plonky2/u32/src/gates/subtraction_u32.rs

use alloc::boxed::Box;
use alloc::string::String;
use alloc::vec::Vec;
use alloc::{format, vec};
use core::marker::PhantomData;

use plonky2::field::extension::Extendable;
use plonky2::field::packed::PackedField;
use plonky2::field::types::Field;
use plonky2::gates::gate::Gate;
use plonky2::gates::packed_util::PackedEvaluableBase;
use plonky2::gates::util::StridedConstraintConsumer;
use plonky2::hash::hash_types::RichField;
use plonky2::iop::ext_target::ExtensionTarget;
use plonky2::iop::generator::{GeneratedValues, SimpleGenerator, WitnessGenerator};
use plonky2::iop::target::Target;
use plonky2::iop::wire::Wire;
use plonky2::iop::witness::{PartitionWitness, Witness, WitnessWrite};
use plonky2::plonk::circuit_builder::CircuitBuilder;
use plonky2::plonk::circuit_data::CircuitConfig;
use plonky2::plonk::vars::{
    EvaluationTargets, EvaluationVars, EvaluationVarsBase, EvaluationVarsBaseBatch,
    EvaluationVarsBasePacked,
};

/// A gate to perform a subtraction on 32-bit limbs: given `x`, `y`, and `borrow`, it returns
/// the result `x - y - borrow` and, if this underflows, a new `borrow`. Inputs are not range-checked.
#[derive(Copy, Clone, Debug)]
pub struct U32SubtractionGate<F: RichField + Extendable<D>, const D: usize> {
    pub num_ops: usize,
    _phantom: PhantomData<F>,
}

impl<F: RichField + Extendable<D>, const D: usize> U32SubtractionGate<F, D> {
    pub fn new_from_config(config: &CircuitConfig) -> Self {
        Self {
            num_ops: Self::num_ops(config),
            _phantom: PhantomData,
        }
    }

    pub(crate) fn num_ops(config: &CircuitConfig) -> usize {
        let wires_per_op = 5 + Self::num_limbs();
        let routed_wires_per_op = 5;
        (config.num_wires / wires_per_op).min(config.num_routed_wires / routed_wires_per_op)
    }

    pub fn wire_ith_input_x(&self, i: usize) -> usize {
        debug_assert!(i < self.num_ops);
        5 * i
    }
    pub fn wire_ith_input_y(&self, i: usize) -> usize {
        debug_assert!(i < self.num_ops);
        5 * i + 1
    }
    pub fn wire_ith_input_borrow(&self, i: usize) -> usize {
        debug_assert!(i < self.num_ops);
        5 * i + 2
    }

    pub fn wire_ith_output_result(&self, i: usize) -> usize {
        debug_assert!(i < self.num_ops);
        5 * i + 3
    }
    pub fn wire_ith_output_borrow(&self, i: usize) -> usize {
        debug_assert!(i < self.num_ops);
        5 * i + 4
    }

    pub fn limb_bits() -> usize {
        2
    }
    // We have limbs for the 32 bits of `output_result`.
    pub fn num_limbs() -> usize {
        32 / Self::limb_bits()
    }

    pub fn wire_ith_output_jth_limb(&self, i: usize, j: usize) -> usize {
        debug_assert!(i < self.num_ops);
        debug_assert!(j < Self::num_limbs());
        5 * self.num_ops + Self::num_limbs() * i + j
    }
}

impl<F: RichField + Extendable<D>, const D: usize> Gate<F, D> for U32SubtractionGate<F, D> {
    fn id(&self) -> String {
        format!("{self:?}")
    }

    fn eval_unfiltered(&self, vars: EvaluationVars<F, D>) -> Vec<F::Extension> {
        let mut constraints = Vec::with_capacity(self.num_constraints());
        for i in 0..self.num_ops {
            let input_x = vars.local_wires[self.wire_ith_input_x(i)];
            let input_y = vars.local_wires[self.wire_ith_input_y(i)];
            let input_borrow = vars.local_wires[self.wire_ith_input_borrow(i)];

            let result_initial = input_x - input_y - input_borrow;
            let base = F::Extension::from_canonical_u64(1 << 32u64);

            let output_result = vars.local_wires[self.wire_ith_output_result(i)];
            let output_borrow = vars.local_wires[self.wire_ith_output_borrow(i)];

            constraints.push(output_result - (result_initial + base * output_borrow));

