A mathematical approach towards hardware design

Today the hardware for embedded systems is often specified in VHDL. However, VHDL describes the system at a rather low level, which is cumbersome and may lead to design faults in large real life applications. There is a need of higher level abstraction mechanisms. In the embedded systems group of the University of Twente we are working on systematic and transformational methods to design hardware architectures, both multi core and single core. The main line in this approach is to start with a straightforward (often mathematical) specification of the problem. The next step is to find some adequate transformations on this specification, in particular to find specific optimizations, to be able to distribute the application over different cores. The result of these transformations is then translated into the functional programming language Haskell since Haskell is close to mathematics and such a translation often is straightforward. Besides, the Haskell code is executable, so one immediately has a simulation of the intended system. Next, the resulting Haskell specification is given to a compiler, called CëaSH (for CAES LAnguage for Synchronous Hardware) which translates the specification into VHDL. The resulting VHDL is synthesizable, so from there on standard VHDL-tooling can be used for synthesis. In this work we primarily focus on streaming applications: i.e. applications that can be modeled as data-flow graphs. At the moment the CëaSH system is ready in prototype form and in the presentation we will give several examples of how it can be used. In these examples it will be shown that the specification code is clear and concise. Furthermore, it is possible to use powerful abstraction mechanisms, such as polymorphism, higher order functions, pattern matching, lambda abstraction, partial application. These features allow a designer to describe circuits in a more natural and concise way than possible with the language elements found in the traditional hardware description languages. In addition we will give some examples of transformations that are possible in a mathematical specification, and which do not suffer from the problems encountered in, e.g., automatic parallelization of nested for-loops in C-programs

Architecture Specifications in CλaSH

This paper introduces CλaSH, a novel hardware specification environment, by discussing several non-trivial examples. CλaSH is based on the functional language Haskell, and exploits many of its powerful abstraction mechanisms such as higher order functions, polymorphism, lambda abstraction, pattern matching, type derivation. As a result, specifications in CλaSH are concise and semantically clear, and simulations can be directly executed within a Haskell evaluation environment. CλaSH generates synthesizable low-level VHDL code by applying several transformation rules to a functional specification of a digital circuit

Using rewriting to synthesize functional languages to digital circuits

A straightforward synthesis from functional languages to digital circuits transforms variables to wires. The types of these variables determine the bit-width of the wires. Assigning a bit-width to polymorphic and function-type variables within this direct synthesis scheme is impossible. Using a term rewrite system, polymorphic and function-type binders can be completely eliminated from a circuit description, given only minor and reasonable restrictions on the input. The presented term rewrite system is used in the compiler for CλaSH: a polymorphic, higher-order, functional hardware description language

Hiding State in CλaSH Hardware Descriptions

Synchronous hardware can be modelled as a mapping from input and state to output and a new state, such mappings are referred to as transition functions. It is natural to use a functional language to implement transition functions. The CaSH compiler is capable of translating transition functions to VHDL. Modelling hardware using multiple components is convenient. Components in CaSH can be considered as instantiations of functions. To avoid packing and unpacking state when composing components, functions are lifted to arrows. By using arrows the chance of making errors will decrease as it is not required to manually (un)pack the state. Furthermore, the Haskell do-syntax for arrows increases the readability of hardware designs. This is demonstrated using a realistic example of a circuit which consists of multiple components

A two step hardware design method using CλaSH

In order to effectively utilize the growing number of resources available on FPGAs, higher level abstraction mechanisms are needed to deal with increasing complexity resulting from large designs. Functional hardware description languages, like the CλaSH HDL, offer adequate abstraction mechanisms such as polymorphism and higher-order functions. This paper describes a two step design method to implement a DSP application on an FPGA, starting from a mathematical specification, followed by an implementation in CλaSH. A non trivial application, a particle filter, is used to evaluate both the method and CλaSH. First, a straightforward translation is performed from the mathematical definition of a particle filtering to Haskell, a functional programming language with syntax and semantics similar to CλaSH. Secondly, minor changes are applied to the Haskell implementation so that it is accepted by the CλaSH compiler. The resulting hardware produced by our method is evaluated and shows that this method eases reasoning about structure and parallelism in both the mathematical definition and the resulting hardware

System-level modelling of dynamic reconfigurable designs using functional programming abstractions

With the increasing size and complexity of designs in electronics, new approaches are required for the description and verification of digital circuits, specifically at the system level. Functional HDLs can appear as an advantageous choice for formal verification and high-level descriptions. In this paper we explain how to use high-level structures and concepts like higher-order functions, and parametrization together with partial evaluation implementation technique, to describe run-time reconfigurable systems in Haskell. We use the CLaSH tool to translate high-level Haskell descriptions into RT level, synthesizable VHDL. A simple design is used to show the ideas and is implemented on Suzaku-sz410 board for practical proof of concept