Formal equivalence checking

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Formal equivalence checking process is a part of electronic design automation (EDA), commonly used during the development of digital integrated circuits, to formally prove that two representations of a circuit design exhibit exactly the same behavior.

Electronic design automation (EDA), also referred to as electronic computer-aided design (ECAD), is a category of software tools for designing electronic systems such as integrated circuits and printed circuit boards. The tools work together in a design flow that chip designers use to design and analyze entire semiconductor chips. Since a modern semiconductor chip can have billions of components, EDA tools are essential for their design.

Integrated circuit electronic circuit manufactured by lithography; set of electronic circuits on one small flat piece (or "chip") of semiconductor material, normally silicon 639-1 ısoo

An integrated circuit or monolithic integrated circuit is a set of electronic circuits on one small flat piece of semiconductor material that is normally silicon. The integration of large numbers of tiny transistors into a small chip results in circuits that are orders of magnitude smaller, cheaper, and faster than those constructed of discrete electronic components. The IC's mass production capability, reliability and building-block approach to circuit design has ensured the rapid adoption of standardized ICs in place of designs using discrete transistors. ICs are now used in virtually all electronic equipment and have revolutionized the world of electronics. Computers, mobile phones, and other digital home appliances are now inextricable parts of the structure of modern societies, made possible by the small size and low cost of ICs.

The process of circuit design can cover systems ranging from complex electronic systems all the way down to the individual transistors within an integrated circuit. For simple circuits the design process can often be done by one person without needing a planned or structured design process, but for more complex designs, teams of designers following a systematic approach with intelligently guided computer simulation are becoming increasingly common. In integrated circuit design automation, the term "circuit design" often refers to the step of the design cycle which outputs the schematics of the integrated circuit. Typically this is the step between logic design and physical design.

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Equivalence checking and levels of abstraction

In general, there is a wide range of possible definitions of functional equivalence covering comparisons between different levels of abstraction and varying granularity of timing details.

A synchronous circuit is a digital circuit in which the changes in the state of memory elements are synchronized by a clock signal. In a sequential digital logic circuit, data is stored in memory devices called flip-flops or latches. The output of a flip-flop is constant until a pulse is applied to its "clock" input, upon which the input of the flip-flop is latched into its output. In a synchronous logic circuit, an electronic oscillator called the clock generates a string of pulses, the "clock signal". This clock signal is applied to every storage element, so in an ideal synchronous circuit, every change in the logical levels of its storage components is simultaneous. Ideally, the input to each storage element has reached its final value before the next clock occurs, so the behaviour of the whole circuit can be predicted exactly. Practically, some delay is required for each logical operation, resulting in a maximum speed at which each synchronous system can run.

Microprocessor computer processor contained on an integrated-circuit chip

A microprocessor is a computer processor that incorporates the functions of a central processing unit on a single integrated circuit (IC), or at most a few integrated circuits. The microprocessor is a multipurpose, clock driven, register based, digital integrated circuit that accepts binary data as input, processes it according to instructions stored in its memory, and provides results as output. Microprocessors contain both combinational logic and sequential digital logic. Microprocessors operate on numbers and symbols represented in the binary number system.

SystemC is a set of C++ classes and macros which provide an event-driven simulation interface. These facilities enable a designer to simulate concurrent processes, each described using plain C++ syntax. SystemC processes can communicate in a simulated real-time environment, using signals of all the datatypes offered by C++, some additional ones offered by the SystemC library, as well as user defined. In certain respects, SystemC deliberately mimics the hardware description languages VHDL and Verilog, but is more aptly described as a system-level modeling language.

Synchronous machine equivalence

The register transfer level (RTL) behavior of a digital chip is usually described with a hardware description language, such as Verilog or VHDL. This description is the golden reference model that describes in detail which operations will be executed during which clock cycle and by which pieces of hardware. Once the logic designers, by simulations and other verification methods, have verified register transfer description, the design is usually converted into a netlist by a logic synthesis tool. Equivalence is not to be confused with functional correctness, which must be determined by functional verification.

