockDim_x, dblockDim_x, sizeof(int), cudaMemcpyDeviceToHost);
  printf("blockDim_x is %d \n", blockDim_x);
  cudaMemcpy(&blockDim_y, dblockDim_y, sizeof(int), cudaMemcpyDeviceToHost);
  printf("blockDim_y is %d \n", blockDim_y);
  cudaMemcpy(&blockDim_z, dblockDim_z, sizeof(int), cudaMemcpyDeviceToHost);
  printf("blockDim_z is %d \n", blockDim_z);

  cudaMemcpy(&gridDim_x, dgridDim_x, sizeof(int), cudaMemcpyDeviceToHost);
  printf("gridDim_x is %d \n", gridDim_x);
  cudaMemcpy(&gridDim_y, dgridDim_y, sizeof(int), cudaMemcpyDeviceToHost);
  printf("gridDim_y is %d \n", gridDim_y);
  cudaMemcpy(&gridDim_z, dgridDim_z, sizeof(int), cudaMemcpyDeviceToHost);
  printf("gridDim_z is %d \n", gridDim_z);

  return 0;
}

cd babel
nvcc gpu_get_variables.cu -o gpu_get_variables
./gpu_get_variables

10.2. Addition dim 1

10.2.1. without parallelism

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <assert.h>
#include <cuda.h>
#include <cuda_runtime.h>

#define N 10000000
#define MAX_ERR 1e-6

__global__ void vector_add(float *out, float *a, float *b, int n) {
  for(int i = 0; i < n; i ++){
    out[i] = a[i] + b[i];
  }
}

int main(){
  float *a, *b, *out;
  float *d_a, *d_b, *d_out; 

  // Allocate host memory
  a   = (float*)malloc(sizeof(float) * N);
  b   = (float*)malloc(sizeof(float) * N);
  out = (float*)malloc(sizeof(float) * N);

  // Initialize host arrays
  for(int i = 0; i < N; i++){
    a[i] = 1.0f;
    b[i] = 2.0f;
  }

  // Allocate device memory
  cudaMalloc((void**)&d_a, sizeof(float) * N);
  cudaMalloc((void**)&d_b, sizeof(float) * N);
  cudaMalloc((void**)&d_out, sizeof(float) * N);

  // Transfer data from host to device memory
  cudaMemcpy(d_a, a, sizeof(float) * N, cudaMemcpyHostToDevice);
  cudaMemcpy(d_b, b, sizeof(float) * N, cudaMemcpyHostToDevice);

  // Executing kernel 
       vector_add<<<1,1>>>(d_out, d_a, d_b, N);

  // Transfer data back to host memory
  cudaMemcpy(out, d_out, sizeof(float) * N, cudaMemcpyDeviceToHost);

  // Verification
  for(int i = 0; i < N; i++){
    assert(fabs(out[i] - a[i] - b[i]) < MAX_ERR);
  }
  printf("out[0] = %f\n", out[0]);
  printf("PASSED\n");

  // Deallocate device memory
  cudaFree(d_a);
  cudaFree(d_b);
  cudaFree(d_out);

  // Deallocate host memory
  free(a); 
  free(b); 
  free(out);
}


cd babel
nvcc gpu_vector_add_withoutpara.cu -o gpu_vector_add_withoutpara
./gpu_vector_add_withoutpara

out[0] = 3.000000
PASSED

10.2.2. dim 1, grid 1, block 256 N10000000

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <assert.h>
#include <cuda.h>
#include <cuda_runtime.h>

#define N 10000000
#define MAX_ERR 1e-6

__global__ void vector_add(float *out, float *a, float *b, int n) {
  int index = threadIdx.x;
  int stride = blockDim.x;

  for(int i = index; i < n; i += stride){
    out[i] = a[i] + b[i];
  }
}

int main(){
  float *a, *b, *out;
  float *d_a, *d_b, *d_out; 

  // Allocate host memory
  a   = (float*)malloc(sizeof(float) * N);
  b   = (float*)malloc(sizeof(float) * N);
  out = (float*)malloc(sizeof(float) * N);

  // Initialize host arrays
  for(int i = 0; i < N; i++){
    a[i] = 1.0f;
    b[i] = 2.0f;
  }

  // Allocate device memory 
  cudaMalloc((void**)&d_a, sizeof(float) * N);
  cudaMalloc((void**)&d_b, sizeof(float) * N);
  cudaMalloc((void**)&d_out, sizeof(float) * N);

  // Transfer data from host to device memory
  cudaMemcpy(d_a, a, sizeof(float) * N, cudaMemcpyHostToDevice);
  cudaMemcpy(d_b, b, sizeof(float) * N, cudaMemcpyHostToDevice);

  // Executing kernel 
  vector_add<<<1,256>>>(d_out, d_a, d_b, N);

  // Transfer data back to host memory
  cudaMemcpy(out, d_out, sizeof(float) * N, cudaMemcpyDeviceToHost);

  // Verification
  for(int i = 0; i < N; i++){
    assert(fabs(out[i] - a[i] - b[i]) < MAX_ERR);
  }

  printf("PASSED\n");

  // Deallocate device memory
  cudaFree(d_a);
  cudaFree(d_b);
  cudaFree(d_out);

  // Deallocate host memory
  free(a); 
  free(b); 
  free(out);
}


cd babel
nvcc gpu_vector_add_dim1_grid1_block256.cu -o gpu_vector_add_dim1_grid1_block256
./gpu_vector_add_dim1_grid1_block256

10.2.3. dim 1, grid 1, block 256 N10000000 with time

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <assert.h>
#include <cuda.h>
#include <cuda_runtime.h>

#define N 10000000
#define MAX_ERR 1e-6

__global__ void vector_add(float *out, float *a, float *b, int n) {
  int index = threadIdx.x;
  int stride = blockDim.x;

  for(int i = index; i < n; i += stride){
    out[i] = a[i] + b[i];
  }
}

int main(){
  float *a, *b, *out;
  float *d_a, *d_b, *d_out; 

  // Allocate host memory
  a   = (float*)malloc(sizeof(float) * N);
  b   = (float*)malloc(sizeof(float) * N);
  out = (float*)malloc(sizeof(float) * N);

  // Initialize host arrays
  for(int i = 0; i < N; i++){
    a[i] = 1.0f;
    b[i] = 2.0f;
  }

  // Allocate device memory 
  cudaMalloc((void**)&d_a, sizeof(float) * N);
  cudaMalloc((void**)&d_b, sizeof(float) * N);
  cudaMalloc((void**)&d_out, sizeof(float) * N);

  cudaEvent_t start, stop;
  cudaEventCreate(&start);
  cudaEventCreate(&stop);

  cudaEventRecord(start, 0);
  // Transfer data from host to device memory
  cudaMemcpy(d_a, a, sizeof(float) * N, cudaMemcpyHostToDevice);
  cudaMemcpy(d_b, b, sizeof(float) * N, cudaMemcpyHostToDevice);

  // Executing kernel 
  vector_add<<<1,256>>>(d_out, d_a, d_b, N);

  // Transfer data back to host memory
  cudaMemcpy(out, d_out, sizeof(float) * N, cudaMemcpyDeviceToHost);

  cudaEventRecord(stop, 0);
  cudaEventSynchronize(stop);
  float elapsedTime;
  cudaEventElapsedTime(&elapsedTime, start, stop);



  // Verification
  for(int i = 0; i < N; i++){
    assert(fabs(out[i] - a[i] - b[i]) < MAX_ERR);
  }

  printf("PASSED with %f ms\n", elapsedTime);

  cudaEventDestroy(start);
  cudaEventDestroy(stop);


  // Deallocate device memory
  cudaFree(d_a);
  cudaFree(d_b);
  cudaFree(d_out);

  // Deallocate host memory
  free(a); 
  free(b); 
  free(out);
}


cd babel
nvcc gpu_vector_add_dim1_grid1_block256_withtime.cu -o gpu_vector_add_dim1_grid1_block256_withtime
./gpu_vector_add_dim1_grid1_block256_withtime

10.2.4. dim 1, grid N, block 1, (N=256)

#include <stdio.h>
#include <cuda.h>
#include <cuda_runtime.h>
#include <curand_kernel.h>
#define N 512
__global__ void add(int *a, int *b, int *c){
  int tid = blockIdx.x; // handle the data at this index
  if(tid < N)
    c[tid] = a[tid] + b[tid];
}
int main()
{
  int a[N], b[N], c[N], i;
  int *dev_a, *dev_b, *dev_c;
  cudaMalloc((void**)&dev_c, N*sizeof(int));
  cudaMalloc((void**)&dev_b, N*sizeof(int));
  cudaMalloc((void**)&dev_a, N*sizeof(int));
  for(i=0; i < N; i++)
    {
      a[i] = -i;
      b[i] = i*i*i;
    }
  cudaMemcpy(dev_a, a, N*sizeof(int), cudaMemcpyHostToDevice);
  cudaMemcpy(dev_b, b, N*sizeof(int), cudaMemcpyHostToDevice);
  add <<<N, 1>>>(dev_a, dev_b, dev_c);
  cudaMemcpy(c, dev_c, N*sizeof(int), cudaMemcpyDeviceToHost);
  for(i=0; i < N; i++)
    printf("%d + %d = %d\n", a[i], b[i], c[i]);
  cudaFree(dev_c);
  cudaFree(dev_b);
  cudaFree(dev_a);
  return 0;
}

