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circuit.rs
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circuit.rs
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use core::cmp::max;
use core::ops::{Add, Mul};
use ff::Field;
use std::collections::HashMap;
use std::{
convert::TryFrom,
ops::{Neg, Sub},
};
use super::{lookup, permutation, Assigned, Error};
use crate::dev::metadata;
use crate::{
circuit::{Layouter, Region, Value},
poly::Rotation,
};
use sealed::SealedPhase;
mod compress_selectors;
/// A column type
pub trait ColumnType:
'static + Sized + Copy + std::fmt::Debug + PartialEq + Eq + Into<Any>
{
}
/// A column with an index and type
#[derive(Clone, Copy, Debug, Eq, PartialEq, Hash)]
pub struct Column<C: ColumnType> {
index: usize,
column_type: C,
}
impl<C: ColumnType> Column<C> {
#[cfg(test)]
pub(crate) fn new(index: usize, column_type: C) -> Self {
Column { index, column_type }
}
/// Index of this column.
pub fn index(&self) -> usize {
self.index
}
/// Type of this column.
pub fn column_type(&self) -> &C {
&self.column_type
}
}
impl<C: ColumnType> Ord for Column<C> {
fn cmp(&self, other: &Self) -> std::cmp::Ordering {
// This ordering is consensus-critical! The layouters rely on deterministic column
// orderings.
match self.column_type.into().cmp(&other.column_type.into()) {
// Indices are assigned within column types.
std::cmp::Ordering::Equal => self.index.cmp(&other.index),
order => order,
}
}
}
impl<C: ColumnType> PartialOrd for Column<C> {
fn partial_cmp(&self, other: &Self) -> Option<std::cmp::Ordering> {
Some(self.cmp(other))
}
}
pub(crate) mod sealed {
/// Phase of advice column
#[derive(Clone, Copy, Debug, Eq, PartialEq, Ord, PartialOrd, Hash)]
pub struct Phase(pub(super) u8);
impl Phase {
pub fn prev(&self) -> Option<Phase> {
self.0.checked_sub(1).map(Phase)
}
}
impl SealedPhase for Phase {
fn to_sealed(self) -> Phase {
self
}
}
/// Sealed trait to help keep `Phase` private.
pub trait SealedPhase {
fn to_sealed(self) -> Phase;
}
}
/// Phase of advice column
pub trait Phase: SealedPhase {}
impl<P: SealedPhase> Phase for P {}
/// First phase
#[derive(Debug)]
pub struct FirstPhase;
impl SealedPhase for super::FirstPhase {
fn to_sealed(self) -> sealed::Phase {
sealed::Phase(0)
}
}
/// Second phase
#[derive(Debug)]
pub struct SecondPhase;
impl SealedPhase for super::SecondPhase {
fn to_sealed(self) -> sealed::Phase {
sealed::Phase(1)
}
}
/// Third phase
#[derive(Debug)]
pub struct ThirdPhase;
impl SealedPhase for super::ThirdPhase {
fn to_sealed(self) -> sealed::Phase {
sealed::Phase(2)
}
}
/// An advice column
#[derive(Clone, Copy, Eq, PartialEq, Hash)]
pub struct Advice {
pub(crate) phase: sealed::Phase,
}
impl Default for Advice {
fn default() -> Advice {
Advice {
phase: FirstPhase.to_sealed(),
}
}
}
impl Advice {
/// Returns `Advice` in given `Phase`
pub fn new<P: Phase>(phase: P) -> Advice {
Advice {
phase: phase.to_sealed(),
}
}
/// Phase of this column
pub fn phase(&self) -> u8 {
self.phase.0
}
}
impl std::fmt::Debug for Advice {
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
let mut debug_struct = f.debug_struct("Advice");
// Only show advice's phase if it's not in first phase.
if self.phase != FirstPhase.to_sealed() {
debug_struct.field("phase", &self.phase);
}
debug_struct.finish()
}
}
/// A fixed column
#[derive(Clone, Copy, Debug, Eq, PartialEq, Hash)]
pub struct Fixed;
/// An instance column
#[derive(Clone, Copy, Debug, Eq, PartialEq, Hash)]
pub struct Instance;
/// An enum over the Advice, Fixed, Instance structs
#[derive(Clone, Copy, Eq, PartialEq, Hash)]
pub enum Any {
/// An Advice variant
Advice(Advice),
/// A Fixed variant
Fixed,
/// An Instance variant
Instance,
}
impl Any {
/// Returns Advice variant in `FirstPhase`
pub fn advice() -> Any {
Any::Advice(Advice::default())
}
/// Returns Advice variant in given `Phase`
pub fn advice_in<P: Phase>(phase: P) -> Any {
Any::Advice(Advice::new(phase))
}
}
impl std::fmt::Debug for Any {
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
match self {
Any::Advice(advice) => {
let mut debug_struct = f.debug_struct("Advice");
// Only show advice's phase if it's not in first phase.
