The key common bottleneck in most stencil codes is data movement, and prior research has shown that improving data locality through optimisations that schedule across loops do particularly well. However, in many large PDE applications it is not possible to apply such optimisations through compilers because there are many options, execution paths and data per grid point, many dependent on run-time parameters, and the code is distributed across different compilation units. In this paper, we adapt the data locality improving optimisation called iteration space slicing for use in large OPS applications both in shared-memory and distributed-memory systems, relying on run-time analysis and delayed execution. We evaluate our approach on a number of applications, observing speedups of 2 @math on the Cloverleaf 2D 3D proxy application, which contain 83 141 loops respectively, @math on the linear solver TeaLeaf, and @math on the compressible Navier-Stokes solver OpenSBLI. We demonstrate strong and weak scalability up to 4608 cores of CINECA's Marconi supercomputer. We also evaluate our algorithms on Intel's Knights Landing, demonstrating maintained throughput as the problem size grows beyond 16GB, and we do scaling studies up to 8704 cores. The approach is generally applicable to any stencil DSL that provides per loop data access information.
Identifying the sequence of loops to tile across and to carry out dependency analysis is a lot easier at run-time, particularly with the help of delayed evaluation or lazy execution @cite_38 @cite_11 , which is a well-known technique used particularly in functional languages that allows expressions to be evaluated only when their results are required. Lazy execution is also used in other fields, such as Apache Spark to plan out the sequence of computations and to skip unnecessary steps. We apply the lazy execution idea to figure out dependencies and compute loops schedules at runtime - to our knowledge these two have not been used together in scientific computing.
@cite_38 @cite_11
1984646543 1600009974 1988072050 2006990447
Implementations of lazy evaluation for nonstrict functional languages usually involve the notion of a delayed representation of the value of an expression, which we call athunk. We present several techniques for implementing thunks and formalize a class of optimizations that reduce both the space and time overhead of these techniques. The optimizations depend on a compile-time inferencing strategy calledpath analysis, a generalization of strictness analysis that uncovers order-of-evaluation information. Although the techniques in this paper are focused on the compilation of a nonstrict functional language for a conventional architecture, they are directly applicable to most of the virtual machines commonly used for implementing such languages. The same techniques also apply to other forms of delayed evaluation such asfutures andpromises. Existing program analysis tools that implement abstraction rely on saturating procedures to compute over-approximations of fixpoints. As an alternative, we propose a new algorithm to compute an over-approximation of the set of reachable states of a program by replacing loops in the control flow graph by their abstract transformer. Our technique is able to generate diagnostic information in case of property violations, which we call leaping counterexamples. We have implemented this technique and report experimental results on a set of large ANSI-C programs using abstract domains that focus on properties related to string-buffers. Existing database systems employ an transaction processing scheme---that is, upon receiving a transaction request, the system executes all the operations entailed in running the transaction (which typically includes reading database records, executing user-specified transaction logic, and logging updates and writes) before reporting to the client that the transaction has completed. We introduce a transaction execution engine, in which a transaction may be considered durably completed after only partial execution, while the bulk of its operations (notably all reads from the database and all execution of transaction logic) may be deferred until an arbitrary future time, such as when a user attempts to read some element of the transaction's write-set---all without modifying the semantics of the transaction or sacrificing ACID guarantees. Lazy transactions are processed deterministically, so that the final state of the database is guaranteed to be equivalent to what the state would have been had all transactions been executed eagerly. Our prototype of a lazy transaction execution engine improves temporal locality when executing related transactions, reduces peak provisioning requirements by deferring more non-urgent work until off-peak load times, and reduces contention footprint of concurrent transactions. However, we find that certain queries suffer increased latency, and therefore lazy database systems may not be appropriate for read-latency sensitive applications. We introduce a lazy transaction execution engine, in which a transaction may be considered durably completed after only partial execution, while the bulk of its operations (notably all reads from the database and all execution of transaction logic) may be deferred until an arbitrary future time, such as when a user attempts to read some element of the transaction's write-set---all without modifying the semantics of the transaction or sacrificing ACID guarantees. Lazy transactions are processed deterministically, so that the final state of the database is guaranteed to be equivalent to what the state would have been had all transactions been executed eagerly. Our prototype of a lazy transaction execution engine improves temporal locality when executing related transactions, reduces peak provisioning requirements by deferring more non-urgent work until off-peak load times, and reduces contention footprint of concurrent transactions. However, we find that certain queries suffer increased latency, and therefore lazy database systems may not be appropriate for read-latency sensitive applications. In recent years much interest has been shown in a class of functional languages including HASKELL, lazy ML, SASL KRC MIRANDA, ALFL, ORWELL, and PONDER. It has been seen that their expressive power is great, programs are compact, and program manipulation and transformation is much easier than with imperative languages or more traditional applicative ones. Common characteristics: they are purely applicative, manipulate trees as data objects, use pattern matching both to determine control flow and to decompose compound data structures, and use a ''lazy'' evaluation strategy. In this paper we describe a technique for data flow analysis of programs in this class by safely approximating the behavior of a certain class of term rewriting systems. In particular we obtain ''safe'' descriptions of program inputs, outputs and intermediate results by regular sets of trees. Potential applications include optimization, strictness analysis and partial evaluation. The technique improves earlier work because of its applicability to programs with higher-order functions, and with either eager or lazy evaluation. The technique addresses the call-by-name aspect of laziness, but not memoization.