cd babel
nvcc dim1_gridN_block1.cu -o dim1_gridN_block1
./dim1_gridN_block1

0 + 0 = 0
-1 + 1 = 0
-2 + 8 = 6
-3 + 27 = 24
-4 + 64 = 60
-5 + 125 = 120
-6 + 216 = 210
-7 + 343 = 336
-8 + 512 = 504
-9 + 729 = 720
-10 + 1000 = 990
-11 + 1331 = 1320
-12 + 1728 = 1716
-13 + 2197 = 2184
-14 + 2744 = 2730
-15 + 3375 = 3360
-16 + 4096 = 4080
-17 + 4913 = 4896
-18 + 5832 = 5814
-19 + 6859 = 6840
-20 + 8000 = 7980
-21 + 9261 = 9240
-22 + 10648 = 10626
-23 + 12167 = 12144
-24 + 13824 = 13800
-25 + 15625 = 15600
-26 + 17576 = 17550
-27 + 19683 = 19656
-28 + 21952 = 21924
-29 + 24389 = 24360
-30 + 27000 = 26970
-31 + 29791 = 29760
-32 + 32768 = 32736
-33 + 35937 = 35904
-34 + 39304 = 39270
-35 + 42875 = 42840
-36 + 46656 = 46620
-37 + 50653 = 50616
-38 + 54872 = 54834
-39 + 59319 = 59280
-40 + 64000 = 63960
-41 + 68921 = 68880
-42 + 74088 = 74046
-43 + 79507 = 79464
-44 + 85184 = 85140
-45 + 91125 = 91080
-46 + 97336 = 97290
-47 + 103823 = 103776
-48 + 110592 = 110544
-49 + 117649 = 117600
-50 + 125000 = 124950
-51 + 132651 = 132600
-52 + 140608 = 140556
-53 + 148877 = 148824
-54 + 157464 = 157410
-55 + 166375 = 166320
-56 + 175616 = 175560
-57 + 185193 = 185136
-58 + 195112 = 195054
-59 + 205379 = 205320
-60 + 216000 = 215940
-61 + 226981 = 226920
-62 + 238328 = 238266
-63 + 250047 = 249984
-64 + 262144 = 262080
-65 + 274625 = 274560
-66 + 287496 = 287430
-67 + 300763 = 300696
-68 + 314432 = 314364
-69 + 328509 = 328440
-70 + 343000 = 342930
-71 + 357911 = 357840
-72 + 373248 = 373176
-73 + 389017 = 388944
-74 + 405224 = 405150
-75 + 421875 = 421800
-76 + 438976 = 438900
-77 + 456533 = 456456
-78 + 474552 = 474474
-79 + 493039 = 492960
-80 + 512000 = 511920
-81 + 531441 = 531360
-82 + 551368 = 551286
-83 + 571787 = 571704
-84 + 592704 = 592620
-85 + 614125 = 614040
-86 + 636056 = 635970
-87 + 658503 = 658416
-88 + 681472 = 681384
-89 + 704969 = 704880
-90 + 729000 = 728910
-91 + 753571 = 753480
-92 + 778688 = 778596
-93 + 804357 = 804264
-94 + 830584 = 830490
-95 + 857375 = 857280
-96 + 884736 = 884640
-97 + 912673 = 912576
-98 + 941192 = 941094
-99 + 970299 = 970200
-100 + 1000000 = 999900
-101 + 1030301 = 1030200
-102 + 1061208 = 1061106
-103 + 1092727 = 1092624
-104 + 1124864 = 1124760
-105 + 1157625 = 1157520
-106 + 1191016 = 1190910
-107 + 1225043 = 1224936
-108 + 1259712 = 1259604
-109 + 1295029 = 1294920
-110 + 1331000 = 1330890
-111 + 1367631 = 1367520
-112 + 1404928 = 1404816
-113 + 1442897 = 1442784
-114 + 1481544 = 1481430
-115 + 1520875 = 1520760
-116 + 1560896 = 1560780
-117 + 1601613 = 1601496
-118 + 1643032 = 1642914
-119 + 1685159 = 1685040
-120 + 1728000 = 1727880
-121 + 1771561 = 1771440
-122 + 1815848 = 1815726
-123 + 1860867 = 1860744
-124 + 1906624 = 1906500
-125 + 1953125 = 1953000
-126 + 2000376 = 2000250
-127 + 2048383 = 2048256
-128 + 2097152 = 2097024
-129 + 2146689 = 2146560
-130 + 2197000 = 2196870
-131 + 2248091 = 2247960
-132 + 2299968 = 2299836
-133 + 2352637 = 2352504
-134 + 2406104 = 2405970
-135 + 2460375 = 2460240
-136 + 2515456 = 2515320
-137 + 2571353 = 2571216
-138 + 2628072 = 2627934
-139 + 2685619 = 2685480
-140 + 2744000 = 2743860
-141 + 2803221 = 2803080
-142 + 2863288 = 2863146
-143 + 2924207 = 2924064
-144 + 2985984 = 2985840
-145 + 3048625 = 3048480
-146 + 3112136 = 3111990
-147 + 3176523 = 3176376
-148 + 3241792 = 3241644
-149 + 3307949 = 3307800
-150 + 3375000 = 3374850
-151 + 3442951 = 3442800
-152 + 3511808 = 3511656
-153 + 3581577 = 3581424
-154 + 3652264 = 3652110
-155 + 3723875 = 3723720
-156 + 3796416 = 3796260
-157 + 3869893 = 3869736
-158 + 3944312 = 3944154
-159 + 4019679 = 4019520
-160 + 4096000 = 4095840
-161 + 4173281 = 4173120
-162 + 4251528 = 4251366
-163 + 4330747 = 4330584
-164 + 4410944 = 4410780
-165 + 4492125 = 4491960
-166 + 4574296 = 4574130
-167 + 4657463 = 4657296
-168 + 4741632 = 4741464
-169 + 4826809 = 4826640
-170 + 4913000 = 4912830
-171 + 5000211 = 5000040
-172 + 5088448 = 5088276
-173 + 5177717 = 5177544
-174 + 5268024 = 5267850
-175 + 5359375 = 5359200
-176 + 5451776 = 5451600
-177 + 5545233 = 5545056
-178 + 5639752 = 5639574
-179 + 5735339 = 5735160
-180 + 5832000 = 5831820
-181 + 5929741 = 5929560
-182 + 6028568 = 6028386
-183 + 6128487 = 6128304
-184 + 6229504 = 6229320
-185 + 6331625 = 6331440
-186 + 6434856 = 6434670
-187 + 6539203 = 6539016
-188 + 6644672 = 6644484
-189 + 6751269 = 6751080
-190 + 6859000 = 6858810
-191 + 6967871 = 6967680
-192 + 7077888 = 7077696
-193 + 7189057 = 7188864
-194 + 7301384 = 7301190
-195 + 7414875 = 7414680
-196 + 7529536 = 7529340
-197 + 7645373 = 7645176
-198 + 7762392 = 7762194
-199 + 7880599 = 7880400
-200 + 8000000 = 7999800
-201 + 8120601 = 8120400
-202 + 8242408 = 8242206
-203 + 8365427 = 8365224
-204 + 8489664 = 8489460
-205 + 8615125 = 8614920
-206 + 8741816 = 8741610
-207 + 8869743 = 8869536
-208 + 8998912 = 8998704
-209 + 9129329 = 9129120
-210 + 9261000 = 9260790
-211 + 9393931 = 9393720
-212 + 9528128 = 9527916
-213 + 9663597 = 9663384
-214 + 9800344 = 9800130
-215 + 9938375 = 9938160
-216 + 10077696 = 10077480
-217 + 10218313 = 10218096
-218 + 10360232 = 10360014
-219 + 10503459 = 10503240
-220 + 10648000 = 10647780
-221 + 10793861 = 10793640
-222 + 10941048 = 10940826
-223 + 11089567 = 11089344
-224 + 11239424 = 11239200
-225 + 11390625 = 11390400
-226 + 11543176 = 11542950
-227 + 11697083 = 11696856
-228 + 11852352 = 11852124
-229 + 12008989 = 12008760
-230 + 12167000 = 12166770
-231 + 12326391 = 12326160
-232 + 12487168 = 12486936
-233 + 12649337 = 12649104
-234 + 12812904 = 12812670
-235 + 12977875 = 12977640
-236 + 13144256 = 13144020
-237 + 13312053 = 13311816
-238 + 13481272 = 13481034
-239 + 13651919 = 13651680
-240 + 13824000 = 13823760
-241 + 13997521 = 13997280
-242 + 14172488 = 14172246
-243 + 14348907 = 14348664
-244 + 14526784 = 14526540
-245 + 14706125 = 14705880
-246 + 14886936 = 14886690
-247 + 15069223 = 15068976
-248 + 15252992 = 15252744
-249 + 15438249 = 15438000
-250 + 15625000 = 15624750
-251 + 15813251 = 15813000
-252 + 16003008 = 16002756
-253 + 16194277 = 16194024
-254 + 16387064 = 16386810
-255 + 16581375 = 16581120
-256 + 16777216 = 16776960
-257 + 16974593 = 16974336
-258 + 17173512 = 17173254
-259 + 17373979 = 17373720
-260 + 17576000 = 17575740
-261 + 17779581 = 17779320
-262 + 17984728 = 17984466
-263 + 18191447 = 18191184
-264 + 18399744 = 18399480
-265 + 18609625 = 18609360
-266 + 18821096 = 18820830
-267 + 19034163 = 19033896
-268 + 19248832 = 19248564
-269 + 19465109 = 19464840
-270 + 19683000 = 19682730
-271 + 19902511 = 19902240
-272 + 20123648 = 20123376
-273 + 20346417 = 20346144
-274 + 20570824 = 20570550
-275 + 20796875 = 20796600
-276 + 21024576 = 21024300
-277 + 21253933 = 21253656
-278 + 21484952 = 21484674
-279 + 21717639 = 21717360
-280 + 21952000 = 21951720
-281 + 22188041 = 22187760
-282 + 22425768 = 22425486
-283 + 22665187 = 22664904
-284 + 22906304 = 22906020
-285 + 23149125 = 23148840
-286 + 23393656 = 23393370
-287 + 23639903 = 23639616
-288 + 23887872 = 23887584
-289 + 24137569 = 24137280
-290 + 24389000 = 24388710
-291 + 24642171 = 24641880
-292 + 24897088 = 24896796
-293 + 25153757 = 25153464
-294 + 25412184 = 25411890
-295 + 25672375 = 25672080
-296 + 25934336 = 25934040
-297 + 26198073 = 26197776
-298 + 26463592 = 26463294
-299 + 26730899 = 26730600
-300 + 27000000 = 26999700
-301 + 27270901 = 27270600
-302 + 27543608 = 27543306
-303 + 27818127 = 27817824
-304 + 28094464 = 28094160
-305 + 28372625 = 28372320
-306 + 28652616 = 28652310
-307 + 28934443 = 28934136
-308 + 29218112 = 29217804
-309 + 29503629 = 29503320
-310 + 29791000 = 29790690
-311 + 30080231 = 30079920
-312 + 30371328 = 30371016
-313 + 30664297 = 30663984
-314 + 30959144 = 30958830
-315 + 31255875 = 31255560
-316 + 31554496 = 31554180
-317 + 31855013 = 31854696
-318 + 32157432 = 32157114
-319 + 32461759 = 32461440
-320 + 32768000 = 32767680
-321 + 33076161 = 33075840
-322 + 33386248 = 33385926
-323 + 33698267 = 33697944
-324 + 34012224 = 34011900
-325 + 34328125 = 34327800
-326 + 34645976 = 34645650
-327 + 34965783 = 34965456
-328 + 35287552 = 35287224
-329 + 35611289 = 35610960
-330 + 35937000 = 35936670
-331 + 36264691 = 36264360
-332 + 36594368 = 36594036
-333 + 36926037 = 36925704
-334 + 37259704 = 37259370
-335 + 37595375 = 37595040
-336 + 37933056 = 37932720
-337 + 38272753 = 38272416
-338 + 38614472 = 38614134
-339 + 38958219 = 38957880
-340 + 39304000 = 39303660
-341 + 39651821 = 39651480
-342 + 40001688 = 40001346
-343 + 40353607 = 40353264
-344 + 40707584 = 40707240
-345 + 41063625 = 41063280
-346 + 41421736 = 41421390
-347 + 41781923 = 41781576
-348 + 42144192 = 42143844
-349 + 42508549 = 42508200
-350 + 42875000 = 42874650
-351 + 43243551 = 43243200
-352 + 43614208 = 43613856
-353 + 43986977 = 43986624
-354 + 44361864 = 44361510
-355 + 44738875 = 44738520
-356 + 45118016 = 45117660
-357 + 45499293 = 45498936
-358 + 45882712 = 45882354
-359 + 46268279 = 46267920
-360 + 46656000 = 46655640
-361 + 47045881 = 47045520
-362 + 47437928 = 47437566
-363 + 47832147 = 47831784
-364 + 48228544 = 48228180
-365 + 48627125 = 48626760
-366 + 49027896 = 49027530
-367 + 49430863 = 49430496
-368 + 49836032 = 49835664
-369 + 50243409 = 50243040
-370 + 50653000 = 50652630
-371 + 51064811 = 51064440
-372 + 51478848 = 51478476
-373 + 51895117 = 51894744
-374 + 52313624 = 52313250
-375 + 52734375 = 52734000
-376 + 53157376 = 53157000
-377 + 53582633 = 53582256
-378 + 54010152 = 54009774
-379 + 54439939 = 54439560
-380 + 54872000 = 54871620
-381 + 55306341 = 55305960
-382 + 55742968 = 55742586
-383 + 56181887 = 56181504
-384 + 56623104 = 56622720
-385 + 57066625 = 57066240
-386 + 57512456 = 57512070
-387 + 57960603 = 57960216
-388 + 58411072 = 58410684
-389 + 58863869 = 58863480
-390 + 59319000 = 59318610
-391 + 59776471 = 59776080
-392 + 60236288 = 60235896
-393 + 60698457 = 60698064
-394 + 61162984 = 61162590
-395 + 61629875 = 61629480
-396 + 62099136 = 62098740
-397 + 62570773 = 62570376
-398 + 63044792 = 63044394
-399 + 63521199 = 63520800
-400 + 64000000 = 63999600
-401 + 64481201 = 64480800
-402 + 64964808 = 64964406
-403 + 65450827 = 65450424
-404 + 65939264 = 65938860
-405 + 66430125 = 66429720
-406 + 66923416 = 66923010
-407 + 67419143 = 67418736
-408 + 67917312 = 67916904
-409 + 68417929 = 68417520
-410 + 68921000 = 68920590
-411 + 69426531 = 69426120
-412 + 69934528 = 69934116
-413 + 70444997 = 70444584
-414 + 70957944 = 70957530
-415 + 71473375 = 71472960
-416 + 71991296 = 71990880
-417 + 72511713 = 72511296
-418 + 73034632 = 73034214
-419 + 73560059 = 73559640
-420 + 74088000 = 74087580
-421 + 74618461 = 74618040
-422 + 75151448 = 75151026
-423 + 75686967 = 75686544
-424 + 76225024 = 76224600
-425 + 76765625 = 76765200
-426 + 77308776 = 77308350
-427 + 77854483 = 77854056
-428 + 78402752 = 78402324
-429 + 78953589 = 78953160
-430 + 79507000 = 79506570
-431 + 80062991 = 80062560
-432 + 80621568 = 80621136
-433 + 81182737 = 81182304
-434 + 81746504 = 81746070
-435 + 82312875 = 82312440
-436 + 82881856 = 82881420
-437 + 83453453 = 83453016
-438 + 84027672 = 84027234
-439 + 84604519 = 84604080
-440 + 85184000 = 85183560
-441 + 85766121 = 85765680
-442 + 86350888 = 86350446
-443 + 86938307 = 86937864
-444 + 87528384 = 87527940
-445 + 88121125 = 88120680
-446 + 88716536 = 88716090
-447 + 89314623 = 89314176
-448 + 89915392 = 89914944
-449 + 90518849 = 90518400
-450 + 91125000 = 91124550
-451 + 91733851 = 91733400
-452 + 92345408 = 92344956
-453 + 92959677 = 92959224
-454 + 93576664 = 93576210
-455 + 94196375 = 94195920
-456 + 94818816 = 94818360
-457 + 95443993 = 95443536
-458 + 96071912 = 96071454
-459 + 96702579 = 96702120
-460 + 97336000 = 97335540
-461 + 97972181 = 97971720
-462 + 98611128 = 98610666
-463 + 99252847 = 99252384
-464 + 99897344 = 99896880
-465 + 100544625 = 100544160
-466 + 101194696 = 101194230
-467 + 101847563 = 101847096
-468 + 102503232 = 102502764
-469 + 103161709 = 103161240
-470 + 103823000 = 103822530
-471 + 104487111 = 104486640
-472 + 105154048 = 105153576
-473 + 105823817 = 105823344
-474 + 106496424 = 106495950
-475 + 107171875 = 107171400
-476 + 107850176 = 107849700
-477 + 108531333 = 108530856
-478 + 109215352 = 109214874
-479 + 109902239 = 109901760
-480 + 110592000 = 110591520
-481 + 111284641 = 111284160
-482 + 111980168 = 111979686
-483 + 112678587 = 112678104
-484 + 113379904 = 113379420
-485 + 114084125 = 114083640
-486 + 114791256 = 114790770
-487 + 115501303 = 115500816
-488 + 116214272 = 116213784
-489 + 116930169 = 116929680
-490 + 117649000 = 117648510
-491 + 118370771 = 118370280
-492 + 119095488 = 119094996
-493 + 119823157 = 119822664
-494 + 120553784 = 120553290
-495 + 121287375 = 121286880
-496 + 122023936 = 122023440
-497 + 122763473 = 122762976
-498 + 123505992 = 123505494
-499 + 124251499 = 124251000
-500 + 125000000 = 124999500
-501 + 125751501 = 125751000
-502 + 126506008 = 126505506
-503 + 127263527 = 127263024
-504 + 128024064 = 128023560
-505 + 128787625 = 128787120
-506 + 129554216 = 129553710
-507 + 130323843 = 130323336
-508 + 131096512 = 131096004
-509 + 131872229 = 131871720
-510 + 132651000 = 132650490
-511 + 133432831 = 133432320

10.2.5. dim 1, grid 1, block N, (N=256)

#include <stdio.h>
#include <cuda.h>
#include <cuda_runtime.h>
#include <curand_kernel.h>
#define N 512
__global__ void add(int *a, int *b, int *c){
  int tid = threadIdx.x; // handle the data at this index
  if(tid < N)
    c[tid] = a[tid] + b[tid];
}
int main()
{
  int a[N], b[N], c[N], i;
  int *dev_a, *dev_b, *dev_c;
  cudaMalloc((void**)&dev_c, N*sizeof(int));
  cudaMalloc((void**)&dev_b, N*sizeof(int));
  cudaMalloc((void**)&dev_a, N*sizeof(int));
  for(i=0; i < N; i++)
    {
      a[i] = -i;
      b[i] = i*i*i;
    }
  cudaMemcpy(dev_a, a, N*sizeof(int), cudaMemcpyHostToDevice);
  cudaMemcpy(dev_b, b, N*sizeof(int), cudaMemcpyHostToDevice);
  add <<<1, N>>>(dev_a, dev_b, dev_c);
  cudaMemcpy(c, dev_c, N*sizeof(int), cudaMemcpyDeviceToHost);
  for(i=0; i < N; i++)
    printf("%d + %d = %d\n", a[i], b[i], c[i]);
  cudaFree(dev_c);
  cudaFree(dev_b);
  cudaFree(dev_a);
  return 0;
}

cd babel
nvcc dim1_gridN_block1_N256.cu -o dim1_gridN_block1_N256
./dim1_gridN_block1_N256