if advice.phase != FirstPhase.to_sealed() {
debug_struct.field("phase", &advice.phase);
}
debug_struct.finish()
}
Any::Fixed => f.debug_struct("Fixed").finish(),
Any::Instance => f.debug_struct("Instance").finish(),
}
}
}
impl Ord for Any {
fn cmp(&self, other: &Self) -> std::cmp::Ordering {
// This ordering is consensus-critical! The layouters rely on deterministic column
// orderings.
match (self, other) {
(Any::Instance, Any::Instance) | (Any::Fixed, Any::Fixed) => std::cmp::Ordering::Equal,
(Any::Advice(lhs), Any::Advice(rhs)) => lhs.phase.cmp(&rhs.phase),
// Across column types, sort Instance < Advice < Fixed.
(Any::Instance, Any::Advice(_))
| (Any::Advice(_), Any::Fixed)
| (Any::Instance, Any::Fixed) => std::cmp::Ordering::Less,
(Any::Fixed, Any::Instance)
| (Any::Fixed, Any::Advice(_))
| (Any::Advice(_), Any::Instance) => std::cmp::Ordering::Greater,
}
}
}
impl PartialOrd for Any {
fn partial_cmp(&self, other: &Self) -> Option<std::cmp::Ordering> {
Some(self.cmp(other))
}
}
impl ColumnType for Advice {}
impl ColumnType for Fixed {}
impl ColumnType for Instance {}
impl ColumnType for Any {}
impl From<Advice> for Any {
fn from(advice: Advice) -> Any {
Any::Advice(advice)
}
}
impl From<Fixed> for Any {
fn from(_: Fixed) -> Any {
Any::Fixed
}
}
impl From<Instance> for Any {
fn from(_: Instance) -> Any {
Any::Instance
}
}
impl From<Column<Advice>> for Column<Any> {
fn from(advice: Column<Advice>) -> Column<Any> {
Column {
index: advice.index(),
column_type: Any::Advice(advice.column_type),
}
}
}
impl From<Column<Fixed>> for Column<Any> {
fn from(advice: Column<Fixed>) -> Column<Any> {
Column {
index: advice.index(),
column_type: Any::Fixed,
}
}
}
impl From<Column<Instance>> for Column<Any> {
fn from(advice: Column<Instance>) -> Column<Any> {
Column {
index: advice.index(),
column_type: Any::Instance,
}
}
}
impl TryFrom<Column<Any>> for Column<Advice> {
type Error = &'static str;
fn try_from(any: Column<Any>) -> Result<Self, Self::Error> {
match any.column_type() {
Any::Advice(advice) => Ok(Column {
index: any.index(),
column_type: *advice,
}),
_ => Err("Cannot convert into Column<Advice>"),
}
}
}
impl TryFrom<Column<Any>> for Column<Fixed> {
type Error = &'static str;
fn try_from(any: Column<Any>) -> Result<Self, Self::Error> {
match any.column_type() {
Any::Fixed => Ok(Column {
index: any.index(),
column_type: Fixed,
}),
_ => Err("Cannot convert into Column<Fixed>"),
}
}
}
impl TryFrom<Column<Any>> for Column<Instance> {
type Error = &'static str;
fn try_from(any: Column<Any>) -> Result<Self, Self::Error> {
match any.column_type() {
Any::Instance => Ok(Column {
index: any.index(),
column_type: Instance,
}),
_ => Err("Cannot convert into Column<Instance>"),
}
}
}
/// A selector, representing a fixed boolean value per row of the circuit.
///
/// Selectors can be used to conditionally enable (portions of) gates:
/// ```
/// use halo2_proofs::poly::Rotation;
/// # use halo2curves::pasta::Fp;
/// # use halo2_proofs::plonk::ConstraintSystem;
///
/// # let mut meta = ConstraintSystem::<Fp>::default();
/// let a = meta.advice_column();
/// let b = meta.advice_column();
/// let s = meta.selector();
///
/// meta.create_gate("foo", |meta| {
/// let a = meta.query_advice(a, Rotation::prev());
/// let b = meta.query_advice(b, Rotation::cur());
/// let s = meta.query_selector(s);
///
/// // On rows where the selector is enabled, a is constrained to equal b.
