Toatie : functional hardware description with dependent types

Describing correct circuits remains a tall order, despite four decades of evolution in Hardware Description Languages (HDLs). Many enticing circuit architectures require recursive structures or complex compile-time computation — two patterns that prove difficult to capture in traditional HDLs. In a signal processing context, the Fast FIR Algorithm (FFA) structure for efficient parallel filtering proves to be naturally recursive, and most Multiple Constant Multiplication (MCM) blocks decompose multiplications into graphs of simple shifts and adds using demanding compile time computation. Generalised versions of both remain mostly in academic folklore. The implementations which do exist are often ad hoc circuit generators, written in software languages. These pose challenges for verification and are resistant to composition. Embedded functional HDLs, that represent circuits as data, allow for these descriptions at the cost of forcing the designer to work at the gate-level. A promising alternative is to use a stand-alone compiler, representing circuits as plain functions, exemplified by the CλaSH HDL. This, however, raises new challenges in capturing a circuit’s staging — which expressions in the single language should be reduced during compile-time elaboration, and which should remain in the circuit’s run-time? To better reflect the physical separation between circuit phases, this work proposes a new functional HDL (representing circuits as functions) with first-class staging constructs. Orthogonal to this, there are also long-standing challenges in the verification of parameterised circuit families. Industry surveys have consistently reported that only a slim minority of FPGA projects reach production without non-trivial bugs. While a healthy growth in the adoption of automatic formal methods is also reported, the majority of testing remains dynamic — presenting difficulties for testing entire circuit families at once. This research offers an alternative verification methodology via the combination of dependent types and automatic synthesis of user-defined data types. Given precise enough types for synthesisable data, this environment can be used to develop circuit families with full functional verification in a correct-by-construction fashion. This approach allows for verification of entire circuit families (not just one concrete member) and side-steps the state-space explosion of model checking methods. Beyond the existing work, this research offers synthesis of combinatorial circuits — not just a software model of their behaviour. This additional step requires careful consideration of staging, erasure & irrelevance, deriving bit representations of user-defined data types, and a new synthesis scheme. This thesis contributes steps towards HDLs with sufficient expressivity for awkward, combinatorial signal processing structures, allowing for a correct-by-construction approach, and a prototype compiler for netlist synthesis.Describing correct circuits remains a tall order, despite four decades of evolution in Hardware Description Languages (HDLs). Many enticing circuit architectures require recursive structures or complex compile-time computation — two patterns that prove difficult to capture in traditional HDLs. In a signal processing context, the Fast FIR Algorithm (FFA) structure for efficient parallel filtering proves to be naturally recursive, and most Multiple Constant Multiplication (MCM) blocks decompose multiplications into graphs of simple shifts and adds using demanding compile time computation. Generalised versions of both remain mostly in academic folklore. The implementations which do exist are often ad hoc circuit generators, written in software languages. These pose challenges for verification and are resistant to composition. Embedded functional HDLs, that represent circuits as data, allow for these descriptions at the cost of forcing the designer to work at the gate-level. A promising alternative is to use a stand-alone compiler, representing circuits as plain functions, exemplified by the CλaSH HDL. This, however, raises new challenges in capturing a circuit’s staging — which expressions in the single language should be reduced during compile-time elaboration, and which should remain in the circuit’s run-time? To better reflect the physical separation between circuit phases, this work proposes a new functional HDL (representing circuits as functions) with first-class staging constructs. Orthogonal to this, there are also long-standing challenges in the verification of parameterised circuit families. Industry surveys have consistently reported that only a slim minority of FPGA projects reach production without non-trivial bugs. While a healthy growth in the adoption of automatic formal methods is also reported, the majority of testing remains dynamic — presenting difficulties for testing entire circuit families at once. This research offers an alternative verification methodology via the combination of dependent types and automatic synthesis of user-defined data types. Given precise enough types for synthesisable data, this environment can be used to develop circuit families with full functional verification in a correct-by-construction fashion. This approach allows for verification of entire circuit families (not just one concrete member) and side-steps the state-space explosion of model checking methods. Beyond the existing work, this research offers synthesis of combinatorial circuits — not just a software model of their behaviour. This additional step requires careful consideration of staging, erasure & irrelevance, deriving bit representations of user-defined data types, and a new synthesis scheme. This thesis contributes steps towards HDLs with sufficient expressivity for awkward, combinatorial signal processing structures, allowing for a correct-by-construction approach, and a prototype compiler for netlist synthesis

