1. TM Parallel Concepts An introduction

2. TM The Goal of Parallelization Reduction of elapsed time of a program Reduction in turnaround time of jobs Overhead: –total increase in cpu time –communication –synchronization –additional work in algorithm –non-parallel part of the program (one processor works, others spin idle) Overhead vs Elapsed time is better expressed as Speedup and Efficiency Elapsed time 1 processor 4 processors start finish Elapsed time cpu time communication overhead 1 processor 2 procs 4 procs 8 procs Reduction in elapsed time

3. TM Speedup and Efficiency Both measure the parallelization properties of a program Let T(p) be the elapsed time on p processors The Speedup S(p) and the Efficiency E(p) are defined as: for ideal parallel speedup we get: Scalable programs remain efficient for large number of processors S(p) = T(1)/T(p) E(p) = S(p)/p T(p) = T(1)/p S(p) = T(1)/T(p) = p E(p) = S(p)/p = 1 or 100% Speedup Number of processors ideal Super-linear Saturation Disaster Efficiency Number of processors 1

4. TM Amdahl’s Law This rule states the following for parallel programs: the non-parallel (serial) fraction s of the program includes the communication and synchronization overhead thus the maximum parallel Speedup S(p) for a program that has parallel fraction f: The non-parallel fraction of the code (I.e. overhead) imposes the upper limit on the scalability of the code (1) 1 = s + f ! program has serial and parallel fractions (2)T(1) = T(parallel) + T(serial) = T(1) *(f + s) = T(1) *(f + (1-f)) (3)T(p)= T(1) *(f/p + (1-f)) (4)S(p)= T(1)/T(p) = 1/(f/p + 1-f) inf. (5) S(p) < 1/(1-f)

5. TM Amdahl’s Law: Time to Solution Hypothetical program run time as function of #processors for several parallel fractions f. Note the log-log plot T(p) = T(1)/S(p) S(p) = 1/(f/p + (1-f))

6. TM Fine-Grained Vs Coarse-Grained Fine-grain parallelism (typically loop level)Fine-grain parallelism (typically loop level) –can be done incrementally, one loop at a time –does not require deep knowledge of the code –a lot of loops have to be parallel for decent speedup –potentially many synchronization points (at the end of each parallel loop) Coarse-grain parallelismCoarse-grain parallelism –make larger loops parallel at higher call-tree level potentially in-closing many small loops –more code is parallel at once –fewer synchronization points, reducing overhead –requires deeper knowledge of the code MAIN A B C D F E G H I J KLM NO pq rs t Coarse-grained Fine-grained

7. TM Other Impediments to Scalability Load imbalance: Load imbalance: the time to complete a parallel execution of a code segment is determined by the longest running thread unequal work load distribution leads to some processors being idle, while others work too much with coarse grain parallelization, more opportunities for load imbalance exist Too many synchronization points Too many synchronization points compiler will put synchronization points at the start and exit of each parallel region if too many small loops have been made parallel, synchronization overhead will compromise scalability. Elapsed time p0 p1 p2 p3 startfinish

8. TM Computing  with DPL Notes: –essentially sequential form –automatic detection of parallelism –automatic work sharing –all variables shared by default –number of processors specified outside of the code compile with: f90 -apo -O3 -mips4 -mplist –the mplist switch will show the intermediate representation  = =  0 1 4 (1+x 2 ) dx 0<i<N 4 N(1+((i+0.5)/N) 2 ) PROGRAM PIPROG INTEGER, PARAMETER:: N = 1000000 REAL (KIND=8):: LS,PI, W = 1.0/N PI = SUM( (/ (4.0*W/(1.0+((I+0.5)*W)**2),I=1,N) /) ) PRINT *, PI END

9. TM Computing  with Shared Memory Notes: –essentially sequential form –automatic work sharing –all variables shared by default –directives to request parallel work distribution –number of processors specified outside of the code  = =  0 1 4 (1+x 2 ) dx 0<i<N 4 N(1+((i+0.5)/N) 2 ) #define n 1000000 main() { double pi, l, ls = 0.0, w = 1.0/n; int i; #pragma omp parallel for private(i,l) reduction(+:ls) for(i=0; i<n; i++) { l = (i+0.5)*w; ls += 4.0/(1.0+l*l); } printf(“pi is %f\n”,ls*w); }

10. TM Computing  with Message Passing Notes: –thread identification first –explicit work sharing –all variables are private –explicit data exchange (reduce) –all code is parallel –number of processors is specified outside of code  = =  0 1 4 (1+x 2 ) dx 0<i<N 4 N(1+((i+0.5)/N) 2 ) #include #define N 1000000 main() { double pi, l, ls = 0.0, w = 1.0/N; int i, mid, nth; MPI_init(&argc, &argv); MPI_comm_rank(MPI_COMM_WORLD,&mid); MPI_comm_size(MPI_COMM_WORLD,&nth); for(i=mid; i<N; i += nth) { l = (i+0.5)*w; ls += 4.0/(1.0+l*l); } MPI_reduce(&ls,&pi,1,MPI_DOUBLE,MPI_SUM,0,MPI_COMM_WORLD); if(mid == 0) printf(“pi is %f\n”,pi*w); MPI_finalize(); }

11. TM Comparing Parallel Paradigms Automatic parallelization combined with explicit Shared Variable programming (compiler directives) used on machines with global memory Automatic parallelization combined with explicit Shared Variable programming (compiler directives) used on machines with global memory –Symmetric Multi-Processors, CC-NUMA, PVP –These methods collectively known as Shared Memory Programming (SMP) –SMP programming model works at loop level, and coarse level parallelism: the coarse level parallelism has to be specified explicitly loop level parallelism can be found by the compiler (implicitly) –Explicit Message Passing Methods are necessary with machines that have no global memory addressability: clusters of all sort, NOW & COW –Message Passing Methods require coarse level parallelism to be scalable Choosing programming model is largely a matter of the application, personal preference and the target machine. it has nothing to do with scalability. Scalability limitations: –communication overhead –process synchronization scalability is mainly a function of the hardware and (your) implementation of the parallelism

12. TMSummary The serial part or the communication overhead of the code limits the scalability of the code (Amdahl Law) programs have to be >99% parallel to use large (>30 proc) machines several Programming Models are in use today: –Shared Memory programming (SMP) (with Automatic Compiler parallelization, Data-Parallel and explicit Shared Memory models) –Message Passing model Choosing a Programming Model is largely a matter of the application, personal choice and target machine. It has nothing to do with scalability. –Don’t confuse Algorithm and implementation machines with a global address space can run applications based on both, SMP and Message Passing programming models