            // Range-check output_result to be at most 32 bits.
            let mut combined_limbs = F::Extension::ZERO;
            let limb_base = F::Extension::from_canonical_u64(1u64 << Self::limb_bits());
            for j in (0..Self::num_limbs()).rev() {
                let this_limb = vars.local_wires[self.wire_ith_output_jth_limb(i, j)];
                let max_limb = 1 << Self::limb_bits();
                let product = (0..max_limb)
                    .map(|x| this_limb - F::Extension::from_canonical_usize(x))
                    .product();
                constraints.push(product);

                combined_limbs = limb_base * combined_limbs + this_limb;
            }
            constraints.push(combined_limbs - output_result);

            // Range-check output_borrow to be one bit.
            constraints.push(output_borrow * (F::Extension::ONE - output_borrow));
        }

        constraints
    }

    fn eval_unfiltered_base_one(
        &self,
        _vars: EvaluationVarsBase<F>,
        _yield_constr: StridedConstraintConsumer<F>,
    ) {
        panic!("use eval_unfiltered_base_packed instead");
    }

    fn eval_unfiltered_base_batch(&self, vars_base: EvaluationVarsBaseBatch<F>) -> Vec<F> {
        self.eval_unfiltered_base_batch_packed(vars_base)
    }

    fn eval_unfiltered_circuit(
        &self,
        builder: &mut CircuitBuilder<F, D>,
        vars: EvaluationTargets<D>,
    ) -> Vec<ExtensionTarget<D>> {
        let mut constraints = Vec::with_capacity(self.num_constraints());
        for i in 0..self.num_ops {
            let input_x = vars.local_wires[self.wire_ith_input_x(i)];
            let input_y = vars.local_wires[self.wire_ith_input_y(i)];
            let input_borrow = vars.local_wires[self.wire_ith_input_borrow(i)];

            let diff = builder.sub_extension(input_x, input_y);
            let result_initial = builder.sub_extension(diff, input_borrow);
            let base = builder.constant_extension(F::Extension::from_canonical_u64(1 << 32u64));

            let output_result = vars.local_wires[self.wire_ith_output_result(i)];
            let output_borrow = vars.local_wires[self.wire_ith_output_borrow(i)];

            let computed_output = builder.mul_add_extension(base, output_borrow, result_initial);
            constraints.push(builder.sub_extension(output_result, computed_output));

            // Range-check output_result to be at most 32 bits.
            let mut combined_limbs = builder.zero_extension();
            let limb_base = builder
                .constant_extension(F::Extension::from_canonical_u64(1u64 << Self::limb_bits()));
            for j in (0..Self::num_limbs()).rev() {
                let this_limb = vars.local_wires[self.wire_ith_output_jth_limb(i, j)];
                let max_limb = 1 << Self::limb_bits();
                let mut product = builder.one_extension();
                for x in 0..max_limb {
                    let x_target =
                        builder.constant_extension(F::Extension::from_canonical_usize(x));
                    let diff = builder.sub_extension(this_limb, x_target);
                    product = builder.mul_extension(product, diff);
                }
                constraints.push(product);

                combined_limbs = builder.mul_add_extension(limb_base, combined_limbs, this_limb);
            }
            constraints.push(builder.sub_extension(combined_limbs, output_result));

            // Range-check output_borrow to be one bit.
            let one = builder.one_extension();
            let not_borrow = builder.sub_extension(one, output_borrow);
            constraints.push(builder.mul_extension(output_borrow, not_borrow));
        }

        constraints
    }

    fn generators(&self, row: usize, _local_constants: &[F]) -> Vec<Box<dyn WitnessGenerator<F>>> {
        (0..self.num_ops)
            .map(|i| {
                let g: Box<dyn WitnessGenerator<F>> = Box::new(
                    U32SubtractionGenerator {
                        gate: *self,
                        row,
                        i,
                        _phantom: PhantomData,
                    }
                    .adapter(),
                );
                g
            })
            .collect()
    }

    fn num_wires(&self) -> usize {
        self.num_ops * (5 + Self::num_limbs())
    }

    fn num_constants(&self) -> usize {
        0
    }

    fn degree(&self) -> usize {
        1 << Self::limb_bits()
    }

    fn num_constraints(&self) -> usize {
        self.num_ops * (3 + Self::num_limbs())
    }
}

