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// SPDX-License-Identifier: Apache-2.0

// Copyright 2023 Consensys Software Inc.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

// Code generated by gnark DO NOT EDIT

pragma solidity ^0.8.19;

import { Utils } from "./Utils.sol";

contract PlonkVerifierFull {
  using Utils for *;
  uint256 private constant r_mod = 21888242871839275222246405745257275088548364400416034343698204186575808495617;
  uint256 private constant p_mod = 21888242871839275222246405745257275088696311157297823662689037894645226208583;

  uint256 private constant g2_srs_0_x_0 = 11559732032986387107991004021392285783925812861821192530917403151452391805634;
  uint256 private constant g2_srs_0_x_1 = 10857046999023057135944570762232829481370756359578518086990519993285655852781;
  uint256 private constant g2_srs_0_y_0 = 4082367875863433681332203403145435568316851327593401208105741076214120093531;
  uint256 private constant g2_srs_0_y_1 = 8495653923123431417604973247489272438418190587263600148770280649306958101930;

  uint256 private constant g2_srs_1_x_0 = 15805639136721018565402881920352193254830339253282065586954346329754995870280;
  uint256 private constant g2_srs_1_x_1 = 19089565590083334368588890253123139704298730990782503769911324779715431555531;
  uint256 private constant g2_srs_1_y_0 = 9779648407879205346559610309258181044130619080926897934572699915909528404984;
  uint256 private constant g2_srs_1_y_1 = 6779728121489434657638426458390319301070371227460768374343986326751507916979;

  // ----------------------- vk ---------------------
  uint256 private constant vk_domain_size = 67108864;
  uint256 private constant vk_inv_domain_size =
    21888242545679039938882419398440172875981108180010270949818755658014750055173;
  uint256 private constant vk_omega = 7419588552507395652481651088034484897579724952953562618697845598160172257810;
  uint256 private constant vk_ql_com_x = 13525709715452455298954926042894212564628036321399789360566793694715937771352;
  uint256 private constant vk_ql_com_y = 16585249180591675138941559203780511979245575412908714775636958360987383792239;
  uint256 private constant vk_qr_com_x = 14148572045886251945792876173080813556116314088794324579574660284762914941669;
  uint256 private constant vk_qr_com_y = 13842239550691491428464191545817225601597189810026701643462638680503957744889;
  uint256 private constant vk_qm_com_x = 13522897959955119652865784834835976361490133655994054434262671514193248404625;
  uint256 private constant vk_qm_com_y = 13493447428329441420851370602159948706574248532218034239617820929323277518001;
  uint256 private constant vk_qo_com_x = 7060690164887603180822709561299613895672597716510049606680499562908505132709;
  uint256 private constant vk_qo_com_y = 17132453280808170663140286188647213203791535181032438058770464109374337899153;
  uint256 private constant vk_qk_com_x = 15216401052757890774219228156239863879308845760439647233724618177408901913570;
  uint256 private constant vk_qk_com_y = 12451956943068853170449619051211352834650857556519559497734074793907719431916;

  uint256 private constant vk_s1_com_x = 14256405778767051587276133608837021203518255961898101394303537378002866419040;
  uint256 private constant vk_s1_com_y = 21038700968212297875313747694611083193187035592187569106720411730639905255252;

  uint256 private constant vk_s2_com_x = 1019109700203543492729048562641359612628812305695299058467746496950485325794;
  uint256 private constant vk_s2_com_y = 490278430319379230242443848913755358662702057338304277498471180434097991836;

  uint256 private constant vk_s3_com_x = 2969427075258365849777260383285616082152301055041585820485498518017437026548;
  uint256 private constant vk_s3_com_y = 16099347285202727295431946911322450887583714417016216619148080599766330871066;

  uint256 private constant vk_coset_shift = 5;

  uint256 private constant vk_selector_commitments_commit_api_0_x =
    21788360697493106829785246939901744021456836473452930837314992369057900122018;
  uint256 private constant vk_selector_commitments_commit_api_0_y =
    16125341249761668633747631072985421243468892447965413965887015388783528206032;

  uint256 private constant vk_selector_commitments_commit_api_1_x =
    9369801914206014217445122279591521815449013590744042826207321226401456655568;
  uint256 private constant vk_selector_commitments_commit_api_1_y =
    20403534275150672051547282308343985824042675377185536764459718189767081861844;

  uint256 private constant vk_selector_commitments_commit_api_2_x =
    15085855314213485493120090850643571722324905485327671636383375594981366630616;
  uint256 private constant vk_selector_commitments_commit_api_2_y =
    9694401959517714837257605548316168182563966590362894961003011860886804708060;

  function load_vk_commitments_indices_commit_api(uint256[] memory v) internal pure {
    assembly {
      let _v := add(v, 0x20)

      mstore(_v, 22612113)
      _v := add(_v, 0x20)

      mstore(_v, 27501766)
      _v := add(_v, 0x20)

      mstore(_v, 60589135)
      _v := add(_v, 0x20)
    }
  }

  uint256 private constant vk_nb_commitments_commit_api = 3;

  // ------------------------------------------------

  // offset proof
  uint256 private constant proof_l_com_x = 0x20;
  uint256 private constant proof_l_com_y = 0x40;
  uint256 private constant proof_r_com_x = 0x60;
  uint256 private constant proof_r_com_y = 0x80;
  uint256 private constant proof_o_com_x = 0xa0;
  uint256 private constant proof_o_com_y = 0xc0;

  // h = h_0 + x^{n+2}h_1 + x^{2(n+2)}h_2
  uint256 private constant proof_h_0_x = 0xe0;
  uint256 private constant proof_h_0_y = 0x100;
  uint256 private constant proof_h_1_x = 0x120;
  uint256 private constant proof_h_1_y = 0x140;
  uint256 private constant proof_h_2_x = 0x160;
  uint256 private constant proof_h_2_y = 0x180;

  // wire values at zeta
  uint256 private constant proof_l_at_zeta = 0x1a0;
  uint256 private constant proof_r_at_zeta = 0x1c0;
  uint256 private constant proof_o_at_zeta = 0x1e0;

  //uint256[STATE_WIDTH-1] permutation_polynomials_at_zeta; // Sσ1(zeta),Sσ2(zeta)
  uint256 private constant proof_s1_at_zeta = 0x200; // Sσ1(zeta)
  uint256 private constant proof_s2_at_zeta = 0x220; // Sσ2(zeta)

  //Bn254.G1Point grand_product_commitment;                 // [z(x)]
  uint256 private constant proof_grand_product_commitment_x = 0x240;
  uint256 private constant proof_grand_product_commitment_y = 0x260;

  uint256 private constant proof_grand_product_at_zeta_omega = 0x280; // z(w*zeta)
  uint256 private constant proof_quotient_polynomial_at_zeta = 0x2a0; // t(zeta)
  uint256 private constant proof_linearised_polynomial_at_zeta = 0x2c0; // r(zeta)

  // Folded proof for the opening of H, linearised poly, l, r, o, s_1, s_2, qcp
  uint256 private constant proof_batch_opening_at_zeta_x = 0x2e0; // [Wzeta]
  uint256 private constant proof_batch_opening_at_zeta_y = 0x300;

  //Bn254.G1Point opening_at_zeta_omega_proof;      // [Wzeta*omega]
  uint256 private constant proof_opening_at_zeta_omega_x = 0x320;
  uint256 private constant proof_opening_at_zeta_omega_y = 0x340;

  uint256 private constant proof_openings_selector_commit_api_at_zeta = 0x360;
  // -> next part of proof is
  // [ openings_selector_commits || commitments_wires_commit_api]

  // -------- offset state

  // challenges to check the claimed quotient
  uint256 private constant state_alpha = 0x00;
  uint256 private constant state_beta = 0x20;
  uint256 private constant state_gamma = 0x40;
  uint256 private constant state_zeta = 0x60;

  // reusable value
  uint256 private constant state_alpha_square_lagrange_0 = 0x80;