In computer engineering, a hardware description language (HDL) is a specialized computer language used to describe the structure and behavior of electronic circuits, and most commonly, digital logic circuits.

Verilog, standardized as IEEE 1364, is a hardware description language (HDL) used to model electronic systems. It is most commonly used in the design and verification of digital circuits at the register-transfer level of abstraction. It is also used in the verification of analog circuits and mixed-signal circuits, as well as in the design of genetic circuits. In 2009, the Verilog standard was merged into the SystemVerilog standard, creating IEEE Standard 1800-2009. Since then, Verilog is officially part of the SystemVerilog language. The current version is IEEE standard 1800-2017.

VHDL hardware description language

VHDL is a hardware description language used in electronic design automation to describe digital and mixed-signal systems such as field-programmable gate arrays and integrated circuits. VHDL can also be used as a general purpose parallel programming language.

The initial netlist will usually undergo a number of transformations such as optimization, addition of Design For Test (DFT) structures, etc., before it is used as the basis for the placement of the logic elements into a physical layout. Contemporary physical design software will occasionally also make significant modifications (such as replacing logic elements with equivalent similar elements that have a higher or lower drive strength and/or area) to the netlist. Throughout every step of a very complex, multi-step procedure, the original functionality and the behavior described by the original code must be maintained. When the final tape-out is made of a digital chip, many different EDA programs and possibly some manual edits will have altered the netlist.

In electronic design, a netlist is a description of the connectivity of an electronic circuit. In its simplest form, a netlist consists of a list of the electronic components in a circuit and a list of the nodes they are connected to. A network (net) is a collection of two or more interconnected components.

In electronics design, tape-out or tapeout is the final result of the design process for integrated circuits or printed circuit boards before they are sent for manufacturing. The tapeout is specifically the point at which the graphic for the photomask of the circuit is sent to the fabrication facility. A synonym used at IBM is RIT. IBM differentiates between RIT-A for the non-metallic structures and RIT-B for the metal layers.

In theory, a logic synthesis tool guarantees that the first netlist is logically equivalent to the RTL source code. All the programs later in the process that make changes to the netlist also, in theory, ensure that these changes are logically equivalent to a previous version.

In logic, statements and are logically equivalent if they have the same logical content. That is, if they have the same truth value in every model. The logical equivalence of and is sometimes expressed as , , or . However, these symbols are also used for material equivalence. Proper interpretation depends on the context. Logical equivalence is different from material equivalence, although the two concepts are closely related.

In practice, programs have bugs and it would be a major risk to assume that all steps from RTL through the final tape-out netlist have been performed without error. Also, in real life, it is common for designers to make manual changes to a netlist, commonly known as Engineering Change Orders, or ECOs, thereby introducing a major additional error factor. Therefore, instead of blindly assuming that no mistakes were made, a verification step is needed to check the logical equivalence of the final version of the netlist to the original description of the design (golden reference model).

Historically, one way to check the equivalence was to re-simulate, using the final netlist, the test cases that were developed for verifying the correctness of the RTL. This process is called gate level logic simulation. However, the problem with this is that the quality of the check is only as good as the quality of the test cases. Also, gate-level simulations are notoriously slow to execute, which is a major problem as the size of digital designs continues to grow exponentially.

An alternative way to solve this is to formally prove that the RTL code and the netlist synthesized from it have exactly the same behavior in all (relevant) cases. This process is called formal equivalence checking and is a problem that is studied under the broader area of formal verification.

A formal equivalence check can be performed between any two representations of a design: RTL <> netlist, netlist <> netlist or RTL <> RTL, though the latter is rare compared to the first two. Typically, a formal equivalence checking tool will also indicate with great precision at which point there exists a difference between two representations.

