Merge pull request #240 from mir-protocol/comparison_gate

Comparison gate

src/gates/comparison.rs

@@ -0,0 +1,582 @@
+use std::marker::PhantomData;
+
+use crate::field::extension_field::target::ExtensionTarget;
+use crate::field::extension_field::Extendable;
+use crate::field::field_types::{Field, PrimeField, RichField};
+use crate::gates::gate::Gate;
+use crate::iop::generator::{GeneratedValues, SimpleGenerator, WitnessGenerator};
+use crate::iop::target::Target;
+use crate::iop::wire::Wire;
+use crate::iop::witness::{PartitionWitness, Witness};
+use crate::plonk::circuit_builder::CircuitBuilder;
+use crate::plonk::plonk_common::{reduce_with_powers, reduce_with_powers_ext_recursive};
+use crate::plonk::vars::{EvaluationTargets, EvaluationVars, EvaluationVarsBase};
+use crate::util::ceil_div_usize;
+
+/// A gate for checking that one value is less than another.
+#[derive(Clone, Debug)]
+pub(crate) struct ComparisonGate<F: PrimeField + Extendable<D>, const D: usize> {
+    pub(crate) num_bits: usize,
+    pub(crate) num_chunks: usize,
+    _phantom: PhantomData<F>,
+}
+
+impl<F: RichField + Extendable<D>, const D: usize> ComparisonGate<F, D> {
+    pub fn new(num_bits: usize, num_chunks: usize) -> Self {
+        Self {
+            num_bits,
+            num_chunks,
+            _phantom: PhantomData,
+        }
+    }
+
+    pub fn chunk_bits(&self) -> usize {
+        ceil_div_usize(self.num_bits, self.num_chunks)
+    }
+
+    pub fn wire_first_input(&self) -> usize {
+        0
+    }
+
+    pub fn wire_second_input(&self) -> usize {
+        1
+    }
+
+    pub fn wire_most_significant_diff(&self) -> usize {
+        2
+    }
+
+    pub fn wire_first_chunk_val(&self, chunk: usize) -> usize {
+        debug_assert!(chunk < self.num_chunks);
+        3 + chunk
+    }
+
+    pub fn wire_second_chunk_val(&self, chunk: usize) -> usize {
+        debug_assert!(chunk < self.num_chunks);
+        3 + self.num_chunks + chunk
+    }
+
+    pub fn wire_equality_dummy(&self, chunk: usize) -> usize {
+        debug_assert!(chunk < self.num_chunks);
+        3 + 2 * self.num_chunks + chunk
+    }
+
+    pub fn wire_chunks_equal(&self, chunk: usize) -> usize {
+        debug_assert!(chunk < self.num_chunks);
+        3 + 3 * self.num_chunks + chunk
+    }
+
+    pub fn wire_intermediate_value(&self, chunk: usize) -> usize {
+        debug_assert!(chunk < self.num_chunks);
+        3 + 4 * self.num_chunks + chunk
+    }
+}
+
+impl<F: RichField + Extendable<D>, const D: usize> Gate<F, D> for ComparisonGate<F, D> {
+    fn id(&self) -> String {
+        format!("{:?}<D={}>", self, D)
+    }
+
+    fn eval_unfiltered(&self, vars: EvaluationVars<F, D>) -> Vec<F::Extension> {
+        let mut constraints = Vec::with_capacity(self.num_constraints());
+
+        let first_input = vars.local_wires[self.wire_first_input()];
+        let second_input = vars.local_wires[self.wire_second_input()];
+
+        // Get chunks and assert that they match
+        let first_chunks: Vec<F::Extension> = (0..self.num_chunks)
+            .map(|i| vars.local_wires[self.wire_first_chunk_val(i)])
+            .collect();
+        let second_chunks: Vec<F::Extension> = (0..self.num_chunks)
+            .map(|i| vars.local_wires[self.wire_second_chunk_val(i)])
+            .collect();
+
+        let first_chunks_combined = reduce_with_powers(
+            &first_chunks,
+            F::Extension::from_canonical_usize(1 << self.chunk_bits()),
+        );
+        let second_chunks_combined = reduce_with_powers(
+            &second_chunks,
+            F::Extension::from_canonical_usize(1 << self.chunk_bits()),
+        );
+
+        constraints.push(first_chunks_combined - first_input);
+        constraints.push(second_chunks_combined - second_input);
+
+        let chunk_size = 1 << self.chunk_bits();
+
+        let mut most_significant_diff_so_far = F::Extension::ZERO;
+
+        for i in 0..self.num_chunks {
+            // Range-check the chunks to be less than `chunk_size`.
