/// contains [Nova](https://eprint.iacr.org/2021/370.pdf) related circuits
use ark_crypto_primitives::sponge::{
    constraints::CryptographicSpongeVar,
    poseidon::{constraints::PoseidonSpongeVar, PoseidonConfig, PoseidonSponge},
    Absorb,
};
use ark_ec::{CurveGroup, Group};
use ark_ff::PrimeField;
use ark_r1cs_std::{
    alloc::AllocVar,
    boolean::Boolean,
    eq::EqGadget,
    fields::{fp::FpVar, FieldVar},
    prelude::CurveVar,
    R1CSVar, ToConstraintFieldGadget,
};
use ark_relations::r1cs::{ConstraintSynthesizer, ConstraintSystemRef, SynthesisError};
use ark_std::{fmt::Debug, One, Zero};
use core::marker::PhantomData;

use super::{
    nifs::{
        nova_circuits::{CommittedInstanceVar, NIFSGadget},
        NIFSGadgetTrait,
    },
    CommittedInstance, NovaCycleFoldConfig,
};
use crate::folding::circuits::{
    cyclefold::{
        CycleFoldChallengeGadget, CycleFoldCommittedInstance, CycleFoldCommittedInstanceVar,
        CycleFoldConfig, NIFSFullGadget,
    },
    nonnative::{affine::NonNativeAffineVar, uint::NonNativeUintVar},
    CF1, CF2,
};
use crate::folding::traits::{CommittedInstanceVarOps, Dummy};
use crate::frontend::FCircuit;
use crate::transcript::AbsorbNonNativeGadget;

/// `AugmentedFCircuit` enhances the original step function `F`, so that it can
/// be used in recursive arguments such as IVC.
///
/// The method for converting `F` to `AugmentedFCircuit` (`F'`) is defined in
/// [Nova](https://eprint.iacr.org/2021/370.pdf), where `AugmentedFCircuit` not
/// only invokes `F`, but also adds additional constraints for verifying the
/// correct folding of primary instances (i.e., Nova's `CommittedInstance`s over
/// `C1`).
///
/// Furthermore, to reduce circuit size over `C2`, we implement the constraints
/// defined in [CycleFold](https://eprint.iacr.org/2023/1192.pdf). These extra
/// constraints verify the correct folding of CycleFold instances.
#[derive(Debug, Clone)]
pub struct AugmentedFCircuit<
    C1: CurveGroup,
    C2: CurveGroup,
    GC2: CurveVar<C2, CF2<C2>>,
    FC: FCircuit<CF1<C1>>,
> {
    pub(super) _gc2: PhantomData<GC2>,
    pub(super) poseidon_config: PoseidonConfig<CF1<C1>>,
    pub(super) pp_hash: Option<CF1<C1>>,
    pub(super) i: Option<CF1<C1>>,
    pub(super) i_usize: Option<usize>,
    pub(super) z_0: Option<Vec<C1::ScalarField>>,
    pub(super) z_i: Option<Vec<C1::ScalarField>>,
    pub(super) external_inputs: Option<Vec<C1::ScalarField>>,
    pub(super) u_i_cmW: Option<C1>,
    pub(super) U_i: Option<CommittedInstance<C1>>,
    pub(super) U_i1_cmE: Option<C1>,
    pub(super) U_i1_cmW: Option<C1>,
    pub(super) cmT: Option<C1>,
    pub(super) F: FC,              // F circuit
    pub(super) x: Option<CF1<C1>>, // public input (u_{i+1}.x[0])