  // commitment to H
  uint256 private constant state_folded_h_x = 0xa0;
  uint256 private constant state_folded_h_y = 0xc0;

  // commitment to the linearised polynomial
  uint256 private constant state_linearised_polynomial_x = 0xe0;
  uint256 private constant state_linearised_polynomial_y = 0x100;

  // Folded proof for the opening of H, linearised poly, l, r, o, s_1, s_2, qcp
  uint256 private constant state_folded_claimed_values = 0x120;

  // folded digests of H, linearised poly, l, r, o, s_1, s_2, qcp
  // Bn254.G1Point folded_digests;
  uint256 private constant state_folded_digests_x = 0x140;
  uint256 private constant state_folded_digests_y = 0x160;

  uint256 private constant state_pi = 0x180;

  uint256 private constant state_zeta_power_n_minus_one = 0x1a0;

  uint256 private constant state_gamma_kzg = 0x1c0;

  uint256 private constant state_success = 0x1e0;
  uint256 private constant state_check_var = 0x200; // /!\ this slot is used for debugging only

  uint256 private constant state_last_mem = 0x220;

  // -------- errors
  uint256 private constant error_string_id = 0x08c379a000000000000000000000000000000000000000000000000000000000; // selector for function Error(string)

  // read the commitments to the wires related to the commit api and store them in wire_commitments.
  // The commitments are points on Bn254(Fp) so they are stored on 2 uint256.
  function load_wire_commitments_commit_api(uint256[] memory wire_commitments, bytes memory proof) internal pure {
    assembly {
      let w := add(wire_commitments, 0x20)
      let p := add(proof, proof_openings_selector_commit_api_at_zeta)
      p := add(p, mul(vk_nb_commitments_commit_api, 0x20))
      for {
        let i := 0
      } lt(i, vk_nb_commitments_commit_api) {
        i := add(i, 1)
      } {
        // x coordinate
        mstore(w, mload(p))
        w := add(w, 0x20)
        p := add(p, 0x20)

        // y coordinate
        mstore(w, mload(p))
        w := add(w, 0x20)
        p := add(p, 0x20)
      }
    }
  }

  function derive_gamma_beta_alpha_zeta(
    bytes memory proof,
    uint256[] memory public_inputs
  ) internal view returns (uint256, uint256, uint256, uint256) {
    uint256 gamma;
    uint256 beta;
    uint256 alpha;
    uint256 zeta;

    assembly {
      let mem := mload(0x40)

      derive_gamma(proof, public_inputs)
      gamma := mload(mem)

      derive_beta(proof, gamma)
      beta := mload(mem)

      derive_alpha(proof, beta)
      alpha := mload(mem)

      derive_zeta(proof, alpha)
      zeta := mload(mem)

      gamma := mod(gamma, r_mod)
      beta := mod(beta, r_mod)
      alpha := mod(alpha, r_mod)
      zeta := mod(zeta, r_mod)

      function error_sha2_256() {
        let ptError := mload(0x40)
        mstore(ptError, error_string_id) // selector for function Error(string)
        mstore(add(ptError, 0x4), 0x20)
        mstore(add(ptError, 0x24), 0x19)
        mstore(add(ptError, 0x44), "error staticcall sha2-256")
        revert(ptError, 0x64)
      }

      // Derive gamma as Sha256(<transcript>)
      // where transcript is the concatenation (in this order) of:
      // * the word "gamma" in ascii, equal to [0x67,0x61,0x6d, 0x6d, 0x61] and encoded as a uint256.
      // * the commitments to the permutation polynomials S1, S2, S3, where we concatenate the coordinates of those points
      // * the commitments of Ql, Qr, Qm, Qo, Qk
      // * the public inputs
      // * the commitments of the wires related to the custom gates (commitments_wires_commit_api)
      // * commitments to L, R, O (proof_<l,r,o>_com_<x,y>)
      // The data described above is written starting at mPtr. "gamma" lies on 5 bytes,
      // and is encoded as a uint256 number n. In basis b = 256, the number looks like this
      // [0 0 0 .. 0x67 0x61 0x6d, 0x6d, 0x61]. The first non zero entry is at position 27=0x1b
      function derive_gamma(aproof, pub_inputs) {
        let mPtr := mload(0x40)

        // gamma
        // gamma in ascii is [0x67,0x61,0x6d, 0x6d, 0x61]
        // (same for alpha, beta, zeta)
        mstore(mPtr, 0x67616d6d61) // "gamma"

        mstore(add(mPtr, 0x20), vk_s1_com_x)
        mstore(add(mPtr, 0x40), vk_s1_com_y)
        mstore(add(mPtr, 0x60), vk_s2_com_x)
        mstore(add(mPtr, 0x80), vk_s2_com_y)
        mstore(add(mPtr, 0xa0), vk_s3_com_x)
        mstore(add(mPtr, 0xc0), vk_s3_com_y)
        mstore(add(mPtr, 0xe0), vk_ql_com_x)
        mstore(add(mPtr, 0x100), vk_ql_com_y)
        mstore(add(mPtr, 0x120), vk_qr_com_x)
        mstore(add(mPtr, 0x140), vk_qr_com_y)
        mstore(add(mPtr, 0x160), vk_qm_com_x)
        mstore(add(mPtr, 0x180), vk_qm_com_y)
        mstore(add(mPtr, 0x1a0), vk_qo_com_x)
        mstore(add(mPtr, 0x1c0), vk_qo_com_y)
        mstore(add(mPtr, 0x1e0), vk_qk_com_x)
        mstore(add(mPtr, 0x200), vk_qk_com_y)

        let pi := add(pub_inputs, 0x20)
        let _mPtr := add(mPtr, 0x220)
        for {
          let i := 0
        } lt(i, mload(pub_inputs)) {
          i := add(i, 1)
        } {
          mstore(_mPtr, mload(pi))
          pi := add(pi, 0x20)
          _mPtr := add(_mPtr, 0x20)
        }

        let _proof := add(aproof, proof_openings_selector_commit_api_at_zeta)
        _proof := add(_proof, mul(vk_nb_commitments_commit_api, 0x20))
        for {
          let i := 0
        } lt(i, vk_nb_commitments_commit_api) {
          i := add(i, 1)
        } {
          mstore(_mPtr, mload(_proof))
          mstore(add(_mPtr, 0x20), mload(add(_proof, 0x20)))
          _mPtr := add(_mPtr, 0x40)
          _proof := add(_proof, 0x40)
        }

        mstore(_mPtr, mload(add(aproof, proof_l_com_x)))
        mstore(add(_mPtr, 0x20), mload(add(aproof, proof_l_com_y)))
        mstore(add(_mPtr, 0x40), mload(add(aproof, proof_r_com_x)))
        mstore(add(_mPtr, 0x60), mload(add(aproof, proof_r_com_y)))
        mstore(add(_mPtr, 0x80), mload(add(aproof, proof_o_com_x)))
        mstore(add(_mPtr, 0xa0), mload(add(aproof, proof_o_com_y)))

        let size := add(0x2c5, mul(mload(pub_inputs), 0x20)) // 0x2c5 = 22*32+5
        size := add(size, mul(vk_nb_commitments_commit_api, 0x40))
        let success := staticcall(sub(gas(), 2000), 0x2, add(mPtr, 0x1b), size, mPtr, 0x20) //0x1b -> 000.."gamma"
        if eq(success, 0) {
          error_sha2_256()
        }
      }

      function derive_beta(aproof, prev_challenge) {
        let mPtr := mload(0x40)
        // beta
        mstore(mPtr, 0x62657461) // "beta"
        mstore(add(mPtr, 0x20), prev_challenge)
        let success := staticcall(sub(gas(), 2000), 0x2, add(mPtr, 0x1c), 0x24, mPtr, 0x20) //0x1b -> 000.."gamma"
        if eq(success, 0) {
          error_sha2_256()
        }
      }

