poly_commitment/

commitment.rs

//! This module implements Dlog-based polynomial commitment schema.
//! The following functionality is implemented
//!
//! 1. Commit to polynomial with its max degree
//! 2. Open polynomial commitment batch at the given evaluation point and
//!    scaling factor scalar producing the batched opening proof
//! 3. Verify batch of batched opening proofs

use ark_ec::{
    models::short_weierstrass::Affine as SWJAffine, short_weierstrass::SWCurveConfig, AffineRepr,
    CurveGroup, VariableBaseMSM,
};
use ark_ff::{BigInteger, Field, One, PrimeField, Zero};
use ark_poly::univariate::DensePolynomial;
use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
use groupmap::{BWParameters, GroupMap};
use mina_poseidon::{sponge::ScalarChallenge, FqSponge};
use o1_utils::{field_helpers::product, ExtendedDensePolynomial as _};
use rayon::prelude::*;
use serde::{de::Visitor, Deserialize, Serialize};
use serde_with::{
    de::DeserializeAsWrap, ser::SerializeAsWrap, serde_as, DeserializeAs, SerializeAs,
};
use std::{
    iter::Iterator,
    marker::PhantomData,
    ops::{Add, AddAssign, Sub},
};

/// Represent a polynomial commitment when the type is instantiated with a
/// curve.
///
/// The structure also handles chunking, i.e. when we aim to handle polynomials
/// whose degree is higher than the SRS size. For this reason, we do use a
/// vector for the field `chunks`.
///
/// Note that the parameter `C` is not constrained to be a curve, therefore in
/// some places in the code, `C` can refer to a scalar field element. For
/// instance, `PolyComm<G::ScalarField>` is used to represent the evaluation of
/// the polynomial bound by a specific commitment, at a particular evaluation
/// point.
#[serde_as]
#[derive(Clone, Debug, Serialize, Deserialize, PartialEq, Eq)]
#[serde(bound = "C: CanonicalDeserialize + CanonicalSerialize")]
pub struct PolyComm<C> {
    #[serde_as(as = "Vec<o1_utils::serialization::SerdeAs>")]
    pub chunks: Vec<C>,
}

impl<C> PolyComm<C>
where
    C: CommitmentCurve,
{
    /// Multiplies each commitment chunk of f with powers of zeta^n
    #[must_use]
    pub fn chunk_commitment(&self, zeta_n: C::ScalarField) -> Self {
        let mut res = C::Group::zero();
        // use Horner's to compute chunk[0] + z^n chunk[1] + z^2n chunk[2] + ...
        // as ( chunk[-1] * z^n + chunk[-2] ) * z^n + chunk[-3]
        // (https://en.wikipedia.org/wiki/Horner%27s_method)
        for chunk in self.chunks.iter().rev() {
            res *= zeta_n;
            res.add_assign(chunk);
        }

        Self {
            chunks: vec![res.into_affine()],
        }
    }
}

impl<F> PolyComm<F>
where
    F: Field,
{
    /// Multiplies each blinding chunk of f with powers of zeta^n
    pub fn chunk_blinding(&self, zeta_n: F) -> F {
        let mut res = F::zero();
        // use Horner's to compute chunk[0] + z^n chunk[1] + z^2n chunk[2] + ...
        // as ( chunk[-1] * z^n + chunk[-2] ) * z^n + chunk[-3]
        // (https://en.wikipedia.org/wiki/Horner%27s_method)
        for chunk in self.chunks.iter().rev() {
            res *= zeta_n;
            res += chunk;
        }
        res
    }
}

impl<G> PolyComm<G> {
    /// Returns an iterator over the chunks.
    pub fn iter(&self) -> std::slice::Iter<'_, G> {
        self.chunks.iter()
    }
}

impl<'a, G> IntoIterator for &'a PolyComm<G> {
    type Item = &'a G;
    type IntoIter = std::slice::Iter<'a, G>;

    fn into_iter(self) -> Self::IntoIter {
        self.chunks.iter()
    }
}

/// A commitment to a polynomial with some blinding factors.
#[derive(Clone, Debug, Serialize, Deserialize)]
pub struct BlindedCommitment<G>
where
    G: CommitmentCurve,
{
    pub commitment: PolyComm<G>,
    pub blinders: PolyComm<G::ScalarField>,
}