+            let first_product = (0..chunk_size)
+                .map(|x| first_chunks[i] - F::Extension::from_canonical_usize(x))
+                .product();
+            let second_product = (0..chunk_size)
+                .map(|x| second_chunks[i] - F::Extension::from_canonical_usize(x))
+                .product();
+            constraints.push(first_product);
+            constraints.push(second_product);
+
+            let difference = second_chunks[i] - first_chunks[i];
+            let equality_dummy = vars.local_wires[self.wire_equality_dummy(i)];
+            let chunks_equal = vars.local_wires[self.wire_chunks_equal(i)];
+
+            // Two constraints to assert that `chunks_equal` is valid.
+            constraints.push(difference * equality_dummy - (F::Extension::ONE - chunks_equal));
+            constraints.push(chunks_equal * difference);
+
+            // Update `most_significant_diff_so_far`.
+            let intermediate_value = vars.local_wires[self.wire_intermediate_value(i)];
+            constraints.push(intermediate_value - chunks_equal * most_significant_diff_so_far);
+            most_significant_diff_so_far =
+                intermediate_value + (F::Extension::ONE - chunks_equal) * difference;
+        }
+
+        let most_significant_diff = vars.local_wires[self.wire_most_significant_diff()];
+        constraints.push(most_significant_diff - most_significant_diff_so_far);
+
+        // Range check `most_significant_diff` to be less than `chunk_size`.
+        let product = (1..chunk_size)
+            .map(|x| most_significant_diff - F::Extension::from_canonical_usize(x))
+            .product();
+        constraints.push(product);
+
+        constraints
+    }
+
+    fn eval_unfiltered_base(&self, vars: EvaluationVarsBase<F>) -> Vec<F> {
+        let mut constraints = Vec::with_capacity(self.num_constraints());
+
+        let first_input = vars.local_wires[self.wire_first_input()];
+        let second_input = vars.local_wires[self.wire_second_input()];
+
+        // Get chunks and assert that they match
+        let first_chunks: Vec<F> = (0..self.num_chunks)
+            .map(|i| vars.local_wires[self.wire_first_chunk_val(i)])
+            .collect();
+        let second_chunks: Vec<F> = (0..self.num_chunks)
+            .map(|i| vars.local_wires[self.wire_second_chunk_val(i)])
+            .collect();
+
+        let first_chunks_combined = reduce_with_powers(
+            &first_chunks,
+            F::from_canonical_usize(1 << self.chunk_bits()),
+        );
+        let second_chunks_combined = reduce_with_powers(
+            &second_chunks,
+            F::from_canonical_usize(1 << self.chunk_bits()),
+        );
+
+        constraints.push(first_chunks_combined - first_input);
+        constraints.push(second_chunks_combined - second_input);
+
+        let chunk_size = 1 << self.chunk_bits();
+
+        let mut most_significant_diff_so_far = F::ZERO;
+
+        for i in 0..self.num_chunks {
+            // Range-check the chunks to be less than `chunk_size`.
+            let first_product = (0..chunk_size)
+                .map(|x| first_chunks[i] - F::from_canonical_usize(x))
+                .product();
+            let second_product = (0..chunk_size)
+                .map(|x| second_chunks[i] - F::from_canonical_usize(x))
+                .product();
+            constraints.push(first_product);
+            constraints.push(second_product);
+
+            let difference = second_chunks[i] - first_chunks[i];
+            let equality_dummy = vars.local_wires[self.wire_equality_dummy(i)];
+            let chunks_equal = vars.local_wires[self.wire_chunks_equal(i)];
+
+            // Two constraints to assert that `chunks_equal` is valid.
