In order to evaluate our approach of developing symbolic models with MA, we have designed a prototype framework. This framework has two main components: a library for instrumenting applications and a post-processing toolset. Figure 1 shows the components of the MA framework. The MA API is used to annotate the source code. As the application executes, the runtime system captures important information in trace files. These trace files are then post-processed to validate, analyze, and construct models. The post-processor currently has three main classes; model validation, control-flow model creation, and symbolic model generation classes. The symbolic model shown in the Figure 1 is generated for the MPI send volume. This symbolic model can be evaluated, and is compatible, with MATLAB⁵ and Octave.⁶

Currently, MA can be used to model computation and communication of applications. The MA API provides a set of functions to annotate a given FORTRAN or C code that uses MPI message-passing for communication. For example, ma_loop_start, a MA API function, can be used to mark the start of a loop. Upon execution, the code instrumented with MA API functions generates trace files. For parallel applications, one trace file is generated for each MPI task. The trace files contain traces for ma_xxx calls and MPI communication events. Most MA calls require a pair of ma_xxx_start and a ma_xxx_end calls. The ma_xxx_end traces are primarily used to validate the modeling assertions against the runtime values. In our current implementation, the assertions for the number of floating-point operations, ma_flop_start/stop, invoke the PAPI hardware counter API⁷ to collect empirical data and compare it to the prediction. The ma_mpi_xxx assertions on the other hand are validated by implementing MPI wrapper functions (PMPI) and by comparing ma_mpi_xxx traces to PMPI_xxx traces. Additional functions are provided in the MA API to control the tracing activity; for example, to control the size of the trace files, by enabling and disabling the tracing at both compile and run time. At runtime, the MA runtime system (MARS) tracks and captures the actual instantiated values as they execute in the application. MARS creates an internal control flow representation of the calls to the MA library as they are executed. It also captures both the symbolic values and the actual values of the expressions. Multiple calls to the same routines with similar parameters is projected onto the same call graph, therefore, the data volume is reduced.