Consistency Analysis of Reconfigurable Dataflow Specifications

Parameterized dataflow is a meta-modeling approach for incorporating dynamic reconfiguration capabilities into broad classes of dataflow-based design frameworks for digital signal processing (DSP). Through a novel formalization of dataflow parameterization, and a disciplined approach to specifying parameter reconfiguration, the parameterized dataflow framework provides for automated synthesis of robust and efficient embedded software. Central to these synthesis objectives is the formulation and analysis of consistency in parameterized dataflow specifications. Consistency analysis of reconfigurable specifications is particularly challenging due to their inherently dynamic behavior. This paper presents a novel framework, based on a concept of local synchrony, for managing consistency when synthesizing implementations from dynamicallyreconfigurable, parameterized dataflow graphs. 1. Motivation and Related Work Dataflow is an established computational model for simulation and synthesis of software for digital signal processing (DSP) applications. The modern trend toward highly dynamic and reconfigurable DSP system behavior, however, poses an important challenge for dataflow-based DSP modeling techniques, which have traditionally been well-suited primarily for applications with significantly static, high-level structure. Parameterized dataflow [1] is a promising new meta-modeling approach that addresses this challenge by systematically incorporating dynamic reconfiguration capabilities into broad classes of dataflow-based design frameworks for digital signal processing (DSP). Through a novel formalization of dataflow parameterization, and a disciplined approach to specifying parameter reconfiguration, the parameterized dataflow framework provides for automated synthesis of robust and efficient embedded software. * This research was sponsored by the U. S. National Science Foundation under Grant #9734275. E.F. Deprettere et al. (Eds.): SAMOS 2001, LNCS 2268, pp. 1–17, 2002. c © Springer-Verlag Berlin Heidelberg 2002 2 Bishnupriya Bhattacharya and Shuvra S. Bhattacharyya Central to these synthesis objectives is the formulation and analysis of consistency in parameterized dataflow specifications. Consistency analysis of reconfigurable specifications is particularly challenging due to their inherently dynamic behavior. This paper presents a novel framework, based on a concept of local synchrony, for managing consistency when synthesizing implementations from dynamically-reconfigurable, parameterized dataflow graphs. Specifically, we examine consistency issues in the context of dataflow graphs that are based on the parameterized synchronous dataflow [1] (PSDF) model of computation (MoC), which is the MoC that results when the parameterized dataflow meta-modeling approach is integrated with the well-known synchronous dataflow MoC. We focus on PSDF in this paper for clarity and uniformity; however, the consistency analysis techniques described in this paper can be adapted to the integration of parameterized dataflow with any dataflow MoC that has a well-defined concept of a graph iteration (e.g., to the parameterized cyclo-static dataflow model that is described in [2]). The organization of this paper is as follows. In the remainder of this section, we review a variety of dataflow modeling approaches for DSP. In Section 2, we present an application example to motivate the PSDF MoC, and in Section 3, we review the fundamental semantics of PSDF. In Sections 4 through 7 we develop and illustrate consistency analysis formulations for PSDF specifications, and relate these formulations precisely to constraints for robust execution of dynamically-reconfigurable applications that are modeled in PSDF. In Section 8, we summarize, and mention promising directions for further study. A restricted version of dataflow, termed synchronous dataflow (SDF) [12], that offers strong compile-time predictability properties, but has limited expressive power, has been studied extensively in the DSP context. The key restriction in SDF is that the number of data values (tokens) produced and consumed by each actor (dataflow graph node) is fixed and known at compile time. Many extensions to SDF have been proposed to increase its expressive power, while maintaining its compile-time predictability properties as much as possible. The primary benefits offered by SDF are static scheduling, and optimization opportunities, leading to a high degree of compile-time predictability. Although an important class of useful DSP applications can be modeled efficiently in SDF, its expressive power is limited to static applications. Thus, many extensions to the SDF model have been proposed, where the objective is to accommodate a broader range of applications, while maintaining a significant part of the compile-time predictability of SDF. Cyclo-static dataflow (CSDF) and scalable synchronous dataflow (SSDF) are the two most popular extensions of SDF in use today. In CSDF, token production and consumption can vary between actor invocations as long as the variation forms a certain type of periodic pattern [4]. Each time an actor is fired, a different piece of code called a phase is executed. For example, consider a distributor actor, which routes data received from a single input to each of two outputs in alternation. In SDF, this actor consumes two tokens and produces one token on each of its two outputs. In CSDF, by contrast, the actor consumes one token on its input, and produces tokens according to the periodic pattern (one token produced on the first invocation, none on the second, and so on) on one output edge, and according to