#![allow(clippy::too_many_arguments)]
use crate::group::CompressedGroup;
use crate::sumcheck::SumcheckInstanceProof;

use super::commitments::{Commitments, MultiCommitGens};
use super::dense_mlpoly::{
  DensePolynomial, EqPolynomial, PolyCommitment, PolyCommitmentGens, PolyEvalProof,
};
use super::errors::ProofVerifyError;
use super::group::{
  CompressGroupElement, DecompressGroupElement, GroupElement, VartimeMultiscalarMul,
};
use super::math::Math;
use super::nizk::{EqualityProof, KnowledgeProof, ProductProof};
use super::r1csinstance::R1CSInstance;
use super::random::RandomTape;
use super::scalar::Scalar;
use super::sparse_mlpoly::{SparsePolyEntry, SparsePolynomial};
use super::sumcheck::ZKSumcheckInstanceProof;
use super::timer::Timer;
use super::transcript::{AppendToTranscript, ProofTranscript};
use ark_ec::ProjectiveCurve;
use ark_ff::PrimeField;
use ark_serialize::*;
use ark_std::{One, Zero};
use core::iter;
use merlin::Transcript;

#[derive(CanonicalSerialize, CanonicalDeserialize, Debug)]
pub struct R1CSProof {
  sc_proof_phase1: SumcheckInstanceProof,
  claims_phase2: (Scalar, Scalar, Scalar, Scalar),
  // pok_claims_phase2: (KnowledgeProof, ProductProof),
  // proof_eq_sc_phase1: EqualityProof,
  sc_proof_phase2: SumcheckInstanceProof,
  eval_vars_at_ry: Scalar,
  // proof_eval_vars_at_ry: PolyEvalProof,
  // proof_eq_sc_phase2: EqualityProof,
}

pub struct R1CSSumcheckGens {
  gens_1: MultiCommitGens,
  gens_3: MultiCommitGens,
  gens_4: MultiCommitGens,
}

// TODO: fix passing gens_1_ref
impl R1CSSumcheckGens {
  pub fn new(label: &'static [u8], gens_1_ref: &MultiCommitGens) -> Self {
    let gens_1 = gens_1_ref.clone();
    let gens_3 = MultiCommitGens::new(3, label);
    let gens_4 = MultiCommitGens::new(4, label);

    R1CSSumcheckGens {
      gens_1,
      gens_3,
      gens_4,
    }
  }
}

pub struct R1CSGens {
  gens_sc: R1CSSumcheckGens,
  gens_pc: PolyCommitmentGens,
}

impl R1CSGens {
  pub fn new(label: &'static [u8], _num_cons: usize, num_vars: usize) -> Self {
    let num_poly_vars = num_vars.log_2() as usize;
    let gens_pc = PolyCommitmentGens::new(num_poly_vars, label);
    let gens_sc = R1CSSumcheckGens::new(label, &gens_pc.gens.gens_1);
    R1CSGens { gens_sc, gens_pc }
  }
}

impl R1CSProof {
  fn prove_phase_one(
    num_rounds: usize,
    evals_tau: &mut DensePolynomial,
    evals_Az: &mut DensePolynomial,
    evals_Bz: &mut DensePolynomial,
    evals_Cz: &mut DensePolynomial,
    transcript: &mut Transcript,
  ) -> (SumcheckInstanceProof, Vec<Scalar>, Vec<Scalar>) {
    let comb_func =
      |poly_tau_comp: &Scalar,
       poly_A_comp: &Scalar,
       poly_B_comp: &Scalar,
       poly_C_comp: &Scalar|
       -> Scalar { (*poly_tau_comp) * ((*poly_A_comp) * poly_B_comp - poly_C_comp) };

    let (sc_proof_phase_one, r, claims) = SumcheckInstanceProof::prove_cubic_with_additive_term(
      &Scalar::zero(), // claim is zero
      num_rounds,
      evals_tau,
      evals_Az,
      evals_Bz,
      evals_Cz,
      comb_func,
      transcript,
    );