+            constraints.push(difference * equality_dummy - (F::ONE - chunks_equal));
+            constraints.push(chunks_equal * difference);
+
+            // Update `most_significant_diff_so_far`.
+            let intermediate_value = vars.local_wires[self.wire_intermediate_value(i)];
+            constraints.push(intermediate_value - chunks_equal * most_significant_diff_so_far);
+            most_significant_diff_so_far =
+                intermediate_value + (F::ONE - chunks_equal) * difference;
+        }
+
+        let most_significant_diff = vars.local_wires[self.wire_most_significant_diff()];
+        constraints.push(most_significant_diff - most_significant_diff_so_far);
+
+        // Range check `most_significant_diff` to be less than `chunk_size`.
+        let product = (1..chunk_size)
+            .map(|x| most_significant_diff - F::from_canonical_usize(x))
+            .product();
+        constraints.push(product);
+
+        constraints
+    }
+
+    fn eval_unfiltered_recursively(
+        &self,
+        builder: &mut CircuitBuilder<F, D>,
+        vars: EvaluationTargets<D>,
+    ) -> Vec<ExtensionTarget<D>> {
+        let mut constraints = Vec::with_capacity(self.num_constraints());
+
+        let first_input = vars.local_wires[self.wire_first_input()];
+        let second_input = vars.local_wires[self.wire_second_input()];
+
+        // Get chunks and assert that they match
+        let first_chunks: Vec<ExtensionTarget<D>> = (0..self.num_chunks)
+            .map(|i| vars.local_wires[self.wire_first_chunk_val(i)])
+            .collect();
+        let second_chunks: Vec<ExtensionTarget<D>> = (0..self.num_chunks)
+            .map(|i| vars.local_wires[self.wire_second_chunk_val(i)])
+            .collect();
+
+        let chunk_base = builder.constant(F::from_canonical_usize(1 << self.chunk_bits()));
+        let first_chunks_combined =
+            reduce_with_powers_ext_recursive(builder, &first_chunks, chunk_base);
+        let second_chunks_combined =
+            reduce_with_powers_ext_recursive(builder, &second_chunks, chunk_base);
+
+        constraints.push(builder.sub_extension(first_chunks_combined, first_input));
+        constraints.push(builder.sub_extension(second_chunks_combined, second_input));
+
+        let chunk_size = 1 << self.chunk_bits();
+
+        let mut most_significant_diff_so_far = builder.zero_extension();
+
+        let one = builder.one_extension();
+        // Find the chosen chunk.
+        for i in 0..self.num_chunks {
+            // Range-check the chunks to be less than `chunk_size`.
+            let mut first_product = one;
+            let mut second_product = one;
+            for x in 0..chunk_size {
+                let x_F = builder.constant_extension(F::Extension::from_canonical_usize(x));
+                let first_diff = builder.sub_extension(first_chunks[i], x_F);
+                let second_diff = builder.sub_extension(second_chunks[i], x_F);
+                first_product = builder.mul_extension(first_product, first_diff);
+                second_product = builder.mul_extension(second_product, second_diff);
+            }
+            constraints.push(first_product);
+            constraints.push(second_product);
+
+            let difference = builder.sub_extension(second_chunks[i], first_chunks[i]);
+            let equality_dummy = vars.local_wires[self.wire_equality_dummy(i)];
+            let chunks_equal = vars.local_wires[self.wire_chunks_equal(i)];
+
+            // Two constraints to assert that `chunks_equal` is valid.
+            let diff_times_equal = builder.mul_extension(difference, equality_dummy);
+            let not_equal = builder.sub_extension(one, chunks_equal);
+            constraints.push(builder.sub_extension(diff_times_equal, not_equal));
+            constraints.push(builder.mul_extension(chunks_equal, difference));
+
+            // Update `most_significant_diff_so_far`.
