---
# System prepended metadata

title: Halo2-base

---

# Halo2-base

Halo2-base provides a streamlined frontend for interacting with the Halo2 API. It simplifies circuit programming to declaring constraints over a single advice and selector column and provides built-in circuit configuration and parellel proving and witness generation.

Programmed circuit constraints are stored in `GateThreadBuilder` as `Vec` of `Context`'s. Each `Context` can be interpreted as a "virtual column" which tracks all witness values and constraints but does not assign them as cells within the Halo2 backend. This allows the number of rows and columns in the circuit to be pre-computed from a `Context` eliminating the need to manually assign circuit parameters before circuit creation. 
In addition, this simplifies parallelizing proving in the Halo2 backend since the number of columns needed in the circuit can be calculated ahead of time, and a `Context` can then be divided into multiple columns for parallel computation. 

A user can also parallelize witness generation by specifying a function and a `Vec` of inputs to perform in parallel using `parallelize_in()` which creates a separate `Context` for each input that performs the specified function. These "virtual columns" are then computed in parallel during witness generation and combined back into a single column "virtual column" before cell assignment in the Halo2 backend.

All assigned values in a circuit are assigned in the Halo2 backend by calling `synthesize()` in `GateCircuitBuilder` which in turn invokes `assign_all()` (or `assign_threads_in` for witness generation) in `GateThreadBuilder` to assign the witness values tracked in a `Context` to their respective `Column` in the circuit within the Halo2 backend.

Halo2-base also provides pre-built [Chips](https://zcash.github.io/halo2/concepts/chips.html) for common arithmetic operations in `GateChip` and lookup arguments in `RangeChip`. Our `Chip` implementations differ slightly from the Zcash's `Chip` implementations. In Zcash, the `Chip` struct stores knowledge about the `Config` and custom gates used. In halo2-base a `Chip` stores only functions while the interaction with a circuits `Config` is done in `GateCircuitBuilder`.

The structure of halo2-base is outlined as follows:

- `builder.rs`: Contains `GateThreadBuilder`, `GateCircuitBuilder`, and `RangeCircuitBuilder` which implement the logic to provide different arithmetization configurations with different performance tradeoffs in the Halo2 backend.
- `lib.rs`: Defines the `QuantumCell`, `ContextCell`, `AssignedValue`, and `Context` types which track assigned values within a circuit across multiple columns and provide a streamlined interface to assign witness values directly to the advice column.
- `utils.rs`: Contains `BigPrimeField`, and `ScalerField` traits which represent field elements within Halo2 and provides methods to decompose field elements into `u64` limbs and convert between field elements and `Biguint`.
- `flex_gate.rs`: Contains the implementation of `GateChip` and the `GateInstructions` trait which provide functions for basic arithmetic operations within Halo2.
- `range.rs:`: Implements `RangeChip` and the `RangeInstructions` trait which provide functions for performing range check and other lookup argument operations.

This readme compliments the in-line documentation of halo2-base providing an overview of `builder.rs` and `lib.rs`.

<br>

## [**Context**](./src/lib.rs)

`Context` holds all information of an execution trace (circuit and its witness values). `Context` represents a "virtual column" that stores unassigned constraint information in the Halo2 backend. Storing the circuit information in a `Context` rather than assigning it directly to the Halo2 backend allows for the pre-computation of circuit parameters and preserves the underlying circuit information allowing for its rearrangement into multiple columns for parallelization in the Halo2 backend.

For parallel proving, the advice values of all `Context` are concatenated in single "virtual column" that is split into multiple at `breakpoints` each representing a different sub-section of the "virtual column". During circuit synthesis, cell assignments are extracted from the `Context` and assigned to a `Region` of a circuit as actual plonkish arithmetization columns within Halo2's backend.