    // cyclefold verifier on C1
    // Here 'cf1, cf2' are for each of the CycleFold circuits, corresponding to the fold of cmW and
    // cmE respectively
    pub(super) cf1_u_i_cmW: Option<C2>, // input
    pub(super) cf2_u_i_cmW: Option<C2>, // input
    pub(super) cf_U_i: Option<CycleFoldCommittedInstance<C2>>, // input
    pub(super) cf1_cmT: Option<C2>,
    pub(super) cf2_cmT: Option<C2>,
    pub(super) cf_x: Option<CF1<C1>>, // public input (u_{i+1}.x[1])
}

impl<C1: CurveGroup, C2: CurveGroup, GC2: CurveVar<C2, CF2<C2>>, FC: FCircuit<CF1<C1>>>
    AugmentedFCircuit<C1, C2, GC2, FC>
{
    pub fn empty(poseidon_config: &PoseidonConfig<CF1<C1>>, F_circuit: FC) -> Self {
        Self {
            _gc2: PhantomData,
            poseidon_config: poseidon_config.clone(),
            pp_hash: None,
            i: None,
            i_usize: None,
            z_0: None,
            z_i: None,
            external_inputs: None,
            u_i_cmW: None,
            U_i: None,
            U_i1_cmE: None,
            U_i1_cmW: None,
            cmT: None,
            F: F_circuit,
            x: None,
            // cyclefold values
            cf1_u_i_cmW: None,
            cf2_u_i_cmW: None,
            cf_U_i: None,
            cf1_cmT: None,
            cf2_cmT: None,
            cf_x: None,
        }
    }
}

impl<C1, C2, GC2, FC> ConstraintSynthesizer<CF1<C1>> for AugmentedFCircuit<C1, C2, GC2, FC>
where
    C1: CurveGroup,
    C2: CurveGroup,
    GC2: CurveVar<C2, CF2<C2>> + ToConstraintFieldGadget<CF2<C2>>,
    FC: FCircuit<CF1<C1>>,
    <C1 as CurveGroup>::BaseField: PrimeField,
    <C2 as CurveGroup>::BaseField: PrimeField,
    <C1 as Group>::ScalarField: Absorb,
    <C2 as Group>::ScalarField: Absorb,
    C1: CurveGroup<BaseField = C2::ScalarField, ScalarField = C2::BaseField>,
{
    fn generate_constraints(self, cs: ConstraintSystemRef<CF1<C1>>) -> Result<(), SynthesisError> {
        let pp_hash = FpVar::<CF1<C1>>::new_witness(cs.clone(), || {
            Ok(self.pp_hash.unwrap_or_else(CF1::<C1>::zero))
        })?;
        let i = FpVar::<CF1<C1>>::new_witness(cs.clone(), || {
            Ok(self.i.unwrap_or_else(CF1::<C1>::zero))
        })?;
        let z_0 = Vec::<FpVar<CF1<C1>>>::new_witness(cs.clone(), || {
            Ok(self
                .z_0
                .unwrap_or(vec![CF1::<C1>::zero(); self.F.state_len()]))
        })?;
        let z_i = Vec::<FpVar<CF1<C1>>>::new_witness(cs.clone(), || {
            Ok(self
                .z_i
                .unwrap_or(vec![CF1::<C1>::zero(); self.F.state_len()]))
        })?;
        let external_inputs = Vec::<FpVar<CF1<C1>>>::new_witness(cs.clone(), || {
            Ok(self
                .external_inputs
                .unwrap_or(vec![CF1::<C1>::zero(); self.F.external_inputs_len()]))
        })?;

        let u_dummy = CommittedInstance::dummy(2);
        let U_i = CommittedInstanceVar::<C1>::new_witness(cs.clone(), || {
            Ok(self.U_i.unwrap_or(u_dummy.clone()))
        })?;
        let U_i1_cmE = NonNativeAffineVar::new_witness(cs.clone(), || {
            Ok(self.U_i1_cmE.unwrap_or_else(C1::zero))
        })?;
        let U_i1_cmW = NonNativeAffineVar::new_witness(cs.clone(), || {
            Ok(self.U_i1_cmW.unwrap_or_else(C1::zero))
        })?;

        let cmT =
            NonNativeAffineVar::new_witness(cs.clone(), || Ok(self.cmT.unwrap_or_else(C1::zero)))?;

        let cf_u_dummy = CycleFoldCommittedInstance::dummy(NovaCycleFoldConfig::<C1>::IO_LEN);
        let cf_U_i = CycleFoldCommittedInstanceVar::<C2, GC2>::new_witness(cs.clone(), || {
            Ok(self.cf_U_i.unwrap_or(cf_u_dummy.clone()))
        })?;
        let cf1_cmT = GC2::new_witness(cs.clone(), || Ok(self.cf1_cmT.unwrap_or_else(C2::zero)))?;
        let cf2_cmT = GC2::new_witness(cs.clone(), || Ok(self.cf2_cmT.unwrap_or_else(C2::zero)))?;