      // alpha depends on the previous challenge (beta) and on the commitment to the grand product polynomial
      function derive_alpha(aproof, prev_challenge) {
        let mPtr := mload(0x40)
        // alpha
        mstore(mPtr, 0x616C706861) // "alpha"
        mstore(add(mPtr, 0x20), prev_challenge)
        mstore(add(mPtr, 0x40), mload(add(aproof, proof_grand_product_commitment_x)))
        mstore(add(mPtr, 0x60), mload(add(aproof, proof_grand_product_commitment_y)))
        let success := staticcall(sub(gas(), 2000), 0x2, add(mPtr, 0x1b), 0x65, mPtr, 0x20) //0x1b -> 000.."gamma"
        if eq(success, 0) {
          error_sha2_256()
        }
      }

      // zeta depends on the previous challenge (alpha) and on the commitment to the quotient polynomial
      function derive_zeta(aproof, prev_challenge) {
        let mPtr := mload(0x40)
        // zeta
        mstore(mPtr, 0x7a657461) // "zeta"
        mstore(add(mPtr, 0x20), prev_challenge)
        mstore(add(mPtr, 0x40), mload(add(aproof, proof_h_0_x)))
        mstore(add(mPtr, 0x60), mload(add(aproof, proof_h_0_y)))
        mstore(add(mPtr, 0x80), mload(add(aproof, proof_h_1_x)))
        mstore(add(mPtr, 0xa0), mload(add(aproof, proof_h_1_y)))
        mstore(add(mPtr, 0xc0), mload(add(aproof, proof_h_2_x)))
        mstore(add(mPtr, 0xe0), mload(add(aproof, proof_h_2_y)))
        let success := staticcall(sub(gas(), 2000), 0x2, add(mPtr, 0x1c), 0xe4, mPtr, 0x20)
        if eq(success, 0) {
          error_sha2_256()
        }
      }
    }

    return (gamma, beta, alpha, zeta);
  }

  // Computes L_i(zeta) =  ωⁱ/n * (ζⁿ-1)/(ζ-ωⁱ) where:
  // * n = vk_domain_size
  // * ω = vk_omega (generator of the multiplicative cyclic group of order n in (ℤ/rℤ)*)
  // * ζ = zeta (challenge derived with Fiat Shamir)
  function compute_ith_lagrange_at_z(uint256 zeta, uint256 i) internal view returns (uint256) {
    uint256 res;
    assembly {
      function error_pow_local() {
        let ptError := mload(0x40)
        mstore(ptError, error_string_id)
        mstore(add(ptError, 0x4), 0x20)
        mstore(add(ptError, 0x24), 0x17)
        mstore(add(ptError, 0x44), "error staticcall modexp")
        revert(ptError, 0x64)
      }

      // _n^_i [r]
      function pow_local(x, e) -> result {
        let mPtr := mload(0x40)
        mstore(mPtr, 0x20)
        mstore(add(mPtr, 0x20), 0x20)
        mstore(add(mPtr, 0x40), 0x20)
        mstore(add(mPtr, 0x60), x)
        mstore(add(mPtr, 0x80), e)
        mstore(add(mPtr, 0xa0), r_mod)
        let success := staticcall(sub(gas(), 2000), 0x05, mPtr, 0xc0, 0x00, 0x20)
        if eq(success, 0) {
          error_pow_local()
        }
        result := mload(0x00)
      }

      let w := pow_local(vk_omega, i) // w**i
      i := addmod(zeta, sub(r_mod, w), r_mod) // z-w**i
      zeta := pow_local(zeta, vk_domain_size) // z**n
      zeta := addmod(zeta, sub(r_mod, 1), r_mod) // z**n-1
      w := mulmod(w, vk_inv_domain_size, r_mod) // w**i/n
      i := pow_local(i, sub(r_mod, 2)) // (z-w**i)**-1
      w := mulmod(w, i, r_mod) // w**i/n*(z-w)**-1
      res := mulmod(w, zeta, r_mod)
    }

    return res;
  }

  function compute_pi(
    uint256[] memory public_inputs,
    uint256 zeta,
    bytes memory proof
  ) internal view returns (uint256) {
    // evaluation of Z=Xⁿ⁻¹ at ζ
    // uint256 zeta_power_n_minus_one = Fr.pow(zeta, vk_domain_size);
    // zeta_power_n_minus_one = Fr.sub(zeta_power_n_minus_one, 1);
    uint256 zeta_power_n_minus_one;

    uint256 pi;

    assembly {
      function error_pow() {
        let ptError := mload(0x40)
        mstore(ptError, error_string_id) // selector for function Error(string)
        mstore(add(ptError, 0x4), 0x20)
        mstore(add(ptError, 0x24), 0x17)
        mstore(add(ptError, 0x44), "error staticcall modexp")
        revert(ptError, 0x64)
      }

      sum_pi_wo_api_commit(add(public_inputs, 0x20), mload(public_inputs), zeta)
      pi := mload(mload(0x40))

      function sum_pi_wo_api_commit(ins, n, z) {
        let li := mload(0x40)
        batch_compute_lagranges_at_z(z, n, li)
        let res := 0
        let tmp := 0
        for {
          let i := 0
        } lt(i, n) {
          i := add(i, 1)
        } {
          tmp := mulmod(mload(li), mload(ins), r_mod)
          res := addmod(res, tmp, r_mod)
          li := add(li, 0x20)
          ins := add(ins, 0x20)
        }
        mstore(mload(0x40), res)
      }

      // mPtr <- [L_0(z), .., L_{n-1}(z)]
      //
      // Here L_i(zeta) =  ωⁱ/n * (ζⁿ-1)/(ζ-ωⁱ) where:
      // * n = vk_domain_size
      // * ω = vk_omega (generator of the multiplicative cyclic group of order n in (ℤ/rℤ)*)
      // * ζ = zeta (challenge derived with Fiat Shamir)
      function batch_compute_lagranges_at_z(z, n, mPtr) {
        let zn := addmod(pow(z, vk_domain_size, mPtr), sub(r_mod, 1), r_mod)
        zn := mulmod(zn, vk_inv_domain_size, r_mod)
        let _w := 1
        let _mPtr := mPtr
        for {
          let i := 0
        } lt(i, n) {
          i := add(i, 1)
        } {
          mstore(_mPtr, addmod(z, sub(r_mod, _w), r_mod))
          _w := mulmod(_w, vk_omega, r_mod)
          _mPtr := add(_mPtr, 0x20)
        }
        batch_invert(mPtr, n, _mPtr)
        _mPtr := mPtr
        _w := 1
        for {
          let i := 0
        } lt(i, n) {
          i := add(i, 1)
        } {
          mstore(_mPtr, mulmod(mulmod(mload(_mPtr), zn, r_mod), _w, r_mod))
          _mPtr := add(_mPtr, 0x20)
          _w := mulmod(_w, vk_omega, r_mod)
        }
      }

      // batch invert (modulo r) in place the nb_ins uint256 inputs starting at ins.
      function batch_invert(ins, nb_ins, mPtr) {
        mstore(mPtr, 1)
        let offset := 0
        for {
          let i := 0
        } lt(i, nb_ins) {
          i := add(i, 1)
        } {
          let prev := mload(add(mPtr, offset))
          let cur := mload(add(ins, offset))
          cur := mulmod(prev, cur, r_mod)
          offset := add(offset, 0x20)
          mstore(add(mPtr, offset), cur)
        }
        ins := add(ins, sub(offset, 0x20))
        mPtr := add(mPtr, offset)
        let inv := pow(mload(mPtr), sub(r_mod, 2), add(mPtr, 0x20))
        for {
          let i := 0
        } lt(i, nb_ins) {
          i := add(i, 1)
        } {
          mPtr := sub(mPtr, 0x20)
          let tmp := mload(ins)
          let cur := mulmod(inv, mload(mPtr), r_mod)
          mstore(ins, cur)
          inv := mulmod(inv, tmp, r_mod)
          ins := sub(ins, 0x20)
        }
      }

