60. MPI OPERATIONS MPI_OP operator MPI_MIN Minimum MPI_SUM Sum MPI_PROD product MPI_MAX maximum MPI_LAND Logical and MPI_BAND Bitwise and MPI_LOR Logical or MPI_BOR Bitwise or MPI_LXOR Logical xor MPI_BXOR Bit-wise xor MPI_MAXLOC Max value and location MPI_MINLOC Min value and location
63. Parallel Trapezoidal Rule Output: Estimate of the integral from a to b of f(x) using the trapezoidal rule and n trapezoids. Algorithm: 1. Each process calculates "its" interval of integration. 2. Each process estimates the integral of f(x) over its interval using the trapezoidal rule. 3a. Each process != 0 sends its integral to 0. 3b. Process 0 sums the calculations received from the individual processes and prints the result. Notes: 1. f(x), a, b, and n are all hardwired. 2. The number of processes (p) should evenly divide the number of trapezoids (n = 1024)
64. Parallelizing the Trapezoidal Rule #include <stdio.h> #include "mpi.h" main(int argc, char** argv) { int my_rank; /* My process rank */ int p; /* The number of processes */ double a = 0.0; /* Left endpoint */ double b = 1.0; /* Right endpoint */ int n = 1024; /* Number of trapezoids */ double h; /* Trapezoid base length */ double local_a; /* Left endpoint my process */ double local_b; /* Right endpoint my process */ int local_n; /* Number of trapezoids for */ /* my calculation */ double integral; /* Integral over my interval */ double total; /* Total integral */ int source; /* Process sending integral */ int dest = 0; /* All messages go to 0 */ int tag = 0; MPI_Status status;
65. Continued… double Trap(double local_a, double local_b, int local_n,double h); /* Calculate local integral */ MPI_Init (&argc, &argv); MPI_Barrier(MPI_COMM_WORLD); double elapsed_time = -MPI_Wtime(); MPI_Comm_rank(MPI_COMM_WORLD, &my_rank); MPI_Comm_size(MPI_COMM_WORLD, &p); h = (b-a)/n; /* h is the same for all processes */ local_n = n/p; /* So is the number of trapezoids */ /* Length of each process' interval of integration = local_n*h. So my interval starts at: */ local_a = a + my_rank*local_n*h; local_b = local_a + local_n*h; integral = Trap(local_a, local_b, local_n, h);
66. Continued… /* Add up the integrals calculated by each process */ if (my_rank == 0) { total = integral; for (source = 1; source < p; source++) { MPI_Recv(&integral, 1, MPI_DOUBLE, source, tag, MPI_COMM_WORLD, &status); total = total + integral; }//End for } else MPI_Send(&integral, 1, MPI_DOUBLE, dest, tag, MPI_COMM_WORLD); MPI_Barrier(MPI_COMM_WORLD); elapsed_time += MPI_Wtime(); /* Print the result */ if (my_rank == 0) { printf("With n = %d trapezoids, our estimate",n); printf("of the integral from %lf to %lf = %lf",a, b, total); printf("time taken: %lf", elapsed_time); }
67. Continued… /* Shut down MPI */ MPI_Finalize(); } /* main */ double Trap( double local_a , double local_b, int local_n, double h) { double integral; /* Store result in integral */ double x; int i; double f(double x); /* function we're integrating */ integral = (f(local_a) + f(local_b))/2.0; x = local_a; for (i = 1; i <= local_n-1; i++) { x = x + h; integral = integral + f(x); } integral = integral*h; return integral; } /* Trap */
68. Continued… double f(double x) { double return_val; /* Calculate f(x). */ /* Store calculation in return_val. */ return_val = 4 / (1+x*x); return return_val; } /* f */
69. Program 2 Process other than root generates the random value less than 1 and sends to root. Root sums up and displays sum.
70. #include <stdio.h> #include <mpi.h> #include<stdlib.h> #include <string.h> #include<time.h> int main(int argc, char **argv) { int myrank, p; int tag =0, dest=0; int i; double randIn,randOut; int source; MPI_Status status; MPI_Init(&argc,&argv); MPI_Comm_rank(MPI_COMM_WORLD,&myrank);
71. MPI_Comm_size(MPI_COMM_WORLD, &p); if(myrank==0)//I am the root { double total=0,average=0; for(source=1;source<p;source++) { MPI_Recv(&randIn,1, MPI_DOUBLE, source, MPI_ANY_TAG, MPI_COMM_WORLD, &status); printf("Message from root: From %d received number %f",source ,randIn); total+=randIn; }//End for average=total/(p-1); }//End if
72. else//I am other than root { srand48((long int) myrank); randOut=drand48(); printf("randout=%f, myrank=%d",randOut,myrank); MPI_Send(&randOut,1,MPI_DOUBLE,dest,tag,MPI_COMM_WORLD); }//End If-Else MPI_Finalize(); return 0; }
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