        // `sponge` is for digest computation.
        let sponge = PoseidonSpongeVar::<C1::ScalarField>::new(cs.clone(), &self.poseidon_config);
        // `transcript` is for challenge generation.
        let mut transcript = sponge.clone();

        let is_basecase = i.is_zero()?;

        // Primary Part
        // P.1. Compute u_i.x
        // u_i.x[0] = H(i, z_0, z_i, U_i)
        let (u_i_x, U_i_vec) = U_i.clone().hash(&sponge, &pp_hash, &i, &z_0, &z_i)?;
        // u_i.x[1] = H(cf_U_i)
        let (cf_u_i_x, cf_U_i_vec) = cf_U_i.clone().hash(&sponge, pp_hash.clone())?;

        // P.2. Construct u_i
        let u_i = CommittedInstanceVar {
            // u_i.cmE = cm(0)
            cmE: NonNativeAffineVar::new_constant(cs.clone(), C1::zero())?,
            // u_i.u = 1
            u: FpVar::one(),
            // u_i.cmW is provided by the prover as witness
            cmW: NonNativeAffineVar::new_witness(cs.clone(), || {
                Ok(self.u_i_cmW.unwrap_or(C1::zero()))
            })?,
            // u_i.x is computed in step 1
            x: vec![u_i_x, cf_u_i_x],
        };

        // P.3. nifs.verify, obtains U_{i+1} by folding u_i & U_i.
        // Notice that NIFSGadget::verify does not fold cmE & cmW.
        // We set `U_i1.cmE` and `U_i1.cmW` to unconstrained witnesses `U_i1_cmE` and `U_i1_cmW`
        // respectively.
        // The correctness of them will be checked on the other curve.
        let (mut U_i1, r_bits) = NIFSGadget::<
            C1,
            PoseidonSponge<C1::ScalarField>,
            PoseidonSpongeVar<C1::ScalarField>,
        >::verify(
            &mut transcript,
            pp_hash.clone(),
            U_i.clone(),
            U_i_vec,
            u_i.clone(),
            Some(cmT.clone()),
        )?;
        U_i1.cmE = U_i1_cmE;
        U_i1.cmW = U_i1_cmW;

        // convert r_bits to a `NonNativeFieldVar`
        let r_nonnat = {
            let mut bits = r_bits;
            bits.resize(C1::BaseField::MODULUS_BIT_SIZE as usize, Boolean::FALSE);
            NonNativeUintVar::from(&bits)
        };

        // P.4.a compute and check the first output of F'

        // get z_{i+1} from the F circuit
        let i_usize = self.i_usize.unwrap_or(0);
        let z_i1 = self
            .F
            .generate_step_constraints(cs.clone(), i_usize, z_i, external_inputs)?;

        // Base case: u_{i+1}.x[0] == H((i+1, z_0, z_{i+1}, U_{\bot})
        // Non-base case: u_{i+1}.x[0] == H((i+1, z_0, z_{i+1}, U_{i+1})
        let (u_i1_x, _) = U_i1.clone().hash(
            &sponge,
            &pp_hash,
            &(i + FpVar::<CF1<C1>>::one()),
            &z_0,
            &z_i1,
        )?;
        let (u_i1_x_base, _) = CommittedInstanceVar::new_constant(cs.clone(), u_dummy)?.hash(
            &sponge,
            &pp_hash,
            &FpVar::<CF1<C1>>::one(),
            &z_0,
            &z_i1,
        )?;
        let x = FpVar::new_input(cs.clone(), || Ok(self.x.unwrap_or(u_i1_x_base.value()?)))?;
        x.enforce_equal(&is_basecase.select(&u_i1_x_base, &u_i1_x)?)?;

