fix: Avoid potential panic in (i)NTT

To improve the performance of NTT, some internal data is cached. The key
for the cache is the log₂ of the input's length. Previously, the empty
input and an input of length 1 mapped to the same cache key. In case
NTT had
1. first been called on an empty input,
2. then called on input of length 1,
the cache would be incorrectly populated, leading to a panic.

Author: jan-ferdinand

twenty-first/src/math/ntt.rs

@@ -153,7 +153,10 @@ where
         [const { OnceLock::new() }; NUM_DOMAINS];
 
     let slice_len = x.len();
-    let log2_slice_len = slice_len.checked_ilog2().unwrap_or(0);
+    let Some(log2_slice_len) = slice_len.checked_ilog2() else {
+        // if the slice is empty, there's nothing to do
+        return;
+    };
     let swap_indices =
         ALL_SWAP_INDICES[log2_slice_len as usize].get_or_init(|| swap_indices(slice_len));
     debug_assert_eq!(swap_indices.len(), slice_len);
@@ -470,6 +473,15 @@ mod tests {
         assert_eq!(vec![bfe], test_vector);
     }
 
+    // Make sure that caches are correctly populated in edge cases.
+    #[test]
+    fn ntt_on_input_of_length_0_then_1_then_0() {
+        let mut empty = Vec::<BFieldElement>::new();
+        ntt(&mut empty);
+        ntt(&mut [BFieldElement::new(0)]);
+        ntt(&mut empty);
+    }
+
     #[proptest(cases = 10)]
     fn ntt_then_intt_is_identity_operation(
         #[strategy((0_usize..18).prop_map(|l| 1 << l))] _vector_length: usize,