+            let intermediate_value = vars.local_wires[self.wire_intermediate_value(i)];
+            let old_diff = builder.mul_extension(chunks_equal, most_significant_diff_so_far);
+            constraints.push(builder.sub_extension(intermediate_value, old_diff));
+
+            let not_equal = builder.sub_extension(one, chunks_equal);
+            let new_diff = builder.mul_extension(not_equal, difference);
+            most_significant_diff_so_far = builder.add_extension(intermediate_value, new_diff);
+        }
+
+        let most_significant_diff = vars.local_wires[self.wire_most_significant_diff()];
+        constraints
+            .push(builder.sub_extension(most_significant_diff, most_significant_diff_so_far));
+
+        // Range check `most_significant_diff` to be less than `chunk_size`.
+        let mut product = builder.one_extension();
+        for x in 1..chunk_size {
+            let x_F = builder.constant_extension(F::Extension::from_canonical_usize(x));
+            let diff = builder.sub_extension(most_significant_diff, x_F);
+            product = builder.mul_extension(product, diff);
+        }
+        constraints.push(product);
+
+        constraints
+    }
+
+    fn generators(
+        &self,
+        gate_index: usize,
+        _local_constants: &[F],
+    ) -> Vec<Box<dyn WitnessGenerator<F>>> {
+        let gen = ComparisonGenerator::<F, D> {
+            gate_index,
+            gate: self.clone(),
+        };
+        vec![Box::new(gen.adapter())]
+    }
+
+    fn num_wires(&self) -> usize {
+        self.wire_intermediate_value(self.num_chunks - 1) + 1
+    }
+
+    fn num_constants(&self) -> usize {
+        0
+    }
+
+    fn degree(&self) -> usize {
+        1 << self.chunk_bits()
+    }
+
+    fn num_constraints(&self) -> usize {
+        4 + 5 * self.num_chunks
+    }
+}
+
+#[derive(Debug)]
+struct ComparisonGenerator<F: RichField + Extendable<D>, const D: usize> {
+    gate_index: usize,
+    gate: ComparisonGate<F, D>,
+}
+
+impl<F: RichField + Extendable<D>, const D: usize> SimpleGenerator<F>
+    for ComparisonGenerator<F, D>
+{
+    fn dependencies(&self) -> Vec<Target> {
+        let local_target = |input| Target::wire(self.gate_index, input);
+
+        let mut deps = Vec::new();
+        deps.push(local_target(self.gate.wire_first_input()));
+        deps.push(local_target(self.gate.wire_second_input()));
+        deps
+    }
+
+    fn run_once(&self, witness: &PartitionWitness<F>, out_buffer: &mut GeneratedValues<F>) {
+        let local_wire = |input| Wire {
+            gate: self.gate_index,
+            input,
+        };
+
+        let get_local_wire = |input| witness.get_wire(local_wire(input));
+
+        let first_input = get_local_wire(self.gate.wire_first_input());
+        let second_input = get_local_wire(self.gate.wire_second_input());
+
+        let first_input_u64 = first_input.to_canonical_u64();
+        let second_input_u64 = second_input.to_canonical_u64();
+
+        debug_assert!(first_input_u64 < second_input_u64);
+
+        let chunk_size = 1 << self.gate.chunk_bits();
+        let first_input_chunks: Vec<F> = (0..self.gate.num_chunks)
+            .scan(first_input_u64, |acc, _| {
+                let tmp = *acc % chunk_size;
+                *acc /= chunk_size;
+                Some(F::from_canonical_u64(tmp))
+            })
+            .collect();
+        let second_input_chunks: Vec<F> = (0..self.gate.num_chunks)
+            .scan(second_input_u64, |acc, _| {
+                let tmp = *acc % chunk_size;
+                *acc /= chunk_size;
+                Some(F::from_canonical_u64(tmp))
+            })
+            .collect();
+
+        let chunks_equal: Vec<F> = (0..self.gate.num_chunks)
+            .map(|i| F::from_bool(first_input_chunks[i] == second_input_chunks[i]))
+            .collect();
+        let equality_dummies: Vec<F> = first_input_chunks
+            .iter()