      // res <- x^e mod r
      function pow(x, e, mPtr) -> res {
        mstore(mPtr, 0x20)
        mstore(add(mPtr, 0x20), 0x20)
        mstore(add(mPtr, 0x40), 0x20)
        mstore(add(mPtr, 0x60), x)
        mstore(add(mPtr, 0x80), e)
        mstore(add(mPtr, 0xa0), r_mod)
        let success := staticcall(sub(gas(), 2000), 0x05, mPtr, 0xc0, mPtr, 0x20)
        if eq(success, 0) {
          error_pow()
        }
        res := mload(mPtr)
      }

      zeta_power_n_minus_one := pow(zeta, vk_domain_size, mload(0x40))
      zeta_power_n_minus_one := addmod(zeta_power_n_minus_one, sub(r_mod, 1), r_mod)
    }

    // compute the contribution of the public inputs whose indices are in commitment_indices,
    // and whose value is hash_fr of the corresponding commitme
    uint256[] memory commitment_indices = new uint256[](vk_nb_commitments_commit_api);
    load_vk_commitments_indices_commit_api(commitment_indices);

    uint256[] memory wire_committed_commitments;
    wire_committed_commitments = new uint256[](2 * vk_nb_commitments_commit_api);

    load_wire_commitments_commit_api(wire_committed_commitments, proof);

    for (uint256 i = 0; i < vk_nb_commitments_commit_api; i++) {
      uint256 hash_res = Utils.hash_fr(wire_committed_commitments[2 * i], wire_committed_commitments[2 * i + 1]);
      uint256 a = compute_ith_lagrange_at_z(zeta, commitment_indices[i] + public_inputs.length);
      assembly {
        a := mulmod(hash_res, a, r_mod)
        pi := addmod(pi, a, r_mod)
      }
    }

    return pi;
  }

  function check_inputs_size(uint256[] memory public_inputs) internal pure {
    bool input_checks = true;
    assembly {
      let s := mload(public_inputs)
      let p := add(public_inputs, 0x20)
      for {
        let i
      } lt(i, s) {
        i := add(i, 1)
      } {
        input_checks := and(input_checks, lt(mload(p), r_mod))
        p := add(p, 0x20)
      }
    }
    require(input_checks, "some inputs are bigger than r");
  }

  function check_proof_size(bytes memory proof) internal pure {
    uint256 expected_proof_size = 0x340 + vk_nb_commitments_commit_api * 0x60;
    uint256 actual_proof_size;
    assembly {
      actual_proof_size := mload(proof)
    }
    require(actual_proof_size == expected_proof_size, "wrong proof size");
  }

  function check_proof_openings_size(bytes memory proof) internal pure {
    bool openings_check = true;
    assembly {
      // linearised polynomial at zeta
      let p := add(proof, proof_linearised_polynomial_at_zeta)
      openings_check := and(openings_check, lt(mload(p), r_mod))

      // quotient polynomial at zeta
      p := add(proof, proof_quotient_polynomial_at_zeta)
      openings_check := and(openings_check, lt(mload(p), r_mod))

      // proof_l_at_zeta
      p := add(proof, proof_l_at_zeta)
      openings_check := and(openings_check, lt(mload(p), r_mod))

      // proof_r_at_zeta
      p := add(proof, proof_r_at_zeta)
      openings_check := and(openings_check, lt(mload(p), r_mod))

      // proof_o_at_zeta
      p := add(proof, proof_o_at_zeta)
      openings_check := and(openings_check, lt(mload(p), r_mod))

      // proof_s1_at_zeta
      p := add(proof, proof_s1_at_zeta)
      openings_check := and(openings_check, lt(mload(p), r_mod))

      // proof_s2_at_zeta
      p := add(proof, proof_s2_at_zeta)
      openings_check := and(openings_check, lt(mload(p), r_mod))

      // proof_grand_product_at_zeta_omega
      p := add(proof, proof_grand_product_at_zeta_omega)
      openings_check := and(openings_check, lt(mload(p), r_mod))

      // proof_openings_selector_commit_api_at_zeta

      p := add(proof, proof_openings_selector_commit_api_at_zeta)
      for {
        let i := 0
      } lt(i, vk_nb_commitments_commit_api) {
        i := add(i, 1)
      } {
        openings_check := and(openings_check, lt(mload(p), r_mod))
        p := add(p, 0x20)
      }
    }
    require(openings_check, "some openings are bigger than r");
  }

  function Verify(bytes memory proof, uint256[] memory public_inputs) public view returns (bool) {
    check_inputs_size(public_inputs);
    check_proof_size(proof);
    check_proof_openings_size(proof);

    uint256 gamma;
    uint256 beta;
    uint256 alpha;
    uint256 zeta;

    (gamma, beta, alpha, zeta) = derive_gamma_beta_alpha_zeta(proof, public_inputs);

    uint256 pi = compute_pi(public_inputs, zeta, proof);

    uint256 check;

    bool success = false;
    // uint256 success;

    assembly {
      let mem := mload(0x40)
      mstore(add(mem, state_alpha), alpha)
      mstore(add(mem, state_gamma), gamma)
      mstore(add(mem, state_zeta), zeta)
      mstore(add(mem, state_beta), beta)
      mstore(add(mem, state_pi), pi)

      compute_alpha_square_lagrange_0()
      verify_quotient_poly_eval_at_zeta(proof)
      fold_h(proof)
      compute_commitment_linearised_polynomial(proof)
      compute_gamma_kzg(proof)
      fold_state(proof)
      batch_verify_multi_points(proof)

      success := mload(add(mem, state_success))

      check := mload(add(mem, state_check_var))

      function error_verify() {
        let ptError := mload(0x40)
        mstore(ptError, error_string_id) // selector for function Error(string)
        mstore(add(ptError, 0x4), 0x20)
        mstore(add(ptError, 0x24), 0xc)
        mstore(add(ptError, 0x44), "error verify")
        revert(ptError, 0x64)
      }

      // compute α² * 1/n * (ζ{n}-1)/(ζ - 1) where
      // * α = challenge derived in derive_gamma_beta_alpha_zeta
      // * n = vk_domain_size
      // * ω = vk_omega (generator of the multiplicative cyclic group of order n in (ℤ/rℤ)*)
      // * ζ = zeta (challenge derived with Fiat Shamir)
      function compute_alpha_square_lagrange_0() {
        let state := mload(0x40)
        let mPtr := add(mload(0x40), state_last_mem)

        // zeta**n - 1
        let res := pow(mload(add(state, state_zeta)), vk_domain_size, mPtr)
        res := addmod(res, sub(r_mod, 1), r_mod)
        mstore(add(state, state_zeta_power_n_minus_one), res)

        // let res := mload(add(state, state_zeta_power_n_minus_one))
        let den := addmod(mload(add(state, state_zeta)), sub(r_mod, 1), r_mod)
        den := pow(den, sub(r_mod, 2), mPtr)
        den := mulmod(den, vk_inv_domain_size, r_mod)
        res := mulmod(den, res, r_mod)

        let l_alpha := mload(add(state, state_alpha))
        res := mulmod(res, l_alpha, r_mod)
        res := mulmod(res, l_alpha, r_mod)
        mstore(add(state, state_alpha_square_lagrange_0), res)
      }

      // follows alg. p.13 of https://eprint.iacr.org/2019/953.pdf
      // with t₁ = t₂ = 1, and the proofs are ([digest] + [quotient] +purported evaluation):
      // * [state_folded_state_digests], [proof_batch_opening_at_zeta_x], state_folded_evals
      // * [proof_grand_product_commitment], [proof_opening_at_zeta_omega_x], [proof_grand_product_at_zeta_omega]
      function batch_verify_multi_points(aproof) {
        let state := mload(0x40)
        let mPtr := add(state, state_last_mem)

