halo2/src/poly.rs

//! Contains utilities for performing arithmetic over univariate polynomials in
//! various forms, including computing commitments to them and provably opening
//! the committed polynomials at arbitrary points.

use crate::arithmetic::{parallelize, Field};

use std::fmt::Debug;
use std::marker::PhantomData;
use std::ops::{Add, Deref, DerefMut, Index, IndexMut, Mul, RangeFrom, RangeFull, Sub};

pub mod commitment;
mod domain;
pub mod multiopen;

pub use domain::*;

/// This is an error that could occur during proving or circuit synthesis.
// TODO: these errors need to be cleaned up
#[derive(Debug)]
pub enum Error {
    /// OpeningProof is not well-formed
    OpeningError,
    /// Caller needs to re-sample a point
    SamplingError,
}

/// The basis over which a polynomial is described.
pub trait Basis: Clone + Debug + Send + Sync {}

/// The polynomial is defined as coefficients
#[derive(Clone, Debug)]
pub struct Coeff;
impl Basis for Coeff {}

/// The polynomial is defined as coefficients of Lagrange basis polynomials
#[derive(Clone, Debug)]
pub struct LagrangeCoeff;
impl Basis for LagrangeCoeff {}

/// The polynomial is defined as coefficients of Lagrange basis polynomials in
/// an extended size domain which supports multiplication
#[derive(Clone, Debug)]
pub struct ExtendedLagrangeCoeff;
impl Basis for ExtendedLagrangeCoeff {}

/// Represents a univariate polynomial defined over a field and a particular
/// basis.
#[derive(Clone, Debug)]
pub struct Polynomial<F, B> {
    values: Vec<F>,
    _marker: PhantomData<B>,
}

impl<F, B> Index<usize> for Polynomial<F, B> {
    type Output = F;

    fn index(&self, index: usize) -> &F {
        self.values.index(index)
    }
}

impl<F, B> IndexMut<usize> for Polynomial<F, B> {
    fn index_mut(&mut self, index: usize) -> &mut F {
        self.values.index_mut(index)
    }
}

impl<F, B> Index<RangeFrom<usize>> for Polynomial<F, B> {
    type Output = [F];

    fn index(&self, index: RangeFrom<usize>) -> &[F] {
        self.values.index(index)
    }
}

impl<F, B> IndexMut<RangeFrom<usize>> for Polynomial<F, B> {
    fn index_mut(&mut self, index: RangeFrom<usize>) -> &mut [F] {
        self.values.index_mut(index)
    }
}

impl<F, B> Index<RangeFull> for Polynomial<F, B> {
    type Output = [F];

    fn index(&self, index: RangeFull) -> &[F] {
        self.values.index(index)
    }
}

impl<F, B> IndexMut<RangeFull> for Polynomial<F, B> {
    fn index_mut(&mut self, index: RangeFull) -> &mut [F] {
        self.values.index_mut(index)
    }
}

impl<F, B> Deref for Polynomial<F, B> {
    type Target = [F];

    fn deref(&self) -> &[F] {
        &self.values[..]
    }
}

impl<F, B> DerefMut for Polynomial<F, B> {
    fn deref_mut(&mut self) -> &mut [F] {
        &mut self.values[..]
    }
}

impl<F, B> Polynomial<F, B> {
    /// Iterate over the values, which are either in coefficient or evaluation
    /// form depending on the basis `B`.
    pub fn iter(&self) -> impl Iterator<Item = &F> {
        self.values.iter()
    }

    /// Iterate over the values mutably, which are either in coefficient or
    /// evaluation form depending on the basis `B`.
    pub fn iter_mut(&mut self) -> impl Iterator<Item = &mut F> {
        self.values.iter_mut()
    }

    /// Gets the size of this polynomial in terms of the number of
    /// coefficients used to describe it.
    pub fn num_coeffs(&self) -> usize {
        self.values.len()
    }
}

impl<'a, F: Field, B: Basis> Add<&'a Polynomial<F, B>> for Polynomial<F, B> {
    type Output = Polynomial<F, B>;

    fn add(mut self, rhs: &'a Polynomial<F, B>) -> Polynomial<F, B> {
        parallelize(&mut self.values, |lhs, start| {
            for (lhs, rhs) in lhs.iter_mut().zip(rhs.values[start..].iter()) {
                *lhs += *rhs;
            }
        });

        self
    }
}

impl<'a, F: Field, B: Basis> Sub<&'a Polynomial<F, B>> for Polynomial<F, B> {
    type Output = Polynomial<F, B>;

    fn sub(mut self, rhs: &'a Polynomial<F, B>) -> Polynomial<F, B> {
        parallelize(&mut self.values, |lhs, start| {
            for (lhs, rhs) in lhs.iter_mut().zip(rhs.values[start..].iter()) {
                *lhs -= *rhs;
            }
        });

        self
    }
}

impl<'a, F: Field> Mul<&'a Polynomial<F, ExtendedLagrangeCoeff>>
    for Polynomial<F, ExtendedLagrangeCoeff>
{
    type Output = Polynomial<F, ExtendedLagrangeCoeff>;

    fn mul(
        mut self,
        rhs: &'a Polynomial<F, ExtendedLagrangeCoeff>,
    ) -> Polynomial<F, ExtendedLagrangeCoeff> {
        parallelize(&mut self.values, |lhs, start| {
            for (lhs, rhs) in lhs.iter_mut().zip(rhs.values[start..].iter()) {
                *lhs *= *rhs;
            }
        });

        self
    }
}

impl<'a, F: Field, B: Basis> Mul<F> for Polynomial<F, B> {
    type Output = Polynomial<F, B>;

    fn mul(mut self, rhs: F) -> Polynomial<F, B> {
        parallelize(&mut self.values, |lhs, _| {
            for lhs in lhs.iter_mut() {
                *lhs *= rhs;
            }
        });

        self
    }
}