/// // On rows where the selector is disabled, a and b can take any value.
/// vec![s * (a - b)]
/// });
/// ```
///
/// Selectors are disabled on all rows by default, and must be explicitly enabled on each
/// row when required:
/// ```
/// use halo2_proofs::{
/// circuit::{Chip, Layouter, Value},
/// plonk::{Advice, Column, Error, Selector},
/// };
/// use ff::Field;
/// # use halo2_proofs::plonk::Fixed;
///
/// struct Config {
/// a: Column<Advice>,
/// b: Column<Advice>,
/// s: Selector,
/// }
///
/// fn circuit_logic<F: Field, C: Chip<F>>(chip: C, mut layouter: impl Layouter<F>) -> Result<(), Error> {
/// let config = chip.config();
/// # let config: Config = todo!();
/// layouter.assign_region(|| "bar", |mut region| {
/// region.assign_advice(|| "a", config.a, 0, || Value::known(F::ONE))?;
/// region.assign_advice(|| "a", config.b, 1, || Value::known(F::ONE))?;
/// config.s.enable(&mut region, 1)
/// })?;
/// Ok(())
/// }
/// ```
#[derive(Clone, Copy, Debug, PartialEq, Eq, Hash)]
pub struct Selector(pub(crate) usize, bool);
impl Selector {
/// Enable this selector at the given offset within the given region.
pub fn enable<F: Field>(&self, region: &mut Region<F>, offset: usize) -> Result<(), Error> {
region.enable_selector(|| "", self, offset)
}
/// Is this selector "simple"? Simple selectors can only be multiplied
/// by expressions that contain no other simple selectors.
pub fn is_simple(&self) -> bool {
self.1
}
}
/// Query of fixed column at a certain relative location
#[derive(Copy, Clone, Debug)]
pub struct FixedQuery {
/// Query index
pub(crate) index: usize,
/// Column index
pub(crate) column_index: usize,
/// Rotation of this query
pub(crate) rotation: Rotation,
}
impl FixedQuery {
/// Column index
pub fn column_index(&self) -> usize {
self.column_index
}
/// Rotation of this query
pub fn rotation(&self) -> Rotation {
self.rotation
}
}
/// Query of advice column at a certain relative location
#[derive(Copy, Clone, Debug)]
pub struct AdviceQuery {
/// Query index
pub(crate) index: usize,
/// Column index
pub(crate) column_index: usize,
/// Rotation of this query
pub(crate) rotation: Rotation,
/// Phase of this advice column
pub(crate) phase: sealed::Phase,
}
impl AdviceQuery {
/// Column index
pub fn column_index(&self) -> usize {
self.column_index
}
/// Rotation of this query
pub fn rotation(&self) -> Rotation {
self.rotation
}
/// Phase of this advice column
pub fn phase(&self) -> u8 {
self.phase.0
}
}
/// Query of instance column at a certain relative location
#[derive(Copy, Clone, Debug)]
pub struct InstanceQuery {
/// Query index
pub(crate) index: usize,
/// Column index
pub(crate) column_index: usize,
/// Rotation of this query
pub(crate) rotation: Rotation,
}
impl InstanceQuery {
/// Column index
pub fn column_index(&self) -> usize {
self.column_index
}
/// Rotation of this query
pub fn rotation(&self) -> Rotation {
self.rotation
}
}
/// A fixed column of a lookup table.
///
/// A lookup table can be loaded into this column via [`Layouter::assign_table`]. Columns
/// can currently only contain a single table, but they may be used in multiple lookup
/// arguments via [`ConstraintSystem::lookup`].
///
/// Lookup table columns are always "encumbered" by the lookup arguments they are used in;
/// they cannot simultaneously be used as general fixed columns.
///
/// [`Layouter::assign_table`]: crate::circuit::Layouter::assign_table
#[derive(Clone, Copy, Debug, Eq, PartialEq, Hash)]
pub struct TableColumn {
/// The fixed column that this table column is stored in.
///
/// # Security
///
/// This inner column MUST NOT be exposed in the public API, or else chip developers
/// can load lookup tables into their circuits without default-value-filling the
/// columns, which can cause soundness bugs.
inner: Column<Fixed>,
}
impl TableColumn {
pub(crate) fn inner(&self) -> Column<Fixed> {
self.inner
}
}
/// A challenge squeezed from transcript after advice columns at the phase have been committed.
