openvm_algebra_circuit/modular_chip/

is_eq.rs

use std::{
    array::{self, from_fn},
    borrow::{Borrow, BorrowMut},
};

use num_bigint::BigUint;
use openvm_algebra_transpiler::Rv32ModularArithmeticOpcode;
use openvm_circuit::{
    arch::*,
    system::memory::{
        online::{GuestMemory, TracingMemory},
        MemoryAuxColsFactory, POINTER_MAX_BITS,
    },
};
use openvm_circuit_primitives::{
    bigint::utils::big_uint_to_limbs,
    bitwise_op_lookup::{BitwiseOperationLookupBus, SharedBitwiseOperationLookupChip},
    is_equal_array::{IsEqArrayIo, IsEqArraySubAir},
    AlignedBytesBorrow, SubAir, TraceSubRowGenerator,
};
use openvm_circuit_primitives_derive::AlignedBorrow;
use openvm_instructions::{
    instruction::Instruction,
    program::DEFAULT_PC_STEP,
    riscv::{RV32_MEMORY_AS, RV32_REGISTER_AS, RV32_REGISTER_NUM_LIMBS},
    LocalOpcode,
};
use openvm_rv32_adapters::Rv32IsEqualModAdapterExecutor;
use openvm_stark_backend::{
    interaction::InteractionBuilder,
    p3_air::{AirBuilder, BaseAir},
    p3_field::{Field, FieldAlgebra, PrimeField32},
    rap::BaseAirWithPublicValues,
};

use crate::modular_chip::VmModularIsEqualExecutor;
// Given two numbers b and c, we want to prove that a) b == c or b != c, depending on
// result of cmp_result and b) b, c < N for some modulus N that is passed into the AIR
// at runtime (i.e. when chip is instantiated).

#[repr(C)]
#[derive(AlignedBorrow, Debug)]
pub struct ModularIsEqualCoreCols<T, const READ_LIMBS: usize> {
    pub is_valid: T,
    pub is_setup: T,
    pub b: [T; READ_LIMBS],
    pub c: [T; READ_LIMBS],
    pub cmp_result: T,

    // Auxiliary columns for subair EQ comparison between b and c.
    pub eq_marker: [T; READ_LIMBS],

    // Auxiliary columns to ensure both b and c are smaller than modulus N. Let b_diff_idx be
    // an index such that b[b_diff_idx] < N[b_diff_idx] and b[i] = N[i] for all i > b_diff_idx,
    // where larger indices correspond to more significant limbs. Such an index exists iff b < N.
    // Define c_diff_idx analogously. Then let b_lt_diff = N[b_diff_idx] - b[b_diff_idx] and
    // c_lt_diff = N[c_diff_idx] - c[c_diff_idx], where both must be in [0, 2^LIMB_BITS).
    //
    // To constrain the above, we will use lt_marker, which will indicate where b_diff_idx and
    // c_diff_idx are. Set lt_marker[b_diff_idx] = 1, lt_marker[c_diff_idx] = c_lt_mark, and 0
    // everywhere else. If b_diff_idx == c_diff_idx then c_lt_mark = 1, else c_lt_mark = 2. The
    // purpose of c_lt_mark is to handle the edge case where b_diff_idx == c_diff_idx (because
    // we cannot set lt_marker[b_diff_idx] to 1 and 2 at the same time).
    pub lt_marker: [T; READ_LIMBS],
    pub b_lt_diff: T,
    pub c_lt_diff: T,
    pub c_lt_mark: T,
}