    (sc_proof_phase_one, r, claims)
  }

  fn prove_phase_two(
    num_rounds: usize,
    claim: &Scalar,
    evals_z: &mut DensePolynomial,
    evals_ABC: &mut DensePolynomial,
    transcript: &mut Transcript,
  ) -> (SumcheckInstanceProof, Vec<Scalar>, Vec<Scalar>) {
    let comb_func =
      |poly_A_comp: &Scalar, poly_B_comp: &Scalar| -> Scalar { (*poly_A_comp) * poly_B_comp };
    let (sc_proof_phase_two, r, claims) = SumcheckInstanceProof::prove_quad(
      claim, num_rounds, evals_z, evals_ABC, comb_func, transcript,
    );

    (sc_proof_phase_two, r, claims)
  }

  fn protocol_name() -> &'static [u8] {
    b"R1CS proof"
  }

  pub fn prove(
    inst: &R1CSInstance,
    vars: Vec<Scalar>,
    input: &[Scalar],
    gens: &R1CSGens,
    transcript: &mut Transcript,
    random_tape: &mut RandomTape,
  ) -> (R1CSProof, Vec<Scalar>, Vec<Scalar>) {
    let timer_prove = Timer::new("R1CSProof::prove");
    transcript.append_protocol_name(R1CSProof::protocol_name());

    // we currently require the number of |inputs| + 1 to be at most number of vars
    assert!(input.len() < vars.len());

    input.append_to_transcript(b"input", transcript);

    let poly_vars = DensePolynomial::new(vars.clone());

    let timer_sc_proof_phase1 = Timer::new("prove_sc_phase_one");

    // append input to variables to create a single vector z
    let z = {
      let num_inputs = input.len();
      let num_vars = vars.len();
      let mut z = vars;
      z.extend(&vec![Scalar::one()]); // add constant term in z
      z.extend(input);
      z.extend(&vec![Scalar::zero(); num_vars - num_inputs - 1]); // we will pad with zeros
      z
    };

    // derive the verifier's challenge tau
    let (num_rounds_x, num_rounds_y) = (
      inst.get_num_cons().log_2() as usize,
      z.len().log_2() as usize,
    );
    let tau = transcript.challenge_vector(b"challenge_tau", num_rounds_x);
    // compute the initial evaluation table for R(\tau, x)
    let mut poly_tau = DensePolynomial::new(EqPolynomial::new(tau).evals());
    let (mut poly_Az, mut poly_Bz, mut poly_Cz) =
      inst.multiply_vec(inst.get_num_cons(), z.len(), &z);

    let (sc_proof_phase1, rx, _claims_phase1) = R1CSProof::prove_phase_one(
      num_rounds_x,
      &mut poly_tau,
      &mut poly_Az,
      &mut poly_Bz,
      &mut poly_Cz,
      transcript,
    );
    assert_eq!(poly_tau.len(), 1);
    assert_eq!(poly_Az.len(), 1);
    assert_eq!(poly_Bz.len(), 1);
    assert_eq!(poly_Cz.len(), 1);
    timer_sc_proof_phase1.stop();

    let (tau_claim, Az_claim, Bz_claim, Cz_claim) =
      (&poly_tau[0], &poly_Az[0], &poly_Bz[0], &poly_Cz[0]);
    let prod_Az_Bz_claims = (*Az_claim) * Bz_claim;

    // prove the final step of sum-check #1
    let taus_bound_rx = tau_claim;
    let claim_post_phase1 = ((*Az_claim) * Bz_claim - Cz_claim) * taus_bound_rx;

    let timer_sc_proof_phase2 = Timer::new("prove_sc_phase_two");
    // combine the three claims into a single claim
    let r_A = transcript.challenge_scalar(b"challenege_Az");
    let r_B = transcript.challenge_scalar(b"challenege_Bz");
    let r_C = transcript.challenge_scalar(b"challenege_Cz");
    let claim_phase2 = r_A * Az_claim + r_B * Bz_claim + r_C * Cz_claim;

    let evals_ABC = {
      // compute the initial evaluation table for R(\tau, x)
      let evals_rx = EqPolynomial::new(rx.clone()).evals();
      let (evals_A, evals_B, evals_C) =
        inst.compute_eval_table_sparse(inst.get_num_cons(), z.len(), &evals_rx);

      assert_eq!(evals_A.len(), evals_B.len());
      assert_eq!(evals_A.len(), evals_C.len());
      (0..evals_A.len())
        .map(|i| r_A * evals_A[i] + r_B * evals_B[i] + r_C * evals_C[i])
        .collect::<Vec<Scalar>>()
    };

