# CIRCT

Circuit IR Compilers and Tools

# FSM Dialect Rationale

This document describes various design points of the FSM dialect, why they are the way they are, and current status. This follows in the spirit of other MLIR Rationale docs.

## Introduction ¶

Finite-state machine (FSM) is an abstract machine that can be in exactly one of a finite number of states at any given time. The FSM can change from one state to another in response to some inputs; the change from one state to another is called a transition. Verification, Hardware IP block control, system state control, hardware design, and software design have aspects that are succinctly described as some form of FSM. For integrated development purposes, late design-time choice, and per-project choice, we want to encode system descriptions in an FSM form. We want a compiler to be able to manipulate, query, and generate code in multiple domains, such as SW drivers, firmware, RTL hardware, and verification.

The FSM dialect in CIRCT is designed to provide a set of abstractions for FSM with the following features:

1. Provide explicit and structural representations of states, transitions, and internal variables of an FSM, allowing convenient analysis and transformation.
2. Provide a target-agnostic representation of FSM, allowing the state machine to be instantiated and attached to other dialects from different domains.
3. By cooperating with two conversion passes, FSMToHW and FSMToStandard, allow to lower the FSM abstraction into HW+Comb+SV (Hardware) and Standard+SCF+MemRef (Software) dialects for the purposes of simulation, code generation, etc.

## Operations ¶

### Two ways of instantiation ¶

A state machine is defined by an fsm.machine operation, which contains all the states and transitions of the state machine. fsm.machine has a list of inputs and outputs and explicit state type:

fsm.machine @foo(%arg0: i1) -> i1 attributes {stateType = i1} {
...
}


FSM dialect provides two ways to instantiate a state machine: fsm.hw_instance is intended for use in HW context (usually described by graph regions) and fsm.instance+fsm.trigger is intended for use in a SW context (usually described by CFG regions). In HW IRs (such as HW+Comb+SV and FIRRTL), although an MLIR value is only defined once in the IR, it is actually “driven” by its predecessors continuously during the runtime and can “hold” different values at different moments. However, in the world of SW IRs (such as Standard+SCF), we don’t have such a semantics – SW IRs “run” sequentially.

Here we define that each trigger causes the possibility of a transition from one state to another state through exactly one transition. In a SW context, fsm.instance generates an InstanceType value to represent a state machine instance. Each fsm.trigger targets a machine instance and explicitly causes a trigger. Therefore, fsm.trigger may change the state of the machine instance thus is a side-effecting operation. The following MLIR code shows an example of instantiating and triggering the state machine defined above:

func @bar() {
%foo_inst = fsm.instance "foo_inst" @foo
%in0 = ...
%out0 = fsm.trigger %foo_inst(%in0) : (i1) -> i1
...
%in1 = ...
%out1 = fsm.trigger %foo_inst(%in1) : (i1) -> i1
return
}


In the contrast, to comply with the HW semantics, fsm.hw_instance directly consumes inputs and generates results. The operand and result types must align with the type of the referenced fsm.machine. In a HW context, triggers are implicitly initiated by the processors of fsm.hw_instance. The following MLIR code shows an example of instantiating the same state machine in HW IRs:

hw.module @qux() {
%in = ...
%out = fsm.hw_instance "foo_inst" @foo(%in) : (i1) -> i1
}


### Explicit state and transition representation ¶

Each state of an FSM is represented explicitly with an fsm.state operation. fsm.state must have an output CFG region representing the combinational logic of generating the state machine’s outputs. The output region must have an fsm.output operation as terminator and the operand types of the fsm.output must align with the result types of the state machine. fsm.state also contains a list of fsm.transition operations representing the outgoing transitions that can be triggered from the current state. fsm.state also has a symbol name that can be referred to by fsm.transitions as the next state. The following MLIR code shows a running example:

fsm.machine @foo(%arg0: i1) -> i1 attributes {stateType = i1} {
fsm.state "IDLE" output  {
%true = constant true
fsm.output %true : i1
} transitions  {
fsm.transition @BUSY ...
}

fsm.state "BUSY" output  {
%false = constant false
fsm.output %false : i1
} transitions  {
fsm.transition @BUSY ...
fsm.transition @IDLE ...
}
}


### Guard region of transitions ¶

fsm.transition has an optional guard CFG region, which must be terminated with an fsm.return operation returning a Boolean value to indicate whether the transition is taken:

fsm.machine @foo(%arg0: i1) -> i1 attributes {stateType = i1} {
fsm.state "IDLE" output  {
%true = constant true
fsm.output %true : i1
} transitions  {
fsm.transition @BUSY guard  {
fsm.return %arg0 : i1
}
}
...
}


If a state has more than one transition, multiple transitions are prioritized in the order that they appear in the transitions region. Guards must also not contain any operations with side effects, enabling the evaluation of guards to be parallelized. Note that an empty guard region is evaluated as true, which means the corresponding transition is always taken.

### Action region of transitions and internal variables ¶

To avoid state explosion, we introduce fsm.variable operation (similar to the extended state in UML state machine) to represent a variable associated with an FSM instance and can hold a value of any type, which can be updated through fsm.update operations.

fsm.transition has an optional action CFG region representing the actions associated with the current transition. The action region can contain side-effecting operations. fsm.update must be contained by the action region of a transition. The following MLIR code shows a running example:

fsm.machine @foo(%arg0: i1) -> i1 attributes {stateType = i1} {
%cnt = fsm.variable "cnt" {initValue = 0 : i16} : i16
fsm.state "IDLE" output  {
%true = constant true
fsm.output %true : i1
} transitions  {
fsm.transition @BUSY guard  {
fsm.return %arg0 : i1
} action  {
%c256_i16 = constant 256 : i16
fsm.update %cnt, %c256_i16 : i16
}
}
...
}