#[derive(Clone, Debug)]
pub struct ModularIsEqualCoreAir<
    const READ_LIMBS: usize,
    const WRITE_LIMBS: usize,
    const LIMB_BITS: usize,
> {
    pub bus: BitwiseOperationLookupBus,
    pub subair: IsEqArraySubAir<READ_LIMBS>,
    pub modulus_limbs: [u32; READ_LIMBS],
    pub offset: usize,
}

impl<const READ_LIMBS: usize, const WRITE_LIMBS: usize, const LIMB_BITS: usize>
    ModularIsEqualCoreAir<READ_LIMBS, WRITE_LIMBS, LIMB_BITS>
{
    pub fn new(modulus: BigUint, bus: BitwiseOperationLookupBus, offset: usize) -> Self {
        let mod_vec = big_uint_to_limbs(&modulus, LIMB_BITS);
        assert!(mod_vec.len() <= READ_LIMBS);
        let modulus_limbs = array::from_fn(|i| {
            if i < mod_vec.len() {
                mod_vec[i] as u32
            } else {
                0
            }
        });
        Self {
            bus,
            subair: IsEqArraySubAir::<READ_LIMBS>,
            modulus_limbs,
            offset,
        }
    }
}

impl<F: Field, const READ_LIMBS: usize, const WRITE_LIMBS: usize, const LIMB_BITS: usize> BaseAir<F>
    for ModularIsEqualCoreAir<READ_LIMBS, WRITE_LIMBS, LIMB_BITS>
{
    fn width(&self) -> usize {
        ModularIsEqualCoreCols::<F, READ_LIMBS>::width()
    }
}
impl<F: Field, const READ_LIMBS: usize, const WRITE_LIMBS: usize, const LIMB_BITS: usize>
    BaseAirWithPublicValues<F> for ModularIsEqualCoreAir<READ_LIMBS, WRITE_LIMBS, LIMB_BITS>
{
}

impl<AB, I, const READ_LIMBS: usize, const WRITE_LIMBS: usize, const LIMB_BITS: usize>
    VmCoreAir<AB, I> for ModularIsEqualCoreAir<READ_LIMBS, WRITE_LIMBS, LIMB_BITS>
where
    AB: InteractionBuilder,
    I: VmAdapterInterface<AB::Expr>,
    I::Reads: From<[[AB::Expr; READ_LIMBS]; 2]>,
    I::Writes: From<[[AB::Expr; WRITE_LIMBS]; 1]>,
    I::ProcessedInstruction: From<MinimalInstruction<AB::Expr>>,
{
    fn eval(
        &self,
        builder: &mut AB,
        local_core: &[AB::Var],
        _from_pc: AB::Var,
    ) -> AdapterAirContext<AB::Expr, I> {
        let cols: &ModularIsEqualCoreCols<_, READ_LIMBS> = local_core.borrow();

        builder.assert_bool(cols.is_valid);
        builder.assert_bool(cols.is_setup);
        builder.when(cols.is_setup).assert_one(cols.is_valid);
        builder.assert_bool(cols.cmp_result);

        // Constrain that either b == c or b != c, depending on the value of cmp_result.
        let eq_subair_io = IsEqArrayIo {
            x: cols.b.map(Into::into),
            y: cols.c.map(Into::into),
            out: cols.cmp_result.into(),
            condition: cols.is_valid - cols.is_setup,
        };
        self.subair.eval(builder, (eq_subair_io, cols.eq_marker));

        // Constrain that auxiliary columns lt_columns and c_lt_mark are as defined above.
        // When c_lt_mark is 1, lt_marker should have exactly one index i where lt_marker[i]
        // is 1, and be 0 elsewhere. When c_lt_mark is 2, lt_marker[i] should have an
        // additional index j such that lt_marker[j] is 2. To constrain this:
        //
        // * When c_lt_mark = 1 the sum of all lt_marker[i] must be 1
        // * When c_lt_mark = 2 the sum of lt_marker[i] * (lt_marker[i] - 1) must be 2.
        //   Additionally, the sum of all lt_marker[i] must be 3.
        //
        // All this doesn't apply when is_setup.
        let lt_marker_sum = cols
            .lt_marker
            .iter()
            .fold(AB::Expr::ZERO, |acc, x| acc + *x);
        let lt_marker_one_check_sum = cols
            .lt_marker
            .iter()
            .fold(AB::Expr::ZERO, |acc, x| acc + (*x) * (*x - AB::F::ONE));