impl<T> PolyComm<T> {
    #[must_use]
    pub const fn new(chunks: Vec<T>) -> Self {
        Self { chunks }
    }
}

impl<T, U> SerializeAs<PolyComm<T>> for PolyComm<U>
where
    U: SerializeAs<T>,
{
    fn serialize_as<S>(source: &PolyComm<T>, serializer: S) -> Result<S::Ok, S::Error>
    where
        S: serde::Serializer,
    {
        serializer.collect_seq(
            source
                .chunks
                .iter()
                .map(|e| SerializeAsWrap::<T, U>::new(e)),
        )
    }
}

impl<'de, T, U> DeserializeAs<'de, PolyComm<T>> for PolyComm<U>
where
    U: DeserializeAs<'de, T>,
{
    fn deserialize_as<D>(deserializer: D) -> Result<PolyComm<T>, D::Error>
    where
        D: serde::Deserializer<'de>,
    {
        struct SeqVisitor<T, U> {
            marker: PhantomData<(T, U)>,
        }

        impl<'de, T, U> Visitor<'de> for SeqVisitor<T, U>
        where
            U: DeserializeAs<'de, T>,
        {
            type Value = PolyComm<T>;

            fn expecting(&self, formatter: &mut core::fmt::Formatter<'_>) -> core::fmt::Result {
                formatter.write_str("a sequence")
            }

            fn visit_seq<A>(self, mut seq: A) -> Result<Self::Value, A::Error>
            where
                A: serde::de::SeqAccess<'de>,
            {
                #[allow(clippy::redundant_closure_call)]
                let mut chunks = vec![];

                while let Some(value) = seq
                    .next_element()?
                    .map(|v: DeserializeAsWrap<T, U>| v.into_inner())
                {
                    chunks.push(value);
                }

                Ok(PolyComm::new(chunks))
            }
        }

        let visitor = SeqVisitor::<T, U> {
            marker: PhantomData,
        };
        deserializer.deserialize_seq(visitor)
    }
}

impl<A: Copy + Clone + CanonicalDeserialize + CanonicalSerialize> PolyComm<A> {
    pub fn map<B, F>(&self, mut f: F) -> PolyComm<B>
    where
        F: FnMut(A) -> B,
        B: CanonicalDeserialize + CanonicalSerialize,
    {
        let chunks = self.chunks.iter().map(|x| f(*x)).collect();
        PolyComm::new(chunks)
    }

    /// Returns the number of chunks.
    #[must_use]
    pub const fn len(&self) -> usize {
        self.chunks.len()
    }

    /// Returns `true` if the commitment is empty.
    #[must_use]
    pub const fn is_empty(&self) -> bool {
        self.chunks.is_empty()
    }

    // TODO: if all callers end up calling unwrap, just call this zip_eq and
    // panic here (and document the panic)
    #[must_use]
    pub fn zip<B: Copy + CanonicalDeserialize + CanonicalSerialize>(
        &self,
        other: &PolyComm<B>,
    ) -> Option<PolyComm<(A, B)>> {
        if self.chunks.len() != other.chunks.len() {
            return None;
        }
        let chunks = self
            .chunks
            .iter()
            .zip(other.chunks.iter())
            .map(|(x, y)| (*x, *y))
            .collect();
        Some(PolyComm::new(chunks))
    }

    /// Return only the first chunk.
    ///
    /// Getting this single value is relatively common in the codebase, even
    /// though we should not do this, and abstract the chunks in the structure.
    #[must_use]
    pub fn get_first_chunk(&self) -> A {
        self.chunks[0]
    }
}