Module-per-Object: a Human-Driven Methodology for C++-based High-Level Synthesis Design

High-Level Synthesis (HLS) brings FPGAs to audiences previously unfamiliar to hardware design. However, achieving the highest Quality-of-Results (QoR) with HLS is still unattainable for most programmers. This requires detailed knowledge of FPGA architecture and hardware design in order to produce FPGA-friendly codes. Moreover, these codes are normally in conflict with best coding practices, which favor code reuse, modularity, and conciseness. To overcome these limitations, we propose Module-per-Object (MpO), a human-driven HLS design methodology intended for both hardware designers and software developers with limited FPGA expertise. MpO exploits modern C++ to raise the abstraction level while improving QoR, code readability and modularity. To guide HLS designers, we present the five characteristics of MpO classes. Each characteristic exploits the power of HLS-supported modern C++ features to build C++-based hardware modules. These characteristics lead to high-quality software descriptions and efficient hardware generation. We also present a use case of MpO, where we use C++ as the intermediate language for FPGA-targeted code generation from P4, a packet processing domain specific language. The MpO methodology is evaluated using three design experiments: a packet parser, a flow-based traffic manager, and a digital up-converter. Based on experiments, we show that MpO can be comparable to hand-written VHDL code while keeping a high abstraction level, human-readable coding style and modularity. Compared to traditional C-based HLS design, MpO leads to more efficient circuit generation, both in terms of performance and resource utilization. Also, the MpO approach notably improves software quality, augmenting parametrization while eliminating the incidence of code duplication.Comment: 9 pages. Paper accepted for publication at The 27th IEEE International Symposium on Field-Programmable Custom Computing Machines, San Diego CA, April 28 - May 1, 201

Tree-Based Hardware Recursion for Divide-and-Conquer Algorithms

It is well-known that custom hardware accelerators implemented as application-specific integrated circuits (ASICs) or on field-programmable gate arrays (FPGAs) can solve many problems much faster than software running on a central processing unit (CPU). This is because FPGAs and ASICs can have handcrafted data and control paths which exploit parallelism in ways that CPUs cannot. However, designing custom hardware is complicated and implementing algorithms in a way that takes advantage of the desired parallelism can be difficult. One class of algorithms that exemplifies this is divide-and-conquer algorithms. A divide-and-conquer algorithm is a type of recursive algorithm that solves a problem by repeatedly dividing it into smaller sub-problems. These algorithms have a lot of parallelism because they generate a large number of sub-problems that can be computed independently of each other. Unfortunately, traditional stack-based approaches to handling recursion in hardware make exploiting this parallelism difficult. This work proposes a new general-purpose approach to implementing recursive functions in hardware, which we call TreeRecur. TreeRecur uses trees to represent the branching recursive function calls of divide-and-conquer algorithms, which makes it possible to take advantage of their procedure-level parallelism. To allow for design flexibility, TreeRecur executes algorithms using a configurable number of independent function processors. These processors are generated using high-level synthesis, making it easy to implement a variety of different algorithms. Our solution was tested on three different algorithms and compared against software implementations of the same algorithms. Performance results were collected in terms of execution speed and energy consumption. TreeRecur was found to have execution speeds comparable to software when differences in clock speed were accounted for and was found to consume up to 11.2 times less energy