        // Constrain that c_lt_mark is either 1 or 2.
        builder
            .when(cols.is_valid - cols.is_setup)
            .assert_bool(cols.c_lt_mark - AB::F::ONE);

        // If c_lt_mark is 1, then lt_marker_sum is 1
        builder
            .when(cols.is_valid - cols.is_setup)
            .when_ne(cols.c_lt_mark, AB::F::from_canonical_u8(2))
            .assert_one(lt_marker_sum.clone());

        // If c_lt_mark is 2, then lt_marker_sum is 3
        builder
            .when(cols.is_valid - cols.is_setup)
            .when_ne(cols.c_lt_mark, AB::F::ONE)
            .assert_eq(lt_marker_sum.clone(), AB::F::from_canonical_u8(3));

        // This constraint, along with the constraint (below) that lt_marker[i] is 0, 1, or 2,
        // ensures that lt_marker has exactly one 2.
        builder.when_ne(cols.c_lt_mark, AB::F::ONE).assert_eq(
            lt_marker_one_check_sum,
            cols.is_valid * AB::F::from_canonical_u8(2),
        );

        // Handle the setup row constraints.
        // When is_setup = 1, constrain c_lt_mark = 2 and lt_marker_sum = 2
        // This ensures that lt_marker has exactly one 2 and the remaining entries are 0.
        // Since lt_marker has no 1, we will end up constraining that b[i] = N[i] for all i
        // instead of just for i > b_diff_idx.
        builder
            .when(cols.is_setup)
            .assert_eq(cols.c_lt_mark, AB::F::from_canonical_u8(2));
        builder
            .when(cols.is_setup)
            .assert_eq(lt_marker_sum.clone(), AB::F::from_canonical_u8(2));

        // Constrain that b, c < N (i.e. modulus).
        let modulus = self.modulus_limbs.map(AB::F::from_canonical_u32);
        let mut prefix_sum = AB::Expr::ZERO;

        for i in (0..READ_LIMBS).rev() {
            prefix_sum += cols.lt_marker[i].into();
            builder.assert_zero(
                cols.lt_marker[i]
                    * (cols.lt_marker[i] - AB::F::ONE)
                    * (cols.lt_marker[i] - cols.c_lt_mark),
            );

            // Constrain b < N.
            // First, we constrain b[i] = N[i] for i > b_diff_idx.
            // We do this by constraining that b[i] = N[i] when prefix_sum is not 1 or
            // lt_marker_sum.
            //  - If is_setup = 0, then lt_marker_sum is either 1 or 3. In this case, prefix_sum is
            //    0, 1, 2, or 3. It can be verified by casework that i > b_diff_idx iff prefix_sum
            //    is not 1 or lt_marker_sum.
            //  - If is_setup = 1, then we want to constrain b[i] = N[i] for all i. In this case,
            //    lt_marker_sum is 2 and prefix_sum is 0 or 2. So we constrain b[i] = N[i] when
            //    prefix_sum is not 1, which works.
            builder
                .when_ne(prefix_sum.clone(), AB::F::ONE)
                .when_ne(prefix_sum.clone(), lt_marker_sum.clone() - cols.is_setup)
                .assert_eq(cols.b[i], modulus[i]);
            // Note that lt_marker[i] is either 0, 1, or 2 and lt_marker[i] being 1 indicates b[i] <
            // N[i] (i.e. i == b_diff_idx).
            builder
                .when_ne(cols.lt_marker[i], AB::F::ZERO)
                .when_ne(cols.lt_marker[i], AB::F::from_canonical_u8(2))
                .assert_eq(AB::Expr::from(modulus[i]) - cols.b[i], cols.b_lt_diff);