/// Inside the circuit, we have a specialized scalar multiplication which
/// computes either
///
/// ```ignore
/// |g: G, x: G::ScalarField| g.scale(x + 2^n)
/// ```
///
/// if the scalar field of G is greater than the size of the base field
/// and
///
/// ```ignore
/// |g: G, x: G::ScalarField| g.scale(2*x + 2^n)
/// ```
///
/// otherwise. So, if we want to actually scale by `x`, we need to apply the
/// inverse function of `|x| x + 2^n` (or of `|x| 2*x + 2^n` in the other case),
/// before supplying the scalar to our in-circuit scalar-multiplication
/// function. This computes that inverse function.
/// Namely,
///
/// ```ignore
/// |x: G::ScalarField| x - 2^n
/// ```
///
/// when the scalar field is larger than the base field and
///
/// ```ignore
/// |x: G::ScalarField| (x - 2^n) / 2
/// ```
///
/// in the other case.
pub fn shift_scalar<G: AffineRepr>(x: G::ScalarField) -> G::ScalarField
where
    G::BaseField: PrimeField,
{
    let n1 = <G::ScalarField as PrimeField>::MODULUS;
    let n2 = <G::ScalarField as PrimeField>::BigInt::from_bits_le(
        &<G::BaseField as PrimeField>::MODULUS.to_bits_le()[..],
    );
    let two: G::ScalarField = (2u64).into();
    let two_pow = two.pow([u64::from(<G::ScalarField as PrimeField>::MODULUS_BIT_SIZE)]);
    if n1 < n2 {
        (x - (two_pow + G::ScalarField::one())) / two
    } else {
        x - two_pow
    }
}

impl<'a, C: AffineRepr> Add<&'a PolyComm<C>> for &PolyComm<C> {
    type Output = PolyComm<C>;

    fn add(self, other: &'a PolyComm<C>) -> PolyComm<C> {
        let mut chunks = vec![];
        let n1 = self.chunks.len();
        let n2 = other.chunks.len();
        for i in 0..std::cmp::max(n1, n2) {
            let pt = if i < n1 && i < n2 {
                (self.chunks[i] + other.chunks[i]).into_affine()
            } else if i < n1 {
                self.chunks[i]
            } else {
                other.chunks[i]
            };
            chunks.push(pt);
        }
        PolyComm::new(chunks)
    }
}

impl<'a, C: AffineRepr + Sub<Output = C::Group>> Sub<&'a PolyComm<C>> for &PolyComm<C> {
    type Output = PolyComm<C>;

    fn sub(self, other: &'a PolyComm<C>) -> PolyComm<C> {
        let mut chunks = vec![];
        let n1 = self.chunks.len();
        let n2 = other.chunks.len();
        for i in 0..std::cmp::max(n1, n2) {
            let pt = if i < n1 && i < n2 {
                (self.chunks[i] - other.chunks[i]).into_affine()
            } else if i < n1 {
                self.chunks[i]
            } else {
                other.chunks[i]
            };
            chunks.push(pt);
        }
        PolyComm::new(chunks)
    }
}

impl<C: AffineRepr> PolyComm<C> {
    #[must_use]
    pub fn scale(&self, c: C::ScalarField) -> Self {
        Self {
            chunks: self.chunks.iter().map(|g| g.mul(c).into_affine()).collect(),
        }
    }

    /// Performs a multi-scalar multiplication between scalars `elm` and
    /// commitments `com`.
    ///
    /// If both are empty, returns a commitment of length 1
    /// containing the point at infinity.
    ///
    /// ## Panics
    ///
    /// Panics if `com` and `elm` are not of the same size.
    #[must_use]
    pub fn multi_scalar_mul(com: &[&Self], elm: &[C::ScalarField]) -> Self {
        assert_eq!(com.len(), elm.len());

        if com.is_empty() || elm.is_empty() {
            return Self::new(vec![C::zero()]);
        }

        let all_scalars: Vec<_> = elm.iter().map(|s| s.into_bigint()).collect();

        let elems_size = Iterator::max(com.iter().map(|c| c.chunks.len())).unwrap();

        let chunks = (0..elems_size)
            .map(|chunk| {
                let (points, scalars): (Vec<_>, Vec<_>) = com
                    .iter()
                    .zip(&all_scalars)
                    // get rid of scalars that don't have an associated chunk
                    .filter_map(|(com, scalar)| com.chunks.get(chunk).map(|c| (c, scalar)))
                    .unzip();