        // here the random is not a challenge, hence no need to use Fiat Shamir, we just
        // need an unpredictible result.
        let random := mod(keccak256(state, 0x20), r_mod)

        let folded_quotients := mPtr
        mPtr := add(folded_quotients, 0x40)
        mstore(folded_quotients, mload(add(aproof, proof_batch_opening_at_zeta_x)))
        mstore(add(folded_quotients, 0x20), mload(add(aproof, proof_batch_opening_at_zeta_y)))
        point_acc_mul(folded_quotients, add(aproof, proof_opening_at_zeta_omega_x), random, mPtr)

        let folded_digests := add(state, state_folded_digests_x)
        point_acc_mul(folded_digests, add(aproof, proof_grand_product_commitment_x), random, mPtr)

        let folded_evals := add(state, state_folded_claimed_values)
        fr_acc_mul(folded_evals, add(aproof, proof_grand_product_at_zeta_omega), random)

        let folded_evals_commit := mPtr
        mPtr := add(folded_evals_commit, 0x40)
        mstore(folded_evals_commit, 14312776538779914388377568895031746459131577658076416373430523308756343304251)
        mstore(
          add(folded_evals_commit, 0x20),
          11763105256161367503191792604679297387056316997144156930871823008787082098465
        )
        mstore(add(folded_evals_commit, 0x40), mload(folded_evals))
        let check_staticcall := staticcall(sub(gas(), 2000), 7, folded_evals_commit, 0x60, folded_evals_commit, 0x40)
        if eq(check_staticcall, 0) {
          error_verify()
        }

        let folded_evals_commit_y := add(folded_evals_commit, 0x20)
        mstore(folded_evals_commit_y, sub(p_mod, mload(folded_evals_commit_y)))
        point_add(folded_digests, folded_digests, folded_evals_commit, mPtr)

        let folded_points_quotients := mPtr
        mPtr := add(mPtr, 0x40)
        point_mul(
          folded_points_quotients,
          add(aproof, proof_batch_opening_at_zeta_x),
          mload(add(state, state_zeta)),
          mPtr
        )
        let zeta_omega := mulmod(mload(add(state, state_zeta)), vk_omega, r_mod)
        random := mulmod(random, zeta_omega, r_mod)
        point_acc_mul(folded_points_quotients, add(aproof, proof_opening_at_zeta_omega_x), random, mPtr)

        point_add(folded_digests, folded_digests, folded_points_quotients, mPtr)

        let folded_quotients_y := add(folded_quotients, 0x20)
        mstore(folded_quotients_y, sub(p_mod, mload(folded_quotients_y)))

        mstore(mPtr, mload(folded_digests))
        mstore(add(mPtr, 0x20), mload(add(folded_digests, 0x20)))
        mstore(add(mPtr, 0x40), g2_srs_0_x_0) // the 4 lines are the canonical G2 point on BN254
        mstore(add(mPtr, 0x60), g2_srs_0_x_1)
        mstore(add(mPtr, 0x80), g2_srs_0_y_0)
        mstore(add(mPtr, 0xa0), g2_srs_0_y_1)
        mstore(add(mPtr, 0xc0), mload(folded_quotients))
        mstore(add(mPtr, 0xe0), mload(add(folded_quotients, 0x20)))
        mstore(add(mPtr, 0x100), g2_srs_1_x_0)
        mstore(add(mPtr, 0x120), g2_srs_1_x_1)
        mstore(add(mPtr, 0x140), g2_srs_1_y_0)
        mstore(add(mPtr, 0x160), g2_srs_1_y_1)
        check_pairing_kzg(mPtr)
      }

      // check_pairing_kzg checks the result of the final pairing product of the batched
      // kzg verification. The purpose of this function is too avoid exhausting the stack
      // in the function batch_verify_multi_points.
      // mPtr: pointer storing the tuple of pairs
      function check_pairing_kzg(mPtr) {
        let state := mload(0x40)

        // TODO test the staticcall using the method from audit_4-5
        let l_success := staticcall(sub(gas(), 2000), 8, mPtr, 0x180, 0x00, 0x20)
        let res_pairing := mload(0x00)
        let s_success := mload(add(state, state_success))
        res_pairing := and(and(res_pairing, l_success), s_success)
        mstore(add(state, state_success), res_pairing)
      }

      // Fold the opening proofs at ζ:
      // * at state+state_folded_digest we store: [H] + γ[Linearised_polynomial]+γ²[L] + γ³[R] + γ⁴[O] + γ⁵[S₁] +γ⁶[S₂] + ∑ᵢγ⁶⁺ⁱ[Pi_{i}]
      // * at state+state_folded_claimed_values we store: H(ζ) + γLinearised_polynomial(ζ)+γ²L(ζ) + γ³R(ζ)+ γ⁴O(ζ) + γ⁵S₁(ζ) +γ⁶S₂(ζ) + ∑ᵢγ⁶⁺ⁱPi_{i}(ζ)
      // acc_gamma stores the γⁱ
      function fold_state(aproof) {
        let state := mload(0x40)
        let mPtr := add(mload(0x40), state_last_mem)

        let l_gamma_kzg := mload(add(state, state_gamma_kzg))
        let acc_gamma := l_gamma_kzg

        let offset := add(0x200, mul(vk_nb_commitments_commit_api, 0x40)) // 0x40 = 2*0x20
        let mPtrOffset := add(mPtr, offset)

        mstore(add(state, state_folded_digests_x), mload(add(mPtr, 0x40)))
        mstore(add(state, state_folded_digests_y), mload(add(mPtr, 0x60)))
        mstore(add(state, state_folded_claimed_values), mload(add(aproof, proof_quotient_polynomial_at_zeta)))

        point_acc_mul(add(state, state_folded_digests_x), add(mPtr, 0x80), acc_gamma, mPtrOffset)
        fr_acc_mul(add(state, state_folded_claimed_values), add(aproof, proof_linearised_polynomial_at_zeta), acc_gamma)
        mstore(add(state, state_check_var), acc_gamma)

        acc_gamma := mulmod(acc_gamma, l_gamma_kzg, r_mod)
        point_acc_mul(add(state, state_folded_digests_x), add(mPtr, 0xc0), acc_gamma, mPtrOffset)
        fr_acc_mul(add(state, state_folded_claimed_values), add(aproof, proof_l_at_zeta), acc_gamma)

        acc_gamma := mulmod(acc_gamma, l_gamma_kzg, r_mod)
        point_acc_mul(add(state, state_folded_digests_x), add(mPtr, 0x100), acc_gamma, add(mPtr, offset))
        fr_acc_mul(add(state, state_folded_claimed_values), add(aproof, proof_r_at_zeta), acc_gamma)

        acc_gamma := mulmod(acc_gamma, l_gamma_kzg, r_mod)
        point_acc_mul(add(state, state_folded_digests_x), add(mPtr, 0x140), acc_gamma, add(mPtr, offset))
        fr_acc_mul(add(state, state_folded_claimed_values), add(aproof, proof_o_at_zeta), acc_gamma)

        acc_gamma := mulmod(acc_gamma, l_gamma_kzg, r_mod)
        point_acc_mul(add(state, state_folded_digests_x), add(mPtr, 0x180), acc_gamma, add(mPtr, offset))
        fr_acc_mul(add(state, state_folded_claimed_values), add(aproof, proof_s1_at_zeta), acc_gamma)

        acc_gamma := mulmod(acc_gamma, l_gamma_kzg, r_mod)
        point_acc_mul(add(state, state_folded_digests_x), add(mPtr, 0x1c0), acc_gamma, add(mPtr, offset))
        fr_acc_mul(add(state, state_folded_claimed_values), add(aproof, proof_s2_at_zeta), acc_gamma)

        let poscaz := add(aproof, proof_openings_selector_commit_api_at_zeta)
        let opca := add(mPtr, 0x200) // offset_proof_commits_api
        for {
          let i := 0
        } lt(i, vk_nb_commitments_commit_api) {
          i := add(i, 1)
        } {
          acc_gamma := mulmod(acc_gamma, l_gamma_kzg, r_mod)
          point_acc_mul(add(state, state_folded_digests_x), opca, acc_gamma, add(mPtr, offset))
          fr_acc_mul(add(state, state_folded_claimed_values), poscaz, acc_gamma)
          poscaz := add(poscaz, 0x20)
          opca := add(opca, 0x40)
        }
      }