            // Constrain c < N.
            // First, we constrain c[i] = N[i] for i > c_diff_idx.
            // We do this by constraining that c[i] = N[i] when prefix_sum is not c_lt_mark or
            // lt_marker_sum. It can be verified by casework that i > c_diff_idx iff
            // prefix_sum is not c_lt_mark or lt_marker_sum.
            builder
                .when_ne(prefix_sum.clone(), cols.c_lt_mark)
                .when_ne(prefix_sum.clone(), lt_marker_sum.clone())
                .assert_eq(cols.c[i], modulus[i]);
            // Note that lt_marker[i] is either 0, 1, or 2 and lt_marker[i] being c_lt_mark
            // indicates c[i] < N[i] (i.e. i == c_diff_idx). Since c_lt_mark is 1 or 2,
            // we have {0, 1, 2} \ {0, 3 - c_lt_mark} = {c_lt_mark}.
            builder
                .when_ne(cols.lt_marker[i], AB::F::ZERO)
                .when_ne(
                    cols.lt_marker[i],
                    AB::Expr::from_canonical_u8(3) - cols.c_lt_mark,
                )
                .assert_eq(AB::Expr::from(modulus[i]) - cols.c[i], cols.c_lt_diff);
        }

        // Check that b_lt_diff and c_lt_diff are positive
        self.bus
            .send_range(
                cols.b_lt_diff - AB::Expr::ONE,
                cols.c_lt_diff - AB::Expr::ONE,
            )
            .eval(builder, cols.is_valid - cols.is_setup);

        let expected_opcode = AB::Expr::from_canonical_usize(self.offset)
            + cols.is_setup
                * AB::Expr::from_canonical_usize(Rv32ModularArithmeticOpcode::SETUP_ISEQ as usize)
            + (AB::Expr::ONE - cols.is_setup)
                * AB::Expr::from_canonical_usize(Rv32ModularArithmeticOpcode::IS_EQ as usize);
        let mut a: [AB::Expr; WRITE_LIMBS] = array::from_fn(|_| AB::Expr::ZERO);
        a[0] = cols.cmp_result.into();

        AdapterAirContext {
            to_pc: None,
            reads: [cols.b.map(Into::into), cols.c.map(Into::into)].into(),
            writes: [a].into(),
            instruction: MinimalInstruction {
                is_valid: cols.is_valid.into(),
                opcode: expected_opcode,
            }
            .into(),
        }
    }

    fn start_offset(&self) -> usize {
        self.offset
    }
}

#[repr(C)]
#[derive(AlignedBytesBorrow, Debug)]
pub struct ModularIsEqualRecord<const READ_LIMBS: usize> {
    pub is_setup: bool,
    pub b: [u8; READ_LIMBS],
    pub c: [u8; READ_LIMBS],
}

#[derive(derive_new::new, Clone)]
pub struct ModularIsEqualExecutor<
    A,
    const READ_LIMBS: usize,
    const WRITE_LIMBS: usize,
    const LIMB_BITS: usize,
> {
    adapter: A,
    pub offset: usize,
    pub modulus_limbs: [u8; READ_LIMBS],
}

#[derive(derive_new::new, Clone)]
pub struct ModularIsEqualFiller<
    A,
    const READ_LIMBS: usize,
    const WRITE_LIMBS: usize,
    const LIMB_BITS: usize,
> {
    adapter: A,
    pub offset: usize,
    pub modulus_limbs: [u8; READ_LIMBS],
    pub bitwise_lookup_chip: SharedBitwiseOperationLookupChip<LIMB_BITS>,
}

impl<F, A, RA, const READ_LIMBS: usize, const WRITE_LIMBS: usize, const LIMB_BITS: usize>
    PreflightExecutor<F, RA> for ModularIsEqualExecutor<A, READ_LIMBS, WRITE_LIMBS, LIMB_BITS>
where
    F: PrimeField32,
    A: 'static
        + AdapterTraceExecutor<
            F,
            ReadData: Into<[[u8; READ_LIMBS]; 2]>,
            WriteData: From<[u8; WRITE_LIMBS]>,
        >,
    for<'buf> RA: RecordArena<
        'buf,
        EmptyAdapterCoreLayout<F, A>,
        (
            A::RecordMut<'buf>,
            &'buf mut ModularIsEqualRecord<READ_LIMBS>,
        ),
    >,
{
    fn execute(
        &self,
        state: VmStateMut<F, TracingMemory, RA>,
        instruction: &Instruction<F>,
    ) -> Result<(), ExecutionError> {
        let Instruction { opcode, .. } = instruction;