        // CycleFold part
        // C.1. Compute cf1_u_i.x and cf2_u_i.x
        let cfW_x = vec![
            r_nonnat.clone(),
            U_i.cmW.x,
            U_i.cmW.y,
            u_i.cmW.x,
            u_i.cmW.y,
            U_i1.cmW.x,
            U_i1.cmW.y,
        ];
        let cfE_x = vec![
            r_nonnat, U_i.cmE.x, U_i.cmE.y, cmT.x, cmT.y, U_i1.cmE.x, U_i1.cmE.y,
        ];

        // ensure that cf1_u & cf2_u have as public inputs the cmW & cmE from main instances U_i,
        // u_i, U_i+1 coordinates of the commitments
        // C.2. Construct `cf1_u_i` and `cf2_u_i`
        let cf1_u_i = CycleFoldCommittedInstanceVar {
            // cf1_u_i.cmE = 0
            cmE: GC2::zero(),
            // cf1_u_i.u = 1
            u: NonNativeUintVar::new_constant(cs.clone(), C1::BaseField::one())?,
            // cf1_u_i.cmW is provided by the prover as witness
            cmW: GC2::new_witness(cs.clone(), || Ok(self.cf1_u_i_cmW.unwrap_or(C2::zero())))?,
            // cf1_u_i.x is computed in step 1
            x: cfW_x,
        };
        let cf2_u_i = CycleFoldCommittedInstanceVar {
            // cf2_u_i.cmE = 0
            cmE: GC2::zero(),
            // cf2_u_i.u = 1
            u: NonNativeUintVar::new_constant(cs.clone(), C1::BaseField::one())?,
            // cf2_u_i.cmW is provided by the prover as witness
            cmW: GC2::new_witness(cs.clone(), || Ok(self.cf2_u_i_cmW.unwrap_or(C2::zero())))?,
            // cf2_u_i.x is computed in step 1
            x: cfE_x,
        };

        // C.3. nifs.verify, obtains cf1_U_{i+1} by folding cf1_u_i & cf_U_i, and then cf_U_{i+1}
        // by folding cf2_u_i & cf1_U_{i+1}.

        // compute cf1_r = H(cf1_u_i, cf_U_i, cf1_cmT)
        // cf_r_bits is denoted by rho* in the paper.
        let cf1_r_bits = CycleFoldChallengeGadget::<C2, GC2>::get_challenge_gadget(
            &mut transcript,
            pp_hash.clone(),
            cf_U_i_vec,
            cf1_u_i.clone(),
            cf1_cmT.clone(),
        )?;
        // Fold cf1_u_i & cf_U_i into cf1_U_{i+1}
        let cf1_U_i1 = NIFSFullGadget::<C2, GC2>::fold_committed_instance(
            cf1_r_bits, cf1_cmT, cf_U_i, cf1_u_i,
        )?;

        // same for cf2_r:
        let cf2_r_bits = CycleFoldChallengeGadget::<C2, GC2>::get_challenge_gadget(
            &mut transcript,
            pp_hash.clone(),
            cf1_U_i1.to_native_sponge_field_elements()?,
            cf2_u_i.clone(),
            cf2_cmT.clone(),
        )?;
        let cf_U_i1 = NIFSFullGadget::<C2, GC2>::fold_committed_instance(
            cf2_r_bits, cf2_cmT, cf1_U_i1, // the output from NIFS.V(cf1_r, cf_U, cfE_u)
            cf2_u_i,
        )?;