For parallel witness generation, multiple `Context`'s are created for each parallel operation. After parallel witness generation, these `Context`'s are combined to form a single "virtual column" which is then, as in parallel proving, split into multiple pre-computed columns for proving in the Halo2 backend.

```rust ignore
pub struct Context<F: ScalarField> {

    witness_gen_only: bool,

    pub context_id: usize,

    pub advice: Vec<Assigned<F>>,

    pub cells_to_lookup: Vec<AssignedValue<F>>,

    pub zero_cell: Option<AssignedValue<F>>,

    pub selector: Vec<bool>,

    pub advice_equality_constraints: Vec<(ContextCell, ContextCell)>,
    
    pub constant_equality_constraints: Vec<(F, ContextCell)>,
}
```
`witness_gen_only` is set only during witness generation, otherwise it is set to false. Setting this flag leads enables parallel witness generation by calling `assign_threads_in()` in `GateCircuitBuilder`. 

A `Context` holds all equality and constant constraints as a `Vec` of `ContextCell` tuples representing the positions of the two cells to constrain. `advice`, and`selector` store the respective column values of the `Context`'s which may represent the entire advice and selector column or a sub-section of the advice and selector column during parellel witness generation. `cells_to_lookup` tracks `AssignedValue`'s of cells to be looked up in a global lookup table shared among all `Context`'s'.

[**ContextCell**](./src/lib.rs):
`ContextCell` Is a pointer to a specific cell within a `Context` identified by the Context's `context_id` and the cell's relative `offset` from the first cell of the advice column of the `Context`.

``` rust ignore
#[derive(Clone, Copy, Debug)]
pub struct ContextCell {
    /// Identifier of the [Context] that this cell belongs to.
    pub context_id: usize,
    /// Relative offset of the cell within this [Context] advice column.
    pub offset: usize,
}
```

[**AssignedValue**](./src/lib.rs):
`AssignedValue` represents a specific `Assigned` value assigned to a specific cell within a `Context` of a circuit referenced by a `ContextCell`. 
```rust ignore
pub struct AssignedValue<F: ScalarField> {
    pub value: Assigned<F>,

    pub cell: Option<ContextCell>,
}
```
    
[**Assigned**](https://github.com/zcash/halo2/blob/76b3f892a9d598923bbb5a747701fff44ae4c0ea/halo2_proofs/src/plonk/assigned.rs#L11)
`Assigned` is a wrapper enum for values assigned to a cell within a circuit which stores the value as a fraction and marks it for batched inversion using [Montgomery's trick](https://zcash.github.io/halo2/background/fields.html#montgomerys-trick). Performing batched inversion allows for the computation of the inverse of all marked values with a single inversion operation.
```rust ignore
pub enum Assigned<F> {
    /// The field element zero.
    Zero,
    /// A value that does not require inversion to evaluate.
    Trivial(F),
    /// A value stored as a fraction to enable batch inversion.
    Rational(F, F),
}
```
    
<br>

## [QuantumCell](./src/lib.rs)

`QuantumCell` is a helper enum that abstracts the scenarios in which a value is assigned to the advice column in Halo2-base. Without `QuantumCell` assigning existing or constant values to the advice column requires manually specifying the enforced constraints on top of assigning the value leading to bloated code. `QuantumCell` handles these technical operations, all a developer needs to do is specify which enum option in `QuantumCell` the value they are adding corresponds to.

```rust ignore
pub enum QuantumCell<F: ScalarField> {

    Existing(AssignedValue<F>),

    Witness(F),

    WitnessFraction(Assigned<F>),

    Constant(F),
}
```
QuantumCell contains the following enum variants.

- **Existing**:
    Assigns a value to the advice column that exists within the advice column. The value is an existing value from some previous part of your computation already in the advice column in the form of an `AssignedValue`. When you add an existing cell into the table a new cell will be assigned into the advice column with value equal to the existing value. An equality constraint will then be added between the new cell and the cell of a so the Verifier has a guarantee that these two cells are always equal.
    ```rust ignore
    QuantumCell::Existing(acell) => {
        self.advice.push(acell.value);