                // Splitting into 2 chunks seems optimal; but in
                // practice elems_size is almost always 1
                //
                // (see the comment to the `benchmark_msm_parallel_vesta` MSM benchmark)
                let subchunk_size = std::cmp::max(points.len() / 2, 1);

                points
                    .into_par_iter()
                    .chunks(subchunk_size)
                    .zip(scalars.into_par_iter().chunks(subchunk_size))
                    .map(|(psc, ssc)| C::Group::msm_bigint(&psc, &ssc).into_affine())
                    .reduce(C::zero, |x, y| (x + y).into())
            })
            .collect();

        Self::new(chunks)
    }
}

/// Evaluates the challenge polynomial `b(X)` at point `x`.
///
/// The challenge polynomial is defined as:
/// ```text
/// b(X) = prod_{i=0}^{k-1} (1 + u_{k-i} * X^{2^i})
/// ```
/// where `chals = [u_1, ..., u_k]` are the IPA challenges.
///
/// This polynomial was introduced in Section 3.2 of the
/// [Halo paper](https://eprint.iacr.org/2019/1021.pdf) as part of the Inner Product
/// Argument. It efficiently encodes the folded evaluation point: after `k` rounds
/// of IPA, the evaluation point vector is reduced to a single value `b(x)`.
///
/// The polynomial has degree `2^k - 1` and can be evaluated in `O(k)` field
/// operations using the product form above. Its coefficients can be computed
/// using [`b_poly_coefficients`].
///
/// # Usage
///
/// - In the verifier (`ipa.rs`), `b_poly` is called to compute evaluations at
///   the challenge points (e.g., `zeta`, `zeta * omega`).
/// - In `RecursionChallenge::evals`, it computes evaluations for the batched
///   polynomial commitment check.
///
/// # References
/// - [Halo paper, Section 3.2](https://eprint.iacr.org/2019/1021.pdf) - original
///   definition of the challenge polynomial
/// - [PCD paper, Appendix A.2, Step 8](https://eprint.iacr.org/2020/499) - use in
///   accumulation context
pub fn b_poly<F: Field>(chals: &[F], x: F) -> F {
    let k = chals.len();

    let mut pow_twos = vec![x];

    for i in 1..k {
        pow_twos.push(pow_twos[i - 1].square());
    }

    product((0..k).map(|i| F::one() + (chals[i] * pow_twos[k - 1 - i])))
}

/// Computes the coefficients of the challenge polynomial `b(X)`.
///
/// Given IPA challenges `chals = [u_1, ..., u_k]`, returns a vector
/// `[s_0, s_1, ..., s_{2^k - 1}]` such that:
/// ```text
/// b(X) = sum_{i=0}^{2^k - 1} s_i * X^i
/// ```
///
/// The coefficients have a closed form: for each index `i` with bit decomposition
/// `i = sum_j b_j * 2^j`, the coefficient is `s_i = prod_{j: b_j = 1} u_{k-j}`.
///
/// # Usage
///
/// This function is used when the full coefficient vector is needed:
/// - In `SRS::verify` (`ipa.rs`): the coefficients are computed and included in
///   the batched MSM to verify the accumulated commitment `<s, G>`.
/// - In `RecursionChallenge::evals`: for chunked polynomial evaluation when the
///   degree exceeds `max_poly_size`.
///
/// # Complexity
///
/// Returns `2^k` coefficients. The MSM `<s, G>` using these coefficients is the
/// expensive operation that gets deferred in recursive proof composition.
///
/// # References
/// - [Halo paper, Section 3.2](https://eprint.iacr.org/2019/1021.pdf)
pub fn b_poly_coefficients<F: Field>(chals: &[F]) -> Vec<F> {
    let rounds = chals.len();
    let s_length = 1 << rounds;
    let mut s = vec![F::one(); s_length];
    let mut k: usize = 0;
    let mut pow: usize = 1;
    for i in 1..s_length {
        k += usize::from(i == pow);
        pow <<= u32::from(i == pow);
        s[i] = s[i - (pow >> 1)] * chals[rounds - 1 - (k - 1)];
    }
    s
}

pub fn squeeze_prechallenge<
    const FULL_ROUNDS: usize,
    Fq: Field,
    G,
    Fr: Field,
    EFqSponge: FqSponge<Fq, G, Fr, FULL_ROUNDS>,
>(
    sponge: &mut EFqSponge,
) -> ScalarChallenge<Fr> {
    ScalarChallenge::new(sponge.challenge())
}