#[derive(Clone, Copy, Debug, Eq, PartialEq, Hash)]
pub struct Challenge {
index: usize,
pub(crate) phase: sealed::Phase,
}
impl Challenge {
/// Index of this challenge.
pub fn index(&self) -> usize {
self.index
}
/// Phase of this challenge.
pub fn phase(&self) -> u8 {
self.phase.0
}
}
/// This trait allows a [`Circuit`] to direct some backend to assign a witness
/// for a constraint system.
pub trait Assignment<F: Field> {
/// Creates a new region and enters into it.
///
/// Panics if we are currently in a region (if `exit_region` was not called).
///
/// Not intended for downstream consumption; use [`Layouter::assign_region`] instead.
///
/// [`Layouter::assign_region`]: crate::circuit::Layouter#method.assign_region
fn enter_region<NR, N>(&mut self, name_fn: N)
where
NR: Into<String>,
N: FnOnce() -> NR;
/// Allows the developer to include an annotation for an specific column within a `Region`.
///
/// This is usually useful for debugging circuit failures.
fn annotate_column<A, AR>(&mut self, annotation: A, column: Column<Any>)
where
A: FnOnce() -> AR,
AR: Into<String>;
/// Exits the current region.
///
/// Panics if we are not currently in a region (if `enter_region` was not called).
///
/// Not intended for downstream consumption; use [`Layouter::assign_region`] instead.
///
/// [`Layouter::assign_region`]: crate::circuit::Layouter#method.assign_region
fn exit_region(&mut self);
/// Enables a selector at the given row.
fn enable_selector<A, AR>(
&mut self,
annotation: A,
selector: &Selector,
row: usize,
) -> Result<(), Error>
where
A: FnOnce() -> AR,
AR: Into<String>;
/// Queries the cell of an instance column at a particular absolute row.
///
/// Returns the cell's value, if known.
fn query_instance(&self, column: Column<Instance>, row: usize) -> Result<Value<F>, Error>;
/// Assign an advice column value (witness)
fn assign_advice<V, VR, A, AR>(
&mut self,
annotation: A,
column: Column<Advice>,
row: usize,
to: V,
) -> Result<(), Error>
where
V: FnOnce() -> Value<VR>,
VR: Into<Assigned<F>>,
A: FnOnce() -> AR,
AR: Into<String>;
/// Assign a fixed value
fn assign_fixed<V, VR, A, AR>(
&mut self,
annotation: A,
column: Column<Fixed>,
row: usize,
to: V,
) -> Result<(), Error>
where
V: FnOnce() -> Value<VR>,
VR: Into<Assigned<F>>,
A: FnOnce() -> AR,
AR: Into<String>;
/// Assign two cells to have the same value
fn copy(
&mut self,
left_column: Column<Any>,
left_row: usize,
right_column: Column<Any>,
right_row: usize,
) -> Result<(), Error>;
/// Fills a fixed `column` starting from the given `row` with value `to`.
fn fill_from_row(
&mut self,
column: Column<Fixed>,
row: usize,
to: Value<Assigned<F>>,
) -> Result<(), Error>;
/// Queries the value of the given challenge.
///
/// Returns `Value::unknown()` if the current synthesis phase is before the challenge can be queried.
fn get_challenge(&self, challenge: Challenge) -> Value<F>;
/// Creates a new (sub)namespace and enters into it.
///
/// Not intended for downstream consumption; use [`Layouter::namespace`] instead.
///
/// [`Layouter::namespace`]: crate::circuit::Layouter#method.namespace
fn push_namespace<NR, N>(&mut self, name_fn: N)
where
NR: Into<String>,
N: FnOnce() -> NR;
/// Exits out of the existing namespace.
///
/// Not intended for downstream consumption; use [`Layouter::namespace`] instead.
///
/// [`Layouter::namespace`]: crate::circuit::Layouter#method.namespace
fn pop_namespace(&mut self, gadget_name: Option<String>);
}
/// A floor planning strategy for a circuit.
///
/// The floor planner is chip-agnostic and applies its strategy to the circuit it is used
/// within.
pub trait FloorPlanner {
/// Given the provided `cs`, synthesize the given circuit.
///
/// `constants` is the list of fixed columns that the layouter may use to assign
/// global constant values. These columns will all have been equality-enabled.
///
/// Internally, a floor planner will perform the following operations:
/// - Instantiate a [`Layouter`] for this floor planner.