        if !self.witness_gen_only {
            let new_cell =
                ContextCell { context_id: self.context_id, offset: self.advice.len() - 1 };
                self.advice_equality_constraints.push((new_cell, acell.cell.unwrap()));
            }
    }
    ```
- **Witness**:
    Assigns an entirely new witness value into the advice column, such as a private input. When `assign_cell()` is called the value is wrapped in as an `Assigned::Trivial()` which marks it for exclusion from batch inversion.
    ``` rust ignore
    QuantumCell::Witness(val) => {
        self.advice.push(Assigned::Trivial(val));
    }
    ```
- **WitnessFraction**:
    Assigns an entirely new witness value to the advice column. `WitnessFraction` exists for optimization purposes and accepts Assigned values wrapped in `Assigned::Rational()` marked for batch inverion.
    ``` rust ignore
    QuantumCell::WitnessFraction(val) => {
        self.advice.push(val);
    }
    ```
- **Constant**:
    A value that is a "known" constant. A "known" refers to known at circuit creation time to both the Prover and Verifier. When you assign a constant value there is exists another secret "Fixed" column in the circuit constraint table whose values are fixed at circuit creation time. When you assign a Constant value, you are adding this value to the Fixed column, adding the value as a witness to the Advice column, and then imposing an equality constraint between the two corresponding cells in the Fixed and Advice columns.
``` rust ignore
QuantumCell::Constant(c) => {
    self.advice.push(Assigned::Trivial(c));
        // If witness generation is not performed, enforce equality constraints between the existing cell and the new cell
    if !self.witness_gen_only {
    let new_cell =
        ContextCell { context_id: self.context_id, offset: self.advice.len() - 1 };
        self.constant_equality_constraints.push((c, new_cell));
        }
}
```

<br>

## [GateThreadBuilder](./src/gates/builder.rs) & [GateCircuitBuilder](./src/gates/builder.rs)

GateThreadBuilder tracks the cell assignments of a circuit as an array of `Vec` of `Context`' where `threads[i]` contains all `Context`'s for that phase. Each array element corresponds to a distinct challenge phase of Halo2's proving system, each of which has its own unique set of rows and columns.

```rust ignore
#[derive(Clone, Debug, Default)]
pub struct GateThreadBuilder<F: ScalarField> {
    /// Threads for each challenge phase
    pub threads: [Vec<Context<F>>; MAX_PHASE],
    /// Max number of threads
    thread_count: usize,
    /// Flag for witness generation. If true, the gate thread builder is used for witness generation only.
    witness_gen_only: bool,
    /// The `unknown` flag is used during key generation. If true, during key generation witness [Value]s are replaced with Value::unknown() for safety.
    use_unknown: bool,
}
```

Once a `GateThreadBuilder` is created, gates may be assigned to a `Context` (or in the case of parallel witness generation multiple `Context`'s) within `threads`. Once the circuit is written `config()` is called to pre-compute the circuits size and set the circuits environment variables.

[**config()**](./src/gates/builder.rs)
```rust ignore
pub fn config(&self, k: usize, minimum_rows: Option<usize>) -> FlexGateConfigParams {
        let max_rows = (1 << k) - minimum_rows.unwrap_or(0);
        let total_advice_per_phase = self
            .threads
            .iter()
            .map(|threads| threads.iter().map(|ctx| ctx.advice.len()).sum::<usize>())
            .collect::<Vec<_>>();
        // we do a rough estimate by taking ceil(advice_cells_per_phase / 2^k )
        // if this is too small, manual configuration will be needed
        let num_advice_per_phase = total_advice_per_phase
            .iter()
            .map(|count| (count + max_rows - 1) / max_rows)
            .collect::<Vec<_>>();

        let total_lookup_advice_per_phase = self
            .threads
            .iter()
            .map(|threads| threads.iter().map(|ctx| ctx.cells_to_lookup.len()).sum::<usize>())
            .collect::<Vec<_>>();
        let num_lookup_advice_per_phase = total_lookup_advice_per_phase
            .iter()
            .map(|count| (count + max_rows - 1) / max_rows)
            .collect::<Vec<_>>();

        let total_fixed: usize = HashSet::<F>::from_iter(self.threads.iter().flat_map(|threads| {
            threads.iter().flat_map(|ctx| ctx.constant_equality_constraints.iter().map(|(c, _)| *c))
        }))
        .len();
        let num_fixed = (total_fixed + (1 << k) - 1) >> k;

        let params = FlexGateConfigParams {
            strategy: GateStrategy::Vertical,
            num_advice_per_phase,
            num_lookup_advice_per_phase,
            num_fixed,
            k,
        };
        #[cfg(feature = "display")]
        {
            for phase in 0..MAX_PHASE {
                if total_advice_per_phase[phase] != 0 || total_lookup_advice_per_phase[phase] != 0 {
                    println!(
                        "Gate Chip | Phase {}: {} advice cells , {} lookup advice cells",
                        phase, total_advice_per_phase[phase], total_lookup_advice_per_phase[phase],
                    );
                }
            }
            println!("Total {total_fixed} fixed cells");
            println!("Auto-calculated config params:\n {params:#?}");
        }
        std::env::set_var("FLEX_GATE_CONFIG_PARAMS", serde_json::to_string(&params).unwrap());
        params
    }
```