pub fn squeeze_challenge<
    const FULL_ROUNDS: usize,
    Fq: Field,
    G,
    Fr: PrimeField,
    EFqSponge: FqSponge<Fq, G, Fr, FULL_ROUNDS>,
>(
    endo_r: &Fr,
    sponge: &mut EFqSponge,
) -> Fr {
    squeeze_prechallenge(sponge).to_field(endo_r)
}

pub fn absorb_commitment<
    const FULL_ROUNDS: usize,
    Fq: Field,
    G: Clone,
    Fr: PrimeField,
    EFqSponge: FqSponge<Fq, G, Fr, FULL_ROUNDS>,
>(
    sponge: &mut EFqSponge,
    commitment: &PolyComm<G>,
) {
    sponge.absorb_g(&commitment.chunks);
}

/// A useful trait extending [`AffineRepr`] for commitments.
///
/// Unfortunately, we can't specify that `AffineRepr<BaseField : PrimeField>`,
/// so usage of this traits must manually bind `G::BaseField: PrimeField`.
pub trait CommitmentCurve: AffineRepr + Sub<Output = Self::Group> {
    type Params: SWCurveConfig;
    type Map: GroupMap<Self::BaseField>;

    fn to_coordinates(&self) -> Option<(Self::BaseField, Self::BaseField)>;
    fn of_coordinates(x: Self::BaseField, y: Self::BaseField) -> Self;
}

/// A trait extending [`CommitmentCurve`] for endomorphisms.
///
/// Unfortunately, we can't specify that `AffineRepr<BaseField : PrimeField>`,
/// so usage of this traits must manually bind `G::BaseField: PrimeField`.
pub trait EndoCurve: CommitmentCurve {
    /// Combine where x1 = one
    fn combine_one(g1: &[Self], g2: &[Self], x2: Self::ScalarField) -> Vec<Self> {
        crate::combine::window_combine(g1, g2, Self::ScalarField::one(), x2)
    }

    /// Combine where x1 = one
    fn combine_one_endo(
        endo_r: Self::ScalarField,
        _endo_q: Self::BaseField,
        g1: &[Self],
        g2: &[Self],
        x2: &ScalarChallenge<Self::ScalarField>,
    ) -> Vec<Self> {
        crate::combine::window_combine(g1, g2, Self::ScalarField::one(), x2.to_field(&endo_r))
    }

    fn combine(
        g1: &[Self],
        g2: &[Self],
        x1: Self::ScalarField,
        x2: Self::ScalarField,
    ) -> Vec<Self> {
        crate::combine::window_combine(g1, g2, x1, x2)
    }
}

impl<P: SWCurveConfig + Clone> CommitmentCurve for SWJAffine<P> {
    type Params = P;
    type Map = BWParameters<P>;

    fn to_coordinates(&self) -> Option<(Self::BaseField, Self::BaseField)> {
        if self.infinity {
            None
        } else {
            Some((self.x, self.y))
        }
    }

    fn of_coordinates(x: P::BaseField, y: P::BaseField) -> Self {
        Self::new_unchecked(x, y)
    }
}

impl<P: SWCurveConfig + Clone> EndoCurve for SWJAffine<P> {
    fn combine_one(g1: &[Self], g2: &[Self], x2: Self::ScalarField) -> Vec<Self> {
        crate::combine::affine_window_combine_one(g1, g2, x2)
    }

    fn combine_one_endo(
        _endo_r: Self::ScalarField,
        endo_q: Self::BaseField,
        g1: &[Self],
        g2: &[Self],
        x2: &ScalarChallenge<Self::ScalarField>,
    ) -> Vec<Self> {
        crate::combine::affine_window_combine_one_endo(endo_q, g1, g2, x2)
    }

    fn combine(
        g1: &[Self],
        g2: &[Self],
        x1: Self::ScalarField,
        x2: Self::ScalarField,
    ) -> Vec<Self> {
        crate::combine::affine_window_combine(g1, g2, x1, x2)
    }
}