      // generate the challenge (using Fiat Shamir) to fold the opening proofs
      // at ζ.
      // The process for deriving γ is the same as in derive_gamma but this time the inputs are
      // in this order (the [] means it's a commitment):
      // * ζ
      // * [H] ( = H₁ + ζᵐ⁺²*H₂ + ζ²⁽ᵐ⁺²⁾*H₃ )
      // * [Linearised polynomial]
      // * [L], [R], [O]
      // * [S₁] [S₂]
      // * [Pi_{i}] (wires associated to custom gates)
      // Then there are the purported evaluations of the previous committed polynomials:
      // * H(ζ)
      // * Linearised_polynomial(ζ)
      // * L(ζ), R(ζ), O(ζ), S₁(ζ), S₂(ζ)
      // * Pi_{i}(ζ)
      function compute_gamma_kzg(aproof) {
        let state := mload(0x40)
        let mPtr := add(mload(0x40), state_last_mem)
        mstore(mPtr, 0x67616d6d61) // "gamma"
        mstore(add(mPtr, 0x20), mload(add(state, state_zeta)))
        mstore(add(mPtr, 0x40), mload(add(state, state_folded_h_x)))
        mstore(add(mPtr, 0x60), mload(add(state, state_folded_h_y)))
        mstore(add(mPtr, 0x80), mload(add(state, state_linearised_polynomial_x)))
        mstore(add(mPtr, 0xa0), mload(add(state, state_linearised_polynomial_y)))
        mstore(add(mPtr, 0xc0), mload(add(aproof, proof_l_com_x)))
        mstore(add(mPtr, 0xe0), mload(add(aproof, proof_l_com_y)))
        mstore(add(mPtr, 0x100), mload(add(aproof, proof_r_com_x)))
        mstore(add(mPtr, 0x120), mload(add(aproof, proof_r_com_y)))
        mstore(add(mPtr, 0x140), mload(add(aproof, proof_o_com_x)))
        mstore(add(mPtr, 0x160), mload(add(aproof, proof_o_com_y)))
        mstore(add(mPtr, 0x180), vk_s1_com_x)
        mstore(add(mPtr, 0x1a0), vk_s1_com_y)
        mstore(add(mPtr, 0x1c0), vk_s2_com_x)
        mstore(add(mPtr, 0x1e0), vk_s2_com_y)

        let offset := 0x200

        mstore(add(mPtr, offset), vk_selector_commitments_commit_api_0_x)
        mstore(add(mPtr, add(offset, 0x20)), vk_selector_commitments_commit_api_0_y)
        offset := add(offset, 0x40)

        mstore(add(mPtr, offset), vk_selector_commitments_commit_api_1_x)
        mstore(add(mPtr, add(offset, 0x20)), vk_selector_commitments_commit_api_1_y)
        offset := add(offset, 0x40)

        mstore(add(mPtr, offset), vk_selector_commitments_commit_api_2_x)
        mstore(add(mPtr, add(offset, 0x20)), vk_selector_commitments_commit_api_2_y)
        offset := add(offset, 0x40)

        mstore(add(mPtr, offset), mload(add(aproof, proof_quotient_polynomial_at_zeta)))
        mstore(add(mPtr, add(offset, 0x20)), mload(add(aproof, proof_linearised_polynomial_at_zeta)))
        mstore(add(mPtr, add(offset, 0x40)), mload(add(aproof, proof_l_at_zeta)))
        mstore(add(mPtr, add(offset, 0x60)), mload(add(aproof, proof_r_at_zeta)))
        mstore(add(mPtr, add(offset, 0x80)), mload(add(aproof, proof_o_at_zeta)))
        mstore(add(mPtr, add(offset, 0xa0)), mload(add(aproof, proof_s1_at_zeta)))
        mstore(add(mPtr, add(offset, 0xc0)), mload(add(aproof, proof_s2_at_zeta)))

        let _mPtr := add(mPtr, add(offset, 0xe0))
        let _poscaz := add(aproof, proof_openings_selector_commit_api_at_zeta)
        for {
          let i := 0
        } lt(i, vk_nb_commitments_commit_api) {
          i := add(i, 1)
        } {
          mstore(_mPtr, mload(_poscaz))
          _poscaz := add(_poscaz, 0x20)
          _mPtr := add(_mPtr, 0x20)
        }

        let start_input := 0x1b // 00.."gamma"
        let size_input := add(0x16, mul(vk_nb_commitments_commit_api, 3)) // number of 32bytes elmts = 0x16 (zeta+2*7+7 for the digests+openings) + 2*vk_nb_commitments_commit_api (for the commitments of the selectors) + vk_nb_commitments_commit_api (for the openings of the selectors)
        size_input := add(0x5, mul(size_input, 0x20)) // size in bytes: 15*32 bytes + 5 bytes for gamma
        let check_staticcall := staticcall(
          sub(gas(), 2000),
          0x2,
          add(mPtr, start_input),
          size_input,
          add(state, state_gamma_kzg),
          0x20
        )
        if eq(check_staticcall, 0) {
          error_verify()
        }
        mstore(add(state, state_gamma_kzg), mod(mload(add(state, state_gamma_kzg)), r_mod))
      }

      function compute_commitment_linearised_polynomial_ec(aproof, s1, s2) {
        let state := mload(0x40)
        let mPtr := add(mload(0x40), state_last_mem)

        mstore(mPtr, vk_ql_com_x)
        mstore(add(mPtr, 0x20), vk_ql_com_y)
        point_mul(add(state, state_linearised_polynomial_x), mPtr, mload(add(aproof, proof_l_at_zeta)), add(mPtr, 0x40))

        mstore(mPtr, vk_qr_com_x)
        mstore(add(mPtr, 0x20), vk_qr_com_y)
        point_acc_mul(
          add(state, state_linearised_polynomial_x),
          mPtr,
          mload(add(aproof, proof_r_at_zeta)),
          add(mPtr, 0x40)
        )

        let rl := mulmod(mload(add(aproof, proof_l_at_zeta)), mload(add(aproof, proof_r_at_zeta)), r_mod)
        mstore(mPtr, vk_qm_com_x)
        mstore(add(mPtr, 0x20), vk_qm_com_y)
        point_acc_mul(add(state, state_linearised_polynomial_x), mPtr, rl, add(mPtr, 0x40))

        mstore(mPtr, vk_qo_com_x)
        mstore(add(mPtr, 0x20), vk_qo_com_y)
        point_acc_mul(
          add(state, state_linearised_polynomial_x),
          mPtr,
          mload(add(aproof, proof_o_at_zeta)),
          add(mPtr, 0x40)
        )

        mstore(mPtr, vk_qk_com_x)
        mstore(add(mPtr, 0x20), vk_qk_com_y)
        point_add(
          add(state, state_linearised_polynomial_x),
          add(state, state_linearised_polynomial_x),
          mPtr,
          add(mPtr, 0x40)
        )

        let commits_api_at_zeta := add(aproof, proof_openings_selector_commit_api_at_zeta)
        let commits_api := add(
          aproof,
          add(proof_openings_selector_commit_api_at_zeta, mul(vk_nb_commitments_commit_api, 0x20))
        )
        for {
          let i := 0
        } lt(i, vk_nb_commitments_commit_api) {
          i := add(i, 1)
        } {
          mstore(mPtr, mload(commits_api))
          mstore(add(mPtr, 0x20), mload(add(commits_api, 0x20)))
          point_acc_mul(add(state, state_linearised_polynomial_x), mPtr, mload(commits_api_at_zeta), add(mPtr, 0x40))
          commits_api_at_zeta := add(commits_api_at_zeta, 0x20)
          commits_api := add(commits_api, 0x40)
        }

        mstore(mPtr, vk_s3_com_x)
        mstore(add(mPtr, 0x20), vk_s3_com_y)
        point_acc_mul(add(state, state_linearised_polynomial_x), mPtr, s1, add(mPtr, 0x40))

        mstore(mPtr, mload(add(aproof, proof_grand_product_commitment_x)))
        mstore(add(mPtr, 0x20), mload(add(aproof, proof_grand_product_commitment_y)))
        point_acc_mul(add(state, state_linearised_polynomial_x), mPtr, s2, add(mPtr, 0x40))
      }