For circuit creation a `GateCircuitBuilder` is created by passing the `GateThreadBuilder` as an argument to `GateCircuitBuilder`'s `keygen`,`mock`, or `prover` functions. `GateCircuitBuilder` acts as a middleman between `GateThreadBuilder` and the Halo2 backend by implementing Halo2's`Circuit` Trait and calling into `GateThreadBuilder` `assign_all()` and `assign_threads_in()` functions to perform circuit assignment.

```rust ignore
/// Vector of vectors tracking the thread break points across different halo2 phases
pub type MultiPhaseThreadBreakPoints = Vec<ThreadBreakPoints>;

#[derive(Clone, Debug)]
pub struct GateCircuitBuilder<F: ScalarField> {
    /// The Thread Builder for the circuit
    pub builder: RefCell<GateThreadBuilder<F>>,
    /// Break points for threads within the circuit
    pub break_points: RefCell<MultiPhaseThreadBreakPoints>,
}

impl<F: ScalarField> Circuit<F> for GateCircuitBuilder<F> {
    type Config = FlexGateConfig<F>;
    type FloorPlanner = SimpleFloorPlanner;
    
    /// Creates a new instance of the circuit without withnesses filled in.
    fn without_witnesses(&self) -> Self {
        unimplemented!()
    }

    /// Configures a new circuit using the the parameters specified [Config].
    fn configure(meta: &mut ConstraintSystem<F>) -> FlexGateConfig<F> {
        let FlexGateConfigParams {
            strategy,
            num_advice_per_phase,
            num_lookup_advice_per_phase: _,
            num_fixed,
            k,
        } = serde_json::from_str(&std::env::var("FLEX_GATE_CONFIG_PARAMS").unwrap()).unwrap();
        FlexGateConfig::configure(meta, strategy, &num_advice_per_phase, num_fixed, k)
    }

    /// Performs the actual computation on the circuit (e.g., witness generation), filling in all the advice values for a particular proof.
    fn synthesize(
        &self,
        config: Self::Config,
        mut layouter: impl Layouter<F>,
    ) -> Result<(), Error> {
        self.sub_synthesize(&config, &[], &[], &mut layouter);
        Ok(())
    }
}
```
During circuit creation `synthesize()` is invoked which passes into `sub_synthesize()` a `FlexGateConfig` containing the actual circuits columns and a mutable reference to a `Layouter` from the Halo2 API which facilitates the final assignment of cells within a `Region` of a circuit in Halo2's backend.

`GateCircuitBuilder` contains a list of breakpoints for each thread across all phases in and `GateThreadBuilder` itself. Both are wrapped in a `RefCell` allowing them to be borrowed mutably so the function performing circuit creation can take ownership of the `builder` and `break_points` can be recorded during circuit creation for later use.

