1. Computer Science 320 Reduction Variables and Operators

2. Get a Histogram of Mandelbrot Set Print to a file the number of points generated on each iteration Same inputs as before, but the output text file will hold a table whose first column runs from 0 to N and whose second column includes the number of points for each I

3. MSHistogramSeq Maintains an array of N + 1 integers Increments the array element at position i after exiting the nested loop Prints the array indexes and contents to a text file // Histogram (array of counters indexed by pixel value). static int[] histogram; … // Create histogram. histogram = new int [maxiter + 1]; … while (i < maxiter && zmagsqr <= 4.0){ // i will be the pixel “value” when the loop exits } // Increment histogram counter for pixel value. ++ histogram[i];

4. Parallelize without Reduction All threads write to the same shared array Use edu.rit.reduction.SharedIntegerArray for multiple-thread-safe incrementAndGet Only minor changes to the structure of the Seq program

5. MSHistogramSmp import edu.rit.pj.reduction.SharedIntegerArray; // Histogram (array of counters indexed by pixel value). static SharedIntegerArray histogram; // Create histogram. histogram = new SharedIntegerArray (maxiter + 1); … execute (0, height-1, new IntegerForLoop() … while (i < maxiter && zmagsqr <= 4.0){ // i will be the pixel “value” when the loop exits } // Increment histogram counter for pixel value. histogram.incrementAndGet(i);

6. Reduction Pattern Shared variable to hold the complete result of the whole program Each thread has its own variable to hold the partial result it computes The partial results are combined in the shared variable as each thread finishes

7. Reduction Variables and Operators A reduction variable holds the complete result A reduction operator combines this variable with a partial result The variable and operator are multiple-thread-safe

8. Using a Reduction Operator // Import integer and operator classes import edu.rit.pj.reduction.SharedInteger; import edu.rit.pj.reduction.IntegerOp; // Initialize an integer SharedInteger x = new SharedInteger(0); // Thread-safe increment x by 4 and return new value of x to result int result = x.reduce(4, IntegerOp.SUM); // Definition of SUM in IntegerOp public static final IntegerOp SUM = new IntegerOp(){ public in op(int x, int y){ return x + y; } }; (x op y) = x.reduce(y, op)

9. Reduction Operator for Arrays // Import shared integer array and operator classes import edu.rit.pj.reduction.SharedIntegerArray; import edu.rit.pj.reduction.IntegerOp; // Initialize a shared integer array and a regular integer array SharedIntegerArray x = new SharedIntegerArray(1000); int[] y = new int[1000]; // Thread-safe increment each x[i] by y[i] x.reduce(y, IntegerOp.SUM); x.length <= y.length

10. Threads Reducing with an Array

11. MSHistogramSmp2 // In the IntegerForLoop // Reduce per-thread histogram into global histogram. public void finish(){ histogram.reduce(thr_histogram, IntegerOp.SUM); }

12. MSHistogramSmp2 // In the ParallelRegion // Per-thread histogram, plus extra padding. int[] thr_histogram = new int [maxiter + 1 + 32]; long p0, p1, p2, p3, p4, p5, p6, p7; long p8, p9, pa, pb, pc, pd, pe, pf; // In the IntegerForLoop // Reduce per-thread histogram into global histogram. public void finish(){ histogram.reduce(thr_histogram, IntegerOp.SUM); }

13. Critical Sections Sometimes you have to do more than appl;y a binary reduction operator to combine results You have to execute a more complex block of code that is multiple-thread-safe Critical sections support the needed synchronization

14. Critical Sections When a thread is executing code in a critical section and another thread enters the same critical section, the second thread blocks until the first thread completes the section And so on, for all the other threads Guarantees mutual exclusion within a critical section: only one thread at a time can be executing in the section

15. Critical Sections in Parallel Java new ParallelTeam().execute(new ParallelRegion(){ public void run(){ // Non-multiple-thread-safe code critical(new ParallelSection(){ public void run(){ // Code for the critical section (multiple-thread-safe) } }); // Non-multiple-thread-safe code } });

16. MSHistogramSmp3 // Create histogram. histogram = new int [maxiter + 1]; // Reduce per-thread histogram into global histogram. public void finish() throws Exception{ region().critical(new ParallelSection(){ public void run(){ for (int i = 0; i <= maxiter; ++ i){ histogram[i] += thr_histogram[i]; } }); } Shared histogram is now a standard array, made thread-safe by being accessed within a critical section