+            .zip(second_input_chunks.iter())
+            .map(|(&f, &s)| if f == s { F::ONE } else { F::ONE / (s - f) })
+            .collect();
+
+        let mut most_significant_diff_so_far = F::ZERO;
+        let mut intermediate_values = Vec::new();
+        for i in 1..self.gate.num_chunks {
+            if first_input_chunks[i] != second_input_chunks[i] {
+                most_significant_diff_so_far = second_input_chunks[i] - first_input_chunks[i];
+                intermediate_values.push(F::ZERO);
+            } else {
+                intermediate_values.push(most_significant_diff_so_far);
+            }
+        }
+        let most_significant_diff = most_significant_diff_so_far;
+
+        out_buffer.set_wire(
+            local_wire(self.gate.wire_most_significant_diff()),
+            most_significant_diff,
+        );
+        for i in 0..self.gate.num_chunks {
+            out_buffer.set_wire(
+                local_wire(self.gate.wire_first_chunk_val(i)),
+                first_input_chunks[i],
+            );
+            out_buffer.set_wire(
+                local_wire(self.gate.wire_second_chunk_val(i)),
+                second_input_chunks[i],
+            );
+            out_buffer.set_wire(
+                local_wire(self.gate.wire_equality_dummy(i)),
+                equality_dummies[i],
+            );
+            out_buffer.set_wire(local_wire(self.gate.wire_chunks_equal(i)), chunks_equal[i]);
+            out_buffer.set_wire(
+                local_wire(self.gate.wire_intermediate_value(i)),
+                intermediate_values[i],
+            );
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use std::marker::PhantomData;
+
+    use anyhow::Result;
+    use rand::Rng;
+
+    use crate::field::crandall_field::CrandallField;
+    use crate::field::extension_field::quartic::QuarticExtension;
+    use crate::field::field_types::{Field, PrimeField};
+    use crate::gates::comparison::ComparisonGate;
+    use crate::gates::gate::Gate;
+    use crate::gates::gate_testing::{test_eval_fns, test_low_degree};
+    use crate::hash::hash_types::HashOut;
+    use crate::plonk::plonk_common::reduce_with_powers;
+    use crate::plonk::vars::EvaluationVars;
+
+    #[test]
+    fn wire_indices() {
+        type CG = ComparisonGate<CrandallField, 4>;
+        let num_bits = 40;
+        let num_chunks = 5;
+
+        let gate = CG {
+            num_bits,
+            num_chunks,
+            _phantom: PhantomData,
+        };
+
+        assert_eq!(gate.wire_first_input(), 0);
+        assert_eq!(gate.wire_second_input(), 1);
+        assert_eq!(gate.wire_most_significant_diff(), 2);
+        assert_eq!(gate.wire_first_chunk_val(0), 3);
+        assert_eq!(gate.wire_first_chunk_val(4), 7);
+        assert_eq!(gate.wire_second_chunk_val(0), 8);
+        assert_eq!(gate.wire_second_chunk_val(4), 12);
+        assert_eq!(gate.wire_equality_dummy(0), 13);
+        assert_eq!(gate.wire_equality_dummy(4), 17);
+        assert_eq!(gate.wire_chunks_equal(0), 18);
+        assert_eq!(gate.wire_chunks_equal(4), 22);
+        assert_eq!(gate.wire_intermediate_value(0), 23);
+        assert_eq!(gate.wire_intermediate_value(4), 27);
+    }
+
+    #[test]
+    fn low_degree() {
+        let num_bits = 40;
+        let num_chunks = 5;
+
+        test_low_degree::<CrandallField, _, 4>(ComparisonGate::<_, 4>::new(num_bits, num_chunks))
+    }
+
+    #[test]
+    fn eval_fns() -> Result<()> {
+        let num_bits = 40;
+        let num_chunks = 5;
+
+        test_eval_fns::<CrandallField, _, 4>(ComparisonGate::<_, 4>::new(num_bits, num_chunks))
+    }
+
+    #[test]
+    fn test_gate_constraint() {
+        type F = CrandallField;
+        type FF = QuarticExtension<CrandallField>;
+        const D: usize = 4;
+
+        let num_bits = 40;
+        let num_chunks = 5;
+        let chunk_bits = num_bits / num_chunks;
+
+        // Returns the local wires for a comparison gate given the two inputs.
