Скачать презентацию CS 351 IT 351 Modeling and Simulation Technologies

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CS 351/ IT 351 Modeling and Simulation Technologies Mapping Data to HPC Architectures Dr. Jim Holten

Overview • Data Parallel Partitioning • Partitions to HW Architecture • Processor Loads • Communications Loads CS 351/ IT 351

Data Parallel Partitioning • Partitioning the primary set members • Projecting to secondary set members • Identifying shared set members • Building communications maps CS 351/ IT 351

Partitioning Primary Set Members • Representing the primary sets partitioning • Sp – the primary set. • Spar – the set of partitions. • Rpar, p – the mapping of partitions to primary set members in each. • Generating the partition assignments • Spi = range(Rpar, pi, i) – partition i subset of the primary set. • Rpi, p – the subset relation for Spi CS 351/ IT 351

Partitioning Secondary Set Members • Sets • Spar – Partitions set • Sp – Primary set • Sk – Secondary set • Subsets • Spi – Primary ith subset • Ski – Secondary ith subset CS 351/ IT 351

Partitioning Secondary Set Members • Main Relations • Rpar, p – Partitions to primaries • Rk, p – Secondary to primary • Rpi, p – Primary’s subset • Desired Relations • Rki, k – Secondary's subset • Rki, pi – Partition secondary to primary • Intermediate Relation • Rpi, k – Primary’s subset to secondary set CS 351/ IT 351

Partitioning Secondary Set Members • Calculate the intermediate relation Rpi, k = Rpi, p * Rk, p-1 – Spi to Sk • Project to partition assignments Rki, k = Range(Rpi, k) Rki, pi = Rki, k * Rpi, k-1 • Repeat for all secondary sets. CS 351/ IT 351

Partitioning Dependent Sets CS 351/ IT 351

Projections of Partitions CS 351/ IT 351

Identifying Sharing of Set Members • Getting shared members (partition subset intersections) • Spij = Spi ∩ Spj for all i ≠ j – primary set members subset to share between partitions i and j • Skij = Ski ∩ Skj for all i ≠ j – kth secondary set members subset to share between partitions i and j • Each gives a subset relation for the shared subset (Rpij, pi and Rkij, ki) enumerating the shared members. CS 351/ IT 351

Partition Set Member Subsets • For each process, each set has three subsets of interest • Private subset – not shared with anyone else • Shared subset – locally modified, then shared • Borrowed – used locally but set by another partition CS 351/ IT 351

Partition Set Member Subsets CS 351/ IT 351

Partition Communications Blocks • For each pair of processes a collection of subsets may be passed as a single communications block • Shared subsets – going out to the other process • Borrowed subsets – come from the other process CS 351/ IT 351

Partition Communication Blocks CS 351/ IT 351

Partition Communications CS 351/ IT 351

Which Processes Must Share? • When must subset field values be shared? • The subset is not empty • The field data values change • Field calculations use the changed data • Empty subsets and empty communications blocks can be ignored. CS 351/ IT 351

Gather/Scatter • Outgoing data must be “gathered” into the communications block • Incoming data must be “scattered” back into the local subset data fields. CS 351/ IT 351

Gather/Scatter CS 351/ IT 351

Actual Data to Be Passed? • Fields of values over the “shared” data subset members that are locally changed must be “shared”. • Fields of data values over the “borrowed” data subset members that are needed in local calculations need “borrowed”. • Field data values order and data types must be standardized for each passed communications block. CS 351/ IT 351

Partitions to HW architecture? • Get a graph of the HW architecture • Each CPU is a node • Shared comms between nodes are the links • • • Ethernet* Direct P 2 P Shared memory* Common file system* (* ) Comms shared among multiple links require comm nodes. • Associate the partitions to the CPU graph nodes • Identifies processor loading • Identifies comm alternatives between partitions • Identifies comm link loading CS 351/ IT 351

Conclusions • Data parallel partitioning can be easily automated for any number of partitions if the dependencies are explicitly given as in SRF relations. • Mapping to an HW architecture can be automated also, including static load balancing. • The same techniques may be extended for dynamic load balancing. CS 351/ IT 351