mul.rs: Explain ordering of mul::incomplete advice columns.

src/circuit/gadget/ecc/chip/add.rs

@@ -70,6 +70,10 @@ impl Config {
         .collect()
     }
 
+    pub(crate) fn output_columns(&self) -> HashSet<Column<Advice>> {
+        core::array::IntoIter::new([self.x_qr, self.y_qr]).collect()
+    }
+
     pub(crate) fn create_gate(&self, meta: &mut ConstraintSystem<pallas::Base>) {
         meta.create_gate("complete addition gates", |meta| {
             let q_add = meta.query_selector(self.q_add);

src/circuit/gadget/ecc/chip/mul.rs

@@ -80,15 +80,20 @@ impl From<&EccConfig> for Config {
             "y_p is shared across hi and lo halves."
         );
 
-        let add_config_advices = config.add_config.advice_columns();
+        // For both hi_config and lo_config:
-        assert!(
+        // z and lambda1 are assigned on the same row as the add_config output.
-            !add_config_advices.contains(&config.hi_config.z),
+        // Therefore, z and lambda1 must not overlap with add_config.x_qr, add_config.y_qr.
-            "hi_config z cannot overlap with complete addition columns."
+        let add_config_outputs = config.add_config.output_columns();
-        );
+        for config in [&(*config.hi_config), &(*config.lo_config)].iter() {
-        assert!(
+            assert!(
-            !add_config_advices.contains(&config.complete_config.z_complete),
+                !add_config_outputs.contains(&config.z),
-            "complete_config z cannot overlap with complete addition columns."
+                "incomplete config z cannot overlap with complete addition columns."
-        );
+            );
+            assert!(
+                !add_config_outputs.contains(&config.lambda1),
+                "incomplete config lambda1 cannot overlap with complete addition columns."
+            );
+        }
 
         config
     }