/// Computes the linearization of evaluations.
///
/// Handles a (potentially split) polynomial.
/// Each polynomial in `polys` is represented by a matrix where the
/// rows correspond to evaluated points, and the columns represent
/// potential segments (if a polynomial was split in several parts).
///
/// Elements in `evaluation_points` are several discrete points on which
/// we evaluate polynomials, e.g. `[zeta,zeta*w]`. See `PointEvaluations`.
///
/// Note that if one of the polynomial comes specified with a degree
/// bound, the evaluation for the last segment is potentially shifted
/// to meet the proof.
///
/// Returns
/// ```text
/// |polys| |segments[k]|
///    Σ         Σ         polyscale^{k*n+i} (Σ polys[k][j][i] * evalscale^j)
///  k = 1     i = 1                          j
/// ```
#[allow(clippy::type_complexity)]
pub fn combined_inner_product<F: PrimeField>(
    polyscale: &F,
    evalscale: &F,
    // TODO(mimoo): needs a type that can get you evaluations or segments
    polys: &[Vec<Vec<F>>],
) -> F {
    // final combined evaluation result
    let mut res = F::zero();
    // polyscale^i
    let mut polyscale_i = F::one();

    for evals_tr in polys.iter().filter(|evals_tr| !evals_tr[0].is_empty()) {
        // Transpose the evaluations.
        // evals[i] = {evals_tr[j][i]}_j now corresponds to a column in
        // evals_tr, representing a segment.
        let evals: Vec<_> = (0..evals_tr[0].len())
            .map(|i| evals_tr.iter().map(|v| v[i]).collect::<Vec<_>>())
            .collect();

        // Iterating over the polynomial segments.
        // Each segment gets its own polyscale^i, each segment element j is
        // multiplied by evalscale^j. Given that polyscale_i = polyscale^i0 at
        // this point, after this loop we have:
        //
        //    res += Σ polyscale^{i0+i} ( Σ evals_tr[j][i] * evalscale^j )
        //           i                    j
        //
        for eval in &evals {
            // p_i(evalscale)
            let term = DensePolynomial::<F>::eval_polynomial(eval, *evalscale);
            res += &(polyscale_i * term);
            polyscale_i *= polyscale;
        }
    }
    res
}

/// Contains the evaluation of a polynomial commitment at a set of points.
pub struct Evaluation<G>
where
    G: AffineRepr,
{
    /// The commitment of the polynomial being evaluated.
    ///
    /// Note that [`PolyComm`] contains a vector of commitments, which handles
    /// the case when chunking is used, i.e. when the polynomial degree is
    /// higher than the SRS size.
    pub commitment: PolyComm<G>,

    /// Contains an evaluation table.
    ///
    /// For instance, for vanilla `PlonK`, it would be a vector of (chunked)
    /// evaluations at zeta and zeta*omega. The outer vector would be the
    /// evaluations at the different points (e.g. zeta and zeta*omega for
    /// vanilla `PlonK`) and the inner vector would be the chunks of the
    /// polynomial.
    pub evaluations: Vec<Vec<G::ScalarField>>,
}

/// Contains the batch evaluation
pub struct BatchEvaluationProof<'a, G, EFqSponge, OpeningProof, const FULL_ROUNDS: usize>
where
    G: AffineRepr,
    EFqSponge: FqSponge<G::BaseField, G, G::ScalarField, FULL_ROUNDS>,
{
    /// Sponge used to coin and absorb values and simulate
    /// non-interactivity using the Fiat-Shamir transformation.
    pub sponge: EFqSponge,
    /// A list of evaluations, each supposed to correspond to a different
    /// polynomial.
    pub evaluations: Vec<Evaluation<G>>,
    /// The actual evaluation points. Each field `evaluations` of each structure
    /// of `Evaluation` should have the same (outer) length.
    pub evaluation_points: Vec<G::ScalarField>,
    /// A challenge to combine polynomials. Powers of this point will be used,
    /// hence the name.
    pub polyscale: G::ScalarField,
    /// A challenge to aggregate multiple evaluation points.
    pub evalscale: G::ScalarField,
    /// The opening proof.
    pub opening: &'a OpeningProof,
    pub combined_inner_product: G::ScalarField,
}