        let local_opcode =
            Rv32ModularArithmeticOpcode::from_usize(opcode.local_opcode_idx(self.offset));
        matches!(
            local_opcode,
            Rv32ModularArithmeticOpcode::IS_EQ | Rv32ModularArithmeticOpcode::SETUP_ISEQ
        );

        let (mut adapter_record, core_record) = state.ctx.alloc(EmptyAdapterCoreLayout::new());

        A::start(*state.pc, state.memory, &mut adapter_record);
        [core_record.b, core_record.c] = self
            .adapter
            .read(state.memory, instruction, &mut adapter_record)
            .into();

        core_record.is_setup = instruction.opcode.local_opcode_idx(self.offset)
            == Rv32ModularArithmeticOpcode::SETUP_ISEQ as usize;

        let mut write_data = [0u8; WRITE_LIMBS];
        write_data[0] = (core_record.b == core_record.c) as u8;

        self.adapter.write(
            state.memory,
            instruction,
            write_data.into(),
            &mut adapter_record,
        );

        *state.pc = state.pc.wrapping_add(DEFAULT_PC_STEP);

        Ok(())
    }

    fn get_opcode_name(&self, opcode: usize) -> String {
        format!(
            "{:?}",
            Rv32ModularArithmeticOpcode::from_usize(opcode - self.offset)
        )
    }
}

impl<F, A, const READ_LIMBS: usize, const WRITE_LIMBS: usize, const LIMB_BITS: usize> TraceFiller<F>
    for ModularIsEqualFiller<A, READ_LIMBS, WRITE_LIMBS, LIMB_BITS>
where
    F: PrimeField32,
    A: 'static + AdapterTraceFiller<F>,
{
    fn fill_trace_row(&self, mem_helper: &MemoryAuxColsFactory<F>, row_slice: &mut [F]) {
        let (adapter_row, mut core_row) = row_slice.split_at_mut(A::WIDTH);
        self.adapter.fill_trace_row(mem_helper, adapter_row);
        // SAFETY:
        // - row_slice is guaranteed by the caller to have at least A::WIDTH +
        //   ModularIsEqualCoreCols::width() elements
        // - caller ensures core_row contains a valid record written by the executor during trace
        //   generation
        let record: &ModularIsEqualRecord<READ_LIMBS> =
            unsafe { get_record_from_slice(&mut core_row, ()) };
        let cols: &mut ModularIsEqualCoreCols<F, READ_LIMBS> = core_row.borrow_mut();
        let (b_cmp, b_diff_idx) =
            run_unsigned_less_than::<READ_LIMBS>(&record.b, &self.modulus_limbs);
        let (c_cmp, c_diff_idx) =
            run_unsigned_less_than::<READ_LIMBS>(&record.c, &self.modulus_limbs);

        if !record.is_setup {
            assert!(b_cmp, "{:?} >= {:?}", record.b, self.modulus_limbs);
        }
        assert!(c_cmp, "{:?} >= {:?}", record.c, self.modulus_limbs);

