On-the-Fly Maintenance of Series-Parallel Relationships in Fork-Join Multithreaded Programs

A key capability of data-race detectors is to determine whether one thread executes logically in parallel with another or whether the threads must operate in series. This paper provides two algorithms, one serial and one parallel, to maintain series-parallel (SP) relationships "on the fly" for fork-join multithreaded programs. The serial SP-order algorithm runs in O(1) amortized time per operation. In contrast, the previously best algorithm requires a time per operation that is proportional to Tarjan’s functional inverse of Ackermann’s function. SP-order employs an order-maintenance data structure that allows us to implement a more efficient "English-Hebrew" labeling scheme than was used in earlier race detectors, which immediately yields an improved determinacy-race detector. In particular, any fork-join program running in T₁ time on a single processor can be checked on the fly for determinacy races in O(T₁) time. Corresponding improved bounds can also be obtained for more sophisticated data-race detectors, for example, those that use locks. By combining SP-order with Feng and Leiserson’s serial SP-bags algorithm, we obtain a parallel SP-maintenance algorithm, called SP-hybrid. Suppose that a fork-join program has n threads, T₁ work, and a critical-path length of T[subscript ∞]. When executed on P processors, we prove that SP-hybrid runs in O((T₁/P + PT[subscript ∞]) lg n) expected time. To understand this bound, consider that the original program obtains linear speed-up over a 1-processor execution when P = O(T₁/T[subscript ∞]). In contrast, SP-hybrid obtains linear speed-up when P = O(√T₁/T[subscript ∞]), but the work is increased by a factor of O(lg n).

A Hierarchical Cache Coherent Protocol

As the number of processors in distributed-memory multiprocessors grows, efficiently supporting a shared-memory programming model becomes difficult. We have designed the Protocol for Hierarchical Directories (PHD) to allow shared-memory support for systems containing massive numbers of processors. PHD eliminates bandwidth problems by using a scalable network, decreases hot-spots by not relying on a single point to distribute blocks, and uses a scalable amount of space for its directories. PHD provides a shared-memory model by synthesizing a global shared memory from the local memories of processors. PHD supports sequentially consistent read, write, and test- and-set operations. This thesis also introduces a method of describing locality for hierarchical protocols and employs this method in the derivation of an abstract model of the protocol behavior. An embedded model, based on the work of Johnson[ISCA19], describes the protocol behavior when mapped to a k-ary n-cube. The thesis uses these two models to study the average height in the hierarchy that operations reach, the longest path messages travel, the number of messages that operations generate, the inter-transaction issue time, and the protocol overhead for different locality parameters, degrees of multithreading, and machine sizes. We determine that multithreading is only useful for approximately two to four threads; any additional interleaving does not decrease the overall latency. For small machines and high locality applications, this limitation is due mainly to the length of the running threads. For large machines with medium to low locality, this limitation is due mainly to the protocol overhead being too large. Our study using the embedded model shows that in situations where the run length between references to shared memory is at least an order of magnitude longer than the time to process a single state transition in the protocol, applications exhibit good performance. If separate controllers for processing protocol requests are included, the protocol scales to 32k processor machines as long as the application exhibits hierarchical locality: at least 22% of the global references must be able to be satisfied locally; at most 35% of the global references are allowed to reach the top level of the hierarchy.