    // another instance of the sum-check protocol
    let (sc_proof_phase2, ry, claims_phase2) = R1CSProof::prove_phase_two(
      num_rounds_y,
      &claim_phase2,
      &mut DensePolynomial::new(z),
      &mut DensePolynomial::new(evals_ABC),
      transcript,
    );
    timer_sc_proof_phase2.stop();

    let timer_polyeval = Timer::new("polyeval");
    let eval_vars_at_ry = poly_vars.evaluate(&ry[1..].to_vec());
    timer_polyeval.stop();

    timer_prove.stop();

    (
      R1CSProof {
        sc_proof_phase1,
        claims_phase2: (*Az_claim, *Bz_claim, *Cz_claim, prod_Az_Bz_claims),
        sc_proof_phase2,
        eval_vars_at_ry,
      },
      rx,
      ry,
    )
  }

  pub fn verify(
    &self,
    num_vars: usize,
    num_cons: usize,
    input: &[Scalar],
    evals: &(Scalar, Scalar, Scalar),
    transcript: &mut Transcript,
    gens: &R1CSGens,
  ) -> Result<(Vec<Scalar>, Vec<Scalar>), ProofVerifyError> {
    transcript.append_protocol_name(R1CSProof::protocol_name());

    input.append_to_transcript(b"input", transcript);

    let n = num_vars;

    let (num_rounds_x, num_rounds_y) = (num_cons.log_2() as usize, (2 * num_vars).log_2() as usize);

    // derive the verifier's challenge tau
    let tau = transcript.challenge_vector(b"challenge_tau", num_rounds_x);

    // verify the first sum-check instance
    let claim_phase1 = Scalar::zero();
    let (claim_post_phase1, rx) =
      self
        .sc_proof_phase1
        .verify(claim_phase1, num_rounds_x, 3, transcript)?;

    // perform the intermediate sum-check test with claimed Az, Bz, and Cz
    let (Az_claim, Bz_claim, Cz_claim, prod_Az_Bz_claims) = &self.claims_phase2;

    let taus_bound_rx: Scalar = (0..rx.len())
      .map(|i| rx[i] * tau[i] + (Scalar::one() - rx[i]) * (Scalar::one() - tau[i]))
      .product();

    let expected_claim_post_phase1 = (*prod_Az_Bz_claims - *Cz_claim) * (taus_bound_rx);

    assert_eq!(claim_post_phase1, expected_claim_post_phase1);

    // derive three public challenges and then derive a joint claim
    let r_A = transcript.challenge_scalar(b"challenege_Az");
    let r_B = transcript.challenge_scalar(b"challenege_Bz");
    let r_C = transcript.challenge_scalar(b"challenege_Cz");

    let claim_phase2 = r_A * Az_claim + r_B * Bz_claim + r_C * Cz_claim;

    // verify the joint claim with a sum-check protocol
    let (claim_post_phase2, ry) =
      self
        .sc_proof_phase2
        .verify(claim_phase2, num_rounds_y, 2, transcript)?;

    let poly_input_eval = {
      // constant term
      let mut input_as_sparse_poly_entries = vec![SparsePolyEntry::new(0, Scalar::one())];
      //remaining inputs
      input_as_sparse_poly_entries.extend(
        (0..input.len())
          .map(|i| SparsePolyEntry::new(i + 1, input[i]))
          .collect::<Vec<SparsePolyEntry>>(),
      );
      SparsePolynomial::new(n.log_2() as usize, input_as_sparse_poly_entries).evaluate(&ry[1..])
    };

    let eval_Z_at_ry = (Scalar::one() - ry[0]) * self.eval_vars_at_ry + ry[0] * poly_input_eval;

    // perform the final check in the second sum-check protocol
    let (eval_A_r, eval_B_r, eval_C_r) = evals;
    let scalar = r_A * eval_A_r + r_B * eval_B_r + r_C * eval_C_r;
    let expected_claim_post_phase2 = eval_Z_at_ry * scalar;

    assert_eq!(expected_claim_post_phase2, claim_post_phase2);