0 + 0 = 0
-1 + 1 = 0
-2 + 8 = 6
-3 + 27 = 24
-4 + 64 = 60
-5 + 125 = 120
-6 + 216 = 210
-7 + 343 = 336
-8 + 512 = 504
-9 + 729 = 720
-10 + 1000 = 990
-11 + 1331 = 1320
-12 + 1728 = 1716
-13 + 2197 = 2184
-14 + 2744 = 2730
-15 + 3375 = 3360
-16 + 4096 = 4080
-17 + 4913 = 4896
-18 + 5832 = 5814
-19 + 6859 = 6840
-20 + 8000 = 7980
-21 + 9261 = 9240
-22 + 10648 = 10626
-23 + 12167 = 12144
-24 + 13824 = 13800
-25 + 15625 = 15600
-26 + 17576 = 17550
-27 + 19683 = 19656
-28 + 21952 = 21924
-29 + 24389 = 24360
-30 + 27000 = 26970
-31 + 29791 = 29760
-32 + 32768 = 32736
-33 + 35937 = 35904
-34 + 39304 = 39270
-35 + 42875 = 42840
-36 + 46656 = 46620
-37 + 50653 = 50616
-38 + 54872 = 54834
-39 + 59319 = 59280
-40 + 64000 = 63960
-41 + 68921 = 68880
-42 + 74088 = 74046
-43 + 79507 = 79464
-44 + 85184 = 85140
-45 + 91125 = 91080
-46 + 97336 = 97290
-47 + 103823 = 103776
-48 + 110592 = 110544
-49 + 117649 = 117600
-50 + 125000 = 124950
-51 + 132651 = 132600
-52 + 140608 = 140556
-53 + 148877 = 148824
-54 + 157464 = 157410
-55 + 166375 = 166320
-56 + 175616 = 175560
-57 + 185193 = 185136
-58 + 195112 = 195054
-59 + 205379 = 205320
-60 + 216000 = 215940
-61 + 226981 = 226920
-62 + 238328 = 238266
-63 + 250047 = 249984
-64 + 262144 = 262080
-65 + 274625 = 274560
-66 + 287496 = 287430
-67 + 300763 = 300696
-68 + 314432 = 314364
-69 + 328509 = 328440
-70 + 343000 = 342930
-71 + 357911 = 357840
-72 + 373248 = 373176
-73 + 389017 = 388944
-74 + 405224 = 405150
-75 + 421875 = 421800
-76 + 438976 = 438900
-77 + 456533 = 456456
-78 + 474552 = 474474
-79 + 493039 = 492960
-80 + 512000 = 511920
-81 + 531441 = 531360
-82 + 551368 = 551286
-83 + 571787 = 571704
-84 + 592704 = 592620
-85 + 614125 = 614040
-86 + 636056 = 635970
-87 + 658503 = 658416
-88 + 681472 = 681384
-89 + 704969 = 704880
-90 + 729000 = 728910
-91 + 753571 = 753480
-92 + 778688 = 778596
-93 + 804357 = 804264
-94 + 830584 = 830490
-95 + 857375 = 857280
-96 + 884736 = 884640
-97 + 912673 = 912576
-98 + 941192 = 941094
-99 + 970299 = 970200
-100 + 1000000 = 999900
-101 + 1030301 = 1030200
-102 + 1061208 = 1061106
-103 + 1092727 = 1092624
-104 + 1124864 = 1124760
-105 + 1157625 = 1157520
-106 + 1191016 = 1190910
-107 + 1225043 = 1224936
-108 + 1259712 = 1259604
-109 + 1295029 = 1294920
-110 + 1331000 = 1330890
-111 + 1367631 = 1367520
-112 + 1404928 = 1404816
-113 + 1442897 = 1442784
-114 + 1481544 = 1481430
-115 + 1520875 = 1520760
-116 + 1560896 = 1560780
-117 + 1601613 = 1601496
-118 + 1643032 = 1642914
-119 + 1685159 = 1685040
-120 + 1728000 = 1727880
-121 + 1771561 = 1771440
-122 + 1815848 = 1815726
-123 + 1860867 = 1860744
-124 + 1906624 = 1906500
-125 + 1953125 = 1953000
-126 + 2000376 = 2000250
-127 + 2048383 = 2048256
-128 + 2097152 = 2097024
-129 + 2146689 = 2146560
-130 + 2197000 = 2196870
-131 + 2248091 = 2247960
-132 + 2299968 = 2299836
-133 + 2352637 = 2352504
-134 + 2406104 = 2405970
-135 + 2460375 = 2460240
-136 + 2515456 = 2515320
-137 + 2571353 = 2571216
-138 + 2628072 = 2627934
-139 + 2685619 = 2685480
-140 + 2744000 = 2743860
-141 + 2803221 = 2803080
-142 + 2863288 = 2863146
-143 + 2924207 = 2924064
-144 + 2985984 = 2985840
-145 + 3048625 = 3048480
-146 + 3112136 = 3111990
-147 + 3176523 = 3176376
-148 + 3241792 = 3241644
-149 + 3307949 = 3307800
-150 + 3375000 = 3374850
-151 + 3442951 = 3442800
-152 + 3511808 = 3511656
-153 + 3581577 = 3581424
-154 + 3652264 = 3652110
-155 + 3723875 = 3723720
-156 + 3796416 = 3796260
-157 + 3869893 = 3869736
-158 + 3944312 = 3944154
-159 + 4019679 = 4019520
-160 + 4096000 = 4095840
-161 + 4173281 = 4173120
-162 + 4251528 = 4251366
-163 + 4330747 = 4330584
-164 + 4410944 = 4410780
-165 + 4492125 = 4491960
-166 + 4574296 = 4574130
-167 + 4657463 = 4657296
-168 + 4741632 = 4741464
-169 + 4826809 = 4826640
-170 + 4913000 = 4912830
-171 + 5000211 = 5000040
-172 + 5088448 = 5088276
-173 + 5177717 = 5177544
-174 + 5268024 = 5267850
-175 + 5359375 = 5359200
-176 + 5451776 = 5451600
-177 + 5545233 = 5545056
-178 + 5639752 = 5639574
-179 + 5735339 = 5735160
-180 + 5832000 = 5831820
-181 + 5929741 = 5929560
-182 + 6028568 = 6028386
-183 + 6128487 = 6128304
-184 + 6229504 = 6229320
-185 + 6331625 = 6331440
-186 + 6434856 = 6434670
-187 + 6539203 = 6539016
-188 + 6644672 = 6644484
-189 + 6751269 = 6751080
-190 + 6859000 = 6858810
-191 + 6967871 = 6967680
-192 + 7077888 = 7077696
-193 + 7189057 = 7188864
-194 + 7301384 = 7301190
-195 + 7414875 = 7414680
-196 + 7529536 = 7529340
-197 + 7645373 = 7645176
-198 + 7762392 = 7762194
-199 + 7880599 = 7880400
-200 + 8000000 = 7999800
-201 + 8120601 = 8120400
-202 + 8242408 = 8242206
-203 + 8365427 = 8365224
-204 + 8489664 = 8489460
-205 + 8615125 = 8614920
-206 + 8741816 = 8741610
-207 + 8869743 = 8869536
-208 + 8998912 = 8998704
-209 + 9129329 = 9129120
-210 + 9261000 = 9260790
-211 + 9393931 = 9393720
-212 + 9528128 = 9527916
-213 + 9663597 = 9663384
-214 + 9800344 = 9800130
-215 + 9938375 = 9938160
-216 + 10077696 = 10077480
-217 + 10218313 = 10218096
-218 + 10360232 = 10360014
-219 + 10503459 = 10503240
-220 + 10648000 = 10647780
-221 + 10793861 = 10793640
-222 + 10941048 = 10940826
-223 + 11089567 = 11089344
-224 + 11239424 = 11239200
-225 + 11390625 = 11390400
-226 + 11543176 = 11542950
-227 + 11697083 = 11696856
-228 + 11852352 = 11852124
-229 + 12008989 = 12008760
-230 + 12167000 = 12166770
-231 + 12326391 = 12326160
-232 + 12487168 = 12486936
-233 + 12649337 = 12649104
-234 + 12812904 = 12812670
-235 + 12977875 = 12977640
-236 + 13144256 = 13144020
-237 + 13312053 = 13311816
-238 + 13481272 = 13481034
-239 + 13651919 = 13651680
-240 + 13824000 = 13823760
-241 + 13997521 = 13997280
-242 + 14172488 = 14172246
-243 + 14348907 = 14348664
-244 + 14526784 = 14526540
-245 + 14706125 = 14705880
-246 + 14886936 = 14886690
-247 + 15069223 = 15068976
-248 + 15252992 = 15252744
-249 + 15438249 = 15438000
-250 + 15625000 = 15624750
-251 + 15813251 = 15813000
-252 + 16003008 = 16002756
-253 + 16194277 = 16194024
-254 + 16387064 = 16386810
-255 + 16581375 = 16581120
-256 + 16777216 = 16776960
-257 + 16974593 = 16974336
-258 + 17173512 = 17173254
-259 + 17373979 = 17373720
-260 + 17576000 = 17575740
-261 + 17779581 = 17779320
-262 + 17984728 = 17984466
-263 + 18191447 = 18191184
-264 + 18399744 = 18399480
-265 + 18609625 = 18609360
-266 + 18821096 = 18820830
-267 + 19034163 = 19033896
-268 + 19248832 = 19248564
-269 + 19465109 = 19464840
-270 + 19683000 = 19682730
-271 + 19902511 = 19902240
-272 + 20123648 = 20123376
-273 + 20346417 = 20346144
-274 + 20570824 = 20570550
-275 + 20796875 = 20796600
-276 + 21024576 = 21024300
-277 + 21253933 = 21253656
-278 + 21484952 = 21484674
-279 + 21717639 = 21717360
-280 + 21952000 = 21951720
-281 + 22188041 = 22187760
-282 + 22425768 = 22425486
-283 + 22665187 = 22664904
-284 + 22906304 = 22906020
-285 + 23149125 = 23148840
-286 + 23393656 = 23393370
-287 + 23639903 = 23639616
-288 + 23887872 = 23887584
-289 + 24137569 = 24137280
-290 + 24389000 = 24388710
-291 + 24642171 = 24641880
-292 + 24897088 = 24896796
-293 + 25153757 = 25153464
-294 + 25412184 = 25411890
-295 + 25672375 = 25672080
-296 + 25934336 = 25934040
-297 + 26198073 = 26197776
-298 + 26463592 = 26463294
-299 + 26730899 = 26730600
-300 + 27000000 = 26999700
-301 + 27270901 = 27270600
-302 + 27543608 = 27543306
-303 + 27818127 = 27817824
-304 + 28094464 = 28094160
-305 + 28372625 = 28372320
-306 + 28652616 = 28652310
-307 + 28934443 = 28934136
-308 + 29218112 = 29217804
-309 + 29503629 = 29503320
-310 + 29791000 = 29790690
-311 + 30080231 = 30079920
-312 + 30371328 = 30371016
-313 + 30664297 = 30663984
-314 + 30959144 = 30958830
-315 + 31255875 = 31255560
-316 + 31554496 = 31554180
-317 + 31855013 = 31854696
-318 + 32157432 = 32157114
-319 + 32461759 = 32461440
-320 + 32768000 = 32767680
-321 + 33076161 = 33075840
-322 + 33386248 = 33385926
-323 + 33698267 = 33697944
-324 + 34012224 = 34011900
-325 + 34328125 = 34327800
-326 + 34645976 = 34645650
-327 + 34965783 = 34965456
-328 + 35287552 = 35287224
-329 + 35611289 = 35610960
-330 + 35937000 = 35936670
-331 + 36264691 = 36264360
-332 + 36594368 = 36594036
-333 + 36926037 = 36925704
-334 + 37259704 = 37259370
-335 + 37595375 = 37595040
-336 + 37933056 = 37932720
-337 + 38272753 = 38272416
-338 + 38614472 = 38614134
-339 + 38958219 = 38957880
-340 + 39304000 = 39303660
-341 + 39651821 = 39651480
-342 + 40001688 = 40001346
-343 + 40353607 = 40353264
-344 + 40707584 = 40707240
-345 + 41063625 = 41063280
-346 + 41421736 = 41421390
-347 + 41781923 = 41781576
-348 + 42144192 = 42143844
-349 + 42508549 = 42508200
-350 + 42875000 = 42874650
-351 + 43243551 = 43243200
-352 + 43614208 = 43613856
-353 + 43986977 = 43986624
-354 + 44361864 = 44361510
-355 + 44738875 = 44738520
-356 + 45118016 = 45117660
-357 + 45499293 = 45498936
-358 + 45882712 = 45882354
-359 + 46268279 = 46267920
-360 + 46656000 = 46655640
-361 + 47045881 = 47045520
-362 + 47437928 = 47437566
-363 + 47832147 = 47831784
-364 + 48228544 = 48228180
-365 + 48627125 = 48626760
-366 + 49027896 = 49027530
-367 + 49430863 = 49430496
-368 + 49836032 = 49835664
-369 + 50243409 = 50243040
-370 + 50653000 = 50652630
-371 + 51064811 = 51064440
-372 + 51478848 = 51478476
-373 + 51895117 = 51894744
-374 + 52313624 = 52313250
-375 + 52734375 = 52734000
-376 + 53157376 = 53157000
-377 + 53582633 = 53582256
-378 + 54010152 = 54009774
-379 + 54439939 = 54439560
-380 + 54872000 = 54871620
-381 + 55306341 = 55305960
-382 + 55742968 = 55742586
-383 + 56181887 = 56181504
-384 + 56623104 = 56622720
-385 + 57066625 = 57066240
-386 + 57512456 = 57512070
-387 + 57960603 = 57960216
-388 + 58411072 = 58410684
-389 + 58863869 = 58863480
-390 + 59319000 = 59318610
-391 + 59776471 = 59776080
-392 + 60236288 = 60235896
-393 + 60698457 = 60698064
-394 + 61162984 = 61162590
-395 + 61629875 = 61629480
-396 + 62099136 = 62098740
-397 + 62570773 = 62570376
-398 + 63044792 = 63044394
-399 + 63521199 = 63520800
-400 + 64000000 = 63999600
-401 + 64481201 = 64480800
-402 + 64964808 = 64964406
-403 + 65450827 = 65450424
-404 + 65939264 = 65938860
-405 + 66430125 = 66429720
-406 + 66923416 = 66923010
-407 + 67419143 = 67418736
-408 + 67917312 = 67916904
-409 + 68417929 = 68417520
-410 + 68921000 = 68920590
-411 + 69426531 = 69426120
-412 + 69934528 = 69934116
-413 + 70444997 = 70444584
-414 + 70957944 = 70957530
-415 + 71473375 = 71472960
-416 + 71991296 = 71990880
-417 + 72511713 = 72511296
-418 + 73034632 = 73034214
-419 + 73560059 = 73559640
-420 + 74088000 = 74087580
-421 + 74618461 = 74618040
-422 + 75151448 = 75151026
-423 + 75686967 = 75686544
-424 + 76225024 = 76224600
-425 + 76765625 = 76765200
-426 + 77308776 = 77308350
-427 + 77854483 = 77854056
-428 + 78402752 = 78402324
-429 + 78953589 = 78953160
-430 + 79507000 = 79506570
-431 + 80062991 = 80062560
-432 + 80621568 = 80621136
-433 + 81182737 = 81182304
-434 + 81746504 = 81746070
-435 + 82312875 = 82312440
-436 + 82881856 = 82881420
-437 + 83453453 = 83453016
-438 + 84027672 = 84027234
-439 + 84604519 = 84604080
-440 + 85184000 = 85183560
-441 + 85766121 = 85765680
-442 + 86350888 = 86350446
-443 + 86938307 = 86937864
-444 + 87528384 = 87527940
-445 + 88121125 = 88120680
-446 + 88716536 = 88716090
-447 + 89314623 = 89314176
-448 + 89915392 = 89914944
-449 + 90518849 = 90518400
-450 + 91125000 = 91124550
-451 + 91733851 = 91733400
-452 + 92345408 = 92344956
-453 + 92959677 = 92959224
-454 + 93576664 = 93576210
-455 + 94196375 = 94195920
-456 + 94818816 = 94818360
-457 + 95443993 = 95443536
-458 + 96071912 = 96071454
-459 + 96702579 = 96702120
-460 + 97336000 = 97335540
-461 + 97972181 = 97971720
-462 + 98611128 = 98610666
-463 + 99252847 = 99252384
-464 + 99897344 = 99896880
-465 + 100544625 = 100544160
-466 + 101194696 = 101194230
-467 + 101847563 = 101847096
-468 + 102503232 = 102502764
-469 + 103161709 = 103161240
-470 + 103823000 = 103822530
-471 + 104487111 = 104486640
-472 + 105154048 = 105153576
-473 + 105823817 = 105823344
-474 + 106496424 = 106495950
-475 + 107171875 = 107171400
-476 + 107850176 = 107849700
-477 + 108531333 = 108530856
-478 + 109215352 = 109214874
-479 + 109902239 = 109901760
-480 + 110592000 = 110591520
-481 + 111284641 = 111284160
-482 + 111980168 = 111979686
-483 + 112678587 = 112678104
-484 + 113379904 = 113379420
-485 + 114084125 = 114083640
-486 + 114791256 = 114790770
-487 + 115501303 = 115500816
-488 + 116214272 = 116213784
-489 + 116930169 = 116929680
-490 + 117649000 = 117648510
-491 + 118370771 = 118370280
-492 + 119095488 = 119094996
-493 + 119823157 = 119822664
-494 + 120553784 = 120553290
-495 + 121287375 = 121286880
-496 + 122023936 = 122023440
-497 + 122763473 = 122762976
-498 + 123505992 = 123505494
-499 + 124251499 = 124251000
-500 + 125000000 = 124999500
-501 + 125751501 = 125751000
-502 + 126506008 = 126505506
-503 + 127263527 = 127263024
-504 + 128024064 = 128023560
-505 + 128787625 = 128787120
-506 + 129554216 = 129553710
-507 + 130323843 = 130323336
-508 + 131096512 = 131096004
-509 + 131872229 = 131871720
-510 + 132651000 = 132650490
-511 + 133432831 = 133432320

10.2.6. dim 1, grid x, block 256

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <assert.h>
#include <cuda.h>
#include <cuda_runtime.h>

#define N 1000000
#define MAX_ERR 1e-6

__global__ void vector_add(float *out, float *a, float *b, int n) {
  int tid = blockIdx.y * blockDim.x + threadIdx.x;
  int stride = blockDim.x;

  // Handling arbitrary vector size
  for(int i = tid; i < n; i += stride){
    if (i < N){
      out[i] = a[i] + b[i];
    }
  }
}

int main(){
  float *a, *b, *out;
  float *d_a, *d_b, *d_out; 

  // Allocate host memory
  a   = (float*)malloc(sizeof(float) * N);
  b   = (float*)malloc(sizeof(float) * N);
  out = (float*)malloc(sizeof(float) * N);

  // Initialize host arrays
  for(int i = 0; i < N; i++){
    a[i] = 1.0f;
    b[i] = 2.0f;
  }

  // Allocate device memory 
  cudaMalloc((void**)&d_a, sizeof(float) * N);
  cudaMalloc((void**)&d_b, sizeof(float) * N);
  cudaMalloc((void**)&d_out, sizeof(float) * N);

  // Transfer data from host to device memory
  cudaMemcpy(d_a, a, sizeof(float) * N, cudaMemcpyHostToDevice);
  cudaMemcpy(d_b, b, sizeof(float) * N, cudaMemcpyHostToDevice);


  // Executing kernel 
  int block_size = 256;
  int grid_size = ((N + block_size) / block_size);
  vector_add<<<grid_size, block_size>>>(d_out, d_a, d_b, N);

  // Transfer data back to host memory
  cudaMemcpy(out, d_out, sizeof(float) * N, cudaMemcpyDeviceToHost);

  // Verification
  for(int i = 0; i < N; i++){
    assert(fabs(out[i] - a[i] - b[i]) < MAX_ERR);
  }

  printf("PASSED\n");

  // Deallocate device memory
  cudaFree(d_a);
  cudaFree(d_b);
  cudaFree(d_out);

  // Deallocate host memory
  free(a); 
  free(b); 
  free(out);
}

cd babel
nvcc gpu_vector_add_dim1_gridx_block256.cu -o gpu_vector_add_dim1_gridx_block256
./gpu_vector_add_dim1_gridx_block256

PASSED

10.3. Addition dim 2 arry in GPU

10.3.1. dim 2, grid 1, block NxN for array

#include <stdio.h>
#include <cuda.h>
#include <assert.h>
#include <cuda_runtime.h>
#include <curand_kernel.h>
#define N 512
__global__ void add(int *a, int *b, int *c){
  int tid = threadIdx.x + threadIdx.y*blockDim.x + blockDim.x*blockDim.y*blockIdx.x; 
  if(tid < N)
    c[tid] = a[tid] + b[tid];
}
int main()
{
  int a[N], b[N], c[N], i;
  int *dev_a, *dev_b, *dev_c;
  cudaMalloc((void**)&dev_c, N*sizeof(int));
  cudaMalloc((void**)&dev_b, N*sizeof(int));
  cudaMalloc((void**)&dev_a, N*sizeof(int));
  for(i=0; i < N; i++)
    {
      a[i] = 1;
      b[i] = 2;
    }
  cudaMemcpy(dev_a, a, N*sizeof(int), cudaMemcpyHostToDevice);
  cudaMemcpy(dev_b, b, N*sizeof(int), cudaMemcpyHostToDevice);
  dim3 BlockPerGrid(1, 1, 1);
  dim3 ThreadsPerBlock(128, 4, 1);
  add <<< BlockPerGrid, ThreadsPerBlock >>>(dev_a, dev_b, dev_c);
  cudaMemcpy(c, dev_c, N*sizeof(int), cudaMemcpyDeviceToHost);
  for(i=0; i < N; i++){
    assert(a[i] + b[i] == c[i]);
  }
  printf("Passed\n");
  cudaFree(dev_c);
  cudaFree(dev_b);
  cudaFree(dev_a);
  return 0;
}




cd babel
nvcc gpu_vector_add_dim2_grid1_blockNxN.cu -o gpu_vector_add_dim2_grid1_blockNxN
./gpu_vector_add_dim2_grid1_blockNxN

Passed

10.3.2. dim 2, grid 1, block NxN for matrix

#include <stdio.h>
#include <cuda.h>
#include <assert.h>
#include <cuda_runtime.h>
#include <curand_kernel.h>
#define n 32
#define N n*n
__global__ void add(float *a, float *b, float *c){
  __shared__ float A[n][n];
  __shared__ float B[n][n];
  __shared__ float C[n][n];
  int tidx = threadIdx.x;
  int tidy = threadIdx.y;

  A[tidy][tidx] = a[tidx +n*tidy];
  B[tidy][tidx] = b[tidx +n*tidy];

  C[tidy][tidx]= A[tidy][tidx] + B[tidy][tidx];

  c[tidx +n*tidy] = C[tidy][tidx];
}
int main()
{
  float a[N], b[N], out[N];
  float *d_a, *d_b, *d_out; 

  for(int i = 0; i < n; i++){
    for (int j = 0; j < n; j++){
      a[i+j*n] = 1.0f + i;
      b[i+j*n] = 1.0f + i;
    }
  }

  // Allocate device memory 
  cudaMalloc((void**)&d_a, sizeof(float) * N);
  cudaMalloc((void**)&d_b, sizeof(float) * N);
  cudaMalloc((void**)&d_out, sizeof(float) * N);