      // Compute the commitment to the linearized polynomial equal to
      //	L(ζ)[Qₗ]+r(ζ)[Qᵣ]+R(ζ)L(ζ)[Qₘ]+O(ζ)[Qₒ]+[Qₖ]+Σᵢqc'ᵢ(ζ)[BsbCommitmentᵢ] +
      //	α*( Z(μζ)(L(ζ)+β*S₁(ζ)+γ)*(R(ζ)+β*S₂(ζ)+γ)[S₃]-[Z](L(ζ)+β*id_{1}(ζ)+γ)*(R(ζ)+β*id_{2(ζ)+γ)*(O(ζ)+β*id_{3}(ζ)+γ) ) +
      //	α²*L₁(ζ)[Z]
      // where
      // * id_1 = id, id_2 = vk_coset_shift*id, id_3 = vk_coset_shift^{2}*id
      // * the [] means that it's a commitment (i.e. a point on Bn254(F_p))
      function compute_commitment_linearised_polynomial(aproof) {
        let state := mload(0x40)
        let l_beta := mload(add(state, state_beta))
        let l_gamma := mload(add(state, state_gamma))
        let l_zeta := mload(add(state, state_zeta))
        let l_alpha := mload(add(state, state_alpha))

        let u := mulmod(mload(add(aproof, proof_grand_product_at_zeta_omega)), l_beta, r_mod)
        let v := mulmod(l_beta, mload(add(aproof, proof_s1_at_zeta)), r_mod)
        v := addmod(v, mload(add(aproof, proof_l_at_zeta)), r_mod)
        v := addmod(v, l_gamma, r_mod)

        let w := mulmod(l_beta, mload(add(aproof, proof_s2_at_zeta)), r_mod)
        w := addmod(w, mload(add(aproof, proof_r_at_zeta)), r_mod)
        w := addmod(w, l_gamma, r_mod)

        let s1 := mulmod(u, v, r_mod)
        s1 := mulmod(s1, w, r_mod)
        s1 := mulmod(s1, l_alpha, r_mod)

        let coset_square := mulmod(vk_coset_shift, vk_coset_shift, r_mod)
        let betazeta := mulmod(l_beta, l_zeta, r_mod)
        u := addmod(betazeta, mload(add(aproof, proof_l_at_zeta)), r_mod)
        u := addmod(u, l_gamma, r_mod)

        v := mulmod(betazeta, vk_coset_shift, r_mod)
        v := addmod(v, mload(add(aproof, proof_r_at_zeta)), r_mod)
        v := addmod(v, l_gamma, r_mod)

        w := mulmod(betazeta, coset_square, r_mod)
        w := addmod(w, mload(add(aproof, proof_o_at_zeta)), r_mod)
        w := addmod(w, l_gamma, r_mod)

        let s2 := mulmod(u, v, r_mod)
        s2 := mulmod(s2, w, r_mod)
        s2 := sub(r_mod, s2)
        s2 := mulmod(s2, l_alpha, r_mod)
        s2 := addmod(s2, mload(add(state, state_alpha_square_lagrange_0)), r_mod)

        // at this stage:
        // * s₁ = α*Z(μζ)(l(ζ)+β*s₁(ζ)+γ)*(r(ζ)+β*s₂(ζ)+γ)*β
        // * s₂ = -α*(l(ζ)+β*ζ+γ)*(r(ζ)+β*u*ζ+γ)*(o(ζ)+β*u²*ζ+γ) + α²*L₁(ζ)

        compute_commitment_linearised_polynomial_ec(aproof, s1, s2)
      }

      // compute H₁ + ζᵐ⁺²*H₂ + ζ²⁽ᵐ⁺²⁾*H₃ and store the result at
      // state + state_folded_h
      function fold_h(aproof) {
        let state := mload(0x40)
        let n_plus_two := add(vk_domain_size, 2)
        let mPtr := add(mload(0x40), state_last_mem)
        let zeta_power_n_plus_two := pow(mload(add(state, state_zeta)), n_plus_two, mPtr)
        point_mul(add(state, state_folded_h_x), add(aproof, proof_h_2_x), zeta_power_n_plus_two, mPtr)
        point_add(add(state, state_folded_h_x), add(state, state_folded_h_x), add(aproof, proof_h_1_x), mPtr)
        point_mul(add(state, state_folded_h_x), add(state, state_folded_h_x), zeta_power_n_plus_two, mPtr)
        point_add(add(state, state_folded_h_x), add(state, state_folded_h_x), add(aproof, proof_h_0_x), mPtr)
      }

      // check that
      //	L(ζ)Qₗ(ζ)+r(ζ)Qᵣ(ζ)+R(ζ)L(ζ)Qₘ(ζ)+O(ζ)Qₒ(ζ)+Qₖ(ζ)+Σᵢqc'ᵢ(ζ)BsbCommitmentᵢ(ζ) +
      //  α*( Z(μζ)(l(ζ)+β*s₁(ζ)+γ)*(r(ζ)+β*s₂(ζ)+γ)*β*s₃(X)-Z(X)(l(ζ)+β*id_1(ζ)+γ)*(r(ζ)+β*id_2(ζ)+γ)*(o(ζ)+β*id_3(ζ)+γ) ) )
      // + α²*L₁(ζ) =
      // (ζⁿ-1)H(ζ)
      function verify_quotient_poly_eval_at_zeta(aproof) {
        let state := mload(0x40)

        // (l(ζ)+β*s1(ζ)+γ)
        let s1 := add(mload(0x40), state_last_mem)
        mstore(s1, mulmod(mload(add(aproof, proof_s1_at_zeta)), mload(add(state, state_beta)), r_mod))
        mstore(s1, addmod(mload(s1), mload(add(state, state_gamma)), r_mod))
        mstore(s1, addmod(mload(s1), mload(add(aproof, proof_l_at_zeta)), r_mod))

        // (r(ζ)+β*s2(ζ)+γ)
        let s2 := add(s1, 0x20)
        mstore(s2, mulmod(mload(add(aproof, proof_s2_at_zeta)), mload(add(state, state_beta)), r_mod))
        mstore(s2, addmod(mload(s2), mload(add(state, state_gamma)), r_mod))
        mstore(s2, addmod(mload(s2), mload(add(aproof, proof_r_at_zeta)), r_mod))
        // _s2 := mload(s2)

        // (o(ζ)+γ)
        let o := add(s1, 0x40)
        mstore(o, addmod(mload(add(aproof, proof_o_at_zeta)), mload(add(state, state_gamma)), r_mod))

        //  α*(Z(μζ))*(l(ζ)+β*s1(ζ)+γ)*(r(ζ)+β*s2(ζ)+γ)*(o(ζ)+γ)
        mstore(s1, mulmod(mload(s1), mload(s2), r_mod))
        mstore(s1, mulmod(mload(s1), mload(o), r_mod))
        mstore(s1, mulmod(mload(s1), mload(add(state, state_alpha)), r_mod))
        mstore(s1, mulmod(mload(s1), mload(add(aproof, proof_grand_product_at_zeta_omega)), r_mod))

        let computed_quotient := add(s1, 0x60)