        // Writing in reverse order
        cols.c_lt_mark = if b_diff_idx == c_diff_idx {
            F::ONE
        } else {
            F::TWO
        };

        cols.c_lt_diff =
            F::from_canonical_u8(self.modulus_limbs[c_diff_idx] - record.c[c_diff_idx]);
        if !record.is_setup {
            cols.b_lt_diff =
                F::from_canonical_u8(self.modulus_limbs[b_diff_idx] - record.b[b_diff_idx]);
            self.bitwise_lookup_chip.request_range(
                (self.modulus_limbs[b_diff_idx] - record.b[b_diff_idx] - 1) as u32,
                (self.modulus_limbs[c_diff_idx] - record.c[c_diff_idx] - 1) as u32,
            );
        } else {
            cols.b_lt_diff = F::ZERO;
        }

        cols.lt_marker = from_fn(|i| {
            if i == b_diff_idx {
                F::ONE
            } else if i == c_diff_idx {
                cols.c_lt_mark
            } else {
                F::ZERO
            }
        });

        cols.c = record.c.map(F::from_canonical_u8);
        cols.b = record.b.map(F::from_canonical_u8);
        let sub_air = IsEqArraySubAir::<READ_LIMBS>;
        sub_air.generate_subrow(
            (&cols.b, &cols.c),
            (&mut cols.eq_marker, &mut cols.cmp_result),
        );

        cols.is_setup = F::from_bool(record.is_setup);
        cols.is_valid = F::ONE;
    }
}

impl<const NUM_LANES: usize, const LANE_SIZE: usize, const TOTAL_LIMBS: usize>
    VmModularIsEqualExecutor<NUM_LANES, LANE_SIZE, TOTAL_LIMBS>
{
    pub fn new(
        adapter: Rv32IsEqualModAdapterExecutor<2, NUM_LANES, LANE_SIZE, TOTAL_LIMBS>,
        offset: usize,
        modulus_limbs: [u8; TOTAL_LIMBS],
    ) -> Self {
        Self(ModularIsEqualExecutor::new(adapter, offset, modulus_limbs))
    }
}

#[derive(AlignedBytesBorrow, Clone)]
#[repr(C)]
struct ModularIsEqualPreCompute<const READ_LIMBS: usize> {
    a: u8,
    rs_addrs: [u8; 2],
    modulus_limbs: [u8; READ_LIMBS],
}

impl<const NUM_LANES: usize, const LANE_SIZE: usize, const TOTAL_READ_SIZE: usize>
    VmModularIsEqualExecutor<NUM_LANES, LANE_SIZE, TOTAL_READ_SIZE>
{
    fn pre_compute_impl<F: PrimeField32>(
        &self,
        pc: u32,
        inst: &Instruction<F>,
        data: &mut ModularIsEqualPreCompute<TOTAL_READ_SIZE>,
    ) -> Result<bool, StaticProgramError> {
        let Instruction {
            opcode,
            a,
            b,
            c,
            d,
            e,
            ..
        } = inst;

        let local_opcode =
            Rv32ModularArithmeticOpcode::from_usize(opcode.local_opcode_idx(self.0.offset));

        // Validate instruction format
        let a = a.as_canonical_u32();
        let b = b.as_canonical_u32();
        let c = c.as_canonical_u32();
        let d = d.as_canonical_u32();
        let e = e.as_canonical_u32();
        if d != RV32_REGISTER_AS || e != RV32_MEMORY_AS {
            return Err(StaticProgramError::InvalidInstruction(pc));
        }

        if !matches!(
            local_opcode,
            Rv32ModularArithmeticOpcode::IS_EQ | Rv32ModularArithmeticOpcode::SETUP_ISEQ
        ) {
            return Err(StaticProgramError::InvalidInstruction(pc));
        }

        let rs_addrs = from_fn(|i| if i == 0 { b } else { c } as u8);
        *data = ModularIsEqualPreCompute {
            a: a as u8,
            rs_addrs,
            modulus_limbs: self.0.modulus_limbs,
        };

        let is_setup = local_opcode == Rv32ModularArithmeticOpcode::SETUP_ISEQ;