the complementary peri1 0 1 0 ... , , , , Consistency Analysis of Reconfigurable Dataflow Specifications 3 4 Bishnupriya Bhattacharya and Shuvra S. Bhattacharyya Furthermore, in contrast to previous work on dataflow modeling, the parameterized dataflow approach achieves increased expressive power entirely through its comprehensive support for parameter definition and parameter value reconfiguration. Actor parameters have been used for years in block diagram DSP design environments. Conventionally, these parameters are assigned static values that remain unchanged throughout execution. The parameterized dataflow approach takes this as a starting point, and develops a comprehensive framework for dynamically reconfiguring the behavior of dataflow actors, edges, graphs, and subsystems by run-time modification of parameter values. SPDF also allows actor parameters to be reconfigured dynamically. However, SPDF is restricted to reconfiguring only those parameters of an actor that do not affect its dataflow behavior (token production/consumption). Parameterized dataflow does not impose this restriction, which greatly enhances the utility of the modeling approach, but significantly complicates scheduling and dataflow consistency analysis. A key consideration in our detailed development of the PSDF MoC (recall that PSDF is the integration of the parameterized dataflow meta-modeling approach with the synchronous dataflow MoC) is addressing these complications in a robust manner, as we will explain in Sections 4 and 7. Such thorough support for parameterization, as well as the associated management of application dynamics in terms of run-time reconfiguration, is not available in any of the previously-developed dataflow modeling techniques. In recent years, several modeling techniques have been proposed that enhance expressive power by providing precise semantics for integrating dataflow graphs with finite state machine (FSM) models. These include El Greco [5], which provides facilities for “control models” to dynamically configure specification parameters; *charts (pronounced “starcharts”) with heterochronous dataflow as the concurrency model [9]; the FunState intermediate representation [17]; the DF* framework developed at K. U. Leuven [8]; and the control flow provisions in bounded dynamic dataflow [14]. In contrast, parameterized dataflow does not require any departure from the dataflow framework. This is advantageous for users of DSP design tools who are already accustomed to working purely in the dataflow domain, and for whom integration with FSMs may presently be an experimental concept. With a longer term view, due to the meta-modeling nature of parameterized dataflow, it appears promising to incorporate our parameterization/reconfiguration techniques into the dataflow components of existing FSM/ dataflow hybrids. This is a useful direction for further investigation. The parameterized dataflow modeling approach was introduced in [1], which provides an overview of its modeling semantics, and quasi-static scheduling of parameterized dataflow specifications was explored in [2]. This paper focuses on consistency analysis of parameterized dataflow specifications, and develops techniques that can be integrated with scheduling to provide robust operation of synthesized implementations. 2. Application Example To motivate the PSDF model, Fig. 1(a) shows a speech compression application, which is modeled by a PSDF subsystem Compress. A speech instance of length is L Consistency Analysis of Reconfigurable Dataflow Specifications 5 6 Bishnupriya Bhattacharya and Shuvra S. Bhattacharyya The size of each speech segment ( ), and the AR model order ( ) are important design parameters for producing a good AR model, which is necessary for achieving high compression ratios. The values of and , along with the zero-padded speech sample length are modeled as subsystem parameters of Compress that are configured in the subinit graph. The select actor in the subinit graph reads the original speech instance, and examines it to determine and , using any of the existing techniques, e.g., the Burg segment size selection algorithm, and the AIC order selection criterion [10]. The zero-padded speech length is computed such that it is the smallest integer greater than that is exactly divided by the segment size, . From these relationships, it is useful to convey to the scheduler the assertion that . Note that for clarity, the above PSDF model does not specify all the details of the application. Our purpose here is to provide an overview of the modeling process, using mixed-grain DSP actors, such that PSDF-specific aspects of the model are emphasized — especially those parameters that are relevant from the scheduler’s perspective. All actor parameters that do not affect dataflow behavior have been omitted from the specification. For example, the quantizers and dequantizers will have actor parameters controlling their quantization levels and thresholds. The select actor could determine two such sets — one for the residual and one for the coefficients. An SDF or CSDF representation of this application will have hard numbers (e.g., 150 instead of ) for the dataflow in Fig. 1(a), corresponding to a particular speech sample. Thus, for processing separate speech samples, the design needs to be modified and the static schedule re-computed. SPDF can accommodate those parameter reconfigurations that do not affect an actor’s dataflow properties (e.g., the threshold parameter of the quantizer actors), but not reconfiguration of the len parameter of the Analyze actor (An), since len affects the dataflow of An. Thus, again separate designs are necessary to process separate speech samples.