/// Populates the parameters `scalars` and `points`.
///
/// It iterates over the evaluations and adds each commitment to the
/// vector `points`.
/// The parameter `scalars` is populated with the values:
/// `rand_base * polyscale^i` for each commitment.
/// For instance, if we have 3 commitments, the `scalars` vector will
/// contain the values
/// ```text
/// [rand_base, rand_base * polyscale, rand_base * polyscale^2]
/// ```
/// and the vector `points` will contain the commitments.
///
/// Note that the function skips the commitments that are empty.
///
/// If more than one commitment is present in a single evaluation (i.e. if
/// `elems` is larger than one), it means that probably chunking was used (i.e.
/// it is a commitment to a polynomial larger than the SRS).
pub fn combine_commitments<G: CommitmentCurve>(
    evaluations: &[Evaluation<G>],
    scalars: &mut Vec<G::ScalarField>,
    points: &mut Vec<G>,
    polyscale: G::ScalarField,
    rand_base: G::ScalarField,
) {
    // will contain the power of polyscale
    let mut polyscale_i = G::ScalarField::one();

    for Evaluation { commitment, .. } in evaluations.iter().filter(|x| !x.commitment.is_empty()) {
        // iterating over the polynomial segments
        for comm_ch in &commitment.chunks {
            scalars.push(rand_base * polyscale_i);
            points.push(*comm_ch);

            // compute next power of polyscale
            polyscale_i *= polyscale;
        }
    }
}

#[cfg(feature = "ocaml_types")]
#[allow(non_local_definitions)]
pub mod caml {
    // polynomial commitment
    use super::PolyComm;
    use ark_ec::AffineRepr;

    #[derive(Clone, Debug, ocaml::IntoValue, ocaml::FromValue, ocaml_gen::Struct)]
    pub struct CamlPolyComm<CamlG> {
        pub unshifted: Vec<CamlG>,
        pub shifted: Option<CamlG>,
    }

    // handy conversions

    impl<G, CamlG> From<PolyComm<G>> for CamlPolyComm<CamlG>
    where
        G: AffineRepr,
        CamlG: From<G>,
    {
        fn from(polycomm: PolyComm<G>) -> Self {
            Self {
                unshifted: polycomm.chunks.into_iter().map(CamlG::from).collect(),
                shifted: None,
            }
        }
    }

    impl<'a, G, CamlG> From<&'a PolyComm<G>> for CamlPolyComm<CamlG>
    where
        G: AffineRepr,
        CamlG: From<G> + From<&'a G>,
    {
        fn from(polycomm: &'a PolyComm<G>) -> Self {
            Self {
                unshifted: polycomm.chunks.iter().map(Into::<CamlG>::into).collect(),
                shifted: None,
            }
        }
    }

    impl<G, CamlG> From<CamlPolyComm<CamlG>> for PolyComm<G>
    where
        G: AffineRepr + From<CamlG>,
    {
        fn from(camlpolycomm: CamlPolyComm<CamlG>) -> Self {
            assert!(
                camlpolycomm.shifted.is_none(),
                "mina#14628: Shifted commitments are deprecated and must not be used"
            );
            Self {
                chunks: camlpolycomm
                    .unshifted
                    .into_iter()
                    .map(Into::<G>::into)
                    .collect(),
            }
        }
    }

    impl<'a, G, CamlG> From<&'a CamlPolyComm<CamlG>> for PolyComm<G>
    where
        G: AffineRepr + From<&'a CamlG> + From<CamlG>,
    {
        fn from(camlpolycomm: &'a CamlPolyComm<CamlG>) -> Self {
            assert!(
                camlpolycomm.shifted.is_none(),
                "mina#14628: Shifted commitments are deprecated and must not be used"
            );
            Self {
                //FIXME something with as_ref()
                chunks: camlpolycomm.unshifted.iter().map(Into::into).collect(),
            }
        }
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use mina_curves::pasta::Fp;
    use std::str::FromStr;

    /// Regression test for `b_poly` evaluation.
    ///
    /// The challenge polynomial b(X) is defined as:
    /// ```text
    /// b(X) = prod_{i=0}^{k-1} (1 + u_{k-i} * X^{2^i})
    /// ```
    /// See Section 3.2 of the [Halo paper](https://eprint.iacr.org/2019/1021.pdf).
    #[test]
    fn test_b_poly_regression() {
        // 15 challenges (typical for domain size 2^15)
        let chals: Vec<Fp> = (2u64..=16).map(Fp::from).collect();

        let zeta = Fp::from(17u64);
        let zeta_omega = Fp::from(19u64);

        let b_at_zeta = b_poly(&chals, zeta);
        let b_at_zeta_omega = b_poly(&chals, zeta_omega);