        Ok(is_setup)
    }
}

macro_rules! dispatch {
    ($execute_impl:ident, $is_setup:ident) => {
        Ok(if $is_setup {
            $execute_impl::<_, _, NUM_LANES, LANE_SIZE, TOTAL_READ_SIZE, true>
        } else {
            $execute_impl::<_, _, NUM_LANES, LANE_SIZE, TOTAL_READ_SIZE, false>
        })
    };
}

impl<F, const NUM_LANES: usize, const LANE_SIZE: usize, const TOTAL_READ_SIZE: usize> Executor<F>
    for VmModularIsEqualExecutor<NUM_LANES, LANE_SIZE, TOTAL_READ_SIZE>
where
    F: PrimeField32,
{
    #[inline(always)]
    fn pre_compute_size(&self) -> usize {
        std::mem::size_of::<ModularIsEqualPreCompute<TOTAL_READ_SIZE>>()
    }

    fn pre_compute<Ctx: ExecutionCtxTrait>(
        &self,
        pc: u32,
        inst: &Instruction<F>,
        data: &mut [u8],
    ) -> Result<ExecuteFunc<F, Ctx>, StaticProgramError> {
        let pre_compute: &mut ModularIsEqualPreCompute<TOTAL_READ_SIZE> = data.borrow_mut();
        let is_setup = self.pre_compute_impl(pc, inst, pre_compute)?;

        dispatch!(execute_e1_impl, is_setup)
    }

    #[cfg(feature = "tco")]
    fn handler<Ctx>(
        &self,
        pc: u32,
        inst: &Instruction<F>,
        data: &mut [u8],
    ) -> Result<Handler<F, Ctx>, StaticProgramError>
    where
        Ctx: ExecutionCtxTrait,
    {
        let pre_compute: &mut ModularIsEqualPreCompute<TOTAL_READ_SIZE> = data.borrow_mut();
        let is_setup = self.pre_compute_impl(pc, inst, pre_compute)?;

        dispatch!(execute_e1_tco_handler, is_setup)
    }
}

impl<F, const NUM_LANES: usize, const LANE_SIZE: usize, const TOTAL_READ_SIZE: usize>
    MeteredExecutor<F> for VmModularIsEqualExecutor<NUM_LANES, LANE_SIZE, TOTAL_READ_SIZE>
where
    F: PrimeField32,
{
    #[inline(always)]
    fn metered_pre_compute_size(&self) -> usize {
        std::mem::size_of::<E2PreCompute<ModularIsEqualPreCompute<TOTAL_READ_SIZE>>>()
    }

    fn metered_pre_compute<Ctx: MeteredExecutionCtxTrait>(
        &self,
        chip_idx: usize,
        pc: u32,
        inst: &Instruction<F>,
        data: &mut [u8],
    ) -> Result<ExecuteFunc<F, Ctx>, StaticProgramError> {
        let pre_compute: &mut E2PreCompute<ModularIsEqualPreCompute<TOTAL_READ_SIZE>> =
            data.borrow_mut();
        pre_compute.chip_idx = chip_idx as u32;

        let is_setup = self.pre_compute_impl(pc, inst, &mut pre_compute.data)?;

        dispatch!(execute_e2_impl, is_setup)
    }

    #[cfg(feature = "tco")]
    fn metered_handler<Ctx: MeteredExecutionCtxTrait>(
        &self,
        chip_idx: usize,
        pc: u32,
        inst: &Instruction<F>,
        data: &mut [u8],
    ) -> Result<Handler<F, Ctx>, StaticProgramError> {
        let pre_compute: &mut E2PreCompute<ModularIsEqualPreCompute<TOTAL_READ_SIZE>> =
            data.borrow_mut();
        pre_compute.chip_idx = chip_idx as u32;

        let is_setup = self.pre_compute_impl(pc, inst, &mut pre_compute.data)?;

        dispatch!(execute_e2_tco_handler, is_setup)
    }
}

#[create_tco_handler]
unsafe fn execute_e1_impl<
    F: PrimeField32,
    CTX: ExecutionCtxTrait,
    const NUM_LANES: usize,
    const LANE_SIZE: usize,
    const TOTAL_READ_SIZE: usize,
    const IS_SETUP: bool,
>(
    pre_compute: &[u8],
    vm_state: &mut VmExecState<F, GuestMemory, CTX>,
) {
    let pre_compute: &ModularIsEqualPreCompute<TOTAL_READ_SIZE> = pre_compute.borrow();

    execute_e12_impl::<_, _, NUM_LANES, LANE_SIZE, TOTAL_READ_SIZE, IS_SETUP>(
        pre_compute,
        vm_state,
    );
}