  // Transfer data from host to device memory
  cudaMemcpy(d_a, a, sizeof(float) * N, cudaMemcpyHostToDevice);
  cudaMemcpy(d_b, b, sizeof(float) * N, cudaMemcpyHostToDevice);

  dim3 BlockPerGrid(1, 1, 1);
  dim3 ThreadsPerBlock(n, n, 1);
  add <<< BlockPerGrid, ThreadsPerBlock >>>(d_a, d_b, d_out);
  cudaMemcpy(out, d_out, sizeof(int) * N, cudaMemcpyDeviceToHost);
  for(int i=0; i < N; i++){
    printf("a[%d] + b[%d] == out[%d] is %f + %f = %f\n", i,i,i, a[i], b[i], out[i]);
  }
  printf("Passed\n");
  cudaFree(d_out);
  cudaFree(d_b);
  cudaFree(d_a);
  return 0;
}


cd babel
nvcc gpu_vector_add_dim2_grid1_blockNxN_matrix.cu -o gpu_vector_add_dim2_grid1_blockNxN_matrix
./gpu_vector_add_dim2_grid1_blockNxN_matrix

a[0] + b[0] == out[0] is 1.000000 + 1.000000 = 2.000000
a[1] + b[1] == out[1] is 2.000000 + 2.000000 = 4.000000
a[2] + b[2] == out[2] is 3.000000 + 3.000000 = 6.000000
a[3] + b[3] == out[3] is 4.000000 + 4.000000 = 8.000000
a[4] + b[4] == out[4] is 5.000000 + 5.000000 = 10.000000
a[5] + b[5] == out[5] is 6.000000 + 6.000000 = 12.000000
a[6] + b[6] == out[6] is 7.000000 + 7.000000 = 14.000000
a[7] + b[7] == out[7] is 8.000000 + 8.000000 = 16.000000
a[8] + b[8] == out[8] is 9.000000 + 9.000000 = 18.000000
a[9] + b[9] == out[9] is 10.000000 + 10.000000 = 20.000000
a[10] + b[10] == out[10] is 11.000000 + 11.000000 = 22.000000
a[11] + b[11] == out[11] is 12.000000 + 12.000000 = 24.000000
a[12] + b[12] == out[12] is 13.000000 + 13.000000 = 26.000000
a[13] + b[13] == out[13] is 14.000000 + 14.000000 = 28.000000
a[14] + b[14] == out[14] is 15.000000 + 15.000000 = 30.000000
a[15] + b[15] == out[15] is 16.000000 + 16.000000 = 32.000000
a[16] + b[16] == out[16] is 17.000000 + 17.000000 = 34.000000
a[17] + b[17] == out[17] is 18.000000 + 18.000000 = 36.000000
a[18] + b[18] == out[18] is 19.000000 + 19.000000 = 38.000000
a[19] + b[19] == out[19] is 20.000000 + 20.000000 = 40.000000
a[20] + b[20] == out[20] is 21.000000 + 21.000000 = 42.000000
a[21] + b[21] == out[21] is 22.000000 + 22.000000 = 44.000000
a[22] + b[22] == out[22] is 23.000000 + 23.000000 = 46.000000
a[23] + b[23] == out[23] is 24.000000 + 24.000000 = 48.000000
a[24] + b[24] == out[24] is 25.000000 + 25.000000 = 50.000000
a[25] + b[25] == out[25] is 26.000000 + 26.000000 = 52.000000
a[26] + b[26] == out[26] is 27.000000 + 27.000000 = 54.000000
a[27] + b[27] == out[27] is 28.000000 + 28.000000 = 56.000000
a[28] + b[28] == out[28] is 29.000000 + 29.000000 = 58.000000
a[29] + b[29] == out[29] is 30.000000 + 30.000000 = 60.000000
a[30] + b[30] == out[30] is 31.000000 + 31.000000 = 62.000000
a[31] + b[31] == out[31] is 32.000000 + 32.000000 = 64.000000
a[32] + b[32] == out[32] is 1.000000 + 1.000000 = 2.000000
a[33] + b[33] == out[33] is 2.000000 + 2.000000 = 4.000000
a[34] + b[34] == out[34] is 3.000000 + 3.000000 = 6.000000
a[35] + b[35] == out[35] is 4.000000 + 4.000000 = 8.000000
a[36] + b[36] == out[36] is 5.000000 + 5.000000 = 10.000000
a[37] + b[37] == out[37] is 6.000000 + 6.000000 = 12.000000
a[38] + b[38] == out[38] is 7.000000 + 7.000000 = 14.000000
a[39] + b[39] == out[39] is 8.000000 + 8.000000 = 16.000000
a[40] + b[40] == out[40] is 9.000000 + 9.000000 = 18.000000
a[41] + b[41] == out[41] is 10.000000 + 10.000000 = 20.000000
a[42] + b[42] == out[42] is 11.000000 + 11.000000 = 22.000000
a[43] + b[43] == out[43] is 12.000000 + 12.000000 = 24.000000
a[44] + b[44] == out[44] is 13.000000 + 13.000000 = 26.000000
a[45] + b[45] == out[45] is 14.000000 + 14.000000 = 28.000000
a[46] + b[46] == out[46] is 15.000000 + 15.000000 = 30.000000
a[47] + b[47] == out[47] is 16.000000 + 16.000000 = 32.000000
a[48] + b[48] == out[48] is 17.000000 + 17.000000 = 34.000000
a[49] + b[49] == out[49] is 18.000000 + 18.000000 = 36.000000
a[50] + b[50] == out[50] is 19.000000 + 19.000000 = 38.000000
a[51] + b[51] == out[51] is 20.000000 + 20.000000 = 40.000000
a[52] + b[52] == out[52] is 21.000000 + 21.000000 = 42.000000
a[53] + b[53] == out[53] is 22.000000 + 22.000000 = 44.000000
a[54] + b[54] == out[54] is 23.000000 + 23.000000 = 46.000000
a[55] + b[55] == out[55] is 24.000000 + 24.000000 = 48.000000
a[56] + b[56] == out[56] is 25.000000 + 25.000000 = 50.000000
a[57] + b[57] == out[57] is 26.000000 + 26.000000 = 52.000000
a[58] + b[58] == out[58] is 27.000000 + 27.000000 = 54.000000
a[59] + b[59] == out[59] is 28.000000 + 28.000000 = 56.000000
a[60] + b[60] == out[60] is 29.000000 + 29.000000 = 58.000000
a[61] + b[61] == out[61] is 30.000000 + 30.000000 = 60.000000
a[62] + b[62] == out[62] is 31.000000 + 31.000000 = 62.000000
a[63] + b[63] == out[63] is 32.000000 + 32.000000 = 64.000000
a[64] + b[64] == out[64] is 1.000000 + 1.000000 = 2.000000
a[65] + b[65] == out[65] is 2.000000 + 2.000000 = 4.000000
a[66] + b[66] == out[66] is 3.000000 + 3.000000 = 6.000000
a[67] + b[67] == out[67] is 4.000000 + 4.000000 = 8.000000
a[68] + b[68] == out[68] is 5.000000 + 5.000000 = 10.000000
a[69] + b[69] == out[69] is 6.000000 + 6.000000 = 12.000000
a[70] + b[70] == out[70] is 7.000000 + 7.000000 = 14.000000
a[71] + b[71] == out[71] is 8.000000 + 8.000000 = 16.000000
a[72] + b[72] == out[72] is 9.000000 + 9.000000 = 18.000000
a[73] + b[73] == out[73] is 10.000000 + 10.000000 = 20.000000
a[74] + b[74] == out[74] is 11.000000 + 11.000000 = 22.000000
a[75] + b[75] == out[75] is 12.000000 + 12.000000 = 24.000000
a[76] + b[76] == out[76] is 13.000000 + 13.000000 = 26.000000
a[77] + b[77] == out[77] is 14.000000 + 14.000000 = 28.000000
a[78] + b[78] == out[78] is 15.000000 + 15.000000 = 30.000000
a[79] + b[79] == out[79] is 16.000000 + 16.000000 = 32.000000
a[80] + b[80] == out[80] is 17.000000 + 17.000000 = 34.000000
a[81] + b[81] == out[81] is 18.000000 + 18.000000 = 36.000000
a[82] + b[82] == out[82] is 19.000000 + 19.000000 = 38.000000
a[83] + b[83] == out[83] is 20.000000 + 20.000000 = 40.000000
a[84] + b[84] == out[84] is 21.000000 + 21.000000 = 42.000000
a[85] + b[85] == out[85] is 22.000000 + 22.000000 = 44.000000
a[86] + b[86] == out[86] is 23.000000 + 23.000000 = 46.000000
a[87] + b[87] == out[87] is 24.000000 + 24.000000 = 48.000000
a[88] + b[88] == out[88] is 25.000000 + 25.000000 = 50.000000
a[89] + b[89] == out[89] is 26.000000 + 26.000000 = 52.000000
a[90] + b[90] == out[90] is 27.000000 + 27.000000 = 54.000000
a[91] + b[91] == out[91] is 28.000000 + 28.000000 = 56.000000
a[92] + b[92] == out[92] is 29.000000 + 29.000000 = 58.000000
a[93] + b[93] == out[93] is 30.000000 + 30.000000 = 60.000000
a[94] + b[94] == out[94] is 31.000000 + 31.000000 = 62.000000
a[95] + b[95] == out[95] is 32.000000 + 32.000000 = 64.000000
a[96] + b[96] == out[96] is 1.000000 + 1.000000 = 2.000000
a[97] + b[97] == out[97] is 2.000000 + 2.000000 = 4.000000
a[98] + b[98] == out[98] is 3.000000 + 3.000000 = 6.000000
a[99] + b[99] == out[99] is 4.000000 + 4.000000 = 8.000000
a[100] + b[100] == out[100] is 5.000000 + 5.000000 = 10.000000
a[101] + b[101] == out[101] is 6.000000 + 6.000000 = 12.000000
a[102] + b[102] == out[102] is 7.000000 + 7.000000 = 14.000000
a[103] + b[103] == out[103] is 8.000000 + 8.000000 = 16.000000
a[104] + b[104] == out[104] is 9.000000 + 9.000000 = 18.000000
a[105] + b[105] == out[105] is 10.000000 + 10.000000 = 20.000000
a[106] + b[106] == out[106] is 11.000000 + 11.000000 = 22.000000
a[107] + b[107] == out[107] is 12.000000 + 12.000000 = 24.000000
a[108] + b[108] == out[108] is 13.000000 + 13.000000 = 26.000000
a[109] + b[109] == out[109] is 14.000000 + 14.000000 = 28.000000
a[110] + b[110] == out[110] is 15.000000 + 15.000000 = 30.000000
a[111] + b[111] == out[111] is 16.000000 + 16.000000 = 32.000000
a[112] + b[112] == out[112] is 17.000000 + 17.000000 = 34.000000
a[113] + b[113] == out[113] is 18.000000 + 18.000000 = 36.000000
a[114] + b[114] == out[114] is 19.000000 + 19.000000 = 38.000000
a[115] + b[115] == out[115] is 20.000000 + 20.000000 = 40.000000
a[116] + b[116] == out[116] is 21.000000 + 21.000000 = 42.000000
a[117] + b[117] == out[117] is 22.000000 + 22.000000 = 44.000000
a[118] + b[118] == out[118] is 23.000000 + 23.000000 = 46.000000
a[119] + b[119] == out[119] is 24.000000 + 24.000000 = 48.000000
a[120] + b[120] == out[120] is 25.000000 + 25.000000 = 50.000000
a[121] + b[121] == out[121] is 26.000000 + 26.000000 = 52.000000
a[122] + b[122] == out[122] is 27.000000 + 27.000000 = 54.000000
a[123] + b[123] == out[123] is 28.000000 + 28.000000 = 56.000000
a[124] + b[124] == out[124] is 29.000000 + 29.000000 = 58.000000
a[125] + b[125] == out[125] is 30.000000 + 30.000000 = 60.000000
a[126] + b[126] == out[126] is 31.000000 + 31.000000 = 62.000000
a[127] + b[127] == out[127] is 32.000000 + 32.000000 = 64.000000
a[128] + b[128] == out[128] is 1.000000 + 1.000000 = 2.000000
a[129] + b[129] == out[129] is 2.000000 + 2.000000 = 4.000000
a[130] + b[130] == out[130] is 3.000000 + 3.000000 = 6.000000
a[131] + b[131] == out[131] is 4.000000 + 4.000000 = 8.000000
a[132] + b[132] == out[132] is 5.000000 + 5.000000 = 10.000000
a[133] + b[133] == out[133] is 6.000000 + 6.000000 = 12.000000
a[134] + b[134] == out[134] is 7.000000 + 7.000000 = 14.000000
a[135] + b[135] == out[135] is 8.000000 + 8.000000 = 16.000000
a[136] + b[136] == out[136] is 9.000000 + 9.000000 = 18.000000
a[137] + b[137] == out[137] is 10.000000 + 10.000000 = 20.000000
a[138] + b[138] == out[138] is 11.000000 + 11.000000 = 22.000000
a[139] + b[139] == out[139] is 12.000000 + 12.000000 = 24.000000
a[140] + b[140] == out[140] is 13.000000 + 13.000000 = 26.000000
a[141] + b[141] == out[141] is 14.000000 + 14.000000 = 28.000000
a[142] + b[142] == out[142] is 15.000000 + 15.000000 = 30.000000
a[143] + b[143] == out[143] is 16.000000 + 16.000000 = 32.000000
a[144] + b[144] == out[144] is 17.000000 + 17.000000 = 34.000000
a[145] + b[145] == out[145] is 18.000000 + 18.000000 = 36.000000
a[146] + b[146] == out[146] is 19.000000 + 19.000000 = 38.000000
a[147] + b[147] == out[147] is 20.000000 + 20.000000 = 40.000000
a[148] + b[148] == out[148] is 21.000000 + 21.000000 = 42.000000
a[149] + b[149] == out[149] is 22.000000 + 22.000000 = 44.000000
a[150] + b[150] == out[150] is 23.000000 + 23.000000 = 46.000000
a[151] + b[151] == out[151] is 24.000000 + 24.000000 = 48.000000
a[152] + b[152] == out[152] is 25.000000 + 25.000000 = 50.000000
a[153] + b[153] == out[153] is 26.000000 + 26.000000 = 52.000000
a[154] + b[154] == out[154] is 27.000000 + 27.000000 = 54.000000
a[155] + b[155] == out[155] is 28.000000 + 28.000000 = 56.000000
a[156] + b[156] == out[156] is 29.000000 + 29.000000 = 58.000000
a[157] + b[157] == out[157] is 30.000000 + 30.000000 = 60.000000
a[158] + b[158] == out[158] is 31.000000 + 31.000000 = 62.000000
a[159] + b[159] == out[159] is 32.000000 + 32.000000 = 64.000000
a[160] + b[160] == out[160] is 1.000000 + 1.000000 = 2.000000
a[161] + b[161] == out[161] is 2.000000 + 2.000000 = 4.000000
a[162] + b[162] == out[162] is 3.000000 + 3.000000 = 6.000000
a[163] + b[163] == out[163] is 4.000000 + 4.000000 = 8.000000
a[164] + b[164] == out[164] is 5.000000 + 5.000000 = 10.000000
a[165] + b[165] == out[165] is 6.000000 + 6.000000 = 12.000000
a[166] + b[166] == out[166] is 7.000000 + 7.000000 = 14.000000
a[167] + b[167] == out[167] is 8.000000 + 8.000000 = 16.000000
a[168] + b[168] == out[168] is 9.000000 + 9.000000 = 18.000000
a[169] + b[169] == out[169] is 10.000000 + 10.000000 = 20.000000
a[170] + b[170] == out[170] is 11.000000 + 11.000000 = 22.000000
a[171] + b[171] == out[171] is 12.000000 + 12.000000 = 24.000000
a[172] + b[172] == out[172] is 13.000000 + 13.000000 = 26.000000
a[173] + b[173] == out[173] is 14.000000 + 14.000000 = 28.000000
a[174] + b[174] == out[174] is 15.000000 + 15.000000 = 30.000000
a[175] + b[175] == out[175] is 16.000000 + 16.000000 = 32.000000
a[176] + b[176] == out[176] is 17.000000 + 17.000000 = 34.000000
a[177] + b[177] == out[177] is 18.000000 + 18.000000 = 36.000000
a[178] + b[178] == out[178] is 19.000000 + 19.000000 = 38.000000
a[179] + b[179] == out[179] is 20.000000 + 20.000000 = 40.000000
a[180] + b[180] == out[180] is 21.000000 + 21.000000 = 42.000000
a[181] + b[181] == out[181] is 22.000000 + 22.000000 = 44.000000
a[182] + b[182] == out[182] is 23.000000 + 23.000000 = 46.000000
a[183] + b[183] == out[183] is 24.000000 + 24.000000 = 48.000000
a[184] + b[184] == out[184] is 25.000000 + 25.000000 = 50.000000
a[185] + b[185] == out[185] is 26.000000 + 26.000000 = 52.000000
a[186] + b[186] == out[186] is 27.000000 + 27.000000 = 54.000000
a[187] + b[187] == out[187] is 28.000000 + 28.000000 = 56.000000
a[188] + b[188] == out[188] is 29.000000 + 29.000000 = 58.000000
a[189] + b[189] == out[189] is 30.000000 + 30.000000 = 60.000000
a[190] + b[190] == out[190] is 31.000000 + 31.000000 = 62.000000
a[191] + b[191] == out[191] is 32.000000 + 32.000000 = 64.000000
a[192] + b[192] == out[192] is 1.000000 + 1.000000 = 2.000000
a[193] + b[193] == out[193] is 2.000000 + 2.000000 = 4.000000
a[194] + b[194] == out[194] is 3.000000 + 3.000000 = 6.000000
a[195] + b[195] == out[195] is 4.000000 + 4.000000 = 8.000000
a[196] + b[196] == out[196] is 5.000000 + 5.000000 = 10.000000
a[197] + b[197] == out[197] is 6.000000 + 6.000000 = 12.000000
a[198] + b[198] == out[198] is 7.000000 + 7.000000 = 14.000000
a[199] + b[199] == out[199] is 8.000000 + 8.000000 = 16.000000
a[200] + b[200] == out[200] is 9.000000 + 9.000000 = 18.000000
a[201] + b[201] == out[201] is 10.000000 + 10.000000 = 20.000000
a[202] + b[202] == out[202] is 11.000000 + 11.000000 = 22.000000
a[203] + b[203] == out[203] is 12.000000 + 12.000000 = 24.000000
a[204] + b[204] == out[204] is 13.000000 + 13.000000 = 26.000000
a[205] + b[205] == out[205] is 14.000000 + 14.000000 = 28.000000
a[206] + b[206] == out[206] is 15.000000 + 15.000000 = 30.000000
a[207] + b[207] == out[207] is 16.000000 + 16.000000 = 32.000000
a[208] + b[208] == out[208] is 17.000000 + 17.000000 = 34.000000
a[209] + b[209] == out[209] is 18.000000 + 18.000000 = 36.000000
a[210] + b[210] == out[210] is 19.000000 + 19.000000 = 38.000000
a[211] + b[211] == out[211] is 20.000000 + 20.000000 = 40.000000
a[212] + b[212] == out[212] is 21.000000 + 21.000000 = 42.000000
a[213] + b[213] == out[213] is 22.000000 + 22.000000 = 44.000000
a[214] + b[214] == out[214] is 23.000000 + 23.000000 = 46.000000
a[215] + b[215] == out[215] is 24.000000 + 24.000000 = 48.000000
a[216] + b[216] == out[216] is 25.000000 + 25.000000 = 50.000000
a[217] + b[217] == out[217] is 26.000000 + 26.000000 = 52.000000
a[218] + b[218] == out[218] is 27.000000 + 27.000000 = 54.000000
a[219] + b[219] == out[219] is 28.000000 + 28.000000 = 56.000000
a[220] + b[220] == out[220] is 29.000000 + 29.000000 = 58.000000
a[221] + b[221] == out[221] is 30.000000 + 30.000000 = 60.000000
a[222] + b[222] == out[222] is 31.000000 + 31.000000 = 62.000000
a[223] + b[223] == out[223] is 32.000000 + 32.000000 = 64.000000
a[224] + b[224] == out[224] is 1.000000 + 1.000000 = 2.000000
a[225] + b[225] == out[225] is 2.000000 + 2.000000 = 4.000000
a[226] + b[226] == out[226] is 3.000000 + 3.000000 = 6.000000
a[227] + b[227] == out[227] is 4.000000 + 4.000000 = 8.000000
a[228] + b[228] == out[228] is 5.000000 + 5.000000 = 10.000000
a[229] + b[229] == out[229] is 6.000000 + 6.000000 = 12.000000
a[230] + b[230] == out[230] is 7.000000 + 7.000000 = 14.000000
a[231] + b[231] == out[231] is 8.000000 + 8.000000 = 16.000000
a[232] + b[232] == out[232] is 9.000000 + 9.000000 = 18.000000
a[233] + b[233] == out[233] is 10.000000 + 10.000000 = 20.000000
a[234] + b[234] == out[234] is 11.000000 + 11.000000 = 22.000000
a[235] + b[235] == out[235] is 12.000000 + 12.000000 = 24.000000
a[236] + b[236] == out[236] is 13.000000 + 13.000000 = 26.000000
a[237] + b[237] == out[237] is 14.000000 + 14.000000 = 28.000000
a[238] + b[238] == out[238] is 15.000000 + 15.000000 = 30.000000
a[239] + b[239] == out[239] is 16.000000 + 16.000000 = 32.000000
a[240] + b[240] == out[240] is 17.000000 + 17.000000 = 34.000000
a[241] + b[241] == out[241] is 18.000000 + 18.000000 = 36.000000
a[242] + b[242] == out[242] is 19.000000 + 19.000000 = 38.000000
a[243] + b[243] == out[243] is 20.000000 + 20.000000 = 40.000000
a[244] + b[244] == out[244] is 21.000000 + 21.000000 = 42.000000
a[245] + b[245] == out[245] is 22.000000 + 22.000000 = 44.000000
a[246] + b[246] == out[246] is 23.000000 + 23.000000 = 46.000000
a[247] + b[247] == out[247] is 24.000000 + 24.000000 = 48.000000
a[248] + b[248] == out[248] is 25.000000 + 25.000000 = 50.000000
a[249] + b[249] == out[249] is 26.000000 + 26.000000 = 52.000000
a[250] + b[250] == out[250] is 27.000000 + 27.000000 = 54.000000
a[251] + b[251] == out[251] is 28.000000 + 28.000000 = 56.000000