/// - Perform any necessary setup or measurement tasks, which may involve one or more
/// calls to `Circuit::default().synthesize(config, &mut layouter)`.
/// - Call `circuit.synthesize(config, &mut layouter)` exactly once.
fn synthesize<F: Field, CS: Assignment<F>, C: Circuit<F>>(
cs: &mut CS,
circuit: &C,
config: C::Config,
constants: Vec<Column<Fixed>>,
) -> Result<(), Error>;
}
/// This is a trait that circuits provide implementations for so that the
/// backend prover can ask the circuit to synthesize using some given
/// [`ConstraintSystem`] implementation.
pub trait Circuit<F: Field> {
/// This is a configuration object that stores things like columns.
type Config: Clone;
/// The floor planner used for this circuit. This is an associated type of the
/// `Circuit` trait because its behaviour is circuit-critical.
type FloorPlanner: FloorPlanner;
/// Optional circuit configuration parameters. Requires the `circuit-params` feature.
#[cfg(feature = "circuit-params")]
type Params: Default;
/// Returns a copy of this circuit with no witness values (i.e. all witnesses set to
/// `None`). For most circuits, this will be equal to `Self::default()`.
fn without_witnesses(&self) -> Self;
/// Returns a reference to the parameters that should be used to configure the circuit.
/// Requires the `circuit-params` feature.
#[cfg(feature = "circuit-params")]
fn params(&self) -> Self::Params {
Self::Params::default()
}
/// The circuit is given an opportunity to describe the exact gate
/// arrangement, column arrangement, etc. Takes a runtime parameter. The default
/// implementation calls `configure` ignoring the `_params` argument in order to easily support
/// circuits that don't use configuration parameters.
#[cfg(feature = "circuit-params")]
fn configure_with_params(
meta: &mut ConstraintSystem<F>,
_params: Self::Params,
) -> Self::Config {
Self::configure(meta)
}
/// The circuit is given an opportunity to describe the exact gate
/// arrangement, column arrangement, etc.
fn configure(meta: &mut ConstraintSystem<F>) -> Self::Config;
/// Given the provided `cs`, synthesize the circuit. The concrete type of
/// the caller will be different depending on the context, and they may or
/// may not expect to have a witness present.
fn synthesize(&self, config: Self::Config, layouter: impl Layouter<F>) -> Result<(), Error>;
}
/// Low-degree expression representing an identity that must hold over the committed columns.
#[derive(Clone)]
pub enum Expression<F> {
/// This is a constant polynomial
Constant(F),
/// This is a virtual selector
Selector(Selector),
/// This is a fixed column queried at a certain relative location
Fixed(FixedQuery),
/// This is an advice (witness) column queried at a certain relative location
Advice(AdviceQuery),
/// This is an instance (external) column queried at a certain relative location
Instance(InstanceQuery),
/// This is a challenge
Challenge(Challenge),
/// This is a negated polynomial
Negated(Box<Expression<F>>),
/// This is the sum of two polynomials
Sum(Box<Expression<F>>, Box<Expression<F>>),
/// This is the product of two polynomials
Product(Box<Expression<F>>, Box<Expression<F>>),
/// This is a scaled polynomial
Scaled(Box<Expression<F>>, F),
}
impl<F: Field> Expression<F> {
/// Evaluate the polynomial using the provided closures to perform the
/// operations.
pub fn evaluate<T>(
&self,
constant: &impl Fn(F) -> T,
selector_column: &impl Fn(Selector) -> T,
fixed_column: &impl Fn(FixedQuery) -> T,
advice_column: &impl Fn(AdviceQuery) -> T,
instance_column: &impl Fn(InstanceQuery) -> T,
challenge: &impl Fn(Challenge) -> T,
negated: &impl Fn(T) -> T,
sum: &impl Fn(T, T) -> T,
product: &impl Fn(T, T) -> T,
scaled: &impl Fn(T, F) -> T,
) -> T {
match self {
Expression::Constant(scalar) => constant(*scalar),
Expression::Selector(selector) => selector_column(*selector),
Expression::Fixed(query) => fixed_column(*query),
Expression::Advice(query) => advice_column(*query),
Expression::Instance(query) => instance_column(*query),
Expression::Challenge(value) => challenge(*value),
Expression::Negated(a) => {
let a = a.evaluate(
constant,
selector_column,
fixed_column,
advice_column,
instance_column,
challenge,
negated,
sum,
product,
scaled,
);
negated(a)
}
Expression::Sum(a, b) => {
let a = a.evaluate(
constant,
selector_column,
fixed_column,
advice_column,
instance_column,
challenge,
negated,
sum,
product,
scaled,
);
let b = b.evaluate(
constant,
selector_column,
fixed_column,
advice_column,
instance_column,
challenge,
negated,
sum,
product,
scaled,
);
sum(a, b)
}
Expression::Product(a, b) => {
let a = a.evaluate(
constant,
selector_column,
fixed_column,
advice_column,
instance_column,
challenge,
negated,
sum,
product,
scaled,
);
let b = b.evaluate(
constant,
selector_column,
fixed_column,
advice_column,
instance_column,
challenge,
negated,
sum,
product,
scaled,
);
product(a, b)
}
Expression::Scaled(a, f) => {
let a = a.evaluate(
constant,
selector_column,
fixed_column,
advice_column,
instance_column,
challenge,
negated,
sum,
product,
scaled,
);
scaled(a, *f)
}
}
}
/// Evaluate the polynomial lazily using the provided closures to perform the
/// operations.