impl<F: RichField + Extendable<D>, const D: usize> PackedEvaluableBase<F, D>
    for U32SubtractionGate<F, D>
{
    fn eval_unfiltered_base_packed<P: PackedField<Scalar = F>>(
        &self,
        vars: EvaluationVarsBasePacked<P>,
        mut yield_constr: StridedConstraintConsumer<P>,
    ) {
        for i in 0..self.num_ops {
            let input_x = vars.local_wires[self.wire_ith_input_x(i)];
            let input_y = vars.local_wires[self.wire_ith_input_y(i)];
            let input_borrow = vars.local_wires[self.wire_ith_input_borrow(i)];

            let result_initial = input_x - input_y - input_borrow;
            let base = F::from_canonical_u64(1 << 32u64);

            let output_result = vars.local_wires[self.wire_ith_output_result(i)];
            let output_borrow = vars.local_wires[self.wire_ith_output_borrow(i)];

            yield_constr.one(output_result - (result_initial + output_borrow * base));

            // Range-check output_result to be at most 32 bits.
            let mut combined_limbs = P::ZEROS;
            let limb_base = F::from_canonical_u64(1u64 << Self::limb_bits());
            for j in (0..Self::num_limbs()).rev() {
                let this_limb = vars.local_wires[self.wire_ith_output_jth_limb(i, j)];
                let max_limb = 1 << Self::limb_bits();
                let product = (0..max_limb)
                    .map(|x| this_limb - F::from_canonical_usize(x))
                    .product();
                yield_constr.one(product);

                combined_limbs = combined_limbs * limb_base + this_limb;
            }
            yield_constr.one(combined_limbs - output_result);

            // Range-check output_borrow to be one bit.
            yield_constr.one(output_borrow * (P::ONES - output_borrow));
        }
    }
}

#[derive(Clone, Debug)]
struct U32SubtractionGenerator<F: RichField + Extendable<D>, const D: usize> {
    gate: U32SubtractionGate<F, D>,
    row: usize,
    i: usize,
    _phantom: PhantomData<F>,
}

impl<F: RichField + Extendable<D>, const D: usize> SimpleGenerator<F>
    for U32SubtractionGenerator<F, D>
{
    fn dependencies(&self) -> Vec<Target> {
        let local_target = |column| Target::wire(self.row, column);

        vec![
            local_target(self.gate.wire_ith_input_x(self.i)),
            local_target(self.gate.wire_ith_input_y(self.i)),
            local_target(self.gate.wire_ith_input_borrow(self.i)),
        ]
    }

    fn run_once(&self, witness: &PartitionWitness<F>, out_buffer: &mut GeneratedValues<F>) {
        let local_wire = |column| Wire {
            row: self.row,
            column,
        };

        let get_local_wire = |column| witness.get_wire(local_wire(column));

        let input_x = get_local_wire(self.gate.wire_ith_input_x(self.i));
        let input_y = get_local_wire(self.gate.wire_ith_input_y(self.i));
        let input_borrow = get_local_wire(self.gate.wire_ith_input_borrow(self.i));

        let result_initial = input_x - input_y - input_borrow;
        let result_initial_u64 = result_initial.to_canonical_u64();
        let output_borrow = if result_initial_u64 > 1 << 32u64 {
            F::ONE
        } else {
            F::ZERO
        };

        let base = F::from_canonical_u64(1 << 32u64);
        let output_result = result_initial + base * output_borrow;

        let output_result_wire = local_wire(self.gate.wire_ith_output_result(self.i));
        let output_borrow_wire = local_wire(self.gate.wire_ith_output_borrow(self.i));

        out_buffer.set_wire(output_result_wire, output_result);
        out_buffer.set_wire(output_borrow_wire, output_borrow);

        let output_result_u64 = output_result.to_canonical_u64();

        let num_limbs = U32SubtractionGate::<F, D>::num_limbs();
        let limb_base = 1 << U32SubtractionGate::<F, D>::limb_bits();
        let output_limbs: Vec<_> = (0..num_limbs)
            .scan(output_result_u64, |acc, _| {
                let tmp = *acc % limb_base;
                *acc /= limb_base;
                Some(F::from_canonical_u64(tmp))
            })
            .collect();

        for j in 0..num_limbs {
            let wire = local_wire(self.gate.wire_ith_output_jth_limb(self.i, j));
            out_buffer.set_wire(wire, output_limbs[j]);
        }
    }
}