a[252] + b[252] == out[252] is 29.000000 + 29.000000 = 58.000000
a[253] + b[253] == out[253] is 30.000000 + 30.000000 = 60.000000
a[254] + b[254] == out[254] is 31.000000 + 31.000000 = 62.000000
a[255] + b[255] == out[255] is 32.000000 + 32.000000 = 64.000000
a[256] + b[256] == out[256] is 1.000000 + 1.000000 = 2.000000
a[257] + b[257] == out[257] is 2.000000 + 2.000000 = 4.000000
a[258] + b[258] == out[258] is 3.000000 + 3.000000 = 6.000000
a[259] + b[259] == out[259] is 4.000000 + 4.000000 = 8.000000
a[260] + b[260] == out[260] is 5.000000 + 5.000000 = 10.000000
a[261] + b[261] == out[261] is 6.000000 + 6.000000 = 12.000000
a[262] + b[262] == out[262] is 7.000000 + 7.000000 = 14.000000
a[263] + b[263] == out[263] is 8.000000 + 8.000000 = 16.000000
a[264] + b[264] == out[264] is 9.000000 + 9.000000 = 18.000000
a[265] + b[265] == out[265] is 10.000000 + 10.000000 = 20.000000
a[266] + b[266] == out[266] is 11.000000 + 11.000000 = 22.000000
a[267] + b[267] == out[267] is 12.000000 + 12.000000 = 24.000000
a[268] + b[268] == out[268] is 13.000000 + 13.000000 = 26.000000
a[269] + b[269] == out[269] is 14.000000 + 14.000000 = 28.000000
a[270] + b[270] == out[270] is 15.000000 + 15.000000 = 30.000000
a[271] + b[271] == out[271] is 16.000000 + 16.000000 = 32.000000
a[272] + b[272] == out[272] is 17.000000 + 17.000000 = 34.000000
a[273] + b[273] == out[273] is 18.000000 + 18.000000 = 36.000000
a[274] + b[274] == out[274] is 19.000000 + 19.000000 = 38.000000
a[275] + b[275] == out[275] is 20.000000 + 20.000000 = 40.000000
a[276] + b[276] == out[276] is 21.000000 + 21.000000 = 42.000000
a[277] + b[277] == out[277] is 22.000000 + 22.000000 = 44.000000
a[278] + b[278] == out[278] is 23.000000 + 23.000000 = 46.000000
a[279] + b[279] == out[279] is 24.000000 + 24.000000 = 48.000000
a[280] + b[280] == out[280] is 25.000000 + 25.000000 = 50.000000
a[281] + b[281] == out[281] is 26.000000 + 26.000000 = 52.000000
a[282] + b[282] == out[282] is 27.000000 + 27.000000 = 54.000000
a[283] + b[283] == out[283] is 28.000000 + 28.000000 = 56.000000
a[284] + b[284] == out[284] is 29.000000 + 29.000000 = 58.000000
a[285] + b[285] == out[285] is 30.000000 + 30.000000 = 60.000000
a[286] + b[286] == out[286] is 31.000000 + 31.000000 = 62.000000
a[287] + b[287] == out[287] is 32.000000 + 32.000000 = 64.000000
a[288] + b[288] == out[288] is 1.000000 + 1.000000 = 2.000000
a[289] + b[289] == out[289] is 2.000000 + 2.000000 = 4.000000
a[290] + b[290] == out[290] is 3.000000 + 3.000000 = 6.000000
a[291] + b[291] == out[291] is 4.000000 + 4.000000 = 8.000000
a[292] + b[292] == out[292] is 5.000000 + 5.000000 = 10.000000
a[293] + b[293] == out[293] is 6.000000 + 6.000000 = 12.000000
a[294] + b[294] == out[294] is 7.000000 + 7.000000 = 14.000000
a[295] + b[295] == out[295] is 8.000000 + 8.000000 = 16.000000
a[296] + b[296] == out[296] is 9.000000 + 9.000000 = 18.000000
a[297] + b[297] == out[297] is 10.000000 + 10.000000 = 20.000000
a[298] + b[298] == out[298] is 11.000000 + 11.000000 = 22.000000
a[299] + b[299] == out[299] is 12.000000 + 12.000000 = 24.000000
a[300] + b[300] == out[300] is 13.000000 + 13.000000 = 26.000000
a[301] + b[301] == out[301] is 14.000000 + 14.000000 = 28.000000
a[302] + b[302] == out[302] is 15.000000 + 15.000000 = 30.000000
a[303] + b[303] == out[303] is 16.000000 + 16.000000 = 32.000000
a[304] + b[304] == out[304] is 17.000000 + 17.000000 = 34.000000
a[305] + b[305] == out[305] is 18.000000 + 18.000000 = 36.000000
a[306] + b[306] == out[306] is 19.000000 + 19.000000 = 38.000000
a[307] + b[307] == out[307] is 20.000000 + 20.000000 = 40.000000
a[308] + b[308] == out[308] is 21.000000 + 21.000000 = 42.000000
a[309] + b[309] == out[309] is 22.000000 + 22.000000 = 44.000000
a[310] + b[310] == out[310] is 23.000000 + 23.000000 = 46.000000
a[311] + b[311] == out[311] is 24.000000 + 24.000000 = 48.000000
a[312] + b[312] == out[312] is 25.000000 + 25.000000 = 50.000000
a[313] + b[313] == out[313] is 26.000000 + 26.000000 = 52.000000
a[314] + b[314] == out[314] is 27.000000 + 27.000000 = 54.000000
a[315] + b[315] == out[315] is 28.000000 + 28.000000 = 56.000000
a[316] + b[316] == out[316] is 29.000000 + 29.000000 = 58.000000
a[317] + b[317] == out[317] is 30.000000 + 30.000000 = 60.000000
a[318] + b[318] == out[318] is 31.000000 + 31.000000 = 62.000000
a[319] + b[319] == out[319] is 32.000000 + 32.000000 = 64.000000
a[320] + b[320] == out[320] is 1.000000 + 1.000000 = 2.000000
a[321] + b[321] == out[321] is 2.000000 + 2.000000 = 4.000000
a[322] + b[322] == out[322] is 3.000000 + 3.000000 = 6.000000
a[323] + b[323] == out[323] is 4.000000 + 4.000000 = 8.000000
a[324] + b[324] == out[324] is 5.000000 + 5.000000 = 10.000000
a[325] + b[325] == out[325] is 6.000000 + 6.000000 = 12.000000
a[326] + b[326] == out[326] is 7.000000 + 7.000000 = 14.000000
a[327] + b[327] == out[327] is 8.000000 + 8.000000 = 16.000000
a[328] + b[328] == out[328] is 9.000000 + 9.000000 = 18.000000
a[329] + b[329] == out[329] is 10.000000 + 10.000000 = 20.000000
a[330] + b[330] == out[330] is 11.000000 + 11.000000 = 22.000000
a[331] + b[331] == out[331] is 12.000000 + 12.000000 = 24.000000
a[332] + b[332] == out[332] is 13.000000 + 13.000000 = 26.000000
a[333] + b[333] == out[333] is 14.000000 + 14.000000 = 28.000000
a[334] + b[334] == out[334] is 15.000000 + 15.000000 = 30.000000
a[335] + b[335] == out[335] is 16.000000 + 16.000000 = 32.000000
a[336] + b[336] == out[336] is 17.000000 + 17.000000 = 34.000000
a[337] + b[337] == out[337] is 18.000000 + 18.000000 = 36.000000
a[338] + b[338] == out[338] is 19.000000 + 19.000000 = 38.000000
a[339] + b[339] == out[339] is 20.000000 + 20.000000 = 40.000000
a[340] + b[340] == out[340] is 21.000000 + 21.000000 = 42.000000
a[341] + b[341] == out[341] is 22.000000 + 22.000000 = 44.000000
a[342] + b[342] == out[342] is 23.000000 + 23.000000 = 46.000000
a[343] + b[343] == out[343] is 24.000000 + 24.000000 = 48.000000
a[344] + b[344] == out[344] is 25.000000 + 25.000000 = 50.000000
a[345] + b[345] == out[345] is 26.000000 + 26.000000 = 52.000000
a[346] + b[346] == out[346] is 27.000000 + 27.000000 = 54.000000
a[347] + b[347] == out[347] is 28.000000 + 28.000000 = 56.000000
a[348] + b[348] == out[348] is 29.000000 + 29.000000 = 58.000000
a[349] + b[349] == out[349] is 30.000000 + 30.000000 = 60.000000
a[350] + b[350] == out[350] is 31.000000 + 31.000000 = 62.000000
a[351] + b[351] == out[351] is 32.000000 + 32.000000 = 64.000000
a[352] + b[352] == out[352] is 1.000000 + 1.000000 = 2.000000
a[353] + b[353] == out[353] is 2.000000 + 2.000000 = 4.000000
a[354] + b[354] == out[354] is 3.000000 + 3.000000 = 6.000000
a[355] + b[355] == out[355] is 4.000000 + 4.000000 = 8.000000
a[356] + b[356] == out[356] is 5.000000 + 5.000000 = 10.000000
a[357] + b[357] == out[357] is 6.000000 + 6.000000 = 12.000000
a[358] + b[358] == out[358] is 7.000000 + 7.000000 = 14.000000
a[359] + b[359] == out[359] is 8.000000 + 8.000000 = 16.000000
a[360] + b[360] == out[360] is 9.000000 + 9.000000 = 18.000000
a[361] + b[361] == out[361] is 10.000000 + 10.000000 = 20.000000
a[362] + b[362] == out[362] is 11.000000 + 11.000000 = 22.000000
a[363] + b[363] == out[363] is 12.000000 + 12.000000 = 24.000000
a[364] + b[364] == out[364] is 13.000000 + 13.000000 = 26.000000
a[365] + b[365] == out[365] is 14.000000 + 14.000000 = 28.000000
a[366] + b[366] == out[366] is 15.000000 + 15.000000 = 30.000000
a[367] + b[367] == out[367] is 16.000000 + 16.000000 = 32.000000
a[368] + b[368] == out[368] is 17.000000 + 17.000000 = 34.000000
a[369] + b[369] == out[369] is 18.000000 + 18.000000 = 36.000000
a[370] + b[370] == out[370] is 19.000000 + 19.000000 = 38.000000
a[371] + b[371] == out[371] is 20.000000 + 20.000000 = 40.000000
a[372] + b[372] == out[372] is 21.000000 + 21.000000 = 42.000000
a[373] + b[373] == out[373] is 22.000000 + 22.000000 = 44.000000
a[374] + b[374] == out[374] is 23.000000 + 23.000000 = 46.000000
a[375] + b[375] == out[375] is 24.000000 + 24.000000 = 48.000000
a[376] + b[376] == out[376] is 25.000000 + 25.000000 = 50.000000
a[377] + b[377] == out[377] is 26.000000 + 26.000000 = 52.000000
a[378] + b[378] == out[378] is 27.000000 + 27.000000 = 54.000000
a[379] + b[379] == out[379] is 28.000000 + 28.000000 = 56.000000
a[380] + b[380] == out[380] is 29.000000 + 29.000000 = 58.000000
a[381] + b[381] == out[381] is 30.000000 + 30.000000 = 60.000000
a[382] + b[382] == out[382] is 31.000000 + 31.000000 = 62.000000
a[383] + b[383] == out[383] is 32.000000 + 32.000000 = 64.000000
a[384] + b[384] == out[384] is 1.000000 + 1.000000 = 2.000000
a[385] + b[385] == out[385] is 2.000000 + 2.000000 = 4.000000
a[386] + b[386] == out[386] is 3.000000 + 3.000000 = 6.000000
a[387] + b[387] == out[387] is 4.000000 + 4.000000 = 8.000000
a[388] + b[388] == out[388] is 5.000000 + 5.000000 = 10.000000
a[389] + b[389] == out[389] is 6.000000 + 6.000000 = 12.000000
a[390] + b[390] == out[390] is 7.000000 + 7.000000 = 14.000000
a[391] + b[391] == out[391] is 8.000000 + 8.000000 = 16.000000
a[392] + b[392] == out[392] is 9.000000 + 9.000000 = 18.000000
a[393] + b[393] == out[393] is 10.000000 + 10.000000 = 20.000000
a[394] + b[394] == out[394] is 11.000000 + 11.000000 = 22.000000
a[395] + b[395] == out[395] is 12.000000 + 12.000000 = 24.000000
a[396] + b[396] == out[396] is 13.000000 + 13.000000 = 26.000000
a[397] + b[397] == out[397] is 14.000000 + 14.000000 = 28.000000
a[398] + b[398] == out[398] is 15.000000 + 15.000000 = 30.000000
a[399] + b[399] == out[399] is 16.000000 + 16.000000 = 32.000000
a[400] + b[400] == out[400] is 17.000000 + 17.000000 = 34.000000
a[401] + b[401] == out[401] is 18.000000 + 18.000000 = 36.000000
a[402] + b[402] == out[402] is 19.000000 + 19.000000 = 38.000000
a[403] + b[403] == out[403] is 20.000000 + 20.000000 = 40.000000
a[404] + b[404] == out[404] is 21.000000 + 21.000000 = 42.000000
a[405] + b[405] == out[405] is 22.000000 + 22.000000 = 44.000000
a[406] + b[406] == out[406] is 23.000000 + 23.000000 = 46.000000
a[407] + b[407] == out[407] is 24.000000 + 24.000000 = 48.000000
a[408] + b[408] == out[408] is 25.000000 + 25.000000 = 50.000000
a[409] + b[409] == out[409] is 26.000000 + 26.000000 = 52.000000
a[410] + b[410] == out[410] is 27.000000 + 27.000000 = 54.000000
a[411] + b[411] == out[411] is 28.000000 + 28.000000 = 56.000000
a[412] + b[412] == out[412] is 29.000000 + 29.000000 = 58.000000
a[413] + b[413] == out[413] is 30.000000 + 30.000000 = 60.000000
a[414] + b[414] == out[414] is 31.000000 + 31.000000 = 62.000000
a[415] + b[415] == out[415] is 32.000000 + 32.000000 = 64.000000
a[416] + b[416] == out[416] is 1.000000 + 1.000000 = 2.000000
a[417] + b[417] == out[417] is 2.000000 + 2.000000 = 4.000000
a[418] + b[418] == out[418] is 3.000000 + 3.000000 = 6.000000
a[419] + b[419] == out[419] is 4.000000 + 4.000000 = 8.000000
a[420] + b[420] == out[420] is 5.000000 + 5.000000 = 10.000000
a[421] + b[421] == out[421] is 6.000000 + 6.000000 = 12.000000
a[422] + b[422] == out[422] is 7.000000 + 7.000000 = 14.000000
a[423] + b[423] == out[423] is 8.000000 + 8.000000 = 16.000000
a[424] + b[424] == out[424] is 9.000000 + 9.000000 = 18.000000
a[425] + b[425] == out[425] is 10.000000 + 10.000000 = 20.000000
a[426] + b[426] == out[426] is 11.000000 + 11.000000 = 22.000000
a[427] + b[427] == out[427] is 12.000000 + 12.000000 = 24.000000
a[428] + b[428] == out[428] is 13.000000 + 13.000000 = 26.000000
a[429] + b[429] == out[429] is 14.000000 + 14.000000 = 28.000000
a[430] + b[430] == out[430] is 15.000000 + 15.000000 = 30.000000
a[431] + b[431] == out[431] is 16.000000 + 16.000000 = 32.000000
a[432] + b[432] == out[432] is 17.000000 + 17.000000 = 34.000000
a[433] + b[433] == out[433] is 18.000000 + 18.000000 = 36.000000
a[434] + b[434] == out[434] is 19.000000 + 19.000000 = 38.000000
a[435] + b[435] == out[435] is 20.000000 + 20.000000 = 40.000000
a[436] + b[436] == out[436] is 21.000000 + 21.000000 = 42.000000
a[437] + b[437] == out[437] is 22.000000 + 22.000000 = 44.000000
a[438] + b[438] == out[438] is 23.000000 + 23.000000 = 46.000000
a[439] + b[439] == out[439] is 24.000000 + 24.000000 = 48.000000
a[440] + b[440] == out[440] is 25.000000 + 25.000000 = 50.000000
a[441] + b[441] == out[441] is 26.000000 + 26.000000 = 52.000000
a[442] + b[442] == out[442] is 27.000000 + 27.000000 = 54.000000
a[443] + b[443] == out[443] is 28.000000 + 28.000000 = 56.000000
a[444] + b[444] == out[444] is 29.000000 + 29.000000 = 58.000000
a[445] + b[445] == out[445] is 30.000000 + 30.000000 = 60.000000
a[446] + b[446] == out[446] is 31.000000 + 31.000000 = 62.000000
a[447] + b[447] == out[447] is 32.000000 + 32.000000 = 64.000000
a[448] + b[448] == out[448] is 1.000000 + 1.000000 = 2.000000
a[449] + b[449] == out[449] is 2.000000 + 2.000000 = 4.000000
a[450] + b[450] == out[450] is 3.000000 + 3.000000 = 6.000000
a[451] + b[451] == out[451] is 4.000000 + 4.000000 = 8.000000
a[452] + b[452] == out[452] is 5.000000 + 5.000000 = 10.000000
a[453] + b[453] == out[453] is 6.000000 + 6.000000 = 12.000000
a[454] + b[454] == out[454] is 7.000000 + 7.000000 = 14.000000
a[455] + b[455] == out[455] is 8.000000 + 8.000000 = 16.000000
a[456] + b[456] == out[456] is 9.000000 + 9.000000 = 18.000000
a[457] + b[457] == out[457] is 10.000000 + 10.000000 = 20.000000
a[458] + b[458] == out[458] is 11.000000 + 11.000000 = 22.000000
a[459] + b[459] == out[459] is 12.000000 + 12.000000 = 24.000000
a[460] + b[460] == out[460] is 13.000000 + 13.000000 = 26.000000
a[461] + b[461] == out[461] is 14.000000 + 14.000000 = 28.000000
a[462] + b[462] == out[462] is 15.000000 + 15.000000 = 30.000000
a[463] + b[463] == out[463] is 16.000000 + 16.000000 = 32.000000
a[464] + b[464] == out[464] is 17.000000 + 17.000000 = 34.000000
a[465] + b[465] == out[465] is 18.000000 + 18.000000 = 36.000000
a[466] + b[466] == out[466] is 19.000000 + 19.000000 = 38.000000
a[467] + b[467] == out[467] is 20.000000 + 20.000000 = 40.000000
a[468] + b[468] == out[468] is 21.000000 + 21.000000 = 42.000000
a[469] + b[469] == out[469] is 22.000000 + 22.000000 = 44.000000
a[470] + b[470] == out[470] is 23.000000 + 23.000000 = 46.000000
a[471] + b[471] == out[471] is 24.000000 + 24.000000 = 48.000000
a[472] + b[472] == out[472] is 25.000000 + 25.000000 = 50.000000
a[473] + b[473] == out[473] is 26.000000 + 26.000000 = 52.000000
a[474] + b[474] == out[474] is 27.000000 + 27.000000 = 54.000000
a[475] + b[475] == out[475] is 28.000000 + 28.000000 = 56.000000
a[476] + b[476] == out[476] is 29.000000 + 29.000000 = 58.000000
a[477] + b[477] == out[477] is 30.000000 + 30.000000 = 60.000000
a[478] + b[478] == out[478] is 31.000000 + 31.000000 = 62.000000
a[479] + b[479] == out[479] is 32.000000 + 32.000000 = 64.000000
a[480] + b[480] == out[480] is 1.000000 + 1.000000 = 2.000000
a[481] + b[481] == out[481] is 2.000000 + 2.000000 = 4.000000
a[482] + b[482] == out[482] is 3.000000 + 3.000000 = 6.000000
a[483] + b[483] == out[483] is 4.000000 + 4.000000 = 8.000000
a[484] + b[484] == out[484] is 5.000000 + 5.000000 = 10.000000
a[485] + b[485] == out[485] is 6.000000 + 6.000000 = 12.000000
a[486] + b[486] == out[486] is 7.000000 + 7.000000 = 14.000000
a[487] + b[487] == out[487] is 8.000000 + 8.000000 = 16.000000
a[488] + b[488] == out[488] is 9.000000 + 9.000000 = 18.000000
a[489] + b[489] == out[489] is 10.000000 + 10.000000 = 20.000000
a[490] + b[490] == out[490] is 11.000000 + 11.000000 = 22.000000
a[491] + b[491] == out[491] is 12.000000 + 12.000000 = 24.000000
a[492] + b[492] == out[492] is 13.000000 + 13.000000 = 26.000000
a[493] + b[493] == out[493] is 14.000000 + 14.000000 = 28.000000
a[494] + b[494] == out[494] is 15.000000 + 15.000000 = 30.000000
a[495] + b[495] == out[495] is 16.000000 + 16.000000 = 32.000000
a[496] + b[496] == out[496] is 17.000000 + 17.000000 = 34.000000
a[497] + b[497] == out[497] is 18.000000 + 18.000000 = 36.000000
a[498] + b[498] == out[498] is 19.000000 + 19.000000 = 38.000000
a[499] + b[499] == out[499] is 20.000000 + 20.000000 = 40.000000
a[500] + b[500] == out[500] is 21.000000 + 21.000000 = 42.000000
a[501] + b[501] == out[501] is 22.000000 + 22.000000 = 44.000000
a[502] + b[502] == out[502] is 23.000000 + 23.000000 = 46.000000
a[503] + b[503] == out[503] is 24.000000 + 24.000000 = 48.000000
a[504] + b[504] == out[504] is 25.000000 + 25.000000 = 50.000000
a[505] + b[505] == out[505] is 26.000000 + 26.000000 = 52.000000
a[506] + b[506] == out[506] is 27.000000 + 27.000000 = 54.000000
a[507] + b[507] == out[507] is 28.000000 + 28.000000 = 56.000000
a[508] + b[508] == out[508] is 29.000000 + 29.000000 = 58.000000
a[509] + b[509] == out[509] is 30.000000 + 30.000000 = 60.000000