pub fn evaluate_lazy<T: PartialEq>(
&self,
constant: &impl Fn(F) -> T,
selector_column: &impl Fn(Selector) -> T,
fixed_column: &impl Fn(FixedQuery) -> T,
advice_column: &impl Fn(AdviceQuery) -> T,
instance_column: &impl Fn(InstanceQuery) -> T,
challenge: &impl Fn(Challenge) -> T,
negated: &impl Fn(T) -> T,
sum: &impl Fn(T, T) -> T,
product: &impl Fn(T, T) -> T,
scaled: &impl Fn(T, F) -> T,
zero: &T,
) -> T {
match self {
Expression::Constant(scalar) => constant(*scalar),
Expression::Selector(selector) => selector_column(*selector),
Expression::Fixed(query) => fixed_column(*query),
Expression::Advice(query) => advice_column(*query),
Expression::Instance(query) => instance_column(*query),
Expression::Challenge(value) => challenge(*value),
Expression::Negated(a) => {
let a = a.evaluate_lazy(
constant,
selector_column,
fixed_column,
advice_column,
instance_column,
challenge,
negated,
sum,
product,
scaled,
zero,
);
negated(a)
}
Expression::Sum(a, b) => {
let a = a.evaluate_lazy(
constant,
selector_column,
fixed_column,
advice_column,
instance_column,
challenge,
negated,
sum,
product,
scaled,
zero,
);
let b = b.evaluate_lazy(
constant,
selector_column,
fixed_column,
advice_column,
instance_column,
challenge,
negated,
sum,
product,
scaled,
zero,
);
sum(a, b)
}
Expression::Product(a, b) => {
let (a, b) = if a.complexity() <= b.complexity() {
(a, b)
} else {
(b, a)
};
let a = a.evaluate_lazy(
constant,
selector_column,
fixed_column,
advice_column,
instance_column,
challenge,
negated,
sum,
product,
scaled,
zero,
);
if a == *zero {
a
} else {
let b = b.evaluate_lazy(
constant,
selector_column,
fixed_column,
advice_column,
instance_column,
challenge,
negated,
sum,
product,
scaled,
zero,
);
product(a, b)
}
}
Expression::Scaled(a, f) => {
let a = a.evaluate_lazy(
constant,
selector_column,
fixed_column,
advice_column,
instance_column,
challenge,
negated,
sum,
product,
scaled,
zero,
);
scaled(a, *f)
}
}
}
fn write_identifier<W: std::io::Write>(&self, writer: &mut W) -> std::io::Result<()> {
match self {
Expression::Constant(scalar) => write!(writer, "{:?}", scalar),
Expression::Selector(selector) => write!(writer, "selector[{}]", selector.0),
Expression::Fixed(query) => {
write!(
writer,
"fixed[{}][{}]",
query.column_index, query.rotation.0
)
}
Expression::Advice(query) => {
write!(
writer,
"advice[{}][{}]",
query.column_index, query.rotation.0
)
}
Expression::Instance(query) => {
write!(
writer,
"instance[{}][{}]",
query.column_index, query.rotation.0
)
}
Expression::Challenge(challenge) => {
write!(writer, "challenge[{}]", challenge.index())
}
Expression::Negated(a) => {
writer.write_all(b"(-")?;
a.write_identifier(writer)?;
writer.write_all(b")")
}
Expression::Sum(a, b) => {
writer.write_all(b"(")?;
a.write_identifier(writer)?;