[**sub_synthesize()**](./src/gates/builder.rs)
```rust ignore
pub fn sub_synthesize(
    &self,
    gate: &FlexGateConfig<F>,
    lookup_advice: &[Vec<Column<Advice>>],
    q_lookup: &[Option<Selector>],
    layouter: &mut impl Layouter<F>,
) -> HashMap<(usize, usize), (circuit::Cell, usize)> {
    let mut first_pass = SKIP_FIRST_PASS;
    let mut assigned_advices = HashMap::new();
    layouter
        .assign_region(
            || "GateCircuitBuilder generated circuit",
            |mut region| {
                if first_pass {
                    first_pass = false;
                    return Ok(());
                }
                    
                if !self.builder.borrow().witness_gen_only {
                // clone the builder so we can re-use the circuit for both vk and pk gen
                    let builder = self.builder.borrow().clone();
                    for threads in builder.threads.iter().skip(1) {
                        assert!(
                            threads.is_empty(),
                            "GateCircuitBuilder only supports FirstPhase for now"
                        );
                    }
                    let assignments = builder.assign_all(
                            gate,
                            lookup_advice,
                            q_lookup,
                            &mut region,
                            Default::default(),
                    );
                    *self.break_points.borrow_mut() = assignments.break_points;
                    assigned_advices = assignments.assigned_advices;
                } else {
                    // If we are only generating witness, we can skip the first pass and assign threads directly
                    let builder = self.builder.take();
                    let break_points = self.break_points.take();
                    for (phase, (threads, break_points)) in builder
                        .threads
                        .into_iter()
                        .zip(break_points.into_iter())
                        .enumerate()
                        .take(1)
                    {
                        assign_threads_in(
                            phase,
                            threads,
                            gate,
                            lookup_advice.get(phase).unwrap_or(&vec![]),
                            &mut region,
                            break_points,
                        );
                    }
                }
                Ok(())
            },
        )
        .unwrap();
    assigned_advices
    }
}

```

Within `sub_synthesize()` `layouter`'s `assign_region()` function is invoked which yields a mutable reference to `Region`. `region` is used to assign cells within a contiguous region of the circuit represented in Halo2's proving system.

If `witness_gen_only` is not set within the `builder` (for keygen, and mock proving) `sub_synthesize` takes ownership of the `builder`, and calls `assign_all()` to assign all cells within this context to a circuit in Halo2's backend. The resulting column breakpoints are recorded in `GateCircuitBuilder`'s `break_points` field. 

`assign_all()` iterates over each `Context` within a `phase` and assigns the values and constraints of the advice, selector, fixed, and lookup columns to the circuit using `region`.

Breakpoints for the advice column are assigned sequentially. If, the `row_offset` of the cell value being currently assigned exceeds the maximum amount of rows allowed in a column a new column is created.

It should be noted this process is only compatible with the first phase of Halo2's proving system as retrieving witness challenges in later phases requires more specialized witness generation during synthesis. Therefore, `assign_all()` must assert all elements in `threads` are unassigned excluding the first phase.