a[510] + b[510] == out[510] is 31.000000 + 31.000000 = 62.000000
a[511] + b[511] == out[511] is 32.000000 + 32.000000 = 64.000000
a[512] + b[512] == out[512] is 1.000000 + 1.000000 = 2.000000
a[513] + b[513] == out[513] is 2.000000 + 2.000000 = 4.000000
a[514] + b[514] == out[514] is 3.000000 + 3.000000 = 6.000000
a[515] + b[515] == out[515] is 4.000000 + 4.000000 = 8.000000
a[516] + b[516] == out[516] is 5.000000 + 5.000000 = 10.000000
a[517] + b[517] == out[517] is 6.000000 + 6.000000 = 12.000000
a[518] + b[518] == out[518] is 7.000000 + 7.000000 = 14.000000
a[519] + b[519] == out[519] is 8.000000 + 8.000000 = 16.000000
a[520] + b[520] == out[520] is 9.000000 + 9.000000 = 18.000000
a[521] + b[521] == out[521] is 10.000000 + 10.000000 = 20.000000
a[522] + b[522] == out[522] is 11.000000 + 11.000000 = 22.000000
a[523] + b[523] == out[523] is 12.000000 + 12.000000 = 24.000000
a[524] + b[524] == out[524] is 13.000000 + 13.000000 = 26.000000
a[525] + b[525] == out[525] is 14.000000 + 14.000000 = 28.000000
a[526] + b[526] == out[526] is 15.000000 + 15.000000 = 30.000000
a[527] + b[527] == out[527] is 16.000000 + 16.000000 = 32.000000
a[528] + b[528] == out[528] is 17.000000 + 17.000000 = 34.000000
a[529] + b[529] == out[529] is 18.000000 + 18.000000 = 36.000000
a[530] + b[530] == out[530] is 19.000000 + 19.000000 = 38.000000
a[531] + b[531] == out[531] is 20.000000 + 20.000000 = 40.000000
a[532] + b[532] == out[532] is 21.000000 + 21.000000 = 42.000000
a[533] + b[533] == out[533] is 22.000000 + 22.000000 = 44.000000
a[534] + b[534] == out[534] is 23.000000 + 23.000000 = 46.000000
a[535] + b[535] == out[535] is 24.000000 + 24.000000 = 48.000000
a[536] + b[536] == out[536] is 25.000000 + 25.000000 = 50.000000
a[537] + b[537] == out[537] is 26.000000 + 26.000000 = 52.000000
a[538] + b[538] == out[538] is 27.000000 + 27.000000 = 54.000000
a[539] + b[539] == out[539] is 28.000000 + 28.000000 = 56.000000
a[540] + b[540] == out[540] is 29.000000 + 29.000000 = 58.000000
a[541] + b[541] == out[541] is 30.000000 + 30.000000 = 60.000000
a[542] + b[542] == out[542] is 31.000000 + 31.000000 = 62.000000
a[543] + b[543] == out[543] is 32.000000 + 32.000000 = 64.000000
a[544] + b[544] == out[544] is 1.000000 + 1.000000 = 2.000000
a[545] + b[545] == out[545] is 2.000000 + 2.000000 = 4.000000
a[546] + b[546] == out[546] is 3.000000 + 3.000000 = 6.000000
a[547] + b[547] == out[547] is 4.000000 + 4.000000 = 8.000000
a[548] + b[548] == out[548] is 5.000000 + 5.000000 = 10.000000
a[549] + b[549] == out[549] is 6.000000 + 6.000000 = 12.000000
a[550] + b[550] == out[550] is 7.000000 + 7.000000 = 14.000000
a[551] + b[551] == out[551] is 8.000000 + 8.000000 = 16.000000
a[552] + b[552] == out[552] is 9.000000 + 9.000000 = 18.000000
a[553] + b[553] == out[553] is 10.000000 + 10.000000 = 20.000000
a[554] + b[554] == out[554] is 11.000000 + 11.000000 = 22.000000
a[555] + b[555] == out[555] is 12.000000 + 12.000000 = 24.000000
a[556] + b[556] == out[556] is 13.000000 + 13.000000 = 26.000000
a[557] + b[557] == out[557] is 14.000000 + 14.000000 = 28.000000
a[558] + b[558] == out[558] is 15.000000 + 15.000000 = 30.000000
a[559] + b[559] == out[559] is 16.000000 + 16.000000 = 32.000000
a[560] + b[560] == out[560] is 17.000000 + 17.000000 = 34.000000
a[561] + b[561] == out[561] is 18.000000 + 18.000000 = 36.000000
a[562] + b[562] == out[562] is 19.000000 + 19.000000 = 38.000000
a[563] + b[563] == out[563] is 20.000000 + 20.000000 = 40.000000
a[564] + b[564] == out[564] is 21.000000 + 21.000000 = 42.000000
a[565] + b[565] == out[565] is 22.000000 + 22.000000 = 44.000000
a[566] + b[566] == out[566] is 23.000000 + 23.000000 = 46.000000
a[567] + b[567] == out[567] is 24.000000 + 24.000000 = 48.000000
a[568] + b[568] == out[568] is 25.000000 + 25.000000 = 50.000000
a[569] + b[569] == out[569] is 26.000000 + 26.000000 = 52.000000
a[570] + b[570] == out[570] is 27.000000 + 27.000000 = 54.000000
a[571] + b[571] == out[571] is 28.000000 + 28.000000 = 56.000000
a[572] + b[572] == out[572] is 29.000000 + 29.000000 = 58.000000
a[573] + b[573] == out[573] is 30.000000 + 30.000000 = 60.000000
a[574] + b[574] == out[574] is 31.000000 + 31.000000 = 62.000000
a[575] + b[575] == out[575] is 32.000000 + 32.000000 = 64.000000
a[576] + b[576] == out[576] is 1.000000 + 1.000000 = 2.000000
a[577] + b[577] == out[577] is 2.000000 + 2.000000 = 4.000000
a[578] + b[578] == out[578] is 3.000000 + 3.000000 = 6.000000
a[579] + b[579] == out[579] is 4.000000 + 4.000000 = 8.000000
a[580] + b[580] == out[580] is 5.000000 + 5.000000 = 10.000000
a[581] + b[581] == out[581] is 6.000000 + 6.000000 = 12.000000
a[582] + b[582] == out[582] is 7.000000 + 7.000000 = 14.000000
a[583] + b[583] == out[583] is 8.000000 + 8.000000 = 16.000000
a[584] + b[584] == out[584] is 9.000000 + 9.000000 = 18.000000
a[585] + b[585] == out[585] is 10.000000 + 10.000000 = 20.000000
a[586] + b[586] == out[586] is 11.000000 + 11.000000 = 22.000000
a[587] + b[587] == out[587] is 12.000000 + 12.000000 = 24.000000
a[588] + b[588] == out[588] is 13.000000 + 13.000000 = 26.000000
a[589] + b[589] == out[589] is 14.000000 + 14.000000 = 28.000000
a[590] + b[590] == out[590] is 15.000000 + 15.000000 = 30.000000
a[591] + b[591] == out[591] is 16.000000 + 16.000000 = 32.000000
a[592] + b[592] == out[592] is 17.000000 + 17.000000 = 34.000000
a[593] + b[593] == out[593] is 18.000000 + 18.000000 = 36.000000
a[594] + b[594] == out[594] is 19.000000 + 19.000000 = 38.000000
a[595] + b[595] == out[595] is 20.000000 + 20.000000 = 40.000000
a[596] + b[596] == out[596] is 21.000000 + 21.000000 = 42.000000
a[597] + b[597] == out[597] is 22.000000 + 22.000000 = 44.000000
a[598] + b[598] == out[598] is 23.000000 + 23.000000 = 46.000000
a[599] + b[599] == out[599] is 24.000000 + 24.000000 = 48.000000
a[600] + b[600] == out[600] is 25.000000 + 25.000000 = 50.000000
a[601] + b[601] == out[601] is 26.000000 + 26.000000 = 52.000000
a[602] + b[602] == out[602] is 27.000000 + 27.000000 = 54.000000
a[603] + b[603] == out[603] is 28.000000 + 28.000000 = 56.000000
a[604] + b[604] == out[604] is 29.000000 + 29.000000 = 58.000000
a[605] + b[605] == out[605] is 30.000000 + 30.000000 = 60.000000
a[606] + b[606] == out[606] is 31.000000 + 31.000000 = 62.000000
a[607] + b[607] == out[607] is 32.000000 + 32.000000 = 64.000000
a[608] + b[608] == out[608] is 1.000000 + 1.000000 = 2.000000
a[609] + b[609] == out[609] is 2.000000 + 2.000000 = 4.000000
a[610] + b[610] == out[610] is 3.000000 + 3.000000 = 6.000000
a[611] + b[611] == out[611] is 4.000000 + 4.000000 = 8.000000
a[612] + b[612] == out[612] is 5.000000 + 5.000000 = 10.000000
a[613] + b[613] == out[613] is 6.000000 + 6.000000 = 12.000000
a[614] + b[614] == out[614] is 7.000000 + 7.000000 = 14.000000
a[615] + b[615] == out[615] is 8.000000 + 8.000000 = 16.000000
a[616] + b[616] == out[616] is 9.000000 + 9.000000 = 18.000000
a[617] + b[617] == out[617] is 10.000000 + 10.000000 = 20.000000
a[618] + b[618] == out[618] is 11.000000 + 11.000000 = 22.000000
a[619] + b[619] == out[619] is 12.000000 + 12.000000 = 24.000000
a[620] + b[620] == out[620] is 13.000000 + 13.000000 = 26.000000
a[621] + b[621] == out[621] is 14.000000 + 14.000000 = 28.000000
a[622] + b[622] == out[622] is 15.000000 + 15.000000 = 30.000000
a[623] + b[623] == out[623] is 16.000000 + 16.000000 = 32.000000
a[624] + b[624] == out[624] is 17.000000 + 17.000000 = 34.000000
a[625] + b[625] == out[625] is 18.000000 + 18.000000 = 36.000000
a[626] + b[626] == out[626] is 19.000000 + 19.000000 = 38.000000
a[627] + b[627] == out[627] is 20.000000 + 20.000000 = 40.000000
a[628] + b[628] == out[628] is 21.000000 + 21.000000 = 42.000000
a[629] + b[629] == out[629] is 22.000000 + 22.000000 = 44.000000
a[630] + b[630] == out[630] is 23.000000 + 23.000000 = 46.000000
a[631] + b[631] == out[631] is 24.000000 + 24.000000 = 48.000000
a[632] + b[632] == out[632] is 25.000000 + 25.000000 = 50.000000
a[633] + b[633] == out[633] is 26.000000 + 26.000000 = 52.000000
a[634] + b[634] == out[634] is 27.000000 + 27.000000 = 54.000000
a[635] + b[635] == out[635] is 28.000000 + 28.000000 = 56.000000
a[636] + b[636] == out[636] is 29.000000 + 29.000000 = 58.000000
a[637] + b[637] == out[637] is 30.000000 + 30.000000 = 60.000000
a[638] + b[638] == out[638] is 31.000000 + 31.000000 = 62.000000
a[639] + b[639] == out[639] is 32.000000 + 32.000000 = 64.000000
a[640] + b[640] == out[640] is 1.000000 + 1.000000 = 2.000000
a[641] + b[641] == out[641] is 2.000000 + 2.000000 = 4.000000
a[642] + b[642] == out[642] is 3.000000 + 3.000000 = 6.000000
a[643] + b[643] == out[643] is 4.000000 + 4.000000 = 8.000000
a[644] + b[644] == out[644] is 5.000000 + 5.000000 = 10.000000
a[645] + b[645] == out[645] is 6.000000 + 6.000000 = 12.000000
a[646] + b[646] == out[646] is 7.000000 + 7.000000 = 14.000000
a[647] + b[647] == out[647] is 8.000000 + 8.000000 = 16.000000
a[648] + b[648] == out[648] is 9.000000 + 9.000000 = 18.000000
a[649] + b[649] == out[649] is 10.000000 + 10.000000 = 20.000000
a[650] + b[650] == out[650] is 11.000000 + 11.000000 = 22.000000
a[651] + b[651] == out[651] is 12.000000 + 12.000000 = 24.000000
a[652] + b[652] == out[652] is 13.000000 + 13.000000 = 26.000000
a[653] + b[653] == out[653] is 14.000000 + 14.000000 = 28.000000
a[654] + b[654] == out[654] is 15.000000 + 15.000000 = 30.000000
a[655] + b[655] == out[655] is 16.000000 + 16.000000 = 32.000000
a[656] + b[656] == out[656] is 17.000000 + 17.000000 = 34.000000
a[657] + b[657] == out[657] is 18.000000 + 18.000000 = 36.000000
a[658] + b[658] == out[658] is 19.000000 + 19.000000 = 38.000000
a[659] + b[659] == out[659] is 20.000000 + 20.000000 = 40.000000
a[660] + b[660] == out[660] is 21.000000 + 21.000000 = 42.000000
a[661] + b[661] == out[661] is 22.000000 + 22.000000 = 44.000000
a[662] + b[662] == out[662] is 23.000000 + 23.000000 = 46.000000
a[663] + b[663] == out[663] is 24.000000 + 24.000000 = 48.000000
a[664] + b[664] == out[664] is 25.000000 + 25.000000 = 50.000000
a[665] + b[665] == out[665] is 26.000000 + 26.000000 = 52.000000
a[666] + b[666] == out[666] is 27.000000 + 27.000000 = 54.000000
a[667] + b[667] == out[667] is 28.000000 + 28.000000 = 56.000000
a[668] + b[668] == out[668] is 29.000000 + 29.000000 = 58.000000
a[669] + b[669] == out[669] is 30.000000 + 30.000000 = 60.000000
a[670] + b[670] == out[670] is 31.000000 + 31.000000 = 62.000000
a[671] + b[671] == out[671] is 32.000000 + 32.000000 = 64.000000
a[672] + b[672] == out[672] is 1.000000 + 1.000000 = 2.000000
a[673] + b[673] == out[673] is 2.000000 + 2.000000 = 4.000000
a[674] + b[674] == out[674] is 3.000000 + 3.000000 = 6.000000
a[675] + b[675] == out[675] is 4.000000 + 4.000000 = 8.000000
a[676] + b[676] == out[676] is 5.000000 + 5.000000 = 10.000000
a[677] + b[677] == out[677] is 6.000000 + 6.000000 = 12.000000
a[678] + b[678] == out[678] is 7.000000 + 7.000000 = 14.000000
a[679] + b[679] == out[679] is 8.000000 + 8.000000 = 16.000000
a[680] + b[680] == out[680] is 9.000000 + 9.000000 = 18.000000
a[681] + b[681] == out[681] is 10.000000 + 10.000000 = 20.000000
a[682] + b[682] == out[682] is 11.000000 + 11.000000 = 22.000000
a[683] + b[683] == out[683] is 12.000000 + 12.000000 = 24.000000
a[684] + b[684] == out[684] is 13.000000 + 13.000000 = 26.000000
a[685] + b[685] == out[685] is 14.000000 + 14.000000 = 28.000000
a[686] + b[686] == out[686] is 15.000000 + 15.000000 = 30.000000
a[687] + b[687] == out[687] is 16.000000 + 16.000000 = 32.000000
a[688] + b[688] == out[688] is 17.000000 + 17.000000 = 34.000000
a[689] + b[689] == out[689] is 18.000000 + 18.000000 = 36.000000
a[690] + b[690] == out[690] is 19.000000 + 19.000000 = 38.000000
a[691] + b[691] == out[691] is 20.000000 + 20.000000 = 40.000000
a[692] + b[692] == out[692] is 21.000000 + 21.000000 = 42.000000
a[693] + b[693] == out[693] is 22.000000 + 22.000000 = 44.000000
a[694] + b[694] == out[694] is 23.000000 + 23.000000 = 46.000000
a[695] + b[695] == out[695] is 24.000000 + 24.000000 = 48.000000
a[696] + b[696] == out[696] is 25.000000 + 25.000000 = 50.000000
a[697] + b[697] == out[697] is 26.000000 + 26.000000 = 52.000000
a[698] + b[698] == out[698] is 27.000000 + 27.000000 = 54.000000
a[699] + b[699] == out[699] is 28.000000 + 28.000000 = 56.000000
a[700] + b[700] == out[700] is 29.000000 + 29.000000 = 58.000000
a[701] + b[701] == out[701] is 30.000000 + 30.000000 = 60.000000
a[702] + b[702] == out[702] is 31.000000 + 31.000000 = 62.000000
a[703] + b[703] == out[703] is 32.000000 + 32.000000 = 64.000000
a[704] + b[704] == out[704] is 1.000000 + 1.000000 = 2.000000
a[705] + b[705] == out[705] is 2.000000 + 2.000000 = 4.000000
a[706] + b[706] == out[706] is 3.000000 + 3.000000 = 6.000000
a[707] + b[707] == out[707] is 4.000000 + 4.000000 = 8.000000
a[708] + b[708] == out[708] is 5.000000 + 5.000000 = 10.000000
a[709] + b[709] == out[709] is 6.000000 + 6.000000 = 12.000000
a[710] + b[710] == out[710] is 7.000000 + 7.000000 = 14.000000
a[711] + b[711] == out[711] is 8.000000 + 8.000000 = 16.000000
a[712] + b[712] == out[712] is 9.000000 + 9.000000 = 18.000000
a[713] + b[713] == out[713] is 10.000000 + 10.000000 = 20.000000
a[714] + b[714] == out[714] is 11.000000 + 11.000000 = 22.000000
a[715] + b[715] == out[715] is 12.000000 + 12.000000 = 24.000000
a[716] + b[716] == out[716] is 13.000000 + 13.000000 = 26.000000
a[717] + b[717] == out[717] is 14.000000 + 14.000000 = 28.000000
a[718] + b[718] == out[718] is 15.000000 + 15.000000 = 30.000000
a[719] + b[719] == out[719] is 16.000000 + 16.000000 = 32.000000
a[720] + b[720] == out[720] is 17.000000 + 17.000000 = 34.000000
a[721] + b[721] == out[721] is 18.000000 + 18.000000 = 36.000000
a[722] + b[722] == out[722] is 19.000000 + 19.000000 = 38.000000
a[723] + b[723] == out[723] is 20.000000 + 20.000000 = 40.000000
a[724] + b[724] == out[724] is 21.000000 + 21.000000 = 42.000000
a[725] + b[725] == out[725] is 22.000000 + 22.000000 = 44.000000
a[726] + b[726] == out[726] is 23.000000 + 23.000000 = 46.000000
a[727] + b[727] == out[727] is 24.000000 + 24.000000 = 48.000000
a[728] + b[728] == out[728] is 25.000000 + 25.000000 = 50.000000
a[729] + b[729] == out[729] is 26.000000 + 26.000000 = 52.000000
a[730] + b[730] == out[730] is 27.000000 + 27.000000 = 54.000000
a[731] + b[731] == out[731] is 28.000000 + 28.000000 = 56.000000
a[732] + b[732] == out[732] is 29.000000 + 29.000000 = 58.000000
a[733] + b[733] == out[733] is 30.000000 + 30.000000 = 60.000000
a[734] + b[734] == out[734] is 31.000000 + 31.000000 = 62.000000
a[735] + b[735] == out[735] is 32.000000 + 32.000000 = 64.000000
a[736] + b[736] == out[736] is 1.000000 + 1.000000 = 2.000000
a[737] + b[737] == out[737] is 2.000000 + 2.000000 = 4.000000
a[738] + b[738] == out[738] is 3.000000 + 3.000000 = 6.000000
a[739] + b[739] == out[739] is 4.000000 + 4.000000 = 8.000000
a[740] + b[740] == out[740] is 5.000000 + 5.000000 = 10.000000
a[741] + b[741] == out[741] is 6.000000 + 6.000000 = 12.000000
a[742] + b[742] == out[742] is 7.000000 + 7.000000 = 14.000000
a[743] + b[743] == out[743] is 8.000000 + 8.000000 = 16.000000
a[744] + b[744] == out[744] is 9.000000 + 9.000000 = 18.000000
a[745] + b[745] == out[745] is 10.000000 + 10.000000 = 20.000000
a[746] + b[746] == out[746] is 11.000000 + 11.000000 = 22.000000
a[747] + b[747] == out[747] is 12.000000 + 12.000000 = 24.000000
a[748] + b[748] == out[748] is 13.000000 + 13.000000 = 26.000000
a[749] + b[749] == out[749] is 14.000000 + 14.000000 = 28.000000
a[750] + b[750] == out[750] is 15.000000 + 15.000000 = 30.000000
a[751] + b[751] == out[751] is 16.000000 + 16.000000 = 32.000000
a[752] + b[752] == out[752] is 17.000000 + 17.000000 = 34.000000
a[753] + b[753] == out[753] is 18.000000 + 18.000000 = 36.000000
a[754] + b[754] == out[754] is 19.000000 + 19.000000 = 38.000000
a[755] + b[755] == out[755] is 20.000000 + 20.000000 = 40.000000
a[756] + b[756] == out[756] is 21.000000 + 21.000000 = 42.000000
a[757] + b[757] == out[757] is 22.000000 + 22.000000 = 44.000000
a[758] + b[758] == out[758] is 23.000000 + 23.000000 = 46.000000
a[759] + b[759] == out[759] is 24.000000 + 24.000000 = 48.000000
a[760] + b[760] == out[760] is 25.000000 + 25.000000 = 50.000000
a[761] + b[761] == out[761] is 26.000000 + 26.000000 = 52.000000
a[762] + b[762] == out[762] is 27.000000 + 27.000000 = 54.000000
a[763] + b[763] == out[763] is 28.000000 + 28.000000 = 56.000000
a[764] + b[764] == out[764] is 29.000000 + 29.000000 = 58.000000
a[765] + b[765] == out[765] is 30.000000 + 30.000000 = 60.000000
a[766] + b[766] == out[766] is 31.000000 + 31.000000 = 62.000000
