1use crate::fields::{fp::FpVar, FieldVar};
 2use ark_ff::{Field, PrimeField};
 3use ark_relations::r1cs::SynthesisError;
 4use ark_std::ops::Sub;
 5
 6/// Struct describing vanishing polynomial for a multiplicative coset H where
 7/// |H| is a power of 2. As H is a coset, every element can be described as
 8/// h*g^i and therefore has vanishing polynomial Z_H(x) = x^|H| - h^|H|
 9#[derive(Clone)]
10pub struct VanishingPolynomial<F: Field> {
11    /// h^|H|
12    pub constant_term: F,
13    /// log_2(|H|)
14    pub dim_h: u64,
15    /// |H|
16    pub order_h: u64,
17}
18
19impl<F: PrimeField> VanishingPolynomial<F> {
20    /// returns a VanishingPolynomial of coset `H = h<g>`.
21    pub fn new(offset: F, dim_h: u64) -> Self {
22        let order_h = 1 << dim_h;
23        let vp = VanishingPolynomial {
24            constant_term: offset.pow([order_h]),
25            dim_h,
26            order_h,
27        };
28        vp
29    }
30
31    /// Evaluates the vanishing polynomial without generating the constraints.
32    pub fn evaluate(&self, x: &F) -> F {
33        let mut result = x.pow([self.order_h]);
34        result -= &self.constant_term;
35        result
36    }
37
38    /// Evaluates the constraints and just gives you the gadget for the result.
39    /// Caution for use in holographic lincheck: The output has 2 entries in one
40    /// matrix
41    pub fn evaluate_constraints(&self, x: &FpVar<F>) -> Result<FpVar<F>, SynthesisError> {
42        if self.dim_h == 1 {
43            let result = x.sub(x);
44            return Ok(result);
45        }
46
47        let mut cur = x.square()?;
48        for _ in 1..self.dim_h {
49            cur.square_in_place()?;
50        }
51        cur -= &FpVar::Constant(self.constant_term);
52        Ok(cur)
53    }
54}
55
56#[cfg(test)]
57mod tests {
58    use crate::{
59        alloc::AllocVar, fields::fp::FpVar, poly::domain::vanishing_poly::VanishingPolynomial,
60        R1CSVar,
61    };
62    use ark_relations::r1cs::ConstraintSystem;
63    use ark_std::{test_rng, UniformRand};
64    use ark_test_curves::bls12_381::Fr;
65
66    #[test]
67    fn constraints_test() {
68        let mut rng = test_rng();
69        let offset = Fr::rand(&mut rng);
70        let cs = ConstraintSystem::new_ref();
71        let x = Fr::rand(&mut rng);
72        let x_var = FpVar::new_witness(ns!(cs, "x_var"), || Ok(x)).unwrap();
73        let vp = VanishingPolynomial::new(offset, 12);
74        let native = vp.evaluate(&x);
75        let result_var = vp.evaluate_constraints(&x_var).unwrap();
76        assert!(cs.is_satisfied().unwrap());
77        assert_eq!(result_var.value().unwrap(), native);
78    }
79}