Add a comment to the rationale for the duplicated-rows range check lookup table

halo2_gadgets/src/utilities/lookup_range_check.rs

@@ -53,7 +53,7 @@
             .map(|inner| Self {
                 inner,
                 num_bits,
                 _phantom: PhantomData::default(),
             })
     }
 }
@@ -129,7 +129,7 @@
         strict: bool,
     ) -> Result<RunningSum<F>, Error> {
         layouter.assign_region(
             || format!("{:?} words range check", num_words),
             |mut region| {
                 // Copy `element` and initialize running sum `z_0 = element` to decompose it.
                 let z_0 =
@@ -253,7 +253,7 @@
     ) -> Result<(), Error> {
         assert!(num_bits < K);
         layouter.assign_region(
             || format!("Range check {:?} bits", num_bits),
             |mut region| {
                 // Copy `element` to use in the k-bit lookup.
                 let element =
@@ -276,7 +276,7 @@
     ) -> Result<AssignedCell<F, F>, Error> {
         assert!(num_bits <= K);
         layouter.assign_region(
             || format!("Range check {:?} bits", num_bits),
             |mut region| {
                 // Witness `element` to use in the k-bit lookup.
                 let element = region.assign_advice(
@@ -471,7 +471,7 @@
         let shifted = element.value().into_field() * F::from(1 << (K - num_bits));
 
         region.assign_advice(
             || format!("element * 2^({}-{})", K, num_bits),
             self.running_sum,
             1,
             || shifted,
@@ -480,7 +480,7 @@
         // Assign 2^{-num_bits} from a fixed column.
         let inv_two_pow_s = F::from(1 << num_bits).invert().unwrap();
         region.assign_advice_from_constant(
             || format!("2^(-{})", num_bits),
             self.running_sum,
             2,
             inv_two_pow_s,
@@ -665,6 +665,25 @@
     /// |     1     |    X(S\[1\])   |    Y(S\[1\])   |           5           |
     /// |    ...    |       ...      |       ...      |           5           |
     /// |   2^5-1   | X(S\[2^5-1\])  | Y(S\[2^5-1\])  |           5           |
+    ///
+    /// # Rationale
+    ///
+    /// While it is possible to avoid duplicated rows by using tags and storing them in an advice
+    /// column, as done in the spread table of the SHA-256 gadget, applying this technique to the
+    /// range check lookup table would significantly increase complexity.
+    ///
+    /// Indeed, in the range check lookup tables, tags are currently computed on the fly and are not
+    /// stored in advice columns. Adopting the no duplicated rows approach would require modifying
+    /// the lookup chip to include an advice column for tags and updating the public API accordingly.
+    /// This tag column would need to be populated each time a range check lookup is performed.
+    /// Additionally, the current lookup range check implementation involves combinations of
+    /// multiple lookups, further complicating this approach.
+    ///
+    /// The performance benefit would be minimal: our current table has 1072 rows (2^10 + 2^4 + 2^5),
+    /// and switching to the no duplicated-rows method would reduce it only slightly to 1024 rows
+    /// (2^10), while adding more logic and infrastructure to manage the tags.
+    ///
+    /// Therefore, we retain the simpler duplicated-rows format for clarity and maintainability.
     fn load(
         &self,
         generator_table_config: &GeneratorTableConfig,