[**assign_all()**](./src/gates/builder.rs)
```rust ignore
pub fn assign_all(
    &self,
    config: &FlexGateConfig<F>,
    lookup_advice: &[Vec<Column<Advice>>],
    q_lookup: &[Option<Selector>],
    region: &mut Region<F>,
    KeygenAssignments {
        mut assigned_advices,
        mut assigned_constants,
        mut break_points
    }: KeygenAssignments<F>,
    ) -> KeygenAssignments<F> {
        ...
        for (phase, threads) in self.threads.iter().enumerate() {
            let mut break_point = vec![];
            let mut gate_index = 0;
            let mut row_offset = 0;
            for ctx in threads {
                let mut basic_gate = config.basic_gates[phase]
                        .get(gate_index)
                        .unwrap_or_else(|| panic!("NOT ENOUGH ADVICE COLUMNS IN PHASE {phase}. Perhaps blinding factors were not taken into account. The max non-poisoned rows is {max_rows}"));
                assert_eq!(ctx.selector.len(), ctx.advice.len());

                for (i, (advice, &q)) in ctx.advice.iter().zip(ctx.selector.iter()).enumerate() {
                    let column = basic_gate.value;
                    let value = if use_unknown { Value::unknown() } else { Value::known(advice) };
                    #[cfg(feature = "halo2-axiom")]
                    let cell = *region.assign_advice(column, row_offset, value).cell();
                    #[cfg(not(feature = "halo2-axiom"))]
                    let cell = region
                        .assign_advice(|| "", column, row_offset, || value.map(|v| *v))
                        .unwrap()
                        .cell();
                    assigned_advices.insert((ctx.context_id, i), (cell, row_offset));
            ...
                    
```
In the case a breakpoint falls on the overlap between two gates (such as chained addition of two cells) the cells the breakpoint falls on must be copied to the next column and a new equality constraint enforced between the value of the cell in the old column and the copied cell in the new column. This prevents the circuit from being undersconstratined and preserves the equality constraint from the overlapping gates.
```rust ignore
if (q && row_offset + 4 > max_rows) || row_offset >= max_rows - 1 {
    break_point.push(row_offset);
    row_offset = 0;
    gate_index += 1;

// when there is a break point, because we may have two gates that overlap at the current cell, we must copy the current cell to the next column for safety
    basic_gate = config.basic_gates[phase]
                .get(gate_index)
                .unwrap_or_else(|| panic!("NOT ENOUGH ADVICE COLUMNS IN PHASE {phase}. Perhaps blinding factors were not taken into account. The max non-poisoned rows is {max_rows}"));
    let column = basic_gate.value;

    #[cfg(feature = "halo2-axiom")]
    {
        let ncell = region.assign_advice(column, row_offset, value);
        region.constrain_equal(ncell.cell(), &cell);
    }
    #[cfg(not(feature = "halo2-axiom"))]
    {
        let ncell = region
                    .assign_advice(|| "", column, row_offset, || value.map(|v| *v))
                    .unwrap()
                    .cell();
        region.constrain_equal(ncell, cell).unwrap();
    }
}

```

If `witness_gen_only` is set, only witness generation is performed, and no copy constraints or selector values are considered. 

Witness generation can be parallelized by a user by calling `parallelize_in()` and specifying a function and a `Vec` of inputs to perform in parallel. `parallelize_in()` which creates a separate `Context` for each input that performs the specified function and appends them to the `Vec` of `Context`'s of a particular phase. 

[**assign_threads_in()**](./src/gates/builder.rs)
```rust ignore
pub fn assign_threads_in<F: ScalarField>(
    phase: usize,
    threads: Vec<Context<F>>,
    config: &FlexGateConfig<F>,
    lookup_advice: &[Column<Advice>],
    region: &mut Region<F>,
    break_points: ThreadBreakPoints,
) {
    if config.basic_gates[phase].is_empty() {
        assert!(threads.is_empty(), "Trying to assign threads in a phase with no columns");
        return;
    }

    let mut break_points = break_points.into_iter();
    let mut break_point = break_points.next();

    let mut gate_index = 0;
    let mut column = config.basic_gates[phase][gate_index].value;
    let mut row_offset = 0;

    let mut lookup_offset = 0;
    let mut lookup_advice = lookup_advice.iter();
    let mut lookup_column = lookup_advice.next();
    for ctx in threads {
        // if lookup_column is [None], that means there should be a single advice column and it has lookup enabled, so we don't need to copy to special lookup advice columns
        if lookup_column.is_some() {
            for advice in ctx.cells_to_lookup {
                if lookup_offset >= config.max_rows {
                    lookup_offset = 0;
                    lookup_column = lookup_advice.next();
                }
                // Assign the lookup advice values to the lookup_column
                let value = advice.value;
                let lookup_column = *lookup_column.unwrap();
                #[cfg(feature = "halo2-axiom")]
                region.assign_advice(lookup_column, lookup_offset, Value::known(value));
                #[cfg(not(feature = "halo2-axiom"))]
                region
                    .assign_advice(|| "", lookup_column, lookup_offset, || Value::known(value))
                    .unwrap();

                lookup_offset += 1;
            }
        }
        // Assign advice values to the advice columns in each [Context]
        for advice in ctx.advice {
            #[cfg(feature = "halo2-axiom")]
            region.assign_advice(column, row_offset, Value::known(advice));
            #[cfg(not(feature = "halo2-axiom"))]
            region.assign_advice(|| "", column, row_offset, || Value::known(advice)).unwrap();

            if break_point == Some(row_offset) {
                break_point = break_points.next();
                row_offset = 0;
                gate_index += 1;
                column = config.basic_gates[phase][gate_index].value;

                #[cfg(feature = "halo2-axiom")]
                region.assign_advice(column, row_offset, Value::known(advice));
                #[cfg(not(feature = "halo2-axiom"))]
                region.assign_advice(|| "", column, row_offset, || Value::known(advice)).unwrap();
            }

            row_offset += 1;
        }
    }