        // Back to Primary Part
        // P.4.b compute and check the second output of F'
        // Base case: u_{i+1}.x[1] == H(cf_U_{\bot})
        // Non-base case: u_{i+1}.x[1] == H(cf_U_{i+1})
        let (cf_u_i1_x, _) = cf_U_i1.clone().hash(&sponge, pp_hash.clone())?;
        let (cf_u_i1_x_base, _) =
            CycleFoldCommittedInstanceVar::<C2, GC2>::new_constant(cs.clone(), cf_u_dummy)?
                .hash(&sponge, pp_hash)?;
        let cf_x = FpVar::new_input(cs.clone(), || {
            Ok(self.cf_x.unwrap_or(cf_u_i1_x_base.value()?))
        })?;
        cf_x.enforce_equal(&is_basecase.select(&cf_u_i1_x_base, &cf_u_i1_x)?)?;

        Ok(())
    }
}

#[cfg(test)]
pub mod tests {
    use super::*;
    use ark_bn254::{Fr, G1Projective as Projective};
    use ark_crypto_primitives::sponge::{poseidon::PoseidonSponge, CryptographicSponge};
    use ark_ff::BigInteger;
    use ark_relations::r1cs::ConstraintSystem;
    use ark_std::UniformRand;

    use crate::folding::nova::nifs::nova::ChallengeGadget;
    use crate::transcript::poseidon::poseidon_canonical_config;

    // checks that the gadget and native implementations of the challenge computation match
    #[test]
    fn test_challenge_gadget() {
        let mut rng = ark_std::test_rng();
        let poseidon_config = poseidon_canonical_config::<Fr>();
        let mut transcript = PoseidonSponge::<Fr>::new(&poseidon_config);

        let u_i = CommittedInstance::<Projective> {
            cmE: Projective::rand(&mut rng),
            u: Fr::rand(&mut rng),
            cmW: Projective::rand(&mut rng),
            x: vec![Fr::rand(&mut rng); 1],
        };
        let U_i = CommittedInstance::<Projective> {
            cmE: Projective::rand(&mut rng),
            u: Fr::rand(&mut rng),
            cmW: Projective::rand(&mut rng),
            x: vec![Fr::rand(&mut rng); 1],
        };
        let cmT = Projective::rand(&mut rng);

        let pp_hash = Fr::from(42u32); // only for testing

        // compute the challenge natively
        let r_bits =
            ChallengeGadget::<Projective, CommittedInstance<Projective>>::get_challenge_native(
                &mut transcript,
                pp_hash,
                &U_i,
                &u_i,
                Some(&cmT),
            );
        let r = Fr::from_bigint(BigInteger::from_bits_le(&r_bits)).unwrap();

        let cs = ConstraintSystem::<Fr>::new_ref();
        let pp_hashVar = FpVar::<Fr>::new_witness(cs.clone(), || Ok(pp_hash)).unwrap();
        let u_iVar =
            CommittedInstanceVar::<Projective>::new_witness(cs.clone(), || Ok(u_i.clone()))
                .unwrap();
        let U_iVar =
            CommittedInstanceVar::<Projective>::new_witness(cs.clone(), || Ok(U_i.clone()))
                .unwrap();
        let cmTVar = NonNativeAffineVar::<Projective>::new_witness(cs.clone(), || Ok(cmT)).unwrap();
        let mut transcriptVar = PoseidonSpongeVar::<Fr>::new(cs.clone(), &poseidon_config);

        // compute the challenge in-circuit
        let U_iVar_vec = [
            vec![U_iVar.u.clone()],
            U_iVar.x.clone(),
            U_iVar.cmE.to_constraint_field().unwrap(),
            U_iVar.cmW.to_constraint_field().unwrap(),
        ]
        .concat();
        let r_bitsVar =
            ChallengeGadget::<Projective, CommittedInstance<Projective>>::get_challenge_gadget(
                &mut transcriptVar,
                pp_hashVar,
                U_iVar_vec,
                u_iVar,
                Some(cmTVar),
            )
            .unwrap();
        assert!(cs.is_satisfied().unwrap());

        // check that the natively computed and in-circuit computed hashes match
        let rVar = Boolean::le_bits_to_fp_var(&r_bitsVar).unwrap();
        assert_eq!(rVar.value().unwrap(), r);
        assert_eq!(r_bitsVar.value().unwrap(), r_bits);
    }
}