a[767] + b[767] == out[767] is 32.000000 + 32.000000 = 64.000000
a[768] + b[768] == out[768] is 1.000000 + 1.000000 = 2.000000
a[769] + b[769] == out[769] is 2.000000 + 2.000000 = 4.000000
a[770] + b[770] == out[770] is 3.000000 + 3.000000 = 6.000000
a[771] + b[771] == out[771] is 4.000000 + 4.000000 = 8.000000
a[772] + b[772] == out[772] is 5.000000 + 5.000000 = 10.000000
a[773] + b[773] == out[773] is 6.000000 + 6.000000 = 12.000000
a[774] + b[774] == out[774] is 7.000000 + 7.000000 = 14.000000
a[775] + b[775] == out[775] is 8.000000 + 8.000000 = 16.000000
a[776] + b[776] == out[776] is 9.000000 + 9.000000 = 18.000000
a[777] + b[777] == out[777] is 10.000000 + 10.000000 = 20.000000
a[778] + b[778] == out[778] is 11.000000 + 11.000000 = 22.000000
a[779] + b[779] == out[779] is 12.000000 + 12.000000 = 24.000000
a[780] + b[780] == out[780] is 13.000000 + 13.000000 = 26.000000
a[781] + b[781] == out[781] is 14.000000 + 14.000000 = 28.000000
a[782] + b[782] == out[782] is 15.000000 + 15.000000 = 30.000000
a[783] + b[783] == out[783] is 16.000000 + 16.000000 = 32.000000
a[784] + b[784] == out[784] is 17.000000 + 17.000000 = 34.000000
a[785] + b[785] == out[785] is 18.000000 + 18.000000 = 36.000000
a[786] + b[786] == out[786] is 19.000000 + 19.000000 = 38.000000
a[787] + b[787] == out[787] is 20.000000 + 20.000000 = 40.000000
a[788] + b[788] == out[788] is 21.000000 + 21.000000 = 42.000000
a[789] + b[789] == out[789] is 22.000000 + 22.000000 = 44.000000
a[790] + b[790] == out[790] is 23.000000 + 23.000000 = 46.000000
a[791] + b[791] == out[791] is 24.000000 + 24.000000 = 48.000000
a[792] + b[792] == out[792] is 25.000000 + 25.000000 = 50.000000
a[793] + b[793] == out[793] is 26.000000 + 26.000000 = 52.000000
a[794] + b[794] == out[794] is 27.000000 + 27.000000 = 54.000000
a[795] + b[795] == out[795] is 28.000000 + 28.000000 = 56.000000
a[796] + b[796] == out[796] is 29.000000 + 29.000000 = 58.000000
a[797] + b[797] == out[797] is 30.000000 + 30.000000 = 60.000000
a[798] + b[798] == out[798] is 31.000000 + 31.000000 = 62.000000
a[799] + b[799] == out[799] is 32.000000 + 32.000000 = 64.000000
a[800] + b[800] == out[800] is 1.000000 + 1.000000 = 2.000000
a[801] + b[801] == out[801] is 2.000000 + 2.000000 = 4.000000
a[802] + b[802] == out[802] is 3.000000 + 3.000000 = 6.000000
a[803] + b[803] == out[803] is 4.000000 + 4.000000 = 8.000000
a[804] + b[804] == out[804] is 5.000000 + 5.000000 = 10.000000
a[805] + b[805] == out[805] is 6.000000 + 6.000000 = 12.000000
a[806] + b[806] == out[806] is 7.000000 + 7.000000 = 14.000000
a[807] + b[807] == out[807] is 8.000000 + 8.000000 = 16.000000
a[808] + b[808] == out[808] is 9.000000 + 9.000000 = 18.000000
a[809] + b[809] == out[809] is 10.000000 + 10.000000 = 20.000000
a[810] + b[810] == out[810] is 11.000000 + 11.000000 = 22.000000
a[811] + b[811] == out[811] is 12.000000 + 12.000000 = 24.000000
a[812] + b[812] == out[812] is 13.000000 + 13.000000 = 26.000000
a[813] + b[813] == out[813] is 14.000000 + 14.000000 = 28.000000
a[814] + b[814] == out[814] is 15.000000 + 15.000000 = 30.000000
a[815] + b[815] == out[815] is 16.000000 + 16.000000 = 32.000000
a[816] + b[816] == out[816] is 17.000000 + 17.000000 = 34.000000
a[817] + b[817] == out[817] is 18.000000 + 18.000000 = 36.000000
a[818] + b[818] == out[818] is 19.000000 + 19.000000 = 38.000000
a[819] + b[819] == out[819] is 20.000000 + 20.000000 = 40.000000
a[820] + b[820] == out[820] is 21.000000 + 21.000000 = 42.000000
a[821] + b[821] == out[821] is 22.000000 + 22.000000 = 44.000000
a[822] + b[822] == out[822] is 23.000000 + 23.000000 = 46.000000
a[823] + b[823] == out[823] is 24.000000 + 24.000000 = 48.000000
a[824] + b[824] == out[824] is 25.000000 + 25.000000 = 50.000000
a[825] + b[825] == out[825] is 26.000000 + 26.000000 = 52.000000
a[826] + b[826] == out[826] is 27.000000 + 27.000000 = 54.000000
a[827] + b[827] == out[827] is 28.000000 + 28.000000 = 56.000000
a[828] + b[828] == out[828] is 29.000000 + 29.000000 = 58.000000
a[829] + b[829] == out[829] is 30.000000 + 30.000000 = 60.000000
a[830] + b[830] == out[830] is 31.000000 + 31.000000 = 62.000000
a[831] + b[831] == out[831] is 32.000000 + 32.000000 = 64.000000
a[832] + b[832] == out[832] is 1.000000 + 1.000000 = 2.000000
a[833] + b[833] == out[833] is 2.000000 + 2.000000 = 4.000000
a[834] + b[834] == out[834] is 3.000000 + 3.000000 = 6.000000
a[835] + b[835] == out[835] is 4.000000 + 4.000000 = 8.000000
a[836] + b[836] == out[836] is 5.000000 + 5.000000 = 10.000000
a[837] + b[837] == out[837] is 6.000000 + 6.000000 = 12.000000
a[838] + b[838] == out[838] is 7.000000 + 7.000000 = 14.000000
a[839] + b[839] == out[839] is 8.000000 + 8.000000 = 16.000000
a[840] + b[840] == out[840] is 9.000000 + 9.000000 = 18.000000
a[841] + b[841] == out[841] is 10.000000 + 10.000000 = 20.000000
a[842] + b[842] == out[842] is 11.000000 + 11.000000 = 22.000000
a[843] + b[843] == out[843] is 12.000000 + 12.000000 = 24.000000
a[844] + b[844] == out[844] is 13.000000 + 13.000000 = 26.000000
a[845] + b[845] == out[845] is 14.000000 + 14.000000 = 28.000000
a[846] + b[846] == out[846] is 15.000000 + 15.000000 = 30.000000
a[847] + b[847] == out[847] is 16.000000 + 16.000000 = 32.000000
a[848] + b[848] == out[848] is 17.000000 + 17.000000 = 34.000000
a[849] + b[849] == out[849] is 18.000000 + 18.000000 = 36.000000
a[850] + b[850] == out[850] is 19.000000 + 19.000000 = 38.000000
a[851] + b[851] == out[851] is 20.000000 + 20.000000 = 40.000000
a[852] + b[852] == out[852] is 21.000000 + 21.000000 = 42.000000
a[853] + b[853] == out[853] is 22.000000 + 22.000000 = 44.000000
a[854] + b[854] == out[854] is 23.000000 + 23.000000 = 46.000000
a[855] + b[855] == out[855] is 24.000000 + 24.000000 = 48.000000
a[856] + b[856] == out[856] is 25.000000 + 25.000000 = 50.000000
a[857] + b[857] == out[857] is 26.000000 + 26.000000 = 52.000000
a[858] + b[858] == out[858] is 27.000000 + 27.000000 = 54.000000
a[859] + b[859] == out[859] is 28.000000 + 28.000000 = 56.000000
a[860] + b[860] == out[860] is 29.000000 + 29.000000 = 58.000000
a[861] + b[861] == out[861] is 30.000000 + 30.000000 = 60.000000
a[862] + b[862] == out[862] is 31.000000 + 31.000000 = 62.000000
a[863] + b[863] == out[863] is 32.000000 + 32.000000 = 64.000000
a[864] + b[864] == out[864] is 1.000000 + 1.000000 = 2.000000
a[865] + b[865] == out[865] is 2.000000 + 2.000000 = 4.000000
a[866] + b[866] == out[866] is 3.000000 + 3.000000 = 6.000000
a[867] + b[867] == out[867] is 4.000000 + 4.000000 = 8.000000
a[868] + b[868] == out[868] is 5.000000 + 5.000000 = 10.000000
a[869] + b[869] == out[869] is 6.000000 + 6.000000 = 12.000000
a[870] + b[870] == out[870] is 7.000000 + 7.000000 = 14.000000
a[871] + b[871] == out[871] is 8.000000 + 8.000000 = 16.000000
a[872] + b[872] == out[872] is 9.000000 + 9.000000 = 18.000000
a[873] + b[873] == out[873] is 10.000000 + 10.000000 = 20.000000
a[874] + b[874] == out[874] is 11.000000 + 11.000000 = 22.000000
a[875] + b[875] == out[875] is 12.000000 + 12.000000 = 24.000000
a[876] + b[876] == out[876] is 13.000000 + 13.000000 = 26.000000
a[877] + b[877] == out[877] is 14.000000 + 14.000000 = 28.000000
a[878] + b[878] == out[878] is 15.000000 + 15.000000 = 30.000000
a[879] + b[879] == out[879] is 16.000000 + 16.000000 = 32.000000
a[880] + b[880] == out[880] is 17.000000 + 17.000000 = 34.000000
a[881] + b[881] == out[881] is 18.000000 + 18.000000 = 36.000000
a[882] + b[882] == out[882] is 19.000000 + 19.000000 = 38.000000
a[883] + b[883] == out[883] is 20.000000 + 20.000000 = 40.000000
a[884] + b[884] == out[884] is 21.000000 + 21.000000 = 42.000000
a[885] + b[885] == out[885] is 22.000000 + 22.000000 = 44.000000
a[886] + b[886] == out[886] is 23.000000 + 23.000000 = 46.000000
a[887] + b[887] == out[887] is 24.000000 + 24.000000 = 48.000000
a[888] + b[888] == out[888] is 25.000000 + 25.000000 = 50.000000
a[889] + b[889] == out[889] is 26.000000 + 26.000000 = 52.000000
a[890] + b[890] == out[890] is 27.000000 + 27.000000 = 54.000000
a[891] + b[891] == out[891] is 28.000000 + 28.000000 = 56.000000
a[892] + b[892] == out[892] is 29.000000 + 29.000000 = 58.000000
a[893] + b[893] == out[893] is 30.000000 + 30.000000 = 60.000000
a[894] + b[894] == out[894] is 31.000000 + 31.000000 = 62.000000
a[895] + b[895] == out[895] is 32.000000 + 32.000000 = 64.000000
a[896] + b[896] == out[896] is 1.000000 + 1.000000 = 2.000000
a[897] + b[897] == out[897] is 2.000000 + 2.000000 = 4.000000
a[898] + b[898] == out[898] is 3.000000 + 3.000000 = 6.000000
a[899] + b[899] == out[899] is 4.000000 + 4.000000 = 8.000000
a[900] + b[900] == out[900] is 5.000000 + 5.000000 = 10.000000
a[901] + b[901] == out[901] is 6.000000 + 6.000000 = 12.000000
a[902] + b[902] == out[902] is 7.000000 + 7.000000 = 14.000000
a[903] + b[903] == out[903] is 8.000000 + 8.000000 = 16.000000
a[904] + b[904] == out[904] is 9.000000 + 9.000000 = 18.000000
a[905] + b[905] == out[905] is 10.000000 + 10.000000 = 20.000000
a[906] + b[906] == out[906] is 11.000000 + 11.000000 = 22.000000
a[907] + b[907] == out[907] is 12.000000 + 12.000000 = 24.000000
a[908] + b[908] == out[908] is 13.000000 + 13.000000 = 26.000000
a[909] + b[909] == out[909] is 14.000000 + 14.000000 = 28.000000
a[910] + b[910] == out[910] is 15.000000 + 15.000000 = 30.000000
a[911] + b[911] == out[911] is 16.000000 + 16.000000 = 32.000000
a[912] + b[912] == out[912] is 17.000000 + 17.000000 = 34.000000
a[913] + b[913] == out[913] is 18.000000 + 18.000000 = 36.000000
a[914] + b[914] == out[914] is 19.000000 + 19.000000 = 38.000000
a[915] + b[915] == out[915] is 20.000000 + 20.000000 = 40.000000
a[916] + b[916] == out[916] is 21.000000 + 21.000000 = 42.000000
a[917] + b[917] == out[917] is 22.000000 + 22.000000 = 44.000000
a[918] + b[918] == out[918] is 23.000000 + 23.000000 = 46.000000
a[919] + b[919] == out[919] is 24.000000 + 24.000000 = 48.000000
a[920] + b[920] == out[920] is 25.000000 + 25.000000 = 50.000000
a[921] + b[921] == out[921] is 26.000000 + 26.000000 = 52.000000
a[922] + b[922] == out[922] is 27.000000 + 27.000000 = 54.000000
a[923] + b[923] == out[923] is 28.000000 + 28.000000 = 56.000000
a[924] + b[924] == out[924] is 29.000000 + 29.000000 = 58.000000
a[925] + b[925] == out[925] is 30.000000 + 30.000000 = 60.000000
a[926] + b[926] == out[926] is 31.000000 + 31.000000 = 62.000000
a[927] + b[927] == out[927] is 32.000000 + 32.000000 = 64.000000
a[928] + b[928] == out[928] is 1.000000 + 1.000000 = 2.000000
a[929] + b[929] == out[929] is 2.000000 + 2.000000 = 4.000000
a[930] + b[930] == out[930] is 3.000000 + 3.000000 = 6.000000
a[931] + b[931] == out[931] is 4.000000 + 4.000000 = 8.000000
a[932] + b[932] == out[932] is 5.000000 + 5.000000 = 10.000000
a[933] + b[933] == out[933] is 6.000000 + 6.000000 = 12.000000
a[934] + b[934] == out[934] is 7.000000 + 7.000000 = 14.000000
a[935] + b[935] == out[935] is 8.000000 + 8.000000 = 16.000000
a[936] + b[936] == out[936] is 9.000000 + 9.000000 = 18.000000
a[937] + b[937] == out[937] is 10.000000 + 10.000000 = 20.000000
a[938] + b[938] == out[938] is 11.000000 + 11.000000 = 22.000000
a[939] + b[939] == out[939] is 12.000000 + 12.000000 = 24.000000
a[940] + b[940] == out[940] is 13.000000 + 13.000000 = 26.000000
a[941] + b[941] == out[941] is 14.000000 + 14.000000 = 28.000000
a[942] + b[942] == out[942] is 15.000000 + 15.000000 = 30.000000
a[943] + b[943] == out[943] is 16.000000 + 16.000000 = 32.000000
a[944] + b[944] == out[944] is 17.000000 + 17.000000 = 34.000000
a[945] + b[945] == out[945] is 18.000000 + 18.000000 = 36.000000
a[946] + b[946] == out[946] is 19.000000 + 19.000000 = 38.000000
a[947] + b[947] == out[947] is 20.000000 + 20.000000 = 40.000000
a[948] + b[948] == out[948] is 21.000000 + 21.000000 = 42.000000
a[949] + b[949] == out[949] is 22.000000 + 22.000000 = 44.000000
a[950] + b[950] == out[950] is 23.000000 + 23.000000 = 46.000000
a[951] + b[951] == out[951] is 24.000000 + 24.000000 = 48.000000
a[952] + b[952] == out[952] is 25.000000 + 25.000000 = 50.000000
a[953] + b[953] == out[953] is 26.000000 + 26.000000 = 52.000000
a[954] + b[954] == out[954] is 27.000000 + 27.000000 = 54.000000
a[955] + b[955] == out[955] is 28.000000 + 28.000000 = 56.000000
a[956] + b[956] == out[956] is 29.000000 + 29.000000 = 58.000000
a[957] + b[957] == out[957] is 30.000000 + 30.000000 = 60.000000
a[958] + b[958] == out[958] is 31.000000 + 31.000000 = 62.000000
a[959] + b[959] == out[959] is 32.000000 + 32.000000 = 64.000000
a[960] + b[960] == out[960] is 1.000000 + 1.000000 = 2.000000
a[961] + b[961] == out[961] is 2.000000 + 2.000000 = 4.000000
a[962] + b[962] == out[962] is 3.000000 + 3.000000 = 6.000000
a[963] + b[963] == out[963] is 4.000000 + 4.000000 = 8.000000
a[964] + b[964] == out[964] is 5.000000 + 5.000000 = 10.000000
a[965] + b[965] == out[965] is 6.000000 + 6.000000 = 12.000000
a[966] + b[966] == out[966] is 7.000000 + 7.000000 = 14.000000
a[967] + b[967] == out[967] is 8.000000 + 8.000000 = 16.000000
a[968] + b[968] == out[968] is 9.000000 + 9.000000 = 18.000000
a[969] + b[969] == out[969] is 10.000000 + 10.000000 = 20.000000
a[970] + b[970] == out[970] is 11.000000 + 11.000000 = 22.000000
a[971] + b[971] == out[971] is 12.000000 + 12.000000 = 24.000000
a[972] + b[972] == out[972] is 13.000000 + 13.000000 = 26.000000
a[973] + b[973] == out[973] is 14.000000 + 14.000000 = 28.000000
a[974] + b[974] == out[974] is 15.000000 + 15.000000 = 30.000000
a[975] + b[975] == out[975] is 16.000000 + 16.000000 = 32.000000
a[976] + b[976] == out[976] is 17.000000 + 17.000000 = 34.000000
a[977] + b[977] == out[977] is 18.000000 + 18.000000 = 36.000000
a[978] + b[978] == out[978] is 19.000000 + 19.000000 = 38.000000
a[979] + b[979] == out[979] is 20.000000 + 20.000000 = 40.000000
a[980] + b[980] == out[980] is 21.000000 + 21.000000 = 42.000000
a[981] + b[981] == out[981] is 22.000000 + 22.000000 = 44.000000
a[982] + b[982] == out[982] is 23.000000 + 23.000000 = 46.000000
a[983] + b[983] == out[983] is 24.000000 + 24.000000 = 48.000000
a[984] + b[984] == out[984] is 25.000000 + 25.000000 = 50.000000
a[985] + b[985] == out[985] is 26.000000 + 26.000000 = 52.000000
a[986] + b[986] == out[986] is 27.000000 + 27.000000 = 54.000000
a[987] + b[987] == out[987] is 28.000000 + 28.000000 = 56.000000
a[988] + b[988] == out[988] is 29.000000 + 29.000000 = 58.000000
a[989] + b[989] == out[989] is 30.000000 + 30.000000 = 60.000000
a[990] + b[990] == out[990] is 31.000000 + 31.000000 = 62.000000
a[991] + b[991] == out[991] is 32.000000 + 32.000000 = 64.000000
a[992] + b[992] == out[992] is 1.000000 + 1.000000 = 2.000000
a[993] + b[993] == out[993] is 2.000000 + 2.000000 = 4.000000
a[994] + b[994] == out[994] is 3.000000 + 3.000000 = 6.000000
a[995] + b[995] == out[995] is 4.000000 + 4.000000 = 8.000000
a[996] + b[996] == out[996] is 5.000000 + 5.000000 = 10.000000
a[997] + b[997] == out[997] is 6.000000 + 6.000000 = 12.000000
a[998] + b[998] == out[998] is 7.000000 + 7.000000 = 14.000000
a[999] + b[999] == out[999] is 8.000000 + 8.000000 = 16.000000
a[1000] + b[1000] == out[1000] is 9.000000 + 9.000000 = 18.000000
a[1001] + b[1001] == out[1001] is 10.000000 + 10.000000 = 20.000000
a[1002] + b[1002] == out[1002] is 11.000000 + 11.000000 = 22.000000
a[1003] + b[1003] == out[1003] is 12.000000 + 12.000000 = 24.000000
a[1004] + b[1004] == out[1004] is 13.000000 + 13.000000 = 26.000000
a[1005] + b[1005] == out[1005] is 14.000000 + 14.000000 = 28.000000
a[1006] + b[1006] == out[1006] is 15.000000 + 15.000000 = 30.000000
a[1007] + b[1007] == out[1007] is 16.000000 + 16.000000 = 32.000000
a[1008] + b[1008] == out[1008] is 17.000000 + 17.000000 = 34.000000
a[1009] + b[1009] == out[1009] is 18.000000 + 18.000000 = 36.000000
a[1010] + b[1010] == out[1010] is 19.000000 + 19.000000 = 38.000000
a[1011] + b[1011] == out[1011] is 20.000000 + 20.000000 = 40.000000
a[1012] + b[1012] == out[1012] is 21.000000 + 21.000000 = 42.000000
a[1013] + b[1013] == out[1013] is 22.000000 + 22.000000 = 44.000000
a[1014] + b[1014] == out[1014] is 23.000000 + 23.000000 = 46.000000
a[1015] + b[1015] == out[1015] is 24.000000 + 24.000000 = 48.000000
a[1016] + b[1016] == out[1016] is 25.000000 + 25.000000 = 50.000000
a[1017] + b[1017] == out[1017] is 26.000000 + 26.000000 = 52.000000
a[1018] + b[1018] == out[1018] is 27.000000 + 27.000000 = 54.000000
a[1019] + b[1019] == out[1019] is 28.000000 + 28.000000 = 56.000000
a[1020] + b[1020] == out[1020] is 29.000000 + 29.000000 = 58.000000
a[1021] + b[1021] == out[1021] is 30.000000 + 30.000000 = 60.000000
a[1022] + b[1022] == out[1022] is 31.000000 + 31.000000 = 62.000000
a[1023] + b[1023] == out[1023] is 32.000000 + 32.000000 = 64.000000
Passed