#[cfg(test)]
mod tests {
    use anyhow::Result;
    use plonky2::field::extension::quartic::QuarticExtension;
    use plonky2::field::goldilocks_field::GoldilocksField;
    use plonky2::field::types::{PrimeField64, Sample};
    use plonky2::gates::gate_testing::{test_eval_fns, test_low_degree};
    use plonky2::hash::hash_types::HashOut;
    use plonky2::plonk::config::{GenericConfig, PoseidonGoldilocksConfig};
    use rand::rngs::OsRng;
    use rand::Rng;

    use super::*;

    #[test]
    fn low_degree() {
        test_low_degree::<GoldilocksField, _, 4>(U32SubtractionGate::<GoldilocksField, 4> {
            num_ops: 3,
            _phantom: PhantomData,
        })
    }

    #[test]
    fn eval_fns() -> Result<()> {
        const D: usize = 2;
        type C = PoseidonGoldilocksConfig;
        type F = <C as GenericConfig<D>>::F;
        test_eval_fns::<F, C, _, D>(U32SubtractionGate::<GoldilocksField, D> {
            num_ops: 3,
            _phantom: PhantomData,
        })
    }

    #[test]
    fn test_gate_constraint() {
        type F = GoldilocksField;
        type FF = QuarticExtension<GoldilocksField>;
        const D: usize = 4;
        const NUM_U32_SUBTRACTION_OPS: usize = 3;

        fn get_wires(inputs_x: Vec<u64>, inputs_y: Vec<u64>, borrows: Vec<u64>) -> Vec<FF> {
            let mut v0 = Vec::new();
            let mut v1 = Vec::new();

            let limb_bits = U32SubtractionGate::<F, D>::limb_bits();
            let num_limbs = U32SubtractionGate::<F, D>::num_limbs();
            let limb_base = 1 << limb_bits;
            for c in 0..NUM_U32_SUBTRACTION_OPS {
                let input_x = F::from_canonical_u64(inputs_x[c]);
                let input_y = F::from_canonical_u64(inputs_y[c]);
                let input_borrow = F::from_canonical_u64(borrows[c]);

                let result_initial = input_x - input_y - input_borrow;
                let result_initial_u64 = result_initial.to_canonical_u64();
                let output_borrow = if result_initial_u64 > 1 << 32u64 {
                    F::ONE
                } else {
                    F::ZERO
                };

                let base = F::from_canonical_u64(1 << 32u64);
                let output_result = result_initial + base * output_borrow;

                let output_result_u64 = output_result.to_canonical_u64();

                let mut output_limbs: Vec<_> = (0..num_limbs)
                    .scan(output_result_u64, |acc, _| {
                        let tmp = *acc % limb_base;
                        *acc /= limb_base;
                        Some(F::from_canonical_u64(tmp))
                    })
                    .collect();

                v0.push(input_x);
                v0.push(input_y);
                v0.push(input_borrow);
                v0.push(output_result);
                v0.push(output_borrow);
                v1.append(&mut output_limbs);
            }

            v0.iter().chain(v1.iter()).map(|&x| x.into()).collect()
        }

        let mut rng = OsRng;
        let inputs_x = (0..NUM_U32_SUBTRACTION_OPS)
            .map(|_| rng.gen::<u32>() as u64)
            .collect();
        let inputs_y = (0..NUM_U32_SUBTRACTION_OPS)
            .map(|_| rng.gen::<u32>() as u64)
            .collect();
        let borrows = (0..NUM_U32_SUBTRACTION_OPS)
            .map(|_| (rng.gen::<u32>() % 2) as u64)
            .collect();

        let gate = U32SubtractionGate::<F, D> {
            num_ops: NUM_U32_SUBTRACTION_OPS,
            _phantom: PhantomData,
        };

        let vars = EvaluationVars {
            local_constants: &[],
            local_wires: &get_wires(inputs_x, inputs_y, borrows),
            public_inputs_hash: &HashOut::rand(),
        };

        assert!(
            gate.eval_unfiltered(vars).iter().all(|x| x.is_zero()),
            "Gate constraints are not satisfied."
        );
    }
}