#[create_tco_handler]
unsafe fn execute_e2_impl<
    F: PrimeField32,
    CTX: MeteredExecutionCtxTrait,
    const NUM_LANES: usize,
    const LANE_SIZE: usize,
    const TOTAL_READ_SIZE: usize,
    const IS_SETUP: bool,
>(
    pre_compute: &[u8],
    vm_state: &mut VmExecState<F, GuestMemory, CTX>,
) {
    let pre_compute: &E2PreCompute<ModularIsEqualPreCompute<TOTAL_READ_SIZE>> =
        pre_compute.borrow();
    vm_state
        .ctx
        .on_height_change(pre_compute.chip_idx as usize, 1);
    execute_e12_impl::<_, _, NUM_LANES, LANE_SIZE, TOTAL_READ_SIZE, IS_SETUP>(
        &pre_compute.data,
        vm_state,
    );
}

unsafe fn execute_e12_impl<
    F: PrimeField32,
    CTX: ExecutionCtxTrait,
    const NUM_LANES: usize,
    const LANE_SIZE: usize,
    const TOTAL_READ_SIZE: usize,
    const IS_SETUP: bool,
>(
    pre_compute: &ModularIsEqualPreCompute<TOTAL_READ_SIZE>,
    vm_state: &mut VmExecState<F, GuestMemory, CTX>,
) {
    // Read register values
    let rs_vals = pre_compute
        .rs_addrs
        .map(|addr| u32::from_le_bytes(vm_state.vm_read(RV32_REGISTER_AS, addr as u32)));

    // Read memory values
    let [b, c]: [[u8; TOTAL_READ_SIZE]; 2] = rs_vals.map(|address| {
        debug_assert!(address as usize + TOTAL_READ_SIZE - 1 < (1 << POINTER_MAX_BITS));
        from_fn::<_, NUM_LANES, _>(|i| {
            vm_state.vm_read::<_, LANE_SIZE>(RV32_MEMORY_AS, address + (i * LANE_SIZE) as u32)
        })
        .concat()
        .try_into()
        .unwrap()
    });

    if !IS_SETUP {
        let (b_cmp, _) = run_unsigned_less_than::<TOTAL_READ_SIZE>(&b, &pre_compute.modulus_limbs);
        debug_assert!(b_cmp, "{:?} >= {:?}", b, pre_compute.modulus_limbs);
    }

    let (c_cmp, _) = run_unsigned_less_than::<TOTAL_READ_SIZE>(&c, &pre_compute.modulus_limbs);
    debug_assert!(c_cmp, "{:?} >= {:?}", c, pre_compute.modulus_limbs);

    // Compute result
    let mut write_data = [0u8; RV32_REGISTER_NUM_LIMBS];
    write_data[0] = (b == c) as u8;

    // Write result to register
    vm_state.vm_write(RV32_REGISTER_AS, pre_compute.a as u32, &write_data);

    vm_state.pc = vm_state.pc.wrapping_add(DEFAULT_PC_STEP);
    vm_state.instret += 1;
}

// Returns (cmp_result, diff_idx)
#[inline(always)]
pub(super) fn run_unsigned_less_than<const NUM_LIMBS: usize>(
    x: &[u8; NUM_LIMBS],
    y: &[u8; NUM_LIMBS],
) -> (bool, usize) {
    for i in (0..NUM_LIMBS).rev() {
        if x[i] != y[i] {
            return (x[i] < y[i], i);
        }
    }
    (false, NUM_LIMBS)
}