changed fft space tests to fri space (#627)

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crates/prover/src/core/backend/cpu/quotients.rs

@@ -179,8 +179,6 @@ mod tests {
     use crate::{m31, qm31};
 
     #[test]
-    // Ignored because we allow polynomials outside of fft-space, hence it is not a bug anymore.
-    #[ignore]
     fn test_quotients_are_low_degree() {
         const LOG_SIZE: u32 = 7;
         let polynomial = CPUCirclePoly::new((0..1 << LOG_SIZE).map(|i| m31!(i)).collect());
@@ -200,6 +198,6 @@ mod tests {
         );
         let quot_poly_base_field =
             CPUCircleEvaluation::new(eval_domain, quot_eval.columns[0].clone()).interpolate();
-        assert!(quot_poly_base_field.is_in_fft_space(LOG_SIZE));
+        assert!(quot_poly_base_field.is_in_fri_space(LOG_SIZE));
     }
 }

crates/prover/src/core/fri.rs

@@ -114,8 +114,9 @@ pub trait FriOps: FieldOps<BaseField> + PolyOps + Sized + FieldOps<SecureField>
         twiddles: &TwiddleTree<Self>,
     );
 
-    /// Decomposes a polynomial of degree N/2 in 'x', into a polynomial inside the fft-space and the
+    /// Decomposes a FRI-space polynomial into a polynomial inside the fft-space and the
     /// remainder term.
+    /// FRI-space: polynomials of total degree n/2.
     /// Based on lemma #12 from the CircleStark paper: f(P) = g(P)+ lambda * alternating(P),
     /// where lambda is the cosset diff of eval, and g is a polynomial in the fft-space.
     fn decompose(eval: &SecureEvaluation<Self>) -> (SecureEvaluation<Self>, SecureField);

crates/prover/src/core/pcs/quotients.rs

@@ -185,10 +185,6 @@ mod tests {
     use crate::{m31, qm31};
 
     #[test]
-    // Ignored because we allow polynomials outside of fft-space, hence it is not a bug anymore.
-    // TODO(Ohad): consider adding a test for the new behavior,
-    //  i.e. polynomials inside the r-h space.
-    #[ignore]
     fn test_quotients_are_low_degree() {
         const LOG_SIZE: u32 = 7;
         let polynomial = CPUCirclePoly::new((0..1 << LOG_SIZE).map(|i| m31!(i)).collect());
@@ -204,6 +200,6 @@ mod tests {
         let quot_poly_base_field =
             CPUCircleEvaluation::new(eval_domain, quot_eval.values.columns[0].clone())
                 .interpolate();
-        assert!(quot_poly_base_field.is_in_fft_space(LOG_SIZE));
+        assert!(quot_poly_base_field.is_in_fri_space(LOG_SIZE));
     }
 }

crates/prover/src/core/poly/circle/poly.rs

@@ -75,7 +75,26 @@ impl crate::core::backend::cpu::CPUCirclePoly {
         while coeffs.last() == Some(&BaseField::zero()) {
             coeffs.pop();
         }
-        coeffs.len() <= 1 << log_fft_size
+
+        // The highest degree monomial in a fft-space polynomial is x^{(n/2) - 1}y.
+        // And it is at offset (n-1). x^{(n/2)} is at offset `n`, and is not allowed.
+        let highest_degree_allowed_monomial_offset = 1 << log_fft_size;
+        coeffs.len() <= highest_degree_allowed_monomial_offset
+    }
+
+    /// Fri space is the space of polynomials of total degree n/2.
+    /// Highest degree monomials are x^{n/2} and x^{(n/2)-1}y.
+    pub fn is_in_fri_space(&self, log_fft_size: u32) -> bool {
+        use num_traits::Zero;
+
+        let mut coeffs = self.coeffs.clone();
+        while coeffs.last() == Some(&BaseField::zero()) {
+            coeffs.pop();
+        }
+
+        // x^{n/2} is at offset `n`, and is the last offset allowed to be non-zero.
+        let highest_degree_monomial_offset = (1 << log_fft_size) + 1;
+        coeffs.len() <= highest_degree_monomial_offset
     }
 }