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Finding the minimum value in an array

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• Example: Find the Minimum value in an array
  • When writing a parallel program, you must divide the work into (preferrably) non-overlapping subtasks

  • Usually there are many different ways to divide a task into subtasks

    (And sometimes, it is not possible to divide the task into non-overlapping tasks and you may have to repeat some steps - necessary evil in parallel programming...

  • You may think that dividing the task of "Finding the minimum value" in an array is pretty straighforward - and yet, there are many ways to do so.

    Some ways are better than others.

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  • Let's do a simple example: split the task of "Finding the minimum value" in an array into 2 subtasks (each subtask performed by one thread).

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  • Solution 1: (2 threads)
    • Split the array into 2 (approximate) equal halfs
    • Thread 1 finds the minimum in the first half of the array
    • Thread 2 finds the minimum in the second half of the array
    • Main thread waits for the results and find the actual minimum.

    Pictorially:

    values handled by values handled by thread 0 thread 1 |<--------------------->|<--------------------->| | | | | V V min[0] min[1] \ / \ / \ / \ / \ / main thread | | V Actual minimum

    In general, the division of the data in the array is as follows

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    Main Thread:

    Create the worker( ) threads (run the function worker( )) The main( ) function passes an id to each worker( ) function thread 0 means: find minimum in array[0 .. n-1] 1 means: find minimum in array[n .. 2n-1] 2 means: find minimum in array[2n .. 3n-1] And so on Wait for the worker( ) function to find the minimum in its range thread 0 will return the minimum value in variable min[0] thread 1 will return the minimum value in variable min[1] thread 2 will return the minimum value in variable min[2] And so on Find the overall minimum among the minimum values min[0], min[1], min[2], ....

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    C++ code for the main( ) function:

    /* Shared Variables */ double x[1000000]; // Must be SHARED (accessed by worker threads !!) int start[100]; // Contain starting array index of each thread double min[100]; // Contain the minimum found by each thread int num_threads; // ----------------------------------- // Create worker threads.... // ----------------------------------- for (i = 0; i < num_threads; i = i + 1) { start[i] = i; // Pass ID to thread in a private variable if ( pthread_create(&tid[i], NULL, worker, (void *)&start[i]) ) { cout << "Cannot create thread" << endl; exit(1); } } // ----------------------------------- // Wait for worker threads to end.... // ----------------------------------- for (i = 0; i < num_threads; i = i + 1) pthread_join(tid[i], NULL); // ---------------------------------------- // Post processing: Find actual minimum // ---------------------------------------- my_min = min[0]; for (i = 1; i < num_threads; i++) if ( min[i] < my_min ) my_min = min[i];

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    Worker Thread:

    Finds the minimum value in its portion of the array Recall how the thread s determines its portion of work:

    The C++ code for worker( ):

    void *worker(void *arg) { int i, s; int n, start, stop; double my_min; n = MAX/num_threads; // number of elements to handle s = * (int *) arg; // Convert arg to an integer start = s * n; // Starting index if ( s != (num_threads-1) ) { stop = start + n; // Ending index } else { stop = MAX; } my_min = x[start]; for (i = start+1; i < stop; i++ ) // Find min in my range { if ( x[i] < my_min ) my_min = x[i]; } min[s] = my_min; // Store min in private slot return(NULL); /* Thread exits (dies) */ }

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  • Example Program: (Demo above code)                        
    • Prog file: click here

    On Solaris compile with: CC -mt min-mt1.C
    On Linux compile with: g++ -pthread min-mt1.C

    Changes that you need to make to compile on Linux:

        #include <iostream.h>   ===>   #include <iostream>
    
        Add line:  using namespace std;