Methods

There are two basic technologies used for boolean reasoning in equivalence checking programs:

Commercial applications for equivalence checking

Major products in the Logic Equivalence Checking (LEC) area of EDA are:

Generalizations

See also

Related Research Articles

Digital electronics Electronic circuits that utilize digital signals

Digital electronics or digital (electronic) circuits are electronics that operate on digital signals. In contrast, analog circuits manipulate analog signals whose performance is more subject to manufacturing tolerance, signal attenuation and noise. Digital techniques are helpful because it is a lot easier to get an electronic device to switch into one of a number of known states than to accurately reproduce a continuous range of values.

In computer science, model checking or property checking refers to the following problem: Given a model of a system, exhaustively and automatically check whether this model meets a given specification. Typically, one has hardware or software systems in mind, whereas the specification contains safety requirements such as the absence of deadlocks and similar critical states that can cause the system to crash. Model checking is a technique for automatically verifying correctness properties of finite-state systems.

In computer science, a binary decision diagram (BDD) or branching program is a data structure that is used to represent a Boolean function. On a more abstract level, BDDs can be considered as a compressed representation of sets or relations. Unlike other compressed representations, operations are performed directly on the compressed representation, i.e. without decompression. Other data structures used to represent Boolean functions include negation normal form (NNF), Zhegalkin polynomials, and propositional directed acyclic graphs (PDAG).

In digital circuit design, register-transfer level (RTL) is a design abstraction which models a synchronous digital circuit in terms of the flow of digital signals (data) between hardware registers, and the logical operations performed on those signals.

In electronics, logic synthesis is a process by which an abstract specification of desired circuit behavior, typically at register transfer level (RTL), is turned into a design implementation in terms of logic gates, typically by a computer program called a synthesis tool. Common examples of this process include synthesis of designs specified in hardware description languages, including VHDL and Verilog. Some synthesis tools generate bitstreams for programmable logic devices such as PALs or FPGAs, while others target the creation of ASICs. Logic synthesis is one aspect of electronic design automation.

In electronic design a semiconductor intellectual property core, IP core, or IP block is a reusable unit of logic, cell, or integrated circuit layout design that is the intellectual property of one party. IP cores may be licensed to another party or can be owned and used by a single party alone. The term is derived from the licensing of the patent and/or source code copyright that exist in the design. IP cores can be used as building blocks within application-specific integrated circuit (ASIC) designs or field-programmable gate array (FPGA) logic designs.

Standard cell group of transistor and interconnect structures that provides a boolean logic function; used to design application-specific integrated circuits with mostly digital-logic features

In semiconductor design, standard cell methodology is a method of designing application-specific integrated circuits (ASICs) with mostly digital-logic features. Standard cell methodology is an example of design abstraction, whereby a low-level very-large-scale integration (VLSI) layout is encapsulated into an abstract logic representation. Cell-based methodology — the general class to which standard cells belong — makes it possible for one designer to focus on the high-level aspect of digital design, while another designer focuses on the implementation (physical) aspect. Along with semiconductor manufacturing advances, standard cell methodology has helped designers scale ASICs from comparatively simple single-function ICs, to complex multi-million gate system-on-a-chip (SoC) devices.

Integrated circuit design Engineering process for electronic hardware

Integrated circuit design, or IC design, is a subset of electronics engineering, encompassing the particular logic and circuit design techniques required to design integrated circuits, or ICs. ICs consist of miniaturized electronic components built into an electrical network on a monolithic semiconductor substrate by photolithography.

In electronic design automation, functional verification is the task of verifying that the logic design conforms to specification. In everyday terms, functional verification attempts to answer the question "Does this proposed design do what is intended?" This is a complex task, and takes the majority of time and effort in most large electronic system design projects. Functional verification is a part of more encompassing design verification, which, besides functional verification, considers non-functional aspects like timing, layout and power.

In VLSI semiconductor manufacturing, the process of Design Closure is a part of the development workflow by which an integrated circuit design is modified from its initial description to meet a growing list of design constraints and objectives.