10.3.3. dim 2, grid 1, block NxN for matrix with one dim array

#include <stdio.h>
#include <cuda.h>
#include <assert.h>
#include <cuda_runtime.h>
#include <curand_kernel.h>
#define n 32
#define N n*n
__global__ void add(float *a, float *b, float *c){
  int tidx = threadIdx.x;
  int tidy = threadIdx.y;
  for(int i = 0; i <= n; i++){
    c[tidx + tidy*i] = a[tidx + tidy*i] + b[tidx + tidy*i];
  }
}
int main()
{
  float a[N], b[N], out[N];
  float *d_a, *d_b, *d_out; 

  for(int i = 0; i < n; i++){
    for (int j = 0; j < n; j++){
      a[i+j*n] = 1.0f;
      b[i+j*n] = 2.0f;
    }
  }

  // Allocate device memory 
  cudaMalloc((void**)&d_a, sizeof(float) * N);
  cudaMalloc((void**)&d_b, sizeof(float) * N);
  cudaMalloc((void**)&d_out, sizeof(float) * N);

  // Transfer data from host to device memory
  cudaMemcpy(d_a, a, sizeof(float) * N, cudaMemcpyHostToDevice);
  cudaMemcpy(d_b, b, sizeof(float) * N, cudaMemcpyHostToDevice);

  dim3 BlockPerGrid(1, 1, 1);
  dim3 ThreadsPerBlock(n, n, 1);
  add <<< BlockPerGrid, ThreadsPerBlock >>>(d_a, d_b, d_out);
  cudaMemcpy(out, d_out, sizeof(int) * N, cudaMemcpyDeviceToHost);
  for(int i=0; i < N; i++){
    printf("a[%d] + b[%d] == out[%d] is %f + %f = %f\n", i,i,i, a[i], b[i], out[i]);
  }
  printf("Passed\n");
  cudaFree(d_out);
  cudaFree(d_b);
  cudaFree(d_a);
  return 0;
}


cd babel
nvcc gpu_vector_add_dim2_grid1_blockNxN_matrix_witharray.cu -o gpu_vector_add_dim2_grid1_blockNxN_matrix_witharray
./gpu_vector_add_dim2_grid1_blockNxN_matrix_witharray

Footnotes:

1

对于新到手的项目可以直接放到容器的nginx根目录（快速部署 /usr/share/nginx/html），可以在映射的本机端口进入

2

to my case: 

sudo docker run -d -p 80:80 -v /home/sx/Documents/Java/ANANProject/layuimini/:/usr/share/nginx/html/ nginx

Beispile 


sudo docker images
sudo docker pull nginx
sudo docker run -d -p 80:80 nginx -> id:xxxxxxx
sudo docker exec -it -v /....../project:/usr/share/nginx/html xxxxxxx
build in - > local host :80

Author: si

Created: 2025-01-24 Fr 19:45

Validate