    Ok((rx, ry))
  }
}

#[cfg(test)]
mod tests {
  use super::*;
  use ark_std::UniformRand;
  use test::Bencher;

  fn produce_tiny_r1cs() -> (R1CSInstance, Vec<Scalar>, Vec<Scalar>) {
    // three constraints over five variables Z1, Z2, Z3, Z4, and Z5
    // rounded to the nearest power of two
    let num_cons = 128;
    let num_vars = 256;
    let num_inputs = 2;

    // encode the above constraints into three matrices
    let mut A: Vec<(usize, usize, Scalar)> = Vec::new();
    let mut B: Vec<(usize, usize, Scalar)> = Vec::new();
    let mut C: Vec<(usize, usize, Scalar)> = Vec::new();

    let one = Scalar::one();
    // constraint 0 entries
    // (Z1 + Z2) * I0 - Z3 = 0;
    A.push((0, 0, one));
    A.push((0, 1, one));
    B.push((0, num_vars + 1, one));
    C.push((0, 2, one));

    // constraint 1 entries
    // (Z1 + I1) * (Z3) - Z4 = 0
    A.push((1, 0, one));
    A.push((1, num_vars + 2, one));
    B.push((1, 2, one));
    C.push((1, 3, one));
    // constraint 3 entries
    // Z5 * 1 - 0 = 0
    A.push((2, 4, one));
    B.push((2, num_vars, one));

    let inst = R1CSInstance::new(num_cons, num_vars, num_inputs, &A, &B, &C);

    // compute a satisfying assignment
    let mut rng = ark_std::rand::thread_rng();
    let i0 = Scalar::rand(&mut rng);
    let i1 = Scalar::rand(&mut rng);
    let z1 = Scalar::rand(&mut rng);
    let z2 = Scalar::rand(&mut rng);
    let z3 = (z1 + z2) * i0; // constraint 1: (Z1 + Z2) * I0 - Z3 = 0;
    let z4 = (z1 + i1) * z3; // constraint 2: (Z1 + I1) * (Z3) - Z4 = 0
    let z5 = Scalar::zero(); //constraint 3

    let mut vars = vec![Scalar::zero(); num_vars];
    vars[0] = z1;
    vars[1] = z2;
    vars[2] = z3;
    vars[3] = z4;
    vars[4] = z5;

    let mut input = vec![Scalar::zero(); num_inputs];
    input[0] = i0;
    input[1] = i1;

    (inst, vars, input)
  }

  #[test]
  fn test_tiny_r1cs() {
    let (inst, vars, input) = tests::produce_tiny_r1cs();
    let is_sat = inst.is_sat(&vars, &input);
    assert!(is_sat);
  }

  #[test]
  fn test_synthetic_r1cs() {
    let (inst, vars, input) = R1CSInstance::produce_synthetic_r1cs(1024, 1024, 10);
    let is_sat = inst.is_sat(&vars, &input);
    assert!(is_sat);
  }

  #[test]
  pub fn check_r1cs_proof() {
    let num_vars = 1024;
    let num_cons = num_vars;
    let num_inputs = 10;
    let (inst, vars, input) = R1CSInstance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);

    let gens = R1CSGens::new(b"test-m", num_cons, num_vars);

    let mut random_tape = RandomTape::new(b"proof");
    let mut prover_transcript = Transcript::new(b"example");
    let (proof, rx, ry) = R1CSProof::prove(
      &inst,
      vars,
      &input,
      &gens,
      &mut prover_transcript,
      &mut random_tape,
    );

    let inst_evals = inst.evaluate(&rx, &ry);

    let mut verifier_transcript = Transcript::new(b"example");
    assert!(proof
      .verify(
        inst.get_num_vars(),
        inst.get_num_cons(),
        &input,
        &inst_evals,
        &mut verifier_transcript,
        &gens,
      )
      .is_ok());
  }

  #[bench]
  fn bench_r1cs_proof(b: &mut Bencher) {
    b.iter(|| check_r1cs_proof());
  }
}