The Layout Versus Schematic (LVS) is the class of electronic design automation (EDA) verification software that determines whether a particular integrated circuit layout corresponds to the original schematic or circuit diagram of the design.

And-inverter graph Graph representing an implementation of the logical functionality of a network

An and-inverter graph (AIG) is a directed, acyclic graph that represents a structural implementation of the logical functionality of a circuit or network. An AIG consists of two-input nodes representing logical conjunction, terminal nodes labeled with variable names, and edges optionally containing markers indicating logical negation. This representation of a logic function is rarely structurally efficient for large circuits, but is an efficient representation for manipulation of boolean functions. Typically, the abstract graph is represented as a data structure in software.

Engineering change orders (ECO) are used for changes in components, assemblies, or documents such as processes and work instructions. They may also be used for changes in specifications. Lastly, it can be "a modification that will have an effect on a manufactured product or manufacturing process."

Timing closure is the process by which a logic design consisting of primitive elements such as combinatorial logic gates and sequential logic gates is modified to meet its timing requirements. Unlike in a computer program where there is no explicit delay to perform a calculation, logic circuits have intrinsic and well defined delays to propagate inputs to outputs. In simple cases, the user can compute the path delay between elements manually. If the design is more than a dozen or so elements this is impractical. For example, the time delay along a path from the output of a D-Flip Flop, through combinatorial logic gates, then into the next D-Flip Flop input must satisfy the time period between synchronizing clock pulses to the two flip flops. When the delay through the elements is greater than the clock cycle time, the elements are said to be on the critical path. The circuit will not function when the path delay exceeds the clock cycle delay so modifying the circuit to remove the timing failure is an important part of the logic design engineer's task.

Physical design (electronics)

In integrated circuit design, physical design is a step in the standard design cycle which follows after the circuit design. At this step, circuit representations of the components of the design are converted into geometric representations of shapes which, when manufactured in the corresponding layers of materials, will ensure the required functioning of the components. This geometric representation is called integrated circuit layout. This step is usually split into several sub-steps, which include both design and verification and validation of the layout.

High-level synthesis (HLS), sometimes referred to as C synthesis, electronic system-level (ESL) synthesis, algorithmic synthesis, or behavioral synthesis, is an automated design process that interprets an algorithmic description of a desired behavior and creates digital hardware that implements that behavior. Synthesis begins with a high-level specification of the problem, where behavior is generally decoupled from e.g. clock-level timing. Early HLS explored a variety of input specification languages., although recent research and commercial applications generally accept synthesizable subsets of ANSI C/C++/SystemC/MATLAB. The code is analyzed, architecturally constrained, and scheduled to transcompile into a register-transfer level (RTL) design in a hardware description language (HDL), which is in turn commonly synthesized to the gate level by the use of a logic synthesis tool. The goal of HLS is to let hardware designers efficiently build and verify hardware, by giving them better control over optimization of their design architecture, and through the nature of allowing the designer to describe the design at a higher level of abstraction while the tool does the RTL implementation. Verification of the RTL is an important part of the process.

In the automated design of integrated circuits, signoff checks is the collective name given to a series of verification steps that the design must pass before it can be taped out. This implies an iterative process involving incremental fixes across the board using one or more check types, and then retesting the design. There are two types of sign-off's: front-end sign-off and back-end sign-off. After back-end sign-off the chip goes to fabrication. After listing out all the features in the specification, the verification engineer will write coverage for those features to identify bugs, and send back the RTL design to the designer. Bugs, or defects, can include issues like missing features, errors in design, etc. When the coverage reaches a maximum% then the verification team will sign it off. By using a methodology like UVM, OVM, or VMM, the verification team develops a reusable environment. Nowadays, UVM is more popular than others.

High-level verification (HLV), or electronic system-level (ESL) verification, is the task to verify ESL designs at high abstraction level, i.e., it is the task to verify a model that represents hardware above register-transfer level (RTL) abstract level. For high-level synthesis, HLV is to HLS as functional verification is to logic synthesis.

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