Leveraging Modern C++ in High-level Synthesis

High-level synthesis (HLS) enables automated conversion of high-level language algorithms into synthesizable register-transfer level code, allowing computation intensive algorithms to be accelerated on FPGAs. Most HLS tools have C++ as their input language, as it is widely known in both software and hardware industry. However, even though C++ receives a new standard every three years, the HLS tool vendors have mostly provided support and examples using C++98/03. Limiting to early C++ standards imposes a productivity penalty, since the newer standards provide both compilation time reductions and more concise, expressive, and maintainable way of writing code. In this study, we make the case for adopting modern C++ in HLS. We inspect the language features of C++11 and forward, and consider their benefits for HLS. We also test the present support for the modern language features with two state-of-the-art commercial HLS tools. Finally, we provide an extended example, demonstrating the increased clarity of code achieved using the newer standards. We note that the investigated HLS tools already have good support for modern C++ features, and urge their adoption to increase designer productivity.publishedVersionPeer reviewe

Separation logic for high-level synthesis

High-level synthesis (HLS) promises a significant shortening of the digital hardware design cycle by raising the abstraction level of the design entry to high-level languages such as C/C++. However, applications using dynamic, pointer-based data structures remain difficult to implement well, yet such constructs are widely used in software. Automated optimisations that leverage the memory bandwidth of dedicated hardware implementations by distributing the application data over separate on-chip memories and parallelise the implementation are often ineffective in the presence of dynamic data structures, due to the lack of an automated analysis that disambiguates pointer-based memory accesses. This thesis takes a step towards closing this gap. We explore recent advances in separation logic, a rigorous mathematical framework that enables formal reasoning about the memory access of heap-manipulating programs. We develop a static analysis that automatically splits heap-allocated data structures into provably disjoint regions. Our algorithm focuses on dynamic data structures accessed in loops and is accompanied by automated source-to-source transformations which enable loop parallelisation and physical memory partitioning by off-the-shelf HLS tools. We then extend the scope of our technique to pointer-based memory-intensive implementations that require access to an off-chip memory. The extended HLS design aid generates parallel on-chip multi-cache architectures. It uses the disjointness property of memory accesses to support non-overlapping memory regions by private caches. It also identifies regions which are shared after parallelisation and which are supported by parallel caches with a coherency mechanism and synchronisation, resulting in automatically specialised memory systems. We show up to 15x acceleration from heap partitioning, parallelisation and the insertion of the custom cache system in demonstrably practical applications.Open Acces

A multi-level functional IR with rewrites for higher-level synthesis of accelerators

Specialised accelerators deliver orders of magnitude higher energy-efficiency than general-purpose processors. Field Programmable Gate Arrays (FPGAs) have become the substrate of choice, because the ever-changing nature of modern workloads, such as machine learning, demands reconfigurability. However, they are notoriously hard to program directly using Hardware Description Languages (HDLs). Traditional High-Level Synthesis (HLS) tools improve productivity, but come with their own problems. They often produce sub-optimal designs and programmers are still required to write hardware-specific code, thus development cycles remain long. This thesis proposes Shir, a higher-level synthesis approach for high-performance accelerator design with a hardware-agnostic programming entry point, a multi-level Intermediate Representation (IR), a compiler and rewrite rules for optimisation. First, a novel, multi-level functional IR structure for accelerator design is described. The IRs operate on different levels of abstraction, cleanly separating different hardware concerns. They enable the expression of different forms of parallelism and standard memory features, such as asynchronous off-chip memories or synchronous on-chip buffers, as well as arbitration of such shared resources. Exposing these features at the IR level is essential for achieving high performance. Next, mechanical lowering procedures are introduced to automatically compile a program specification through Shir’s functional IRs until low-level HDL code for FPGA synthesis is emitted. Each lowering step gradually adds implementation details. Finally, this thesis presents rewrite rules for automatic optimisations around parallelisation, buffering and data reshaping. Reshaping operations pose a challenge to functional approaches in particular. They introduce overheads that compromise performance or even prevent the generation of synthesisable hardware designs altogether. This fundamental issue is solved by the application of rewrite rules. The viability of this approach is demonstrated by running matrix multiplication and 2D convolution on an Intel Arria 10 FPGA. A limited design space exploration is conducted, confirming the ability of the IR to exploit various hardware features. Using rewrite rules for optimisation, it is possible to generate high-performance designs that are competitive with highly tuned OpenCL implementations and that outperform hardware-agnostic OpenCL code. The performance impact of the optimisations is further evaluated showing that they are essential to achieving high performance, and in many cases also necessary to produce hardware that fits the resource constraints