        // linearizedpolynomial + pi(zeta)
        mstore(
          computed_quotient,
          addmod(mload(add(aproof, proof_linearised_polynomial_at_zeta)), mload(add(state, state_pi)), r_mod)
        )
        mstore(computed_quotient, addmod(mload(computed_quotient), mload(s1), r_mod))
        mstore(
          computed_quotient,
          addmod(mload(computed_quotient), sub(r_mod, mload(add(state, state_alpha_square_lagrange_0))), r_mod)
        )
        mstore(
          s2,
          mulmod(
            mload(add(aproof, proof_quotient_polynomial_at_zeta)),
            mload(add(state, state_zeta_power_n_minus_one)),
            r_mod
          )
        )

        mstore(add(state, state_success), eq(mload(computed_quotient), mload(s2)))
      }

      function point_add(dst, p, q, mPtr) {
        // let mPtr := add(mload(0x40), state_last_mem)
        let state := mload(0x40)
        mstore(mPtr, mload(p))
        mstore(add(mPtr, 0x20), mload(add(p, 0x20)))
        mstore(add(mPtr, 0x40), mload(q))
        mstore(add(mPtr, 0x60), mload(add(q, 0x20)))
        let l_success := staticcall(sub(gas(), 2000), 6, mPtr, 0x80, dst, 0x40)
        mstore(add(state, state_success), and(l_success, mload(add(state, state_success))))
      }

      // dst <- [s]src
      function point_mul(dst, src, s, mPtr) {
        // let mPtr := add(mload(0x40), state_last_mem)
        let state := mload(0x40)
        mstore(mPtr, mload(src))
        mstore(add(mPtr, 0x20), mload(add(src, 0x20)))
        mstore(add(mPtr, 0x40), s)
        let l_success := staticcall(sub(gas(), 2000), 7, mPtr, 0x60, dst, 0x40)
        mstore(add(state, state_success), and(l_success, mload(add(state, state_success))))
      }

      // dst <- dst + [s]src (Elliptic curve)
      function point_acc_mul(dst, src, s, mPtr) {
        let state := mload(0x40)
        mstore(mPtr, mload(src))
        mstore(add(mPtr, 0x20), mload(add(src, 0x20)))
        mstore(add(mPtr, 0x40), s)
        let l_success := staticcall(sub(gas(), 2000), 7, mPtr, 0x60, mPtr, 0x40)
        mstore(add(mPtr, 0x40), mload(dst))
        mstore(add(mPtr, 0x60), mload(add(dst, 0x20)))
        l_success := and(l_success, staticcall(sub(gas(), 2000), 6, mPtr, 0x80, dst, 0x40))
        mstore(add(state, state_success), and(l_success, mload(add(state, state_success))))
      }

      // dst <- dst + src (Fr) dst,src are addresses, s is a value
      function fr_acc_mul(dst, src, s) {
        let tmp := mulmod(mload(src), s, r_mod)
        mstore(dst, addmod(mload(dst), tmp, r_mod))
      }

      // dst <- x ** e mod r (x, e are values, not pointers)
      function pow(x, e, mPtr) -> res {
        mstore(mPtr, 0x20)
        mstore(add(mPtr, 0x20), 0x20)
        mstore(add(mPtr, 0x40), 0x20)
        mstore(add(mPtr, 0x60), x)
        mstore(add(mPtr, 0x80), e)
        mstore(add(mPtr, 0xa0), r_mod)
        let check_staticcall := staticcall(sub(gas(), 2000), 0x05, mPtr, 0xc0, mPtr, 0x20)
        if eq(check_staticcall, 0) {
          error_verify()
        }
        res := mload(mPtr)
      }
    }

    return success;
  }
}

// SPDX-License-Identifier: AGPL-3.0

// It has not been audited and is provided as-is, we make no guarantees or warranties to its safety and reliability.
//
// According to https://eprint.iacr.org/archive/2019/953/1585767119.pdf
pragma solidity ^0.8.19;

library Utils {
  uint256 private constant r_mod = 21888242871839275222246405745257275088548364400416034343698204186575808495617;

  /**
   * @dev ExpandMsgXmd expands msg to a slice of lenInBytes bytes.
   *      https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06#section-5
   *      https://tools.ietf.org/html/rfc8017#section-4.1 (I2OSP/O2ISP)
   */
  function expand_msg(uint256 x, uint256 y) public pure returns (uint8[48] memory res) {
    string memory dst = "BSB22-Plonk";

    //uint8[64] memory pad; // 64 is sha256 block size.
    // sha256(pad || msg || (0 || 48 || 0) || dst || 11)
    bytes memory tmp;
    uint8 zero = 0;
    uint8 lenInBytes = 48;
    uint8 sizeDomain = 11; // size of dst

    for (uint i = 0; i < 64; i++) {
      tmp = abi.encodePacked(tmp, zero);
    }
    tmp = abi.encodePacked(tmp, x, y, zero, lenInBytes, zero, dst, sizeDomain);
    bytes32 b0 = sha256(tmp);

    tmp = abi.encodePacked(b0, uint8(1), dst, sizeDomain);
    bytes32 b1 = sha256(tmp);
    for (uint i = 0; i < 32; i++) {
      res[i] = uint8(b1[i]);
    }

    tmp = abi.encodePacked(uint8(b0[0]) ^ uint8(b1[0]));
    for (uint i = 1; i < 32; i++) {
      tmp = abi.encodePacked(tmp, uint8(b0[i]) ^ uint8(b1[i]));
    }

    tmp = abi.encodePacked(tmp, uint8(2), dst, sizeDomain);
    b1 = sha256(tmp);

    // TODO handle the size of the dst (check gnark-crypto)
    for (uint i = 0; i < 16; i++) {
      res[i + 32] = uint8(b1[i]);
    }

    return res;
  }

  /**
   * @dev cf https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06#section-5.2
   * corresponds to https://github.com/ConsenSys/gnark-crypto/blob/develop/ecc/bn254/fr/element.go
   */
  function hash_fr(uint256 x, uint256 y) internal pure returns (uint256 res) {
    // interpret a as a bigEndian integer and reduce it mod r
    uint8[48] memory xmsg = expand_msg(x, y);
    // uint8[48] memory xmsg = [0x44, 0x74, 0xb5, 0x29, 0xd7, 0xfb, 0x29, 0x88, 0x3a, 0x7a, 0xc1, 0x65, 0xfd, 0x72, 0xce, 0xd0, 0xd4, 0xd1, 0x3f, 0x9e, 0x85, 0x8a, 0x3, 0x86, 0x1c, 0x90, 0x83, 0x1e, 0x94, 0xdc, 0xfc, 0x1d, 0x70, 0x82, 0xf5, 0xbf, 0x30, 0x3, 0x39, 0x87, 0x21, 0x38, 0x15, 0xed, 0x12, 0x75, 0x44, 0x6a];

    // reduce xmsg mod r, where xmsg is intrepreted in big endian
    // (as SetBytes does for golang's Big.Int library).
    for (uint i = 0; i < 32; i++) {
      res += uint256(xmsg[47 - i]) << (8 * i);
    }
    res = res % r_mod;
    uint256 tmp;
    for (uint i = 0; i < 16; i++) {
      tmp += uint256(xmsg[15 - i]) << (8 * i);
    }

    // 2**256%r
    uint256 b = 6350874878119819312338956282401532410528162663560392320966563075034087161851;
    assembly {
      tmp := mulmod(tmp, b, r_mod)
      res := addmod(res, tmp, r_mod)
    }

    return res;
  }
}

{
  "optimizer": {
    "enabled": true,
    "runs": 100000
  },
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "devdoc",
        "userdoc",
        "metadata",
        "abi"
      ]
    }
  },
  "libraries": {}
}

• No Contract Security Audit Submitted- Submit Audit Here

[{"inputs":[{"internalType":"bytes","name":"proof","type":"bytes"},{"internalType":"uint256[]","name":"public_inputs","type":"uint256[]"}],"name":"Verify","outputs":[{"internalType":"bool","name":"","type":"bool"}],"stateMutability":"view","type":"function"}]

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