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\begin{document}

Name: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

Directions: {\bf \Large Work only on this sheet.}  Put all your ``fill
the blank'' answers in one place, say the lower-right part of this side,
or on the back.  Format:

\begin{Verbatim}[fontsize=\relsize{-2}]
#1a.
x+y
#1b
if(u > v) w = 3;
...
\end{Verbatim}

MAKE SURE TO COPY YOUR ANSWERS TO A SEPARATE SHEET FOR SENDING
ME AN ELECTRONIC COPY LATER.

{\bf 1.}  Below is an MPI version of the bucket sort in our OpenMP
example (except that the bin boundaries are assumed known ahead of time,
rather than calculated from a sample).  The message-passing strategy is
outline in the comments at the beginning of the code.  Fill in the
blanks.

\begin{Verbatim}[fontsize=\relsize{-2},numbers=left]
// bucket sort, bin boundaries known in advance

// node 0 is manager, all else worker nodes; node 0 sends full data, bin
// boundaries to all worker nodes; i-th worker node extracts data for
// bin i-1, sorts it, sends sorted chunk back to node 0; node 0 places
// sorted results back in original array

// not claimed efficient; e.g. could be better to have manager place
// items into bins

#include <mpi.h>

#define MAX_N 100000  // max size of original data array
#define MAX_NPROCS 100  // max number of MPI processes
#define DATA_MSG 0  // manager sending original data
#define BDRIES_MSG 0  // manager sending bin boundaries
#define CHUNKS_MSG 2  // workers sending their sorted chunks

int nnodes,  // 
    n,  // size of full array
    me,  // my node number 
    fulldata[MAX_N],
    tmp[MAX_N],
    nbdries,  // number of bin boundaries
    counts[MAX_NPROCS];
float bdries[MAX_NPROCS-2];  // bin boundaries

int debug,debugme; 

init(int argc, char **argv)
{  
   int i;
   debug = atoi(argv[3]); 
   debugme = atoi(argv[4]); 
   MPI_Init(&argc,&argv);
   MPI_Comm_size(MPI_COMM_WORLD,&nnodes);
   MPI_Comm_rank(MPI_COMM_WORLD,&me); 
   nbdries = nnodes - 2;
   n = atoi(argv[1]); 
   int k = atoi(argv[2]);  // for random # gen
   // generate random data for test purposes
   for (i = 0; i < n; i++) fulldata[i] = rand() % k;
   // generate bin boundaries for test purposes
   for (i = 0; i < nbdries; i++) {
      bdries[i] = i * (k+1) / ((float) nnodes);
   }
}

void managernode()
{  
   MPI_Status status;
   int i;
   int lenchunk;  // length of a chunk received from a worker
   // send full data, bin boundaries to workers
   for (i = 1; i < nnodes; i++) {
      MPI_Send(BLANKa,BLANKb,MPI_INT,BLANKc,DATA_MSG,MPI_COMM_WORLD);
      MPI_Send(BLANKd,BLANKe,MPI_FLOAT,BLANKf,BDRIES_MSG,MPI_COMM_WORLD);
   }
   // collect sorted chunks from workers, place them in their proper
   // positions within the original array
   int currposition = 0;
   for (i = 1; i < nnodes; i++) {
      MPI_Recv(tmp,MAX_N,MPI_INT,BLANKg,CHUNKS_MSG,MPI_COMM_WORLD,&status);
      MPI_Get_count(&status,MPI_INT,BLANKh);
      // memcpy(d,s,nb) copies nb bytes from s to d
      memcpy(BLANKi);
      BLANKj;
   }
   if (n < 25) {
      for (i = 0; i < n; i++) printf("%d ",fulldata[i]);
      printf("\n");
   }
}

// adds xi to the part array, increments npart, the length of part
void grab(int xi, int *part, int *npart)
{
    part[*npart] = xi;
    *npart += 1;
}

int cmpints(int *u, int *v)
{  if (*u < *v) return -1;
   if (*u > *v) return 1;
   return 0;
}

void getandsortmychunk(int *tmp, int n, int *chunk, int *lenchunk)
{
   int i,count = 0;
   int workernumber = me - 1;
   for (i = 0; i < n; i++) {
       if (workernumber == 0) {
          if (tmp[i] <= bdries[0]) grab(tmp[i],chunk,&count);
       }
       else if (workernumber < nbdries-1) {
          if (tmp[i] > bdries[workernumber-1] && 
              tmp[i] <= bdries[workernumber]) grab(tmp[i],chunk,&count);
       } else
          if (tmp[i] > bdries[nbdries-1]) grab(tmp[i],chunk,&count);
   }
   qsort(chunk,count,sizeof(int),cmpints);
   *lenchunk = count;
}

void workernode()
{
   int n,fulldata[MAX_N],  // size and storage of full data
       chunk[MAX_N],
       lenchunk,
       nbdries;  // number of bin boundaries
   float bdries[MAX_NPROCS-1];  // bin boundaries
   MPI_Status status;
   MPI_Recv(fulldata,MAX_N,MPI_INT,BLANKk,DATA_MSG,MPI_COMM_WORLD,&status);
   MPI_Get_count(&status,MPI_INT,BLANKl);
   MPI_Recv(bdries,MAX_NPROCS-2,MPI_FLOAT,BLANKm,BDRIES_MSG,
      MPI_COMM_WORLD,&status);
   MPI_Get_count(&status,MPI_FLOAT,BLANKn);
   getandsortmychunk(fulldata,n,chunk,&lenchunk);
   MPI_Send(chunk,lenchunk,MPI_INT,BLANKo,CHUNKS_MSG,MPI_COMM_WORLD);
}

int main(int argc,char **argv)
{  
   int i;
   init(argc,argv);
   if (me == 0) managernode();
   else workernode();
   MPI_Finalize();
}