+        let get_wires = |first_input: F, second_input: F| -> Vec<FF> {
+            let mut v = Vec::new();
+
+            let first_input_u64 = first_input.to_canonical_u64();
+            let second_input_u64 = second_input.to_canonical_u64();
+
+            let chunk_size = 1 << chunk_bits;
+            let mut first_input_chunks: Vec<F> = (0..num_chunks)
+                .scan(first_input_u64, |acc, _| {
+                    let tmp = *acc % chunk_size;
+                    *acc /= chunk_size;
+                    Some(F::from_canonical_u64(tmp))
+                })
+                .collect();
+            let mut second_input_chunks: Vec<F> = (0..num_chunks)
+                .scan(second_input_u64, |acc, _| {
+                    let tmp = *acc % chunk_size;
+                    *acc /= chunk_size;
+                    Some(F::from_canonical_u64(tmp))
+                })
+                .collect();
+
+            let mut chunks_equal: Vec<F> = (0..num_chunks)
+                .map(|i| F::from_bool(first_input_chunks[i] == second_input_chunks[i]))
+                .collect();
+            let mut equality_dummies: Vec<F> = first_input_chunks
+                .iter()
+                .zip(second_input_chunks.iter())
+                .map(|(&f, &s)| if f == s { F::ONE } else { F::ONE / (s - f) })
+                .collect();
+
+            let mut most_significant_diff_so_far = F::ZERO;
+            let mut intermediate_values = Vec::new();
+            for i in 0..num_chunks {
+                if first_input_chunks[i] != second_input_chunks[i] {
+                    most_significant_diff_so_far = second_input_chunks[i] - first_input_chunks[i];
+                    intermediate_values.push(F::ZERO);
+                } else {
+                    intermediate_values.push(most_significant_diff_so_far);
+                }
+            }
+            let most_significant_diff = most_significant_diff_so_far;
+
+            v.push(first_input);
+            v.push(second_input);
+            v.push(most_significant_diff);
+            v.append(&mut first_input_chunks);
+            v.append(&mut second_input_chunks);
+            v.append(&mut equality_dummies);
+            v.append(&mut chunks_equal);
+            v.append(&mut intermediate_values);
+
+            v.iter().map(|&x| x.into()).collect::<Vec<_>>()
+        };
+
+        let mut rng = rand::thread_rng();
+        let max: u64 = 1 << num_bits - 1;
+        let first_input_u64 = rng.gen_range(0..max);
+        let second_input_u64 = {
+            let mut val = rng.gen_range(0..max);
+            while val <= first_input_u64 {
+                val = rng.gen_range(0..max);
+            }
+            val
+        };
+
+        let first_input = F::from_canonical_u64(first_input_u64);
+        let second_input = F::from_canonical_u64(second_input_u64);
+
+        let gate = ComparisonGate::<F, D> {
+            num_bits,
+            num_chunks,
+            _phantom: PhantomData,
+        };
+
+        let vars = EvaluationVars {
+            local_constants: &[],
+            local_wires: &get_wires(first_input, second_input),
+            public_inputs_hash: &HashOut::rand(),
+        };
+
+        assert!(
+            gate.eval_unfiltered(vars).iter().all(|x| x.is_zero()),
+            "Gate constraints are not satisfied."
+        );
+    }
+}

src/gates/mod.rs

@@ -3,6 +3,7 @@
 
 pub mod arithmetic;
 pub mod base_sum;
+pub mod comparison;
 pub mod constant;
 pub mod exponentiation;
 pub mod gate;