        // Expected values (computed and verified)
        let expected_at_zeta = Fp::from_str(
            "21115683812642620361045381629886583866877919362491419134086003378733605776328",
        )
        .unwrap();
        let expected_at_zeta_omega = Fp::from_str(
            "2298325069360593860729719174291433577456794311517767070156020442825391962511",
        )
        .unwrap();

        assert_eq!(b_at_zeta, expected_at_zeta, "b(zeta) mismatch");
        assert_eq!(
            b_at_zeta_omega, expected_at_zeta_omega,
            "b(zeta*omega) mismatch"
        );
    }

    /// Regression test for `b_poly_coefficients`.
    ///
    /// Verifies that the coefficients satisfy: `b(x) = sum_i s_i * x^i`
    /// where `s_i = prod_{j: bit_j(i) = 1} u_{k-j}`
    #[test]
    fn test_b_poly_coefficients_regression() {
        // Use 4 challenges for manageable output (2^4 = 16 coefficients)
        let chals: Vec<Fp> = vec![
            Fp::from(2u64),
            Fp::from(3u64),
            Fp::from(5u64),
            Fp::from(7u64),
        ];

        let coeffs = b_poly_coefficients(&chals);

        assert_eq!(coeffs.len(), 16, "Should have 2^4 = 16 coefficients");

        // Expected coefficients (computed and verified)
        // s_i = prod_{j: bit_j(i) = 1} u_{k-j}
        // chals = [2, 3, 5, 7] means u_1=2, u_2=3, u_3=5, u_4=7
        // Index 0 (0000): 1
        // Index 1 (0001): u_4 = 7
        // Index 2 (0010): u_3 = 5
        // Index 3 (0011): u_3 * u_4 = 35
        // etc.
        let expected: Vec<Fp> = vec![
            Fp::from(1u64),   // 0: 1
            Fp::from(7u64),   // 1: u_4
            Fp::from(5u64),   // 2: u_3
            Fp::from(35u64),  // 3: u_3 * u_4
            Fp::from(3u64),   // 4: u_2
            Fp::from(21u64),  // 5: u_2 * u_4
            Fp::from(15u64),  // 6: u_2 * u_3
            Fp::from(105u64), // 7: u_2 * u_3 * u_4
            Fp::from(2u64),   // 8: u_1
            Fp::from(14u64),  // 9: u_1 * u_4
            Fp::from(10u64),  // 10: u_1 * u_3
            Fp::from(70u64),  // 11: u_1 * u_3 * u_4
            Fp::from(6u64),   // 12: u_1 * u_2
            Fp::from(42u64),  // 13: u_1 * u_2 * u_4
            Fp::from(30u64),  // 14: u_1 * u_2 * u_3
            Fp::from(210u64), // 15: u_1 * u_2 * u_3 * u_4
        ];

        assert_eq!(coeffs, expected, "Coefficients mismatch");
    }

    /// Test that `b_poly` and `b_poly_coefficients` are consistent:
    /// evaluating b(x) via the product form should equal evaluating via coefficients.
    #[test]
    fn test_b_poly_consistency() {
        let chals: Vec<Fp> = (2u64..=10).map(Fp::from).collect();
        let coeffs = b_poly_coefficients(&chals);

        // Test at several points
        for x_val in [1u64, 7, 13, 42, 100] {
            let x = Fp::from(x_val);

            // Evaluate via product form
            let b_product = b_poly(&chals, x);

            // Evaluate via coefficients: sum_i s_i * x^i
            let mut b_coeffs = Fp::zero();
            let mut x_pow = Fp::one();
            for coeff in &coeffs {
                b_coeffs += *coeff * x_pow;
                x_pow *= x;
            }

            assert_eq!(
                b_product, b_coeffs,
                "b_poly and b_poly_coefficients inconsistent at x={x_val}"
            );
        }
    }
}