Rapid Digital Architecture Design of Computationally Complex Algorithms

Traditional digital design techniques hardly keep up with the rising abundance of programmable circuitry found on recent Field-Programmable Gate Arrays. Therefore, the novel Rapid Data Type-Agnostic Digital Design Methodology (RDAM) elevates the design perspective of digital design engineers away from the register-transfer level to the algorithmic level. It is founded on the capabilities of High-Level Synthesis tools. By consequently working with data type-agnostic source codes, the RDAM brings significant simplifications to the fixed-point conversion of algorithms and the design of complex-valued architectures. Signal processing applications from the field of Compressed Sensing illustrate the efficacy of the RDAM in the context of multi-user wireless communications. For instance, a complex-valued digital architecture of Orthogonal Matching Pursuit with rank-1 updating has successfully been implemented and tested

Late-bound code generation

Each time a function or method is invoked during the execution of a program, a stream of instructions is issued to some underlying hardware platform. But exactly what underlying hardware, and which instructions, is usually left implicit. However in certain situations it becomes important to control these decisions. For example, particular problems can only be solved in real-time when scheduled on specialised accelerators, such as graphics coprocessors or computing clusters. We introduce a novel operator for hygienically reifying the behaviour of a runtime function instance as a syntactic fragment, in a language which may in general differ from the source function definition. Translation and optimisation are performed by recursively invoked, dynamically dispatched code generators. Side-effecting operations are permitted, and their ordering is preserved. We compare our operator with other techniques for pragmatic control, observing that: the use of our operator supports lifting arbitrary mutable objects, and neither requires rewriting sections of the source program in a multi-level language, nor interferes with the interface to individual software components. Due to its lack of interference at the abstraction level at which software is composed, we believe that our approach poses a significantly lower barrier to practical adoption than current methods. The practical efficacy of our operator is demonstrated by using it to offload the user interface rendering of a smartphone application to an FPGA coprocessor, including both statically and procedurally defined user interface components. The generated pipeline is an application-specific, statically scheduled processor-per-primitive rendering pipeline, suitable for place-and-route style optimisation. To demonstrate the compatibility of our operator with existing languages, we show how it may be defined within the Python programming language. We introduce a transformation for weakening mutable to immutable named bindings, termed let-weakening, to solve the problem of propagating information pertaining to named variables between modular code generating units.Open Acces

Wiring Circuits Is Easy as {0,1,ω}, or Is It...

Quantitative Type-Systems support fine-grained reasoning about term usage in our programming languages. Hardware Design Languages are another style of language in which quantitative typing would be beneficial. When wiring components together we must ensure that there are no unused ports, dangling wires, or accidental fan-ins and fan-outs. Although many wire usage checks are detectable using static analysis tools, such as Verilator, quantitative typing supports making these extrinsic checks an intrinsic aspect of the type-system. With quantitative typing of bound terms, we can provide design-time checks that all wires and ports have been used, and ensure that all wiring decisions are explicitly made, and are neither implicit nor accidental. We showcase the use of quantitative types in hardware design languages by detailing how we can retrofit quantitative types onto SystemVerilog netlists, and the impact that such a quantitative type-system has when creating designs. Netlists are gate-level descriptions of hardware that are produced as the result of synthesis, and it is from these netlists that hardware is generated (fabless or fabbed). First, we present a simple structural type-system for a featherweight version of SystemVerilog netlists that demonstrates how we can type netlists using standard structural techniques, and what it means for netlists to be type-safe but still lead to ill-wired designs. We then detail how to retrofit the language with quantitative types, make the type-system sub-structural, and detail how our new type-safety result ensures that wires and ports are used once. Our ideas have been proven both practically and formally by realising our work in Idris2, through which we can construct a verified language implementation that can type-check existing designs. From this work we can look to promote quantitative typing back up the synthesis chain to a more comprehensive hardware description language; and to help develop new and better hardware description languages with quantitative typing