\end{Verbatim}

\onecolumn

{\bf Solutions:}

\begin{Verbatim}[fontsize=\relsize{-2},numbers=left]
// bucket sort, bin boundaries known in advance

// node 0 is manager, all else worker nodes; node 0 sends full data, bin
// boundaries to all worker nodes; i-th worker node extracts data for
// bin i-1, sorts it, sends sorted chunk back to node 0; node 0 places
// sorted results back in original array

// not claimed efficient; e.g. could be better to have manager place
// items into bins

#include <mpi.h>

#define MAX_N 100000  // max size of original data array
#define MAX_NPROCS 100  // max number of MPI processes
#define DATA_MSG 0  // manager sending original data
#define BDRIES_MSG 0  // manager sending bin boundaries
#define CHUNKS_MSG 2  // workers sending their sorted chunks

int nnodes,  // 
    n,  // size of full array
    me,  // my node number 
    fulldata[MAX_N],
    tmp[MAX_N],
    nbdries,  // number of bin boundaries
    counts[MAX_NPROCS];
float bdries[MAX_NPROCS-2];  // bin boundaries

int debug,debugme; 

init(int argc, char **argv)
{  
   int i;
   debug = atoi(argv[3]); 
   debugme = atoi(argv[4]); 
   MPI_Init(&argc,&argv);
   MPI_Comm_size(MPI_COMM_WORLD,&nnodes);
   MPI_Comm_rank(MPI_COMM_WORLD,&me); 
   nbdries = nnodes - 2;
   n = atoi(argv[1]); 
   int k = atoi(argv[2]);  // for random # gen
   // generate random data for test purposes
   for (i = 0; i < n; i++) fulldata[i] = rand() % k;
   // generate bin boundaries for test purposes
   for (i = 0; i < nbdries; i++) {
      bdries[i] = i * (k+1) / ((float) nnodes);
   }
}

void managernode()
{  
   MPI_Status status;
   int i;
   int lenchunk;  // length of a chunk received from a worker
   // send full data, bin boundaries to workers
   for (i = 1; i < nnodes; i++) {
      MPI_Send(fulldata,n,MPI_INT,i,DATA_MSG,MPI_COMM_WORLD);
      MPI_Send(bdries,nbdries,MPI_FLOAT,i,BDRIES_MSG,MPI_COMM_WORLD);
   }
   // collect sorted chunks from workers, place them in their proper
   // positions within the original array
   int currposition = 0;
   for (i = 1; i < nnodes; i++) {
      MPI_Recv(tmp,MAX_N,MPI_INT,i,CHUNKS_MSG,MPI_COMM_WORLD,&status);
      MPI_Get_count(&status,MPI_INT,&lenchunk);
      memcpy(fulldata+currposition,tmp,lenchunk*sizeof(int));
      currposition += lenchunk;
   }
   if (n < 25) {
      for (i = 0; i < n; i++) printf("%d ",fulldata[i]);
      printf("\n");
   }
}

// adds xi to the part array, increments npart, the length of part
void grab(int xi, int *part, int *npart)
{
    part[*npart] = xi;
    *npart += 1;
}

int cmpints(int *u, int *v)
{  if (*u < *v) return -1;
   if (*u > *v) return 1;
   return 0;
}

void getandsortmychunk(int *tmp, int n, int *chunk, int *lenchunk)
{
   int i,count = 0;
   int workernumber = me - 1;
      if (me == debugme) while (debug) ;
   for (i = 0; i < n; i++) {
       if (workernumber == 0) {
          if (tmp[i] <= bdries[0]) grab(tmp[i],chunk,&count);
       }
       else if (workernumber < nbdries-1) {
          if (tmp[i] > bdries[workernumber-1] && 
              tmp[i] <= bdries[workernumber]) grab(tmp[i],chunk,&count);
       } else
          if (tmp[i] > bdries[nbdries-1]) grab(tmp[i],chunk,&count);
   }
   qsort(chunk,count,sizeof(int),cmpints);
   *lenchunk = count;
}

void workernode()
{
   int n,fulldata[MAX_N],  // size and storage of full data
       chunk[MAX_N],
       lenchunk,
       nbdries;  // number of bin boundaries
   float bdries[MAX_NPROCS-1];  // bin boundaries
   MPI_Status status;
   MPI_Recv(fulldata,MAX_N,MPI_INT,0,DATA_MSG,MPI_COMM_WORLD,&status);
   MPI_Get_count(&status,MPI_INT,&n);
   MPI_Recv(bdries,MAX_NPROCS-2,MPI_FLOAT,0,BDRIES_MSG,MPI_COMM_WORLD,&status);
   MPI_Get_count(&status,MPI_FLOAT,&nbdries);
   getandsortmychunk(fulldata,n,chunk,&lenchunk);
   MPI_Send(chunk,lenchunk,MPI_INT,0,CHUNKS_MSG,MPI_COMM_WORLD);
}

int main(int argc,char **argv)
{  
   int i;
   init(argc,argv);
   if (me == 0) managernode();
   else workernode();
   MPI_Finalize();
}

\end{Verbatim}

\end{document}