```
`sub_synthesize` iterates over all phases and calls `assign_threads_in()` for that phase. `assign_threads_in()` terates over all`Context`'s within that phase and assigns all lookup and advice values in the `Context` creating a new advice column at every pre-computed "breakpoint" by incrementing `gate_index` and assigning `column` to a new advice column found at `config.basic_gates[phase][gate_index].value`. Since, break points are assigned at the end of a `Context` within `assign_all()` (`row_offset >= max_rows - 1`) a new column is created for each `Context` within that phase enabling parallel witness generation.

## [RangeCircuitBuilder](./src/gates/builder.rs)

`RangeCircuitBuilder` is a wrapper struct around `GateCircuitBuilder`. Like `GateCircuitBuilder` it acts as a middleman between `GateThreadBuilder` and the Halo2 backend by implementing Halo2's`Circuit` Trait. 
```rust ignore
#[derive(Clone, Debug)]
pub struct RangeCircuitBuilder<F: ScalarField>(pub GateCircuitBuilder<F>);

impl<F: ScalarField> Circuit<F> for RangeCircuitBuilder<F> {
    type Config = RangeConfig<F>;
    type FloorPlanner = SimpleFloorPlanner;

    /// Creates a new instance of the [RangeCircuitBuilder] without witnesses by setting the witness_gen_only flag to false
    fn without_witnesses(&self) -> Self {
        unimplemented!()
    }

    /// Configures a new circuit using the the parameters specified [Config] and environment variable `LOOKUP_BITS`.
    fn configure(meta: &mut ConstraintSystem<F>) -> Self::Config {
        let FlexGateConfigParams {
            strategy,
            num_advice_per_phase,
            num_lookup_advice_per_phase,
            num_fixed,
            k,
        } = serde_json::from_str(&var("FLEX_GATE_CONFIG_PARAMS").unwrap()).unwrap();
        let strategy = match strategy {
            GateStrategy::Vertical => RangeStrategy::Vertical,
        };
        let lookup_bits = var("LOOKUP_BITS").unwrap_or_else(|_| "0".to_string()).parse().unwrap();
        RangeConfig::configure(
            meta,
            strategy,
            &num_advice_per_phase,
            &num_lookup_advice_per_phase,
            num_fixed,
            lookup_bits,
            k,
        )
    }

    /// Performs the actual computation on the circuit (e.g., witness generation), populating the lookup table and filling in all the advice values for a particular proof.
    fn synthesize(
        &self,
        config: Self::Config,
        mut layouter: impl Layouter<F>,
    ) -> Result<(), Error> {
        // only load lookup table if we are actually doing lookups
        if config.lookup_advice.iter().map(|a| a.len()).sum::<usize>() != 0
            || !config.q_lookup.iter().all(|q| q.is_none())
        {
            config.load_lookup_table(&mut layouter).expect("load lookup table should not fail");
        }
        self.0.sub_synthesize(&config.gate, &config.lookup_advice, &config.q_lookup, &mut layouter);
        Ok(())
    }
}
```
`RangeCircuitBuilder` differs from `GateCircuitBuilder` in that it contains a `RangeConfig` instead of a `FlexGateConfig` as its `Config`. `RangeConfig` contains a `lookup` table needed to declare lookup arguments within Halo2's backend. When creating a circuit that uses lookup tables `GateThreadBuilder` must be wrapped with `RangeCircuitBuilder` instead of `GateCircuitBuilder` otherwise circuit synthesis will fail as a lookup table is not present within the Halo2 backend.
